Commit | Line | Data |
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8e43ed5d | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006, 2007, 2008, 2009, 2010, 2011 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 | ||
0f2d19dd | 48 | #include <math.h> |
fc194577 | 49 | #include <string.h> |
3f47e526 MG |
50 | #include <unicase.h> |
51 | #include <unictype.h> | |
f92e85f7 | 52 | |
8ab3d8a0 KR |
53 | #if HAVE_COMPLEX_H |
54 | #include <complex.h> | |
55 | #endif | |
56 | ||
a0599745 | 57 | #include "libguile/_scm.h" |
a0599745 MD |
58 | #include "libguile/feature.h" |
59 | #include "libguile/ports.h" | |
60 | #include "libguile/root.h" | |
61 | #include "libguile/smob.h" | |
62 | #include "libguile/strings.h" | |
864e7d42 | 63 | #include "libguile/bdw-gc.h" |
a0599745 MD |
64 | |
65 | #include "libguile/validate.h" | |
66 | #include "libguile/numbers.h" | |
1be6b49c | 67 | #include "libguile/deprecation.h" |
f4c627b3 | 68 | |
f92e85f7 MV |
69 | #include "libguile/eq.h" |
70 | ||
8ab3d8a0 KR |
71 | /* values per glibc, if not already defined */ |
72 | #ifndef M_LOG10E | |
73 | #define M_LOG10E 0.43429448190325182765 | |
74 | #endif | |
75 | #ifndef M_PI | |
76 | #define M_PI 3.14159265358979323846 | |
77 | #endif | |
78 | ||
e25f3727 AW |
79 | typedef scm_t_signed_bits scm_t_inum; |
80 | #define scm_from_inum(x) (scm_from_signed_integer (x)) | |
81 | ||
7112615f MW |
82 | /* Tests to see if a C double is neither infinite nor a NaN. |
83 | TODO: if it's available, use C99's isfinite(x) instead */ | |
84 | #define DOUBLE_IS_FINITE(x) (!isinf(x) && !isnan(x)) | |
85 | ||
041fccf6 MW |
86 | /* On some platforms, isinf(x) returns 0, 1 or -1, indicating the sign |
87 | of the infinity, but other platforms return a boolean only. */ | |
88 | #define DOUBLE_IS_POSITIVE_INFINITY(x) (isinf(x) && ((x) > 0)) | |
89 | #define DOUBLE_IS_NEGATIVE_INFINITY(x) (isinf(x) && ((x) < 0)) | |
90 | ||
0f2d19dd | 91 | \f |
f4c627b3 | 92 | |
ca46fb90 RB |
93 | /* |
94 | Wonder if this might be faster for some of our code? A switch on | |
95 | the numtag would jump directly to the right case, and the | |
96 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
97 | ||
98 | #define SCM_I_NUMTAG_NOTNUM 0 | |
99 | #define SCM_I_NUMTAG_INUM 1 | |
100 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
101 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
102 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
103 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 104 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 105 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 106 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
107 | : SCM_I_NUMTAG_NOTNUM))) |
108 | */ | |
f92e85f7 | 109 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
110 | |
111 | ||
e7efe8e7 | 112 | static SCM flo0; |
ff62c168 | 113 | static SCM exactly_one_half; |
e7efe8e7 | 114 | |
34d19ef6 | 115 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 116 | |
56e55ac7 | 117 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
118 | * printed or scm_string representation of an inexact number. |
119 | */ | |
0b799eea | 120 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 121 | |
b127c712 | 122 | |
ad79736c AW |
123 | #if !defined (HAVE_ASINH) |
124 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } | |
125 | #endif | |
126 | #if !defined (HAVE_ACOSH) | |
127 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } | |
128 | #endif | |
129 | #if !defined (HAVE_ATANH) | |
130 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } | |
131 | #endif | |
132 | ||
f8a8200b KR |
133 | /* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses |
134 | an explicit check. In some future gmp (don't know what version number), | |
135 | mpz_cmp_d is supposed to do this itself. */ | |
136 | #if 1 | |
b127c712 | 137 | #define xmpz_cmp_d(z, d) \ |
2e65b52f | 138 | (isinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) |
b127c712 KR |
139 | #else |
140 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
141 | #endif | |
142 | ||
f92e85f7 | 143 | |
4b26c03e | 144 | #if defined (GUILE_I) |
bca69a9f | 145 | #if HAVE_COMPLEX_DOUBLE |
8ab3d8a0 KR |
146 | |
147 | /* For an SCM object Z which is a complex number (ie. satisfies | |
148 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
149 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 150 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 151 | |
7a35784c | 152 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
8ab3d8a0 KR |
153 | |
154 | /* Convert a C "complex double" to an SCM value. */ | |
7a35784c | 155 | static inline SCM |
8ab3d8a0 KR |
156 | scm_from_complex_double (complex double z) |
157 | { | |
158 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
159 | } | |
bca69a9f | 160 | |
8ab3d8a0 | 161 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 162 | #endif /* GUILE_I */ |
8ab3d8a0 | 163 | |
0f2d19dd JB |
164 | \f |
165 | ||
713a4259 | 166 | static mpz_t z_negative_one; |
ac0c002c DH |
167 | |
168 | \f | |
864e7d42 LC |
169 | /* Clear the `mpz_t' embedded in bignum PTR. */ |
170 | static void | |
171 | finalize_bignum (GC_PTR ptr, GC_PTR data) | |
172 | { | |
173 | SCM bignum; | |
174 | ||
175 | bignum = PTR2SCM (ptr); | |
176 | mpz_clear (SCM_I_BIG_MPZ (bignum)); | |
177 | } | |
178 | ||
d017fcdf LC |
179 | /* Return a new uninitialized bignum. */ |
180 | static inline SCM | |
181 | make_bignum (void) | |
182 | { | |
183 | scm_t_bits *p; | |
864e7d42 LC |
184 | GC_finalization_proc prev_finalizer; |
185 | GC_PTR prev_finalizer_data; | |
d017fcdf LC |
186 | |
187 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ | |
188 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), | |
189 | "bignum"); | |
190 | p[0] = scm_tc16_big; | |
191 | ||
864e7d42 LC |
192 | GC_REGISTER_FINALIZER_NO_ORDER (p, finalize_bignum, NULL, |
193 | &prev_finalizer, | |
194 | &prev_finalizer_data); | |
195 | ||
d017fcdf LC |
196 | return SCM_PACK (p); |
197 | } | |
ac0c002c | 198 | |
864e7d42 | 199 | |
189171c5 | 200 | SCM |
ca46fb90 RB |
201 | scm_i_mkbig () |
202 | { | |
203 | /* Return a newly created bignum. */ | |
d017fcdf | 204 | SCM z = make_bignum (); |
ca46fb90 RB |
205 | mpz_init (SCM_I_BIG_MPZ (z)); |
206 | return z; | |
207 | } | |
208 | ||
e25f3727 AW |
209 | static SCM |
210 | scm_i_inum2big (scm_t_inum x) | |
211 | { | |
212 | /* Return a newly created bignum initialized to X. */ | |
213 | SCM z = make_bignum (); | |
214 | #if SIZEOF_VOID_P == SIZEOF_LONG | |
215 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
216 | #else | |
217 | /* Note that in this case, you'll also have to check all mpz_*_ui and | |
218 | mpz_*_si invocations in Guile. */ | |
219 | #error creation of mpz not implemented for this inum size | |
220 | #endif | |
221 | return z; | |
222 | } | |
223 | ||
189171c5 | 224 | SCM |
c71b0706 MV |
225 | scm_i_long2big (long x) |
226 | { | |
227 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 228 | SCM z = make_bignum (); |
c71b0706 MV |
229 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
230 | return z; | |
231 | } | |
232 | ||
189171c5 | 233 | SCM |
c71b0706 MV |
234 | scm_i_ulong2big (unsigned long x) |
235 | { | |
236 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 237 | SCM z = make_bignum (); |
c71b0706 MV |
238 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
239 | return z; | |
240 | } | |
241 | ||
189171c5 | 242 | SCM |
ca46fb90 RB |
243 | scm_i_clonebig (SCM src_big, int same_sign_p) |
244 | { | |
245 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
d017fcdf | 246 | SCM z = make_bignum (); |
ca46fb90 | 247 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
0aacf84e MD |
248 | if (!same_sign_p) |
249 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
250 | return z; |
251 | } | |
252 | ||
189171c5 | 253 | int |
ca46fb90 RB |
254 | scm_i_bigcmp (SCM x, SCM y) |
255 | { | |
256 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
257 | /* presume we already know x and y are bignums */ | |
258 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
259 | scm_remember_upto_here_2 (x, y); | |
260 | return result; | |
261 | } | |
262 | ||
189171c5 | 263 | SCM |
ca46fb90 RB |
264 | scm_i_dbl2big (double d) |
265 | { | |
266 | /* results are only defined if d is an integer */ | |
d017fcdf | 267 | SCM z = make_bignum (); |
ca46fb90 RB |
268 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
269 | return z; | |
270 | } | |
271 | ||
f92e85f7 MV |
272 | /* Convert a integer in double representation to a SCM number. */ |
273 | ||
189171c5 | 274 | SCM |
f92e85f7 MV |
275 | scm_i_dbl2num (double u) |
276 | { | |
277 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
278 | powers of 2, so there's no rounding when making "double" values | |
279 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
280 | get rounded on a 64-bit machine, hence the "+1". | |
281 | ||
282 | The use of floor() to force to an integer value ensures we get a | |
283 | "numerically closest" value without depending on how a | |
284 | double->long cast or how mpz_set_d will round. For reference, | |
285 | double->long probably follows the hardware rounding mode, | |
286 | mpz_set_d truncates towards zero. */ | |
287 | ||
288 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
289 | representable as a double? */ | |
290 | ||
291 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
292 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
e25f3727 | 293 | return SCM_I_MAKINUM ((scm_t_inum) u); |
f92e85f7 MV |
294 | else |
295 | return scm_i_dbl2big (u); | |
296 | } | |
297 | ||
089c9a59 KR |
298 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
299 | with R5RS exact->inexact. | |
300 | ||
301 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
302 | (ie. truncate towards zero), then adjust to get the closest double by |
303 | examining the next lower bit and adding 1 (to the absolute value) if | |
304 | necessary. | |
305 | ||
306 | Bignums exactly half way between representable doubles are rounded to the | |
307 | next higher absolute value (ie. away from zero). This seems like an | |
308 | adequate interpretation of R5RS "numerically closest", and it's easier | |
309 | and faster than a full "nearest-even" style. | |
310 | ||
311 | The bit test must be done on the absolute value of the mpz_t, which means | |
312 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
313 | negatives as twos complement. | |
314 | ||
315 | In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up | |
316 | following the hardware rounding mode, but applied to the absolute value | |
317 | of the mpz_t operand. This is not what we want so we put the high | |
318 | DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when, | |
319 | mpz_get_d is supposed to always truncate towards zero. | |
320 | ||
321 | ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3 | |
322 | is a slowdown. It'd be faster to pick out the relevant high bits with | |
323 | mpz_getlimbn if we could be bothered coding that, and if the new | |
324 | truncating gmp doesn't come out. */ | |
089c9a59 KR |
325 | |
326 | double | |
ca46fb90 RB |
327 | scm_i_big2dbl (SCM b) |
328 | { | |
089c9a59 KR |
329 | double result; |
330 | size_t bits; | |
331 | ||
332 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
333 | ||
f8a8200b | 334 | #if 1 |
089c9a59 | 335 | { |
f8a8200b | 336 | /* Current GMP, eg. 4.1.3, force truncation towards zero */ |
089c9a59 KR |
337 | mpz_t tmp; |
338 | if (bits > DBL_MANT_DIG) | |
339 | { | |
340 | size_t shift = bits - DBL_MANT_DIG; | |
341 | mpz_init2 (tmp, DBL_MANT_DIG); | |
342 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
343 | result = ldexp (mpz_get_d (tmp), shift); | |
344 | mpz_clear (tmp); | |
345 | } | |
346 | else | |
347 | { | |
348 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
349 | } | |
350 | } | |
351 | #else | |
f8a8200b | 352 | /* Future GMP */ |
089c9a59 KR |
353 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
354 | #endif | |
355 | ||
356 | if (bits > DBL_MANT_DIG) | |
357 | { | |
358 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
359 | /* test bit number "pos" in absolute value */ | |
360 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
361 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
362 | { | |
363 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
364 | } | |
365 | } | |
366 | ||
ca46fb90 RB |
367 | scm_remember_upto_here_1 (b); |
368 | return result; | |
369 | } | |
370 | ||
189171c5 | 371 | SCM |
ca46fb90 RB |
372 | scm_i_normbig (SCM b) |
373 | { | |
374 | /* convert a big back to a fixnum if it'll fit */ | |
375 | /* presume b is a bignum */ | |
376 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
377 | { | |
e25f3727 | 378 | scm_t_inum val = mpz_get_si (SCM_I_BIG_MPZ (b)); |
ca46fb90 | 379 | if (SCM_FIXABLE (val)) |
d956fa6f | 380 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
381 | } |
382 | return b; | |
383 | } | |
f872b822 | 384 | |
f92e85f7 MV |
385 | static SCM_C_INLINE_KEYWORD SCM |
386 | scm_i_mpz2num (mpz_t b) | |
387 | { | |
388 | /* convert a mpz number to a SCM number. */ | |
389 | if (mpz_fits_slong_p (b)) | |
390 | { | |
e25f3727 | 391 | scm_t_inum val = mpz_get_si (b); |
f92e85f7 | 392 | if (SCM_FIXABLE (val)) |
d956fa6f | 393 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
394 | } |
395 | ||
396 | { | |
d017fcdf | 397 | SCM z = make_bignum (); |
f92e85f7 MV |
398 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
399 | return z; | |
400 | } | |
401 | } | |
402 | ||
403 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
404 | static SCM scm_divide2real (SCM x, SCM y); | |
405 | ||
cba42c93 MV |
406 | static SCM |
407 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 408 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 409 | { |
c60e130c MV |
410 | /* First make sure the arguments are proper. |
411 | */ | |
e11e83f3 | 412 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 413 | { |
bc36d050 | 414 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 415 | scm_num_overflow ("make-ratio"); |
cff5fa33 | 416 | if (scm_is_eq (denominator, SCM_INUM1)) |
f92e85f7 MV |
417 | return numerator; |
418 | } | |
419 | else | |
420 | { | |
421 | if (!(SCM_BIGP(denominator))) | |
422 | SCM_WRONG_TYPE_ARG (2, denominator); | |
423 | } | |
e11e83f3 | 424 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
425 | SCM_WRONG_TYPE_ARG (1, numerator); |
426 | ||
427 | /* Then flip signs so that the denominator is positive. | |
428 | */ | |
73e4de09 | 429 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
430 | { |
431 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
432 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
433 | } | |
434 | ||
435 | /* Now consider for each of the four fixnum/bignum combinations | |
436 | whether the rational number is really an integer. | |
437 | */ | |
e11e83f3 | 438 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 439 | { |
e25f3727 | 440 | scm_t_inum x = SCM_I_INUM (numerator); |
bc36d050 | 441 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 442 | return SCM_INUM0; |
e11e83f3 | 443 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 444 | { |
e25f3727 | 445 | scm_t_inum y; |
e11e83f3 | 446 | y = SCM_I_INUM (denominator); |
f92e85f7 | 447 | if (x == y) |
cff5fa33 | 448 | return SCM_INUM1; |
f92e85f7 | 449 | if ((x % y) == 0) |
d956fa6f | 450 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 451 | } |
dd5130ca KR |
452 | else |
453 | { | |
454 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
455 | of that value for the denominator, as a bignum. Apart from |
456 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
457 | integer. */ | |
458 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
459 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
460 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 461 | return SCM_I_MAKINUM(-1); |
dd5130ca | 462 | } |
f92e85f7 | 463 | } |
c60e130c | 464 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 465 | { |
e11e83f3 | 466 | if (SCM_I_INUMP (denominator)) |
c60e130c | 467 | { |
e25f3727 | 468 | scm_t_inum yy = SCM_I_INUM (denominator); |
c60e130c MV |
469 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
470 | return scm_divide (numerator, denominator); | |
471 | } | |
472 | else | |
f92e85f7 | 473 | { |
bc36d050 | 474 | if (scm_is_eq (numerator, denominator)) |
cff5fa33 | 475 | return SCM_INUM1; |
c60e130c MV |
476 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
477 | SCM_I_BIG_MPZ (denominator))) | |
478 | return scm_divide(numerator, denominator); | |
f92e85f7 | 479 | } |
f92e85f7 | 480 | } |
c60e130c MV |
481 | |
482 | /* No, it's a proper fraction. | |
483 | */ | |
e2bf3b19 HWN |
484 | { |
485 | SCM divisor = scm_gcd (numerator, denominator); | |
cff5fa33 | 486 | if (!(scm_is_eq (divisor, SCM_INUM1))) |
e2bf3b19 HWN |
487 | { |
488 | numerator = scm_divide (numerator, divisor); | |
489 | denominator = scm_divide (denominator, divisor); | |
490 | } | |
491 | ||
492 | return scm_double_cell (scm_tc16_fraction, | |
493 | SCM_UNPACK (numerator), | |
494 | SCM_UNPACK (denominator), 0); | |
495 | } | |
f92e85f7 | 496 | } |
c60e130c | 497 | #undef FUNC_NAME |
f92e85f7 | 498 | |
f92e85f7 MV |
499 | double |
500 | scm_i_fraction2double (SCM z) | |
501 | { | |
55f26379 MV |
502 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
503 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
504 | } |
505 | ||
2e274311 MW |
506 | static int |
507 | double_is_non_negative_zero (double x) | |
508 | { | |
509 | static double zero = 0.0; | |
510 | ||
511 | return !memcmp (&x, &zero, sizeof(double)); | |
512 | } | |
513 | ||
2519490c MW |
514 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
515 | (SCM x), | |
942e5b91 MG |
516 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
517 | "otherwise.") | |
1bbd0b84 | 518 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 519 | { |
41df63cf MW |
520 | if (SCM_INEXACTP (x)) |
521 | return SCM_BOOL_F; | |
522 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 523 | return SCM_BOOL_T; |
41df63cf | 524 | else |
2519490c | 525 | SCM_WTA_DISPATCH_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
526 | } |
527 | #undef FUNC_NAME | |
528 | ||
529 | ||
2519490c | 530 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
531 | (SCM x), |
532 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
533 | "else.") | |
534 | #define FUNC_NAME s_scm_inexact_p | |
535 | { | |
536 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 537 | return SCM_BOOL_T; |
41df63cf | 538 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 539 | return SCM_BOOL_F; |
41df63cf | 540 | else |
2519490c | 541 | SCM_WTA_DISPATCH_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 542 | } |
1bbd0b84 | 543 | #undef FUNC_NAME |
0f2d19dd | 544 | |
4219f20d | 545 | |
2519490c | 546 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 547 | (SCM n), |
942e5b91 MG |
548 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
549 | "otherwise.") | |
1bbd0b84 | 550 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 551 | { |
e11e83f3 | 552 | if (SCM_I_INUMP (n)) |
0aacf84e | 553 | { |
e25f3727 | 554 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 555 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
556 | } |
557 | else if (SCM_BIGP (n)) | |
558 | { | |
559 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
560 | scm_remember_upto_here_1 (n); | |
73e4de09 | 561 | return scm_from_bool (odd_p); |
0aacf84e | 562 | } |
f92e85f7 MV |
563 | else if (SCM_REALP (n)) |
564 | { | |
2519490c MW |
565 | double val = SCM_REAL_VALUE (n); |
566 | if (DOUBLE_IS_FINITE (val)) | |
567 | { | |
568 | double rem = fabs (fmod (val, 2.0)); | |
569 | if (rem == 1.0) | |
570 | return SCM_BOOL_T; | |
571 | else if (rem == 0.0) | |
572 | return SCM_BOOL_F; | |
573 | } | |
f92e85f7 | 574 | } |
2519490c | 575 | SCM_WTA_DISPATCH_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 576 | } |
1bbd0b84 | 577 | #undef FUNC_NAME |
0f2d19dd | 578 | |
4219f20d | 579 | |
2519490c | 580 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 581 | (SCM n), |
942e5b91 MG |
582 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
583 | "otherwise.") | |
1bbd0b84 | 584 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 585 | { |
e11e83f3 | 586 | if (SCM_I_INUMP (n)) |
0aacf84e | 587 | { |
e25f3727 | 588 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 589 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
590 | } |
591 | else if (SCM_BIGP (n)) | |
592 | { | |
593 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
594 | scm_remember_upto_here_1 (n); | |
73e4de09 | 595 | return scm_from_bool (even_p); |
0aacf84e | 596 | } |
f92e85f7 MV |
597 | else if (SCM_REALP (n)) |
598 | { | |
2519490c MW |
599 | double val = SCM_REAL_VALUE (n); |
600 | if (DOUBLE_IS_FINITE (val)) | |
601 | { | |
602 | double rem = fabs (fmod (val, 2.0)); | |
603 | if (rem == 1.0) | |
604 | return SCM_BOOL_F; | |
605 | else if (rem == 0.0) | |
606 | return SCM_BOOL_T; | |
607 | } | |
f92e85f7 | 608 | } |
2519490c | 609 | SCM_WTA_DISPATCH_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 610 | } |
1bbd0b84 | 611 | #undef FUNC_NAME |
0f2d19dd | 612 | |
2519490c MW |
613 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
614 | (SCM x), | |
10391e06 AW |
615 | "Return @code{#t} if the real number @var{x} is neither\n" |
616 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
617 | #define FUNC_NAME s_scm_finite_p |
618 | { | |
619 | if (SCM_REALP (x)) | |
620 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 621 | else if (scm_is_real (x)) |
7112615f MW |
622 | return SCM_BOOL_T; |
623 | else | |
2519490c | 624 | SCM_WTA_DISPATCH_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
625 | } |
626 | #undef FUNC_NAME | |
627 | ||
2519490c MW |
628 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
629 | (SCM x), | |
630 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
631 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
632 | #define FUNC_NAME s_scm_inf_p |
633 | { | |
b1092b3a | 634 | if (SCM_REALP (x)) |
2e65b52f | 635 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 636 | else if (scm_is_real (x)) |
7351e207 | 637 | return SCM_BOOL_F; |
10391e06 | 638 | else |
2519490c | 639 | SCM_WTA_DISPATCH_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
640 | } |
641 | #undef FUNC_NAME | |
642 | ||
2519490c MW |
643 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
644 | (SCM x), | |
10391e06 AW |
645 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
646 | "or @code{#f} otherwise.") | |
7351e207 MV |
647 | #define FUNC_NAME s_scm_nan_p |
648 | { | |
10391e06 AW |
649 | if (SCM_REALP (x)) |
650 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
651 | else if (scm_is_real (x)) | |
7351e207 | 652 | return SCM_BOOL_F; |
10391e06 | 653 | else |
2519490c | 654 | SCM_WTA_DISPATCH_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
655 | } |
656 | #undef FUNC_NAME | |
657 | ||
658 | /* Guile's idea of infinity. */ | |
659 | static double guile_Inf; | |
660 | ||
661 | /* Guile's idea of not a number. */ | |
662 | static double guile_NaN; | |
663 | ||
664 | static void | |
665 | guile_ieee_init (void) | |
666 | { | |
7351e207 MV |
667 | /* Some version of gcc on some old version of Linux used to crash when |
668 | trying to make Inf and NaN. */ | |
669 | ||
240a27d2 KR |
670 | #ifdef INFINITY |
671 | /* C99 INFINITY, when available. | |
672 | FIXME: The standard allows for INFINITY to be something that overflows | |
673 | at compile time. We ought to have a configure test to check for that | |
674 | before trying to use it. (But in practice we believe this is not a | |
675 | problem on any system guile is likely to target.) */ | |
676 | guile_Inf = INFINITY; | |
56a3dcd4 | 677 | #elif defined HAVE_DINFINITY |
240a27d2 | 678 | /* OSF */ |
7351e207 | 679 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 680 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
681 | #else |
682 | double tmp = 1e+10; | |
683 | guile_Inf = tmp; | |
684 | for (;;) | |
685 | { | |
686 | guile_Inf *= 1e+10; | |
687 | if (guile_Inf == tmp) | |
688 | break; | |
689 | tmp = guile_Inf; | |
690 | } | |
691 | #endif | |
692 | ||
240a27d2 KR |
693 | #ifdef NAN |
694 | /* C99 NAN, when available */ | |
695 | guile_NaN = NAN; | |
56a3dcd4 | 696 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
697 | { |
698 | /* OSF */ | |
699 | extern unsigned int DQNAN[2]; | |
700 | guile_NaN = (*((double *)(DQNAN))); | |
701 | } | |
7351e207 MV |
702 | #else |
703 | guile_NaN = guile_Inf / guile_Inf; | |
704 | #endif | |
7351e207 MV |
705 | } |
706 | ||
707 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
708 | (void), | |
709 | "Return Inf.") | |
710 | #define FUNC_NAME s_scm_inf | |
711 | { | |
712 | static int initialized = 0; | |
713 | if (! initialized) | |
714 | { | |
715 | guile_ieee_init (); | |
716 | initialized = 1; | |
717 | } | |
55f26379 | 718 | return scm_from_double (guile_Inf); |
7351e207 MV |
719 | } |
720 | #undef FUNC_NAME | |
721 | ||
722 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
723 | (void), | |
724 | "Return NaN.") | |
725 | #define FUNC_NAME s_scm_nan | |
726 | { | |
727 | static int initialized = 0; | |
0aacf84e | 728 | if (!initialized) |
7351e207 MV |
729 | { |
730 | guile_ieee_init (); | |
731 | initialized = 1; | |
732 | } | |
55f26379 | 733 | return scm_from_double (guile_NaN); |
7351e207 MV |
734 | } |
735 | #undef FUNC_NAME | |
736 | ||
4219f20d | 737 | |
a48d60b1 MD |
738 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
739 | (SCM x), | |
740 | "Return the absolute value of @var{x}.") | |
2519490c | 741 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 742 | { |
e11e83f3 | 743 | if (SCM_I_INUMP (x)) |
0aacf84e | 744 | { |
e25f3727 | 745 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
746 | if (xx >= 0) |
747 | return x; | |
748 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 749 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 750 | else |
e25f3727 | 751 | return scm_i_inum2big (-xx); |
4219f20d | 752 | } |
9b9ef10c MW |
753 | else if (SCM_LIKELY (SCM_REALP (x))) |
754 | { | |
755 | double xx = SCM_REAL_VALUE (x); | |
756 | /* If x is a NaN then xx<0 is false so we return x unchanged */ | |
757 | if (xx < 0.0) | |
758 | return scm_from_double (-xx); | |
759 | /* Handle signed zeroes properly */ | |
760 | else if (SCM_UNLIKELY (xx == 0.0)) | |
761 | return flo0; | |
762 | else | |
763 | return x; | |
764 | } | |
0aacf84e MD |
765 | else if (SCM_BIGP (x)) |
766 | { | |
767 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
768 | if (sgn < 0) | |
769 | return scm_i_clonebig (x, 0); | |
770 | else | |
771 | return x; | |
4219f20d | 772 | } |
f92e85f7 MV |
773 | else if (SCM_FRACTIONP (x)) |
774 | { | |
73e4de09 | 775 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 776 | return x; |
cba42c93 | 777 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
778 | SCM_FRACTION_DENOMINATOR (x)); |
779 | } | |
0aacf84e | 780 | else |
a48d60b1 | 781 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 782 | } |
a48d60b1 | 783 | #undef FUNC_NAME |
0f2d19dd | 784 | |
4219f20d | 785 | |
2519490c MW |
786 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
787 | (SCM x, SCM y), | |
788 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
789 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 790 | { |
a16982ca | 791 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 792 | { |
e25f3727 | 793 | scm_t_inum xx = SCM_I_INUM (x); |
a16982ca | 794 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 795 | { |
e25f3727 | 796 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 797 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 798 | scm_num_overflow (s_scm_quotient); |
0aacf84e MD |
799 | else |
800 | { | |
e25f3727 | 801 | scm_t_inum z = xx / yy; |
a16982ca | 802 | if (SCM_LIKELY (SCM_FIXABLE (z))) |
d956fa6f | 803 | return SCM_I_MAKINUM (z); |
0aacf84e | 804 | else |
e25f3727 | 805 | return scm_i_inum2big (z); |
0aacf84e | 806 | } |
828865c3 | 807 | } |
0aacf84e | 808 | else if (SCM_BIGP (y)) |
ac0c002c | 809 | { |
e11e83f3 | 810 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
811 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
812 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
813 | { | |
814 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
815 | scm_remember_upto_here_1 (y); | |
d956fa6f | 816 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 817 | } |
0aacf84e | 818 | else |
cff5fa33 | 819 | return SCM_INUM0; |
ac0c002c DH |
820 | } |
821 | else | |
2519490c | 822 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
828865c3 | 823 | } |
0aacf84e MD |
824 | else if (SCM_BIGP (x)) |
825 | { | |
a16982ca | 826 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 827 | { |
e25f3727 | 828 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 829 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 830 | scm_num_overflow (s_scm_quotient); |
a16982ca | 831 | else if (SCM_UNLIKELY (yy == 1)) |
0aacf84e MD |
832 | return x; |
833 | else | |
834 | { | |
835 | SCM result = scm_i_mkbig (); | |
836 | if (yy < 0) | |
837 | { | |
838 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
839 | SCM_I_BIG_MPZ (x), | |
840 | - yy); | |
841 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
842 | } | |
843 | else | |
844 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
845 | scm_remember_upto_here_1 (x); | |
846 | return scm_i_normbig (result); | |
847 | } | |
848 | } | |
849 | else if (SCM_BIGP (y)) | |
850 | { | |
851 | SCM result = scm_i_mkbig (); | |
852 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
853 | SCM_I_BIG_MPZ (x), | |
854 | SCM_I_BIG_MPZ (y)); | |
855 | scm_remember_upto_here_2 (x, y); | |
856 | return scm_i_normbig (result); | |
857 | } | |
858 | else | |
2519490c | 859 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 860 | } |
0aacf84e | 861 | else |
2519490c | 862 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 863 | } |
2519490c | 864 | #undef FUNC_NAME |
0f2d19dd | 865 | |
2519490c MW |
866 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
867 | (SCM x, SCM y), | |
868 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
869 | "@lisp\n" | |
870 | "(remainder 13 4) @result{} 1\n" | |
871 | "(remainder -13 4) @result{} -1\n" | |
872 | "@end lisp") | |
873 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 874 | { |
a16982ca | 875 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 876 | { |
a16982ca | 877 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 878 | { |
e25f3727 | 879 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 880 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 881 | scm_num_overflow (s_scm_remainder); |
0aacf84e MD |
882 | else |
883 | { | |
a16982ca MW |
884 | /* C99 specifies that "%" is the remainder corresponding to a |
885 | quotient rounded towards zero, and that's also traditional | |
886 | for machine division, so z here should be well defined. */ | |
e25f3727 | 887 | scm_t_inum z = SCM_I_INUM (x) % yy; |
d956fa6f | 888 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
889 | } |
890 | } | |
891 | else if (SCM_BIGP (y)) | |
ac0c002c | 892 | { |
e11e83f3 | 893 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
894 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
895 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
896 | { | |
897 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
898 | scm_remember_upto_here_1 (y); | |
cff5fa33 | 899 | return SCM_INUM0; |
4dc09ee4 | 900 | } |
0aacf84e MD |
901 | else |
902 | return x; | |
ac0c002c DH |
903 | } |
904 | else | |
2519490c | 905 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
89a7e495 | 906 | } |
0aacf84e MD |
907 | else if (SCM_BIGP (x)) |
908 | { | |
a16982ca | 909 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 910 | { |
e25f3727 | 911 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 912 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 913 | scm_num_overflow (s_scm_remainder); |
0aacf84e MD |
914 | else |
915 | { | |
916 | SCM result = scm_i_mkbig (); | |
917 | if (yy < 0) | |
918 | yy = - yy; | |
919 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
920 | scm_remember_upto_here_1 (x); | |
921 | return scm_i_normbig (result); | |
922 | } | |
923 | } | |
924 | else if (SCM_BIGP (y)) | |
925 | { | |
926 | SCM result = scm_i_mkbig (); | |
927 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
928 | SCM_I_BIG_MPZ (x), | |
929 | SCM_I_BIG_MPZ (y)); | |
930 | scm_remember_upto_here_2 (x, y); | |
931 | return scm_i_normbig (result); | |
932 | } | |
933 | else | |
2519490c | 934 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 935 | } |
0aacf84e | 936 | else |
2519490c | 937 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 938 | } |
2519490c | 939 | #undef FUNC_NAME |
0f2d19dd | 940 | |
89a7e495 | 941 | |
2519490c MW |
942 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
943 | (SCM x, SCM y), | |
944 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
945 | "@lisp\n" | |
946 | "(modulo 13 4) @result{} 1\n" | |
947 | "(modulo -13 4) @result{} 3\n" | |
948 | "@end lisp") | |
949 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 950 | { |
a16982ca | 951 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 952 | { |
e25f3727 | 953 | scm_t_inum xx = SCM_I_INUM (x); |
a16982ca | 954 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 955 | { |
e25f3727 | 956 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 957 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 958 | scm_num_overflow (s_scm_modulo); |
0aacf84e MD |
959 | else |
960 | { | |
66b1c775 KR |
961 | /* C99 specifies that "%" is the remainder corresponding to a |
962 | quotient rounded towards zero, and that's also traditional | |
963 | for machine division, so z here should be well defined. */ | |
e25f3727 AW |
964 | scm_t_inum z = xx % yy; |
965 | scm_t_inum result; | |
0aacf84e MD |
966 | |
967 | if (yy < 0) | |
968 | { | |
969 | if (z > 0) | |
970 | result = z + yy; | |
971 | else | |
972 | result = z; | |
973 | } | |
974 | else | |
975 | { | |
976 | if (z < 0) | |
977 | result = z + yy; | |
978 | else | |
979 | result = z; | |
980 | } | |
d956fa6f | 981 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
982 | } |
983 | } | |
984 | else if (SCM_BIGP (y)) | |
985 | { | |
986 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
987 | { |
988 | mpz_t z_x; | |
989 | SCM result; | |
990 | ||
991 | if (sgn_y < 0) | |
992 | { | |
993 | SCM pos_y = scm_i_clonebig (y, 0); | |
994 | /* do this after the last scm_op */ | |
995 | mpz_init_set_si (z_x, xx); | |
996 | result = pos_y; /* re-use this bignum */ | |
997 | mpz_mod (SCM_I_BIG_MPZ (result), | |
998 | z_x, | |
999 | SCM_I_BIG_MPZ (pos_y)); | |
1000 | scm_remember_upto_here_1 (pos_y); | |
1001 | } | |
1002 | else | |
1003 | { | |
1004 | result = scm_i_mkbig (); | |
1005 | /* do this after the last scm_op */ | |
1006 | mpz_init_set_si (z_x, xx); | |
1007 | mpz_mod (SCM_I_BIG_MPZ (result), | |
1008 | z_x, | |
1009 | SCM_I_BIG_MPZ (y)); | |
1010 | scm_remember_upto_here_1 (y); | |
1011 | } | |
ca46fb90 | 1012 | |
0aacf84e MD |
1013 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
1014 | mpz_add (SCM_I_BIG_MPZ (result), | |
1015 | SCM_I_BIG_MPZ (y), | |
1016 | SCM_I_BIG_MPZ (result)); | |
1017 | scm_remember_upto_here_1 (y); | |
1018 | /* and do this before the next one */ | |
1019 | mpz_clear (z_x); | |
1020 | return scm_i_normbig (result); | |
1021 | } | |
1022 | } | |
1023 | else | |
2519490c | 1024 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
f872b822 | 1025 | } |
0aacf84e MD |
1026 | else if (SCM_BIGP (x)) |
1027 | { | |
a16982ca | 1028 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 1029 | { |
e25f3727 | 1030 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 1031 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 1032 | scm_num_overflow (s_scm_modulo); |
0aacf84e MD |
1033 | else |
1034 | { | |
1035 | SCM result = scm_i_mkbig (); | |
1036 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
1037 | SCM_I_BIG_MPZ (x), | |
1038 | (yy < 0) ? - yy : yy); | |
1039 | scm_remember_upto_here_1 (x); | |
1040 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1041 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
1042 | SCM_I_BIG_MPZ (result), | |
1043 | - yy); | |
1044 | return scm_i_normbig (result); | |
1045 | } | |
1046 | } | |
1047 | else if (SCM_BIGP (y)) | |
1048 | { | |
a16982ca MW |
1049 | SCM result = scm_i_mkbig (); |
1050 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1051 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
1052 | mpz_mod (SCM_I_BIG_MPZ (result), | |
1053 | SCM_I_BIG_MPZ (x), | |
1054 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 1055 | |
a16982ca MW |
1056 | scm_remember_upto_here_1 (x); |
1057 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1058 | mpz_add (SCM_I_BIG_MPZ (result), | |
1059 | SCM_I_BIG_MPZ (y), | |
1060 | SCM_I_BIG_MPZ (result)); | |
1061 | scm_remember_upto_here_2 (y, pos_y); | |
1062 | return scm_i_normbig (result); | |
0aacf84e MD |
1063 | } |
1064 | else | |
2519490c | 1065 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 1066 | } |
0aacf84e | 1067 | else |
2519490c | 1068 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 1069 | } |
2519490c | 1070 | #undef FUNC_NAME |
0f2d19dd | 1071 | |
5fbf680b MW |
1072 | /* two_valued_wta_dispatch_2 is a version of SCM_WTA_DISPATCH_2 for |
1073 | two-valued functions. It is called from primitive generics that take | |
1074 | two arguments and return two values, when the core procedure is | |
1075 | unable to handle the given argument types. If there are GOOPS | |
1076 | methods for this primitive generic, it dispatches to GOOPS and, if | |
1077 | successful, expects two values to be returned, which are placed in | |
1078 | *rp1 and *rp2. If there are no GOOPS methods, it throws a | |
1079 | wrong-type-arg exception. | |
1080 | ||
1081 | FIXME: This obviously belongs somewhere else, but until we decide on | |
1082 | the right API, it is here as a static function, because it is needed | |
1083 | by the *_divide functions below. | |
1084 | */ | |
1085 | static void | |
1086 | two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos, | |
1087 | const char *subr, SCM *rp1, SCM *rp2) | |
1088 | { | |
1089 | if (SCM_UNPACK (gf)) | |
1090 | scm_i_extract_values_2 (scm_call_generic_2 (gf, a1, a2), rp1, rp2); | |
1091 | else | |
1092 | scm_wrong_type_arg (subr, pos, (pos == SCM_ARG1) ? a1 : a2); | |
1093 | } | |
1094 | ||
ff62c168 | 1095 | static SCM scm_i_inexact_euclidean_quotient (double x, double y); |
03ddd15b | 1096 | static SCM scm_i_exact_rational_euclidean_quotient (SCM x, SCM y); |
ff62c168 MW |
1097 | |
1098 | SCM_PRIMITIVE_GENERIC (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, | |
1099 | (SCM x, SCM y), | |
1100 | "Return the integer @var{q} such that\n" | |
1101 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1102 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1103 | "@lisp\n" | |
1104 | "(euclidean-quotient 123 10) @result{} 12\n" | |
1105 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
1106 | "(euclidean-quotient -123 10) @result{} -13\n" | |
1107 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
1108 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
1109 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
1110 | "@end lisp") | |
1111 | #define FUNC_NAME s_scm_euclidean_quotient | |
1112 | { | |
1113 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1114 | { | |
4a46bc2a | 1115 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
1116 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
1117 | { | |
1118 | scm_t_inum yy = SCM_I_INUM (y); | |
1119 | if (SCM_UNLIKELY (yy == 0)) | |
1120 | scm_num_overflow (s_scm_euclidean_quotient); | |
1121 | else | |
1122 | { | |
ff62c168 MW |
1123 | scm_t_inum qq = xx / yy; |
1124 | if (xx < qq * yy) | |
1125 | { | |
1126 | if (yy > 0) | |
1127 | qq--; | |
1128 | else | |
1129 | qq++; | |
1130 | } | |
4a46bc2a MW |
1131 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
1132 | return SCM_I_MAKINUM (qq); | |
1133 | else | |
1134 | return scm_i_inum2big (qq); | |
ff62c168 MW |
1135 | } |
1136 | } | |
1137 | else if (SCM_BIGP (y)) | |
1138 | { | |
4a46bc2a | 1139 | if (xx >= 0) |
ff62c168 MW |
1140 | return SCM_INUM0; |
1141 | else | |
4a46bc2a MW |
1142 | { |
1143 | scm_t_inum qq = - mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1144 | scm_remember_upto_here_1 (y); | |
1145 | return SCM_I_MAKINUM (qq); | |
1146 | } | |
ff62c168 MW |
1147 | } |
1148 | else if (SCM_REALP (y)) | |
4a46bc2a | 1149 | return scm_i_inexact_euclidean_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 1150 | else if (SCM_FRACTIONP (y)) |
03ddd15b | 1151 | return scm_i_exact_rational_euclidean_quotient (x, y); |
ff62c168 MW |
1152 | else |
1153 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1154 | s_scm_euclidean_quotient); | |
1155 | } | |
1156 | else if (SCM_BIGP (x)) | |
1157 | { | |
1158 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1159 | { | |
1160 | scm_t_inum yy = SCM_I_INUM (y); | |
1161 | if (SCM_UNLIKELY (yy == 0)) | |
1162 | scm_num_overflow (s_scm_euclidean_quotient); | |
4a46bc2a MW |
1163 | else if (SCM_UNLIKELY (yy == 1)) |
1164 | return x; | |
ff62c168 MW |
1165 | else |
1166 | { | |
1167 | SCM q = scm_i_mkbig (); | |
1168 | if (yy > 0) | |
1169 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1170 | else | |
1171 | { | |
1172 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1173 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1174 | } | |
1175 | scm_remember_upto_here_1 (x); | |
1176 | return scm_i_normbig (q); | |
1177 | } | |
1178 | } | |
1179 | else if (SCM_BIGP (y)) | |
1180 | { | |
1181 | SCM q = scm_i_mkbig (); | |
1182 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1183 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1184 | SCM_I_BIG_MPZ (x), | |
1185 | SCM_I_BIG_MPZ (y)); | |
1186 | else | |
1187 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1188 | SCM_I_BIG_MPZ (x), | |
1189 | SCM_I_BIG_MPZ (y)); | |
1190 | scm_remember_upto_here_2 (x, y); | |
1191 | return scm_i_normbig (q); | |
1192 | } | |
1193 | else if (SCM_REALP (y)) | |
1194 | return scm_i_inexact_euclidean_quotient | |
1195 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1196 | else if (SCM_FRACTIONP (y)) | |
03ddd15b | 1197 | return scm_i_exact_rational_euclidean_quotient (x, y); |
ff62c168 MW |
1198 | else |
1199 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1200 | s_scm_euclidean_quotient); | |
1201 | } | |
1202 | else if (SCM_REALP (x)) | |
1203 | { | |
1204 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1205 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1206 | return scm_i_inexact_euclidean_quotient | |
1207 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1208 | else | |
1209 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1210 | s_scm_euclidean_quotient); | |
1211 | } | |
1212 | else if (SCM_FRACTIONP (x)) | |
1213 | { | |
1214 | if (SCM_REALP (y)) | |
1215 | return scm_i_inexact_euclidean_quotient | |
1216 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
03ddd15b MW |
1217 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
1218 | return scm_i_exact_rational_euclidean_quotient (x, y); | |
ff62c168 | 1219 | else |
03ddd15b MW |
1220 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, |
1221 | s_scm_euclidean_quotient); | |
ff62c168 MW |
1222 | } |
1223 | else | |
1224 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG1, | |
1225 | s_scm_euclidean_quotient); | |
1226 | } | |
1227 | #undef FUNC_NAME | |
1228 | ||
1229 | static SCM | |
1230 | scm_i_inexact_euclidean_quotient (double x, double y) | |
1231 | { | |
1232 | if (SCM_LIKELY (y > 0)) | |
1233 | return scm_from_double (floor (x / y)); | |
1234 | else if (SCM_LIKELY (y < 0)) | |
1235 | return scm_from_double (ceil (x / y)); | |
1236 | else if (y == 0) | |
1237 | scm_num_overflow (s_scm_euclidean_quotient); /* or return a NaN? */ | |
1238 | else | |
1239 | return scm_nan (); | |
1240 | } | |
1241 | ||
ff62c168 | 1242 | static SCM |
03ddd15b | 1243 | scm_i_exact_rational_euclidean_quotient (SCM x, SCM y) |
ff62c168 | 1244 | { |
03ddd15b MW |
1245 | return scm_euclidean_quotient |
1246 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1247 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
1248 | } |
1249 | ||
1250 | static SCM scm_i_inexact_euclidean_remainder (double x, double y); | |
03ddd15b | 1251 | static SCM scm_i_exact_rational_euclidean_remainder (SCM x, SCM y); |
ff62c168 MW |
1252 | |
1253 | SCM_PRIMITIVE_GENERIC (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, | |
1254 | (SCM x, SCM y), | |
1255 | "Return the real number @var{r} such that\n" | |
1256 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
1257 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1258 | "for some integer @var{q}.\n" | |
1259 | "@lisp\n" | |
1260 | "(euclidean-remainder 123 10) @result{} 3\n" | |
1261 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
1262 | "(euclidean-remainder -123 10) @result{} 7\n" | |
1263 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
1264 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
1265 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
1266 | "@end lisp") | |
1267 | #define FUNC_NAME s_scm_euclidean_remainder | |
1268 | { | |
1269 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1270 | { | |
4a46bc2a | 1271 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
1272 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
1273 | { | |
1274 | scm_t_inum yy = SCM_I_INUM (y); | |
1275 | if (SCM_UNLIKELY (yy == 0)) | |
1276 | scm_num_overflow (s_scm_euclidean_remainder); | |
1277 | else | |
1278 | { | |
4a46bc2a | 1279 | scm_t_inum rr = xx % yy; |
ff62c168 MW |
1280 | if (rr >= 0) |
1281 | return SCM_I_MAKINUM (rr); | |
1282 | else if (yy > 0) | |
1283 | return SCM_I_MAKINUM (rr + yy); | |
1284 | else | |
1285 | return SCM_I_MAKINUM (rr - yy); | |
1286 | } | |
1287 | } | |
1288 | else if (SCM_BIGP (y)) | |
1289 | { | |
ff62c168 MW |
1290 | if (xx >= 0) |
1291 | return x; | |
1292 | else if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1293 | { | |
1294 | SCM r = scm_i_mkbig (); | |
1295 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1296 | scm_remember_upto_here_1 (y); | |
1297 | return scm_i_normbig (r); | |
1298 | } | |
1299 | else | |
1300 | { | |
1301 | SCM r = scm_i_mkbig (); | |
1302 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1303 | scm_remember_upto_here_1 (y); | |
1304 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1305 | return scm_i_normbig (r); | |
1306 | } | |
1307 | } | |
1308 | else if (SCM_REALP (y)) | |
4a46bc2a | 1309 | return scm_i_inexact_euclidean_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 1310 | else if (SCM_FRACTIONP (y)) |
03ddd15b | 1311 | return scm_i_exact_rational_euclidean_remainder (x, y); |
ff62c168 MW |
1312 | else |
1313 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1314 | s_scm_euclidean_remainder); | |
1315 | } | |
1316 | else if (SCM_BIGP (x)) | |
1317 | { | |
1318 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1319 | { | |
1320 | scm_t_inum yy = SCM_I_INUM (y); | |
1321 | if (SCM_UNLIKELY (yy == 0)) | |
1322 | scm_num_overflow (s_scm_euclidean_remainder); | |
1323 | else | |
1324 | { | |
1325 | scm_t_inum rr; | |
1326 | if (yy < 0) | |
1327 | yy = -yy; | |
1328 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1329 | scm_remember_upto_here_1 (x); | |
1330 | return SCM_I_MAKINUM (rr); | |
1331 | } | |
1332 | } | |
1333 | else if (SCM_BIGP (y)) | |
1334 | { | |
1335 | SCM r = scm_i_mkbig (); | |
1336 | mpz_mod (SCM_I_BIG_MPZ (r), | |
1337 | SCM_I_BIG_MPZ (x), | |
1338 | SCM_I_BIG_MPZ (y)); | |
1339 | scm_remember_upto_here_2 (x, y); | |
1340 | return scm_i_normbig (r); | |
1341 | } | |
1342 | else if (SCM_REALP (y)) | |
1343 | return scm_i_inexact_euclidean_remainder | |
1344 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1345 | else if (SCM_FRACTIONP (y)) | |
03ddd15b | 1346 | return scm_i_exact_rational_euclidean_remainder (x, y); |
ff62c168 MW |
1347 | else |
1348 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1349 | s_scm_euclidean_remainder); | |
1350 | } | |
1351 | else if (SCM_REALP (x)) | |
1352 | { | |
1353 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1354 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1355 | return scm_i_inexact_euclidean_remainder | |
1356 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1357 | else | |
1358 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1359 | s_scm_euclidean_remainder); | |
1360 | } | |
1361 | else if (SCM_FRACTIONP (x)) | |
1362 | { | |
1363 | if (SCM_REALP (y)) | |
1364 | return scm_i_inexact_euclidean_remainder | |
1365 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
03ddd15b MW |
1366 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
1367 | return scm_i_exact_rational_euclidean_remainder (x, y); | |
ff62c168 | 1368 | else |
03ddd15b MW |
1369 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, |
1370 | s_scm_euclidean_remainder); | |
ff62c168 MW |
1371 | } |
1372 | else | |
1373 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG1, | |
1374 | s_scm_euclidean_remainder); | |
1375 | } | |
1376 | #undef FUNC_NAME | |
1377 | ||
1378 | static SCM | |
1379 | scm_i_inexact_euclidean_remainder (double x, double y) | |
1380 | { | |
1381 | double q; | |
1382 | ||
1383 | /* Although it would be more efficient to use fmod here, we can't | |
1384 | because it would in some cases produce results inconsistent with | |
1385 | scm_i_inexact_euclidean_quotient, such that x != q * y + r (not | |
1386 | even close). In particular, when x is very close to a multiple of | |
1387 | y, then r might be either 0.0 or abs(y)-epsilon, but those two | |
1388 | cases must correspond to different choices of q. If r = 0.0 then q | |
1389 | must be x/y, and if r = abs(y) then q must be (x-r)/y. If quotient | |
1390 | chooses one and remainder chooses the other, it would be bad. This | |
1391 | problem was observed with x = 130.0 and y = 10/7. */ | |
1392 | if (SCM_LIKELY (y > 0)) | |
1393 | q = floor (x / y); | |
1394 | else if (SCM_LIKELY (y < 0)) | |
1395 | q = ceil (x / y); | |
1396 | else if (y == 0) | |
1397 | scm_num_overflow (s_scm_euclidean_remainder); /* or return a NaN? */ | |
1398 | else | |
1399 | return scm_nan (); | |
1400 | return scm_from_double (x - q * y); | |
1401 | } | |
1402 | ||
ff62c168 | 1403 | static SCM |
03ddd15b | 1404 | scm_i_exact_rational_euclidean_remainder (SCM x, SCM y) |
ff62c168 | 1405 | { |
03ddd15b MW |
1406 | SCM xd = scm_denominator (x); |
1407 | SCM yd = scm_denominator (y); | |
1408 | SCM r1 = scm_euclidean_remainder (scm_product (scm_numerator (x), yd), | |
1409 | scm_product (scm_numerator (y), xd)); | |
1410 | return scm_divide (r1, scm_product (xd, yd)); | |
ff62c168 MW |
1411 | } |
1412 | ||
1413 | ||
5fbf680b MW |
1414 | static void scm_i_inexact_euclidean_divide (double x, double y, |
1415 | SCM *qp, SCM *rp); | |
03ddd15b MW |
1416 | static void scm_i_exact_rational_euclidean_divide (SCM x, SCM y, |
1417 | SCM *qp, SCM *rp); | |
ff62c168 | 1418 | |
5fbf680b | 1419 | SCM_PRIMITIVE_GENERIC (scm_i_euclidean_divide, "euclidean/", 2, 0, 0, |
ff62c168 MW |
1420 | (SCM x, SCM y), |
1421 | "Return the integer @var{q} and the real number @var{r}\n" | |
1422 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1423 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1424 | "@lisp\n" | |
1425 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
1426 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
1427 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
1428 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
1429 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1430 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1431 | "@end lisp") | |
5fbf680b MW |
1432 | #define FUNC_NAME s_scm_i_euclidean_divide |
1433 | { | |
1434 | SCM q, r; | |
1435 | ||
1436 | scm_euclidean_divide(x, y, &q, &r); | |
1437 | return scm_values (scm_list_2 (q, r)); | |
1438 | } | |
1439 | #undef FUNC_NAME | |
1440 | ||
1441 | #define s_scm_euclidean_divide s_scm_i_euclidean_divide | |
1442 | #define g_scm_euclidean_divide g_scm_i_euclidean_divide | |
1443 | ||
1444 | void | |
1445 | scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 MW |
1446 | { |
1447 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1448 | { | |
4a46bc2a | 1449 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
1450 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
1451 | { | |
1452 | scm_t_inum yy = SCM_I_INUM (y); | |
1453 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 1454 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1455 | else |
1456 | { | |
ff62c168 | 1457 | scm_t_inum qq = xx / yy; |
4a46bc2a | 1458 | scm_t_inum rr = xx % yy; |
ff62c168 MW |
1459 | if (rr < 0) |
1460 | { | |
1461 | if (yy > 0) | |
1462 | { rr += yy; qq--; } | |
1463 | else | |
1464 | { rr -= yy; qq++; } | |
1465 | } | |
4a46bc2a | 1466 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 1467 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 1468 | else |
5fbf680b MW |
1469 | *qp = scm_i_inum2big (qq); |
1470 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 1471 | } |
5fbf680b | 1472 | return; |
ff62c168 MW |
1473 | } |
1474 | else if (SCM_BIGP (y)) | |
1475 | { | |
ff62c168 | 1476 | if (xx >= 0) |
5fbf680b MW |
1477 | { |
1478 | *qp = SCM_INUM0; | |
1479 | *rp = x; | |
1480 | } | |
ff62c168 MW |
1481 | else if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) |
1482 | { | |
1483 | SCM r = scm_i_mkbig (); | |
1484 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1485 | scm_remember_upto_here_1 (y); | |
5fbf680b MW |
1486 | *qp = SCM_I_MAKINUM (-1); |
1487 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
1488 | } |
1489 | else | |
1490 | { | |
1491 | SCM r = scm_i_mkbig (); | |
1492 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1493 | scm_remember_upto_here_1 (y); | |
1494 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
5fbf680b MW |
1495 | *qp = SCM_INUM1; |
1496 | *rp = scm_i_normbig (r); | |
ff62c168 | 1497 | } |
5fbf680b | 1498 | return; |
ff62c168 MW |
1499 | } |
1500 | else if (SCM_REALP (y)) | |
5fbf680b | 1501 | return scm_i_inexact_euclidean_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 1502 | else if (SCM_FRACTIONP (y)) |
03ddd15b | 1503 | return scm_i_exact_rational_euclidean_divide (x, y, qp, rp); |
ff62c168 | 1504 | else |
5fbf680b MW |
1505 | return two_valued_wta_dispatch_2 |
1506 | (g_scm_euclidean_divide, x, y, SCM_ARG2, | |
1507 | s_scm_euclidean_divide, qp, rp); | |
ff62c168 MW |
1508 | } |
1509 | else if (SCM_BIGP (x)) | |
1510 | { | |
1511 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1512 | { | |
1513 | scm_t_inum yy = SCM_I_INUM (y); | |
1514 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 1515 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1516 | else |
1517 | { | |
1518 | SCM q = scm_i_mkbig (); | |
4a46bc2a | 1519 | scm_t_inum rr; |
ff62c168 | 1520 | if (yy > 0) |
4a46bc2a MW |
1521 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
1522 | SCM_I_BIG_MPZ (x), yy); | |
ff62c168 MW |
1523 | else |
1524 | { | |
4a46bc2a MW |
1525 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
1526 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 MW |
1527 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
1528 | } | |
1529 | scm_remember_upto_here_1 (x); | |
5fbf680b MW |
1530 | *qp = scm_i_normbig (q); |
1531 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 1532 | } |
5fbf680b | 1533 | return; |
ff62c168 MW |
1534 | } |
1535 | else if (SCM_BIGP (y)) | |
1536 | { | |
1537 | SCM q = scm_i_mkbig (); | |
1538 | SCM r = scm_i_mkbig (); | |
1539 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1540 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1541 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1542 | else | |
1543 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1544 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1545 | scm_remember_upto_here_2 (x, y); | |
5fbf680b MW |
1546 | *qp = scm_i_normbig (q); |
1547 | *rp = scm_i_normbig (r); | |
1548 | return; | |
ff62c168 MW |
1549 | } |
1550 | else if (SCM_REALP (y)) | |
ac6ce16b | 1551 | return scm_i_inexact_euclidean_divide |
5fbf680b | 1552 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 1553 | else if (SCM_FRACTIONP (y)) |
03ddd15b | 1554 | return scm_i_exact_rational_euclidean_divide (x, y, qp, rp); |
ff62c168 | 1555 | else |
5fbf680b MW |
1556 | return two_valued_wta_dispatch_2 |
1557 | (g_scm_euclidean_divide, x, y, SCM_ARG2, | |
1558 | s_scm_euclidean_divide, qp, rp); | |
ff62c168 MW |
1559 | } |
1560 | else if (SCM_REALP (x)) | |
1561 | { | |
1562 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1563 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
ac6ce16b | 1564 | return scm_i_inexact_euclidean_divide |
5fbf680b | 1565 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
ff62c168 | 1566 | else |
5fbf680b MW |
1567 | return two_valued_wta_dispatch_2 |
1568 | (g_scm_euclidean_divide, x, y, SCM_ARG2, | |
1569 | s_scm_euclidean_divide, qp, rp); | |
ff62c168 MW |
1570 | } |
1571 | else if (SCM_FRACTIONP (x)) | |
1572 | { | |
1573 | if (SCM_REALP (y)) | |
ac6ce16b | 1574 | return scm_i_inexact_euclidean_divide |
5fbf680b | 1575 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b MW |
1576 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
1577 | return scm_i_exact_rational_euclidean_divide (x, y, qp, rp); | |
ff62c168 | 1578 | else |
03ddd15b MW |
1579 | return two_valued_wta_dispatch_2 |
1580 | (g_scm_euclidean_divide, x, y, SCM_ARG2, | |
1581 | s_scm_euclidean_divide, qp, rp); | |
ff62c168 MW |
1582 | } |
1583 | else | |
5fbf680b MW |
1584 | return two_valued_wta_dispatch_2 (g_scm_euclidean_divide, x, y, SCM_ARG1, |
1585 | s_scm_euclidean_divide, qp, rp); | |
ff62c168 | 1586 | } |
ff62c168 | 1587 | |
5fbf680b MW |
1588 | static void |
1589 | scm_i_inexact_euclidean_divide (double x, double y, SCM *qp, SCM *rp) | |
ff62c168 MW |
1590 | { |
1591 | double q, r; | |
1592 | ||
1593 | if (SCM_LIKELY (y > 0)) | |
1594 | q = floor (x / y); | |
1595 | else if (SCM_LIKELY (y < 0)) | |
1596 | q = ceil (x / y); | |
1597 | else if (y == 0) | |
ac6ce16b | 1598 | scm_num_overflow (s_scm_euclidean_divide); /* or return a NaN? */ |
ff62c168 MW |
1599 | else |
1600 | q = guile_NaN; | |
1601 | r = x - q * y; | |
5fbf680b MW |
1602 | *qp = scm_from_double (q); |
1603 | *rp = scm_from_double (r); | |
ff62c168 MW |
1604 | } |
1605 | ||
5fbf680b | 1606 | static void |
03ddd15b | 1607 | scm_i_exact_rational_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 1608 | { |
03ddd15b MW |
1609 | SCM r1; |
1610 | SCM xd = scm_denominator (x); | |
1611 | SCM yd = scm_denominator (y); | |
1612 | ||
1613 | scm_euclidean_divide (scm_product (scm_numerator (x), yd), | |
1614 | scm_product (scm_numerator (y), xd), | |
1615 | qp, &r1); | |
1616 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
ff62c168 MW |
1617 | } |
1618 | ||
8f9da340 MW |
1619 | static SCM scm_i_inexact_floor_quotient (double x, double y); |
1620 | static SCM scm_i_exact_rational_floor_quotient (SCM x, SCM y); | |
1621 | ||
1622 | SCM_PRIMITIVE_GENERIC (scm_floor_quotient, "floor-quotient", 2, 0, 0, | |
1623 | (SCM x, SCM y), | |
1624 | "Return the floor of @math{@var{x} / @var{y}}.\n" | |
1625 | "@lisp\n" | |
1626 | "(floor-quotient 123 10) @result{} 12\n" | |
1627 | "(floor-quotient 123 -10) @result{} -13\n" | |
1628 | "(floor-quotient -123 10) @result{} -13\n" | |
1629 | "(floor-quotient -123 -10) @result{} 12\n" | |
1630 | "(floor-quotient -123.2 -63.5) @result{} 1.0\n" | |
1631 | "(floor-quotient 16/3 -10/7) @result{} -4\n" | |
1632 | "@end lisp") | |
1633 | #define FUNC_NAME s_scm_floor_quotient | |
1634 | { | |
1635 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1636 | { | |
1637 | scm_t_inum xx = SCM_I_INUM (x); | |
1638 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1639 | { | |
1640 | scm_t_inum yy = SCM_I_INUM (y); | |
1641 | scm_t_inum xx1 = xx; | |
1642 | scm_t_inum qq; | |
1643 | if (SCM_LIKELY (yy > 0)) | |
1644 | { | |
1645 | if (SCM_UNLIKELY (xx < 0)) | |
1646 | xx1 = xx - yy + 1; | |
1647 | } | |
1648 | else if (SCM_UNLIKELY (yy == 0)) | |
1649 | scm_num_overflow (s_scm_floor_quotient); | |
1650 | else if (xx > 0) | |
1651 | xx1 = xx - yy - 1; | |
1652 | qq = xx1 / yy; | |
1653 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1654 | return SCM_I_MAKINUM (qq); | |
1655 | else | |
1656 | return scm_i_inum2big (qq); | |
1657 | } | |
1658 | else if (SCM_BIGP (y)) | |
1659 | { | |
1660 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1661 | scm_remember_upto_here_1 (y); | |
1662 | if (sign > 0) | |
1663 | return SCM_I_MAKINUM ((xx < 0) ? -1 : 0); | |
1664 | else | |
1665 | return SCM_I_MAKINUM ((xx > 0) ? -1 : 0); | |
1666 | } | |
1667 | else if (SCM_REALP (y)) | |
1668 | return scm_i_inexact_floor_quotient (xx, SCM_REAL_VALUE (y)); | |
1669 | else if (SCM_FRACTIONP (y)) | |
1670 | return scm_i_exact_rational_floor_quotient (x, y); | |
1671 | else | |
1672 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1673 | s_scm_floor_quotient); | |
1674 | } | |
1675 | else if (SCM_BIGP (x)) | |
1676 | { | |
1677 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1678 | { | |
1679 | scm_t_inum yy = SCM_I_INUM (y); | |
1680 | if (SCM_UNLIKELY (yy == 0)) | |
1681 | scm_num_overflow (s_scm_floor_quotient); | |
1682 | else if (SCM_UNLIKELY (yy == 1)) | |
1683 | return x; | |
1684 | else | |
1685 | { | |
1686 | SCM q = scm_i_mkbig (); | |
1687 | if (yy > 0) | |
1688 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1689 | else | |
1690 | { | |
1691 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1692 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1693 | } | |
1694 | scm_remember_upto_here_1 (x); | |
1695 | return scm_i_normbig (q); | |
1696 | } | |
1697 | } | |
1698 | else if (SCM_BIGP (y)) | |
1699 | { | |
1700 | SCM q = scm_i_mkbig (); | |
1701 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1702 | SCM_I_BIG_MPZ (x), | |
1703 | SCM_I_BIG_MPZ (y)); | |
1704 | scm_remember_upto_here_2 (x, y); | |
1705 | return scm_i_normbig (q); | |
1706 | } | |
1707 | else if (SCM_REALP (y)) | |
1708 | return scm_i_inexact_floor_quotient | |
1709 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1710 | else if (SCM_FRACTIONP (y)) | |
1711 | return scm_i_exact_rational_floor_quotient (x, y); | |
1712 | else | |
1713 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1714 | s_scm_floor_quotient); | |
1715 | } | |
1716 | else if (SCM_REALP (x)) | |
1717 | { | |
1718 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1719 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1720 | return scm_i_inexact_floor_quotient | |
1721 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1722 | else | |
1723 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1724 | s_scm_floor_quotient); | |
1725 | } | |
1726 | else if (SCM_FRACTIONP (x)) | |
1727 | { | |
1728 | if (SCM_REALP (y)) | |
1729 | return scm_i_inexact_floor_quotient | |
1730 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1731 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1732 | return scm_i_exact_rational_floor_quotient (x, y); | |
1733 | else | |
1734 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1735 | s_scm_floor_quotient); | |
1736 | } | |
1737 | else | |
1738 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG1, | |
1739 | s_scm_floor_quotient); | |
1740 | } | |
1741 | #undef FUNC_NAME | |
1742 | ||
1743 | static SCM | |
1744 | scm_i_inexact_floor_quotient (double x, double y) | |
1745 | { | |
1746 | if (SCM_UNLIKELY (y == 0)) | |
1747 | scm_num_overflow (s_scm_floor_quotient); /* or return a NaN? */ | |
1748 | else | |
1749 | return scm_from_double (floor (x / y)); | |
1750 | } | |
1751 | ||
1752 | static SCM | |
1753 | scm_i_exact_rational_floor_quotient (SCM x, SCM y) | |
1754 | { | |
1755 | return scm_floor_quotient | |
1756 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1757 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1758 | } | |
1759 | ||
1760 | static SCM scm_i_inexact_floor_remainder (double x, double y); | |
1761 | static SCM scm_i_exact_rational_floor_remainder (SCM x, SCM y); | |
1762 | ||
1763 | SCM_PRIMITIVE_GENERIC (scm_floor_remainder, "floor-remainder", 2, 0, 0, | |
1764 | (SCM x, SCM y), | |
1765 | "Return the real number @var{r} such that\n" | |
1766 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1767 | "where @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1768 | "@lisp\n" | |
1769 | "(floor-remainder 123 10) @result{} 3\n" | |
1770 | "(floor-remainder 123 -10) @result{} -7\n" | |
1771 | "(floor-remainder -123 10) @result{} 7\n" | |
1772 | "(floor-remainder -123 -10) @result{} -3\n" | |
1773 | "(floor-remainder -123.2 -63.5) @result{} -59.7\n" | |
1774 | "(floor-remainder 16/3 -10/7) @result{} -8/21\n" | |
1775 | "@end lisp") | |
1776 | #define FUNC_NAME s_scm_floor_remainder | |
1777 | { | |
1778 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1779 | { | |
1780 | scm_t_inum xx = SCM_I_INUM (x); | |
1781 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1782 | { | |
1783 | scm_t_inum yy = SCM_I_INUM (y); | |
1784 | if (SCM_UNLIKELY (yy == 0)) | |
1785 | scm_num_overflow (s_scm_floor_remainder); | |
1786 | else | |
1787 | { | |
1788 | scm_t_inum rr = xx % yy; | |
1789 | int needs_adjustment; | |
1790 | ||
1791 | if (SCM_LIKELY (yy > 0)) | |
1792 | needs_adjustment = (rr < 0); | |
1793 | else | |
1794 | needs_adjustment = (rr > 0); | |
1795 | ||
1796 | if (needs_adjustment) | |
1797 | rr += yy; | |
1798 | return SCM_I_MAKINUM (rr); | |
1799 | } | |
1800 | } | |
1801 | else if (SCM_BIGP (y)) | |
1802 | { | |
1803 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1804 | scm_remember_upto_here_1 (y); | |
1805 | if (sign > 0) | |
1806 | { | |
1807 | if (xx < 0) | |
1808 | { | |
1809 | SCM r = scm_i_mkbig (); | |
1810 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1811 | scm_remember_upto_here_1 (y); | |
1812 | return scm_i_normbig (r); | |
1813 | } | |
1814 | else | |
1815 | return x; | |
1816 | } | |
1817 | else if (xx <= 0) | |
1818 | return x; | |
1819 | else | |
1820 | { | |
1821 | SCM r = scm_i_mkbig (); | |
1822 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1823 | scm_remember_upto_here_1 (y); | |
1824 | return scm_i_normbig (r); | |
1825 | } | |
1826 | } | |
1827 | else if (SCM_REALP (y)) | |
1828 | return scm_i_inexact_floor_remainder (xx, SCM_REAL_VALUE (y)); | |
1829 | else if (SCM_FRACTIONP (y)) | |
1830 | return scm_i_exact_rational_floor_remainder (x, y); | |
1831 | else | |
1832 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1833 | s_scm_floor_remainder); | |
1834 | } | |
1835 | else if (SCM_BIGP (x)) | |
1836 | { | |
1837 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1838 | { | |
1839 | scm_t_inum yy = SCM_I_INUM (y); | |
1840 | if (SCM_UNLIKELY (yy == 0)) | |
1841 | scm_num_overflow (s_scm_floor_remainder); | |
1842 | else | |
1843 | { | |
1844 | scm_t_inum rr; | |
1845 | if (yy > 0) | |
1846 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1847 | else | |
1848 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1849 | scm_remember_upto_here_1 (x); | |
1850 | return SCM_I_MAKINUM (rr); | |
1851 | } | |
1852 | } | |
1853 | else if (SCM_BIGP (y)) | |
1854 | { | |
1855 | SCM r = scm_i_mkbig (); | |
1856 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
1857 | SCM_I_BIG_MPZ (x), | |
1858 | SCM_I_BIG_MPZ (y)); | |
1859 | scm_remember_upto_here_2 (x, y); | |
1860 | return scm_i_normbig (r); | |
1861 | } | |
1862 | else if (SCM_REALP (y)) | |
1863 | return scm_i_inexact_floor_remainder | |
1864 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1865 | else if (SCM_FRACTIONP (y)) | |
1866 | return scm_i_exact_rational_floor_remainder (x, y); | |
1867 | else | |
1868 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1869 | s_scm_floor_remainder); | |
1870 | } | |
1871 | else if (SCM_REALP (x)) | |
1872 | { | |
1873 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1874 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1875 | return scm_i_inexact_floor_remainder | |
1876 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1877 | else | |
1878 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1879 | s_scm_floor_remainder); | |
1880 | } | |
1881 | else if (SCM_FRACTIONP (x)) | |
1882 | { | |
1883 | if (SCM_REALP (y)) | |
1884 | return scm_i_inexact_floor_remainder | |
1885 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1886 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1887 | return scm_i_exact_rational_floor_remainder (x, y); | |
1888 | else | |
1889 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1890 | s_scm_floor_remainder); | |
1891 | } | |
1892 | else | |
1893 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG1, | |
1894 | s_scm_floor_remainder); | |
1895 | } | |
1896 | #undef FUNC_NAME | |
1897 | ||
1898 | static SCM | |
1899 | scm_i_inexact_floor_remainder (double x, double y) | |
1900 | { | |
1901 | /* Although it would be more efficient to use fmod here, we can't | |
1902 | because it would in some cases produce results inconsistent with | |
1903 | scm_i_inexact_floor_quotient, such that x != q * y + r (not even | |
1904 | close). In particular, when x is very close to a multiple of y, | |
1905 | then r might be either 0.0 or y, but those two cases must | |
1906 | correspond to different choices of q. If r = 0.0 then q must be | |
1907 | x/y, and if r = y then q must be x/y-1. If quotient chooses one | |
1908 | and remainder chooses the other, it would be bad. */ | |
1909 | if (SCM_UNLIKELY (y == 0)) | |
1910 | scm_num_overflow (s_scm_floor_remainder); /* or return a NaN? */ | |
1911 | else | |
1912 | return scm_from_double (x - y * floor (x / y)); | |
1913 | } | |
1914 | ||
1915 | static SCM | |
1916 | scm_i_exact_rational_floor_remainder (SCM x, SCM y) | |
1917 | { | |
1918 | SCM xd = scm_denominator (x); | |
1919 | SCM yd = scm_denominator (y); | |
1920 | SCM r1 = scm_floor_remainder (scm_product (scm_numerator (x), yd), | |
1921 | scm_product (scm_numerator (y), xd)); | |
1922 | return scm_divide (r1, scm_product (xd, yd)); | |
1923 | } | |
1924 | ||
1925 | ||
1926 | static void scm_i_inexact_floor_divide (double x, double y, | |
1927 | SCM *qp, SCM *rp); | |
1928 | static void scm_i_exact_rational_floor_divide (SCM x, SCM y, | |
1929 | SCM *qp, SCM *rp); | |
1930 | ||
1931 | SCM_PRIMITIVE_GENERIC (scm_i_floor_divide, "floor/", 2, 0, 0, | |
1932 | (SCM x, SCM y), | |
1933 | "Return the integer @var{q} and the real number @var{r}\n" | |
1934 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1935 | "and @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1936 | "@lisp\n" | |
1937 | "(floor/ 123 10) @result{} 12 and 3\n" | |
1938 | "(floor/ 123 -10) @result{} -13 and -7\n" | |
1939 | "(floor/ -123 10) @result{} -13 and 7\n" | |
1940 | "(floor/ -123 -10) @result{} 12 and -3\n" | |
1941 | "(floor/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
1942 | "(floor/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
1943 | "@end lisp") | |
1944 | #define FUNC_NAME s_scm_i_floor_divide | |
1945 | { | |
1946 | SCM q, r; | |
1947 | ||
1948 | scm_floor_divide(x, y, &q, &r); | |
1949 | return scm_values (scm_list_2 (q, r)); | |
1950 | } | |
1951 | #undef FUNC_NAME | |
1952 | ||
1953 | #define s_scm_floor_divide s_scm_i_floor_divide | |
1954 | #define g_scm_floor_divide g_scm_i_floor_divide | |
1955 | ||
1956 | void | |
1957 | scm_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1958 | { | |
1959 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1960 | { | |
1961 | scm_t_inum xx = SCM_I_INUM (x); | |
1962 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1963 | { | |
1964 | scm_t_inum yy = SCM_I_INUM (y); | |
1965 | if (SCM_UNLIKELY (yy == 0)) | |
1966 | scm_num_overflow (s_scm_floor_divide); | |
1967 | else | |
1968 | { | |
1969 | scm_t_inum qq = xx / yy; | |
1970 | scm_t_inum rr = xx % yy; | |
1971 | int needs_adjustment; | |
1972 | ||
1973 | if (SCM_LIKELY (yy > 0)) | |
1974 | needs_adjustment = (rr < 0); | |
1975 | else | |
1976 | needs_adjustment = (rr > 0); | |
1977 | ||
1978 | if (needs_adjustment) | |
1979 | { | |
1980 | rr += yy; | |
1981 | qq--; | |
1982 | } | |
1983 | ||
1984 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1985 | *qp = SCM_I_MAKINUM (qq); | |
1986 | else | |
1987 | *qp = scm_i_inum2big (qq); | |
1988 | *rp = SCM_I_MAKINUM (rr); | |
1989 | } | |
1990 | return; | |
1991 | } | |
1992 | else if (SCM_BIGP (y)) | |
1993 | { | |
1994 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1995 | scm_remember_upto_here_1 (y); | |
1996 | if (sign > 0) | |
1997 | { | |
1998 | if (xx < 0) | |
1999 | { | |
2000 | SCM r = scm_i_mkbig (); | |
2001 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
2002 | scm_remember_upto_here_1 (y); | |
2003 | *qp = SCM_I_MAKINUM (-1); | |
2004 | *rp = scm_i_normbig (r); | |
2005 | } | |
2006 | else | |
2007 | { | |
2008 | *qp = SCM_INUM0; | |
2009 | *rp = x; | |
2010 | } | |
2011 | } | |
2012 | else if (xx <= 0) | |
2013 | { | |
2014 | *qp = SCM_INUM0; | |
2015 | *rp = x; | |
2016 | } | |
2017 | else | |
2018 | { | |
2019 | SCM r = scm_i_mkbig (); | |
2020 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
2021 | scm_remember_upto_here_1 (y); | |
2022 | *qp = SCM_I_MAKINUM (-1); | |
2023 | *rp = scm_i_normbig (r); | |
2024 | } | |
2025 | return; | |
2026 | } | |
2027 | else if (SCM_REALP (y)) | |
2028 | return scm_i_inexact_floor_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2029 | else if (SCM_FRACTIONP (y)) | |
2030 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
2031 | else | |
2032 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
2033 | s_scm_floor_divide, qp, rp); | |
2034 | } | |
2035 | else if (SCM_BIGP (x)) | |
2036 | { | |
2037 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2038 | { | |
2039 | scm_t_inum yy = SCM_I_INUM (y); | |
2040 | if (SCM_UNLIKELY (yy == 0)) | |
2041 | scm_num_overflow (s_scm_floor_divide); | |
2042 | else | |
2043 | { | |
2044 | SCM q = scm_i_mkbig (); | |
2045 | SCM r = scm_i_mkbig (); | |
2046 | if (yy > 0) | |
2047 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2048 | SCM_I_BIG_MPZ (x), yy); | |
2049 | else | |
2050 | { | |
2051 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2052 | SCM_I_BIG_MPZ (x), -yy); | |
2053 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2054 | } | |
2055 | scm_remember_upto_here_1 (x); | |
2056 | *qp = scm_i_normbig (q); | |
2057 | *rp = scm_i_normbig (r); | |
2058 | } | |
2059 | return; | |
2060 | } | |
2061 | else if (SCM_BIGP (y)) | |
2062 | { | |
2063 | SCM q = scm_i_mkbig (); | |
2064 | SCM r = scm_i_mkbig (); | |
2065 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2066 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2067 | scm_remember_upto_here_2 (x, y); | |
2068 | *qp = scm_i_normbig (q); | |
2069 | *rp = scm_i_normbig (r); | |
2070 | return; | |
2071 | } | |
2072 | else if (SCM_REALP (y)) | |
2073 | return scm_i_inexact_floor_divide | |
2074 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2075 | else if (SCM_FRACTIONP (y)) | |
2076 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
2077 | else | |
2078 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
2079 | s_scm_floor_divide, qp, rp); | |
2080 | } | |
2081 | else if (SCM_REALP (x)) | |
2082 | { | |
2083 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2084 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2085 | return scm_i_inexact_floor_divide | |
2086 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2087 | else | |
2088 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
2089 | s_scm_floor_divide, qp, rp); | |
2090 | } | |
2091 | else if (SCM_FRACTIONP (x)) | |
2092 | { | |
2093 | if (SCM_REALP (y)) | |
2094 | return scm_i_inexact_floor_divide | |
2095 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2096 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2097 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
2098 | else | |
2099 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
2100 | s_scm_floor_divide, qp, rp); | |
2101 | } | |
2102 | else | |
2103 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG1, | |
2104 | s_scm_floor_divide, qp, rp); | |
2105 | } | |
2106 | ||
2107 | static void | |
2108 | scm_i_inexact_floor_divide (double x, double y, SCM *qp, SCM *rp) | |
2109 | { | |
2110 | if (SCM_UNLIKELY (y == 0)) | |
2111 | scm_num_overflow (s_scm_floor_divide); /* or return a NaN? */ | |
2112 | else | |
2113 | { | |
2114 | double q = floor (x / y); | |
2115 | double r = x - q * y; | |
2116 | *qp = scm_from_double (q); | |
2117 | *rp = scm_from_double (r); | |
2118 | } | |
2119 | } | |
2120 | ||
2121 | static void | |
2122 | scm_i_exact_rational_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2123 | { | |
2124 | SCM r1; | |
2125 | SCM xd = scm_denominator (x); | |
2126 | SCM yd = scm_denominator (y); | |
2127 | ||
2128 | scm_floor_divide (scm_product (scm_numerator (x), yd), | |
2129 | scm_product (scm_numerator (y), xd), | |
2130 | qp, &r1); | |
2131 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2132 | } | |
2133 | ||
2134 | static SCM scm_i_inexact_ceiling_quotient (double x, double y); | |
2135 | static SCM scm_i_exact_rational_ceiling_quotient (SCM x, SCM y); | |
2136 | ||
2137 | SCM_PRIMITIVE_GENERIC (scm_ceiling_quotient, "ceiling-quotient", 2, 0, 0, | |
2138 | (SCM x, SCM y), | |
2139 | "Return the ceiling of @math{@var{x} / @var{y}}.\n" | |
2140 | "@lisp\n" | |
2141 | "(ceiling-quotient 123 10) @result{} 13\n" | |
2142 | "(ceiling-quotient 123 -10) @result{} -12\n" | |
2143 | "(ceiling-quotient -123 10) @result{} -12\n" | |
2144 | "(ceiling-quotient -123 -10) @result{} 13\n" | |
2145 | "(ceiling-quotient -123.2 -63.5) @result{} 2.0\n" | |
2146 | "(ceiling-quotient 16/3 -10/7) @result{} -3\n" | |
2147 | "@end lisp") | |
2148 | #define FUNC_NAME s_scm_ceiling_quotient | |
2149 | { | |
2150 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2151 | { | |
2152 | scm_t_inum xx = SCM_I_INUM (x); | |
2153 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2154 | { | |
2155 | scm_t_inum yy = SCM_I_INUM (y); | |
2156 | if (SCM_UNLIKELY (yy == 0)) | |
2157 | scm_num_overflow (s_scm_ceiling_quotient); | |
2158 | else | |
2159 | { | |
2160 | scm_t_inum xx1 = xx; | |
2161 | scm_t_inum qq; | |
2162 | if (SCM_LIKELY (yy > 0)) | |
2163 | { | |
2164 | if (SCM_LIKELY (xx >= 0)) | |
2165 | xx1 = xx + yy - 1; | |
2166 | } | |
2167 | else if (SCM_UNLIKELY (yy == 0)) | |
2168 | scm_num_overflow (s_scm_ceiling_quotient); | |
2169 | else if (xx < 0) | |
2170 | xx1 = xx + yy + 1; | |
2171 | qq = xx1 / yy; | |
2172 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2173 | return SCM_I_MAKINUM (qq); | |
2174 | else | |
2175 | return scm_i_inum2big (qq); | |
2176 | } | |
2177 | } | |
2178 | else if (SCM_BIGP (y)) | |
2179 | { | |
2180 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
2181 | scm_remember_upto_here_1 (y); | |
2182 | if (SCM_LIKELY (sign > 0)) | |
2183 | { | |
2184 | if (SCM_LIKELY (xx > 0)) | |
2185 | return SCM_INUM1; | |
2186 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2187 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2188 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2189 | { | |
2190 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2191 | scm_remember_upto_here_1 (y); | |
2192 | return SCM_I_MAKINUM (-1); | |
2193 | } | |
2194 | else | |
2195 | return SCM_INUM0; | |
2196 | } | |
2197 | else if (xx >= 0) | |
2198 | return SCM_INUM0; | |
2199 | else | |
2200 | return SCM_INUM1; | |
2201 | } | |
2202 | else if (SCM_REALP (y)) | |
2203 | return scm_i_inexact_ceiling_quotient (xx, SCM_REAL_VALUE (y)); | |
2204 | else if (SCM_FRACTIONP (y)) | |
2205 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
2206 | else | |
2207 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
2208 | s_scm_ceiling_quotient); | |
2209 | } | |
2210 | else if (SCM_BIGP (x)) | |
2211 | { | |
2212 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2213 | { | |
2214 | scm_t_inum yy = SCM_I_INUM (y); | |
2215 | if (SCM_UNLIKELY (yy == 0)) | |
2216 | scm_num_overflow (s_scm_ceiling_quotient); | |
2217 | else if (SCM_UNLIKELY (yy == 1)) | |
2218 | return x; | |
2219 | else | |
2220 | { | |
2221 | SCM q = scm_i_mkbig (); | |
2222 | if (yy > 0) | |
2223 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
2224 | else | |
2225 | { | |
2226 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
2227 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2228 | } | |
2229 | scm_remember_upto_here_1 (x); | |
2230 | return scm_i_normbig (q); | |
2231 | } | |
2232 | } | |
2233 | else if (SCM_BIGP (y)) | |
2234 | { | |
2235 | SCM q = scm_i_mkbig (); | |
2236 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
2237 | SCM_I_BIG_MPZ (x), | |
2238 | SCM_I_BIG_MPZ (y)); | |
2239 | scm_remember_upto_here_2 (x, y); | |
2240 | return scm_i_normbig (q); | |
2241 | } | |
2242 | else if (SCM_REALP (y)) | |
2243 | return scm_i_inexact_ceiling_quotient | |
2244 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2245 | else if (SCM_FRACTIONP (y)) | |
2246 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
2247 | else | |
2248 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
2249 | s_scm_ceiling_quotient); | |
2250 | } | |
2251 | else if (SCM_REALP (x)) | |
2252 | { | |
2253 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2254 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2255 | return scm_i_inexact_ceiling_quotient | |
2256 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2257 | else | |
2258 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
2259 | s_scm_ceiling_quotient); | |
2260 | } | |
2261 | else if (SCM_FRACTIONP (x)) | |
2262 | { | |
2263 | if (SCM_REALP (y)) | |
2264 | return scm_i_inexact_ceiling_quotient | |
2265 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2266 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2267 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
2268 | else | |
2269 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
2270 | s_scm_ceiling_quotient); | |
2271 | } | |
2272 | else | |
2273 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG1, | |
2274 | s_scm_ceiling_quotient); | |
2275 | } | |
2276 | #undef FUNC_NAME | |
2277 | ||
2278 | static SCM | |
2279 | scm_i_inexact_ceiling_quotient (double x, double y) | |
2280 | { | |
2281 | if (SCM_UNLIKELY (y == 0)) | |
2282 | scm_num_overflow (s_scm_ceiling_quotient); /* or return a NaN? */ | |
2283 | else | |
2284 | return scm_from_double (ceil (x / y)); | |
2285 | } | |
2286 | ||
2287 | static SCM | |
2288 | scm_i_exact_rational_ceiling_quotient (SCM x, SCM y) | |
2289 | { | |
2290 | return scm_ceiling_quotient | |
2291 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2292 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2293 | } | |
2294 | ||
2295 | static SCM scm_i_inexact_ceiling_remainder (double x, double y); | |
2296 | static SCM scm_i_exact_rational_ceiling_remainder (SCM x, SCM y); | |
2297 | ||
2298 | SCM_PRIMITIVE_GENERIC (scm_ceiling_remainder, "ceiling-remainder", 2, 0, 0, | |
2299 | (SCM x, SCM y), | |
2300 | "Return the real number @var{r} such that\n" | |
2301 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2302 | "where @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
2303 | "@lisp\n" | |
2304 | "(ceiling-remainder 123 10) @result{} -7\n" | |
2305 | "(ceiling-remainder 123 -10) @result{} 3\n" | |
2306 | "(ceiling-remainder -123 10) @result{} -3\n" | |
2307 | "(ceiling-remainder -123 -10) @result{} 7\n" | |
2308 | "(ceiling-remainder -123.2 -63.5) @result{} 3.8\n" | |
2309 | "(ceiling-remainder 16/3 -10/7) @result{} 22/21\n" | |
2310 | "@end lisp") | |
2311 | #define FUNC_NAME s_scm_ceiling_remainder | |
2312 | { | |
2313 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2314 | { | |
2315 | scm_t_inum xx = SCM_I_INUM (x); | |
2316 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2317 | { | |
2318 | scm_t_inum yy = SCM_I_INUM (y); | |
2319 | if (SCM_UNLIKELY (yy == 0)) | |
2320 | scm_num_overflow (s_scm_ceiling_remainder); | |
2321 | else | |
2322 | { | |
2323 | scm_t_inum rr = xx % yy; | |
2324 | int needs_adjustment; | |
2325 | ||
2326 | if (SCM_LIKELY (yy > 0)) | |
2327 | needs_adjustment = (rr > 0); | |
2328 | else | |
2329 | needs_adjustment = (rr < 0); | |
2330 | ||
2331 | if (needs_adjustment) | |
2332 | rr -= yy; | |
2333 | return SCM_I_MAKINUM (rr); | |
2334 | } | |
2335 | } | |
2336 | else if (SCM_BIGP (y)) | |
2337 | { | |
2338 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
2339 | scm_remember_upto_here_1 (y); | |
2340 | if (SCM_LIKELY (sign > 0)) | |
2341 | { | |
2342 | if (SCM_LIKELY (xx > 0)) | |
2343 | { | |
2344 | SCM r = scm_i_mkbig (); | |
2345 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
2346 | scm_remember_upto_here_1 (y); | |
2347 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
2348 | return scm_i_normbig (r); | |
2349 | } | |
2350 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2351 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2352 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2353 | { | |
2354 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2355 | scm_remember_upto_here_1 (y); | |
2356 | return SCM_INUM0; | |
2357 | } | |
2358 | else | |
2359 | return x; | |
2360 | } | |
2361 | else if (xx >= 0) | |
2362 | return x; | |
2363 | else | |
2364 | { | |
2365 | SCM r = scm_i_mkbig (); | |
2366 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
2367 | scm_remember_upto_here_1 (y); | |
2368 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
2369 | return scm_i_normbig (r); | |
2370 | } | |
2371 | } | |
2372 | else if (SCM_REALP (y)) | |
2373 | return scm_i_inexact_ceiling_remainder (xx, SCM_REAL_VALUE (y)); | |
2374 | else if (SCM_FRACTIONP (y)) | |
2375 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
2376 | else | |
2377 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
2378 | s_scm_ceiling_remainder); | |
2379 | } | |
2380 | else if (SCM_BIGP (x)) | |
2381 | { | |
2382 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2383 | { | |
2384 | scm_t_inum yy = SCM_I_INUM (y); | |
2385 | if (SCM_UNLIKELY (yy == 0)) | |
2386 | scm_num_overflow (s_scm_ceiling_remainder); | |
2387 | else | |
2388 | { | |
2389 | scm_t_inum rr; | |
2390 | if (yy > 0) | |
2391 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
2392 | else | |
2393 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
2394 | scm_remember_upto_here_1 (x); | |
2395 | return SCM_I_MAKINUM (rr); | |
2396 | } | |
2397 | } | |
2398 | else if (SCM_BIGP (y)) | |
2399 | { | |
2400 | SCM r = scm_i_mkbig (); | |
2401 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
2402 | SCM_I_BIG_MPZ (x), | |
2403 | SCM_I_BIG_MPZ (y)); | |
2404 | scm_remember_upto_here_2 (x, y); | |
2405 | return scm_i_normbig (r); | |
2406 | } | |
2407 | else if (SCM_REALP (y)) | |
2408 | return scm_i_inexact_ceiling_remainder | |
2409 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2410 | else if (SCM_FRACTIONP (y)) | |
2411 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
2412 | else | |
2413 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
2414 | s_scm_ceiling_remainder); | |
2415 | } | |
2416 | else if (SCM_REALP (x)) | |
2417 | { | |
2418 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2419 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2420 | return scm_i_inexact_ceiling_remainder | |
2421 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2422 | else | |
2423 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
2424 | s_scm_ceiling_remainder); | |
2425 | } | |
2426 | else if (SCM_FRACTIONP (x)) | |
2427 | { | |
2428 | if (SCM_REALP (y)) | |
2429 | return scm_i_inexact_ceiling_remainder | |
2430 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2431 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2432 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
2433 | else | |
2434 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
2435 | s_scm_ceiling_remainder); | |
2436 | } | |
2437 | else | |
2438 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG1, | |
2439 | s_scm_ceiling_remainder); | |
2440 | } | |
2441 | #undef FUNC_NAME | |
2442 | ||
2443 | static SCM | |
2444 | scm_i_inexact_ceiling_remainder (double x, double y) | |
2445 | { | |
2446 | /* Although it would be more efficient to use fmod here, we can't | |
2447 | because it would in some cases produce results inconsistent with | |
2448 | scm_i_inexact_ceiling_quotient, such that x != q * y + r (not even | |
2449 | close). In particular, when x is very close to a multiple of y, | |
2450 | then r might be either 0.0 or -y, but those two cases must | |
2451 | correspond to different choices of q. If r = 0.0 then q must be | |
2452 | x/y, and if r = -y then q must be x/y+1. If quotient chooses one | |
2453 | and remainder chooses the other, it would be bad. */ | |
2454 | if (SCM_UNLIKELY (y == 0)) | |
2455 | scm_num_overflow (s_scm_ceiling_remainder); /* or return a NaN? */ | |
2456 | else | |
2457 | return scm_from_double (x - y * ceil (x / y)); | |
2458 | } | |
2459 | ||
2460 | static SCM | |
2461 | scm_i_exact_rational_ceiling_remainder (SCM x, SCM y) | |
2462 | { | |
2463 | SCM xd = scm_denominator (x); | |
2464 | SCM yd = scm_denominator (y); | |
2465 | SCM r1 = scm_ceiling_remainder (scm_product (scm_numerator (x), yd), | |
2466 | scm_product (scm_numerator (y), xd)); | |
2467 | return scm_divide (r1, scm_product (xd, yd)); | |
2468 | } | |
2469 | ||
2470 | static void scm_i_inexact_ceiling_divide (double x, double y, | |
2471 | SCM *qp, SCM *rp); | |
2472 | static void scm_i_exact_rational_ceiling_divide (SCM x, SCM y, | |
2473 | SCM *qp, SCM *rp); | |
2474 | ||
2475 | SCM_PRIMITIVE_GENERIC (scm_i_ceiling_divide, "ceiling/", 2, 0, 0, | |
2476 | (SCM x, SCM y), | |
2477 | "Return the integer @var{q} and the real number @var{r}\n" | |
2478 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2479 | "and @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
2480 | "@lisp\n" | |
2481 | "(ceiling/ 123 10) @result{} 13 and -7\n" | |
2482 | "(ceiling/ 123 -10) @result{} -12 and 3\n" | |
2483 | "(ceiling/ -123 10) @result{} -12 and -3\n" | |
2484 | "(ceiling/ -123 -10) @result{} 13 and 7\n" | |
2485 | "(ceiling/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2486 | "(ceiling/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2487 | "@end lisp") | |
2488 | #define FUNC_NAME s_scm_i_ceiling_divide | |
2489 | { | |
2490 | SCM q, r; | |
2491 | ||
2492 | scm_ceiling_divide(x, y, &q, &r); | |
2493 | return scm_values (scm_list_2 (q, r)); | |
2494 | } | |
2495 | #undef FUNC_NAME | |
2496 | ||
2497 | #define s_scm_ceiling_divide s_scm_i_ceiling_divide | |
2498 | #define g_scm_ceiling_divide g_scm_i_ceiling_divide | |
2499 | ||
2500 | void | |
2501 | scm_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2502 | { | |
2503 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2504 | { | |
2505 | scm_t_inum xx = SCM_I_INUM (x); | |
2506 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2507 | { | |
2508 | scm_t_inum yy = SCM_I_INUM (y); | |
2509 | if (SCM_UNLIKELY (yy == 0)) | |
2510 | scm_num_overflow (s_scm_ceiling_divide); | |
2511 | else | |
2512 | { | |
2513 | scm_t_inum qq = xx / yy; | |
2514 | scm_t_inum rr = xx % yy; | |
2515 | int needs_adjustment; | |
2516 | ||
2517 | if (SCM_LIKELY (yy > 0)) | |
2518 | needs_adjustment = (rr > 0); | |
2519 | else | |
2520 | needs_adjustment = (rr < 0); | |
2521 | ||
2522 | if (needs_adjustment) | |
2523 | { | |
2524 | rr -= yy; | |
2525 | qq++; | |
2526 | } | |
2527 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2528 | *qp = SCM_I_MAKINUM (qq); | |
2529 | else | |
2530 | *qp = scm_i_inum2big (qq); | |
2531 | *rp = SCM_I_MAKINUM (rr); | |
2532 | } | |
2533 | return; | |
2534 | } | |
2535 | else if (SCM_BIGP (y)) | |
2536 | { | |
2537 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
2538 | scm_remember_upto_here_1 (y); | |
2539 | if (SCM_LIKELY (sign > 0)) | |
2540 | { | |
2541 | if (SCM_LIKELY (xx > 0)) | |
2542 | { | |
2543 | SCM r = scm_i_mkbig (); | |
2544 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
2545 | scm_remember_upto_here_1 (y); | |
2546 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
2547 | *qp = SCM_INUM1; | |
2548 | *rp = scm_i_normbig (r); | |
2549 | } | |
2550 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2551 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2552 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2553 | { | |
2554 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2555 | scm_remember_upto_here_1 (y); | |
2556 | *qp = SCM_I_MAKINUM (-1); | |
2557 | *rp = SCM_INUM0; | |
2558 | } | |
2559 | else | |
2560 | { | |
2561 | *qp = SCM_INUM0; | |
2562 | *rp = x; | |
2563 | } | |
2564 | } | |
2565 | else if (xx >= 0) | |
2566 | { | |
2567 | *qp = SCM_INUM0; | |
2568 | *rp = x; | |
2569 | } | |
2570 | else | |
2571 | { | |
2572 | SCM r = scm_i_mkbig (); | |
2573 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
2574 | scm_remember_upto_here_1 (y); | |
2575 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
2576 | *qp = SCM_INUM1; | |
2577 | *rp = scm_i_normbig (r); | |
2578 | } | |
2579 | return; | |
2580 | } | |
2581 | else if (SCM_REALP (y)) | |
2582 | return scm_i_inexact_ceiling_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2583 | else if (SCM_FRACTIONP (y)) | |
2584 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2585 | else | |
2586 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2587 | s_scm_ceiling_divide, qp, rp); | |
2588 | } | |
2589 | else if (SCM_BIGP (x)) | |
2590 | { | |
2591 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2592 | { | |
2593 | scm_t_inum yy = SCM_I_INUM (y); | |
2594 | if (SCM_UNLIKELY (yy == 0)) | |
2595 | scm_num_overflow (s_scm_ceiling_divide); | |
2596 | else | |
2597 | { | |
2598 | SCM q = scm_i_mkbig (); | |
2599 | SCM r = scm_i_mkbig (); | |
2600 | if (yy > 0) | |
2601 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2602 | SCM_I_BIG_MPZ (x), yy); | |
2603 | else | |
2604 | { | |
2605 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2606 | SCM_I_BIG_MPZ (x), -yy); | |
2607 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2608 | } | |
2609 | scm_remember_upto_here_1 (x); | |
2610 | *qp = scm_i_normbig (q); | |
2611 | *rp = scm_i_normbig (r); | |
2612 | } | |
2613 | return; | |
2614 | } | |
2615 | else if (SCM_BIGP (y)) | |
2616 | { | |
2617 | SCM q = scm_i_mkbig (); | |
2618 | SCM r = scm_i_mkbig (); | |
2619 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2620 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2621 | scm_remember_upto_here_2 (x, y); | |
2622 | *qp = scm_i_normbig (q); | |
2623 | *rp = scm_i_normbig (r); | |
2624 | return; | |
2625 | } | |
2626 | else if (SCM_REALP (y)) | |
2627 | return scm_i_inexact_ceiling_divide | |
2628 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2629 | else if (SCM_FRACTIONP (y)) | |
2630 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2631 | else | |
2632 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2633 | s_scm_ceiling_divide, qp, rp); | |
2634 | } | |
2635 | else if (SCM_REALP (x)) | |
2636 | { | |
2637 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2638 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2639 | return scm_i_inexact_ceiling_divide | |
2640 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2641 | else | |
2642 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2643 | s_scm_ceiling_divide, qp, rp); | |
2644 | } | |
2645 | else if (SCM_FRACTIONP (x)) | |
2646 | { | |
2647 | if (SCM_REALP (y)) | |
2648 | return scm_i_inexact_ceiling_divide | |
2649 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2650 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2651 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
2652 | else | |
2653 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
2654 | s_scm_ceiling_divide, qp, rp); | |
2655 | } | |
2656 | else | |
2657 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG1, | |
2658 | s_scm_ceiling_divide, qp, rp); | |
2659 | } | |
2660 | ||
2661 | static void | |
2662 | scm_i_inexact_ceiling_divide (double x, double y, SCM *qp, SCM *rp) | |
2663 | { | |
2664 | if (SCM_UNLIKELY (y == 0)) | |
2665 | scm_num_overflow (s_scm_ceiling_divide); /* or return a NaN? */ | |
2666 | else | |
2667 | { | |
2668 | double q = ceil (x / y); | |
2669 | double r = x - q * y; | |
2670 | *qp = scm_from_double (q); | |
2671 | *rp = scm_from_double (r); | |
2672 | } | |
2673 | } | |
2674 | ||
2675 | static void | |
2676 | scm_i_exact_rational_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2677 | { | |
2678 | SCM r1; | |
2679 | SCM xd = scm_denominator (x); | |
2680 | SCM yd = scm_denominator (y); | |
2681 | ||
2682 | scm_ceiling_divide (scm_product (scm_numerator (x), yd), | |
2683 | scm_product (scm_numerator (y), xd), | |
2684 | qp, &r1); | |
2685 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2686 | } | |
2687 | ||
2688 | static SCM scm_i_inexact_truncate_quotient (double x, double y); | |
2689 | static SCM scm_i_exact_rational_truncate_quotient (SCM x, SCM y); | |
2690 | ||
2691 | SCM_PRIMITIVE_GENERIC (scm_truncate_quotient, "truncate-quotient", 2, 0, 0, | |
2692 | (SCM x, SCM y), | |
2693 | "Return @math{@var{x} / @var{y}} rounded toward zero.\n" | |
2694 | "@lisp\n" | |
2695 | "(truncate-quotient 123 10) @result{} 12\n" | |
2696 | "(truncate-quotient 123 -10) @result{} -12\n" | |
2697 | "(truncate-quotient -123 10) @result{} -12\n" | |
2698 | "(truncate-quotient -123 -10) @result{} 12\n" | |
2699 | "(truncate-quotient -123.2 -63.5) @result{} 1.0\n" | |
2700 | "(truncate-quotient 16/3 -10/7) @result{} -3\n" | |
2701 | "@end lisp") | |
2702 | #define FUNC_NAME s_scm_truncate_quotient | |
2703 | { | |
2704 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2705 | { | |
2706 | scm_t_inum xx = SCM_I_INUM (x); | |
2707 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2708 | { | |
2709 | scm_t_inum yy = SCM_I_INUM (y); | |
2710 | if (SCM_UNLIKELY (yy == 0)) | |
2711 | scm_num_overflow (s_scm_truncate_quotient); | |
2712 | else | |
2713 | { | |
2714 | scm_t_inum qq = xx / yy; | |
2715 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2716 | return SCM_I_MAKINUM (qq); | |
2717 | else | |
2718 | return scm_i_inum2big (qq); | |
2719 | } | |
2720 | } | |
2721 | else if (SCM_BIGP (y)) | |
2722 | { | |
2723 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2724 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2725 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2726 | { | |
2727 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2728 | scm_remember_upto_here_1 (y); | |
2729 | return SCM_I_MAKINUM (-1); | |
2730 | } | |
2731 | else | |
2732 | return SCM_INUM0; | |
2733 | } | |
2734 | else if (SCM_REALP (y)) | |
2735 | return scm_i_inexact_truncate_quotient (xx, SCM_REAL_VALUE (y)); | |
2736 | else if (SCM_FRACTIONP (y)) | |
2737 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2738 | else | |
2739 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2740 | s_scm_truncate_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_truncate_quotient); | |
2749 | else if (SCM_UNLIKELY (yy == 1)) | |
2750 | return x; | |
2751 | else | |
2752 | { | |
2753 | SCM q = scm_i_mkbig (); | |
2754 | if (yy > 0) | |
2755 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
2756 | else | |
2757 | { | |
2758 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
2759 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2760 | } | |
2761 | scm_remember_upto_here_1 (x); | |
2762 | return scm_i_normbig (q); | |
2763 | } | |
2764 | } | |
2765 | else if (SCM_BIGP (y)) | |
2766 | { | |
2767 | SCM q = scm_i_mkbig (); | |
2768 | mpz_tdiv_q (SCM_I_BIG_MPZ (q), | |
2769 | SCM_I_BIG_MPZ (x), | |
2770 | SCM_I_BIG_MPZ (y)); | |
2771 | scm_remember_upto_here_2 (x, y); | |
2772 | return scm_i_normbig (q); | |
2773 | } | |
2774 | else if (SCM_REALP (y)) | |
2775 | return scm_i_inexact_truncate_quotient | |
2776 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2777 | else if (SCM_FRACTIONP (y)) | |
2778 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2779 | else | |
2780 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2781 | s_scm_truncate_quotient); | |
2782 | } | |
2783 | else if (SCM_REALP (x)) | |
2784 | { | |
2785 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2786 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2787 | return scm_i_inexact_truncate_quotient | |
2788 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2789 | else | |
2790 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2791 | s_scm_truncate_quotient); | |
2792 | } | |
2793 | else if (SCM_FRACTIONP (x)) | |
2794 | { | |
2795 | if (SCM_REALP (y)) | |
2796 | return scm_i_inexact_truncate_quotient | |
2797 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2798 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2799 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2800 | else | |
2801 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2802 | s_scm_truncate_quotient); | |
2803 | } | |
2804 | else | |
2805 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG1, | |
2806 | s_scm_truncate_quotient); | |
2807 | } | |
2808 | #undef FUNC_NAME | |
2809 | ||
2810 | static SCM | |
2811 | scm_i_inexact_truncate_quotient (double x, double y) | |
2812 | { | |
2813 | if (SCM_UNLIKELY (y == 0)) | |
2814 | scm_num_overflow (s_scm_truncate_quotient); /* or return a NaN? */ | |
2815 | else | |
2816 | return scm_from_double (scm_c_truncate (x / y)); | |
2817 | } | |
2818 | ||
2819 | static SCM | |
2820 | scm_i_exact_rational_truncate_quotient (SCM x, SCM y) | |
2821 | { | |
2822 | return scm_truncate_quotient | |
2823 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2824 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2825 | } | |
2826 | ||
2827 | static SCM scm_i_inexact_truncate_remainder (double x, double y); | |
2828 | static SCM scm_i_exact_rational_truncate_remainder (SCM x, SCM y); | |
2829 | ||
2830 | SCM_PRIMITIVE_GENERIC (scm_truncate_remainder, "truncate-remainder", 2, 0, 0, | |
2831 | (SCM x, SCM y), | |
2832 | "Return the real number @var{r} such that\n" | |
2833 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2834 | "where @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2835 | "@lisp\n" | |
2836 | "(truncate-remainder 123 10) @result{} 3\n" | |
2837 | "(truncate-remainder 123 -10) @result{} 3\n" | |
2838 | "(truncate-remainder -123 10) @result{} -3\n" | |
2839 | "(truncate-remainder -123 -10) @result{} -3\n" | |
2840 | "(truncate-remainder -123.2 -63.5) @result{} -59.7\n" | |
2841 | "(truncate-remainder 16/3 -10/7) @result{} 22/21\n" | |
2842 | "@end lisp") | |
2843 | #define FUNC_NAME s_scm_truncate_remainder | |
2844 | { | |
2845 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2846 | { | |
2847 | scm_t_inum xx = SCM_I_INUM (x); | |
2848 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2849 | { | |
2850 | scm_t_inum yy = SCM_I_INUM (y); | |
2851 | if (SCM_UNLIKELY (yy == 0)) | |
2852 | scm_num_overflow (s_scm_truncate_remainder); | |
2853 | else | |
2854 | return SCM_I_MAKINUM (xx % yy); | |
2855 | } | |
2856 | else if (SCM_BIGP (y)) | |
2857 | { | |
2858 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2859 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2860 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2861 | { | |
2862 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2863 | scm_remember_upto_here_1 (y); | |
2864 | return SCM_INUM0; | |
2865 | } | |
2866 | else | |
2867 | return x; | |
2868 | } | |
2869 | else if (SCM_REALP (y)) | |
2870 | return scm_i_inexact_truncate_remainder (xx, SCM_REAL_VALUE (y)); | |
2871 | else if (SCM_FRACTIONP (y)) | |
2872 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2873 | else | |
2874 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2875 | s_scm_truncate_remainder); | |
2876 | } | |
2877 | else if (SCM_BIGP (x)) | |
2878 | { | |
2879 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2880 | { | |
2881 | scm_t_inum yy = SCM_I_INUM (y); | |
2882 | if (SCM_UNLIKELY (yy == 0)) | |
2883 | scm_num_overflow (s_scm_truncate_remainder); | |
2884 | else | |
2885 | { | |
2886 | scm_t_inum rr = (mpz_tdiv_ui (SCM_I_BIG_MPZ (x), | |
2887 | (yy > 0) ? yy : -yy) | |
2888 | * mpz_sgn (SCM_I_BIG_MPZ (x))); | |
2889 | scm_remember_upto_here_1 (x); | |
2890 | return SCM_I_MAKINUM (rr); | |
2891 | } | |
2892 | } | |
2893 | else if (SCM_BIGP (y)) | |
2894 | { | |
2895 | SCM r = scm_i_mkbig (); | |
2896 | mpz_tdiv_r (SCM_I_BIG_MPZ (r), | |
2897 | SCM_I_BIG_MPZ (x), | |
2898 | SCM_I_BIG_MPZ (y)); | |
2899 | scm_remember_upto_here_2 (x, y); | |
2900 | return scm_i_normbig (r); | |
2901 | } | |
2902 | else if (SCM_REALP (y)) | |
2903 | return scm_i_inexact_truncate_remainder | |
2904 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2905 | else if (SCM_FRACTIONP (y)) | |
2906 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2907 | else | |
2908 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2909 | s_scm_truncate_remainder); | |
2910 | } | |
2911 | else if (SCM_REALP (x)) | |
2912 | { | |
2913 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2914 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2915 | return scm_i_inexact_truncate_remainder | |
2916 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2917 | else | |
2918 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2919 | s_scm_truncate_remainder); | |
2920 | } | |
2921 | else if (SCM_FRACTIONP (x)) | |
2922 | { | |
2923 | if (SCM_REALP (y)) | |
2924 | return scm_i_inexact_truncate_remainder | |
2925 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2926 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2927 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2928 | else | |
2929 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2930 | s_scm_truncate_remainder); | |
2931 | } | |
2932 | else | |
2933 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG1, | |
2934 | s_scm_truncate_remainder); | |
2935 | } | |
2936 | #undef FUNC_NAME | |
2937 | ||
2938 | static SCM | |
2939 | scm_i_inexact_truncate_remainder (double x, double y) | |
2940 | { | |
2941 | /* Although it would be more efficient to use fmod here, we can't | |
2942 | because it would in some cases produce results inconsistent with | |
2943 | scm_i_inexact_truncate_quotient, such that x != q * y + r (not even | |
2944 | close). In particular, when x is very close to a multiple of y, | |
2945 | then r might be either 0.0 or sgn(x)*|y|, but those two cases must | |
2946 | correspond to different choices of q. If quotient chooses one and | |
2947 | remainder chooses the other, it would be bad. */ | |
2948 | if (SCM_UNLIKELY (y == 0)) | |
2949 | scm_num_overflow (s_scm_truncate_remainder); /* or return a NaN? */ | |
2950 | else | |
2951 | return scm_from_double (x - y * scm_c_truncate (x / y)); | |
2952 | } | |
2953 | ||
2954 | static SCM | |
2955 | scm_i_exact_rational_truncate_remainder (SCM x, SCM y) | |
2956 | { | |
2957 | SCM xd = scm_denominator (x); | |
2958 | SCM yd = scm_denominator (y); | |
2959 | SCM r1 = scm_truncate_remainder (scm_product (scm_numerator (x), yd), | |
2960 | scm_product (scm_numerator (y), xd)); | |
2961 | return scm_divide (r1, scm_product (xd, yd)); | |
2962 | } | |
2963 | ||
2964 | ||
2965 | static void scm_i_inexact_truncate_divide (double x, double y, | |
2966 | SCM *qp, SCM *rp); | |
2967 | static void scm_i_exact_rational_truncate_divide (SCM x, SCM y, | |
2968 | SCM *qp, SCM *rp); | |
2969 | ||
2970 | SCM_PRIMITIVE_GENERIC (scm_i_truncate_divide, "truncate/", 2, 0, 0, | |
2971 | (SCM x, SCM y), | |
2972 | "Return the integer @var{q} and the real number @var{r}\n" | |
2973 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2974 | "and @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2975 | "@lisp\n" | |
2976 | "(truncate/ 123 10) @result{} 12 and 3\n" | |
2977 | "(truncate/ 123 -10) @result{} -12 and 3\n" | |
2978 | "(truncate/ -123 10) @result{} -12 and -3\n" | |
2979 | "(truncate/ -123 -10) @result{} 12 and -3\n" | |
2980 | "(truncate/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
2981 | "(truncate/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2982 | "@end lisp") | |
2983 | #define FUNC_NAME s_scm_i_truncate_divide | |
2984 | { | |
2985 | SCM q, r; | |
2986 | ||
2987 | scm_truncate_divide(x, y, &q, &r); | |
2988 | return scm_values (scm_list_2 (q, r)); | |
2989 | } | |
2990 | #undef FUNC_NAME | |
2991 | ||
2992 | #define s_scm_truncate_divide s_scm_i_truncate_divide | |
2993 | #define g_scm_truncate_divide g_scm_i_truncate_divide | |
2994 | ||
2995 | void | |
2996 | scm_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2997 | { | |
2998 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2999 | { | |
3000 | scm_t_inum xx = SCM_I_INUM (x); | |
3001 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3002 | { | |
3003 | scm_t_inum yy = SCM_I_INUM (y); | |
3004 | if (SCM_UNLIKELY (yy == 0)) | |
3005 | scm_num_overflow (s_scm_truncate_divide); | |
3006 | else | |
3007 | { | |
3008 | scm_t_inum qq = xx / yy; | |
3009 | scm_t_inum rr = xx % yy; | |
3010 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
3011 | *qp = SCM_I_MAKINUM (qq); | |
3012 | else | |
3013 | *qp = scm_i_inum2big (qq); | |
3014 | *rp = SCM_I_MAKINUM (rr); | |
3015 | } | |
3016 | return; | |
3017 | } | |
3018 | else if (SCM_BIGP (y)) | |
3019 | { | |
3020 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
3021 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
3022 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
3023 | { | |
3024 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
3025 | scm_remember_upto_here_1 (y); | |
3026 | *qp = SCM_I_MAKINUM (-1); | |
3027 | *rp = SCM_INUM0; | |
3028 | } | |
3029 | else | |
3030 | { | |
3031 | *qp = SCM_INUM0; | |
3032 | *rp = x; | |
3033 | } | |
3034 | return; | |
3035 | } | |
3036 | else if (SCM_REALP (y)) | |
3037 | return scm_i_inexact_truncate_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
3038 | else if (SCM_FRACTIONP (y)) | |
3039 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
3040 | else | |
3041 | return two_valued_wta_dispatch_2 | |
3042 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
3043 | s_scm_truncate_divide, qp, rp); | |
3044 | } | |
3045 | else if (SCM_BIGP (x)) | |
3046 | { | |
3047 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3048 | { | |
3049 | scm_t_inum yy = SCM_I_INUM (y); | |
3050 | if (SCM_UNLIKELY (yy == 0)) | |
3051 | scm_num_overflow (s_scm_truncate_divide); | |
3052 | else | |
3053 | { | |
3054 | SCM q = scm_i_mkbig (); | |
3055 | scm_t_inum rr; | |
3056 | if (yy > 0) | |
3057 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3058 | SCM_I_BIG_MPZ (x), yy); | |
3059 | else | |
3060 | { | |
3061 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3062 | SCM_I_BIG_MPZ (x), -yy); | |
3063 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
3064 | } | |
3065 | rr *= mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3066 | scm_remember_upto_here_1 (x); | |
3067 | *qp = scm_i_normbig (q); | |
3068 | *rp = SCM_I_MAKINUM (rr); | |
3069 | } | |
3070 | return; | |
3071 | } | |
3072 | else if (SCM_BIGP (y)) | |
3073 | { | |
3074 | SCM q = scm_i_mkbig (); | |
3075 | SCM r = scm_i_mkbig (); | |
3076 | mpz_tdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3077 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3078 | scm_remember_upto_here_2 (x, y); | |
3079 | *qp = scm_i_normbig (q); | |
3080 | *rp = scm_i_normbig (r); | |
3081 | } | |
3082 | else if (SCM_REALP (y)) | |
3083 | return scm_i_inexact_truncate_divide | |
3084 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
3085 | else if (SCM_FRACTIONP (y)) | |
3086 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
3087 | else | |
3088 | return two_valued_wta_dispatch_2 | |
3089 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
3090 | s_scm_truncate_divide, qp, rp); | |
3091 | } | |
3092 | else if (SCM_REALP (x)) | |
3093 | { | |
3094 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3095 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3096 | return scm_i_inexact_truncate_divide | |
3097 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
3098 | else | |
3099 | return two_valued_wta_dispatch_2 | |
3100 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
3101 | s_scm_truncate_divide, qp, rp); | |
3102 | } | |
3103 | else if (SCM_FRACTIONP (x)) | |
3104 | { | |
3105 | if (SCM_REALP (y)) | |
3106 | return scm_i_inexact_truncate_divide | |
3107 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
3108 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3109 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
3110 | else | |
3111 | return two_valued_wta_dispatch_2 | |
3112 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
3113 | s_scm_truncate_divide, qp, rp); | |
3114 | } | |
3115 | else | |
3116 | return two_valued_wta_dispatch_2 (g_scm_truncate_divide, x, y, SCM_ARG1, | |
3117 | s_scm_truncate_divide, qp, rp); | |
3118 | } | |
3119 | ||
3120 | static void | |
3121 | scm_i_inexact_truncate_divide (double x, double y, SCM *qp, SCM *rp) | |
3122 | { | |
3123 | if (SCM_UNLIKELY (y == 0)) | |
3124 | scm_num_overflow (s_scm_truncate_divide); /* or return a NaN? */ | |
3125 | else | |
3126 | { | |
3127 | double q, r, q1; | |
3128 | /* FIXME: Use trunc, after it has been imported from gnulib */ | |
3129 | q1 = x / y; | |
3130 | q = (q1 >= 0) ? floor (q1) : ceil (q1); | |
3131 | r = x - q * y; | |
3132 | *qp = scm_from_double (q); | |
3133 | *rp = scm_from_double (r); | |
3134 | } | |
3135 | } | |
3136 | ||
3137 | static void | |
3138 | scm_i_exact_rational_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3139 | { | |
3140 | SCM r1; | |
3141 | SCM xd = scm_denominator (x); | |
3142 | SCM yd = scm_denominator (y); | |
3143 | ||
3144 | scm_truncate_divide (scm_product (scm_numerator (x), yd), | |
3145 | scm_product (scm_numerator (y), xd), | |
3146 | qp, &r1); | |
3147 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
3148 | } | |
3149 | ||
ff62c168 MW |
3150 | static SCM scm_i_inexact_centered_quotient (double x, double y); |
3151 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
03ddd15b | 3152 | static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y); |
ff62c168 | 3153 | |
8f9da340 MW |
3154 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, |
3155 | (SCM x, SCM y), | |
3156 | "Return the integer @var{q} such that\n" | |
3157 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
3158 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
3159 | "@lisp\n" | |
3160 | "(centered-quotient 123 10) @result{} 12\n" | |
3161 | "(centered-quotient 123 -10) @result{} -12\n" | |
3162 | "(centered-quotient -123 10) @result{} -12\n" | |
3163 | "(centered-quotient -123 -10) @result{} 12\n" | |
3164 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
3165 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
3166 | "@end lisp") | |
3167 | #define FUNC_NAME s_scm_centered_quotient | |
3168 | { | |
3169 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3170 | { | |
3171 | scm_t_inum xx = SCM_I_INUM (x); | |
3172 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3173 | { | |
3174 | scm_t_inum yy = SCM_I_INUM (y); | |
3175 | if (SCM_UNLIKELY (yy == 0)) | |
3176 | scm_num_overflow (s_scm_centered_quotient); | |
3177 | else | |
3178 | { | |
3179 | scm_t_inum qq = xx / yy; | |
3180 | scm_t_inum rr = xx % yy; | |
3181 | if (SCM_LIKELY (xx > 0)) | |
3182 | { | |
3183 | if (SCM_LIKELY (yy > 0)) | |
3184 | { | |
3185 | if (rr >= (yy + 1) / 2) | |
3186 | qq++; | |
3187 | } | |
3188 | else | |
3189 | { | |
3190 | if (rr >= (1 - yy) / 2) | |
3191 | qq--; | |
3192 | } | |
3193 | } | |
3194 | else | |
3195 | { | |
3196 | if (SCM_LIKELY (yy > 0)) | |
3197 | { | |
3198 | if (rr < -yy / 2) | |
3199 | qq--; | |
3200 | } | |
3201 | else | |
3202 | { | |
3203 | if (rr < yy / 2) | |
3204 | qq++; | |
3205 | } | |
3206 | } | |
3207 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
3208 | return SCM_I_MAKINUM (qq); | |
3209 | else | |
3210 | return scm_i_inum2big (qq); | |
3211 | } | |
3212 | } | |
3213 | else if (SCM_BIGP (y)) | |
3214 | { | |
3215 | /* Pass a denormalized bignum version of x (even though it | |
3216 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
3217 | return scm_i_bigint_centered_quotient (scm_i_long2big (xx), y); | |
3218 | } | |
3219 | else if (SCM_REALP (y)) | |
3220 | return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y)); | |
3221 | else if (SCM_FRACTIONP (y)) | |
3222 | return scm_i_exact_rational_centered_quotient (x, y); | |
3223 | else | |
3224 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
3225 | s_scm_centered_quotient); | |
3226 | } | |
3227 | else if (SCM_BIGP (x)) | |
3228 | { | |
3229 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3230 | { | |
3231 | scm_t_inum yy = SCM_I_INUM (y); | |
3232 | if (SCM_UNLIKELY (yy == 0)) | |
3233 | scm_num_overflow (s_scm_centered_quotient); | |
3234 | else if (SCM_UNLIKELY (yy == 1)) | |
3235 | return x; | |
3236 | else | |
3237 | { | |
3238 | SCM q = scm_i_mkbig (); | |
3239 | scm_t_inum rr; | |
3240 | /* Arrange for rr to initially be non-positive, | |
3241 | because that simplifies the test to see | |
3242 | if it is within the needed bounds. */ | |
3243 | if (yy > 0) | |
3244 | { | |
3245 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3246 | SCM_I_BIG_MPZ (x), yy); | |
3247 | scm_remember_upto_here_1 (x); | |
3248 | if (rr < -yy / 2) | |
3249 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3250 | SCM_I_BIG_MPZ (q), 1); | |
3251 | } | |
3252 | else | |
3253 | { | |
3254 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3255 | SCM_I_BIG_MPZ (x), -yy); | |
3256 | scm_remember_upto_here_1 (x); | |
3257 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
3258 | if (rr < yy / 2) | |
3259 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3260 | SCM_I_BIG_MPZ (q), 1); | |
3261 | } | |
3262 | return scm_i_normbig (q); | |
3263 | } | |
3264 | } | |
3265 | else if (SCM_BIGP (y)) | |
3266 | return scm_i_bigint_centered_quotient (x, y); | |
3267 | else if (SCM_REALP (y)) | |
3268 | return scm_i_inexact_centered_quotient | |
3269 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
3270 | else if (SCM_FRACTIONP (y)) | |
3271 | return scm_i_exact_rational_centered_quotient (x, y); | |
3272 | else | |
3273 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
3274 | s_scm_centered_quotient); | |
3275 | } | |
3276 | else if (SCM_REALP (x)) | |
3277 | { | |
3278 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3279 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3280 | return scm_i_inexact_centered_quotient | |
3281 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
3282 | else | |
3283 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
3284 | s_scm_centered_quotient); | |
3285 | } | |
3286 | else if (SCM_FRACTIONP (x)) | |
3287 | { | |
3288 | if (SCM_REALP (y)) | |
3289 | return scm_i_inexact_centered_quotient | |
3290 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
3291 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3292 | return scm_i_exact_rational_centered_quotient (x, y); | |
3293 | else | |
3294 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
3295 | s_scm_centered_quotient); | |
3296 | } | |
3297 | else | |
3298 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
3299 | s_scm_centered_quotient); | |
3300 | } | |
3301 | #undef FUNC_NAME | |
3302 | ||
3303 | static SCM | |
3304 | scm_i_inexact_centered_quotient (double x, double y) | |
3305 | { | |
3306 | if (SCM_LIKELY (y > 0)) | |
3307 | return scm_from_double (floor (x/y + 0.5)); | |
3308 | else if (SCM_LIKELY (y < 0)) | |
3309 | return scm_from_double (ceil (x/y - 0.5)); | |
3310 | else if (y == 0) | |
3311 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
3312 | else | |
3313 | return scm_nan (); | |
3314 | } | |
3315 | ||
3316 | /* Assumes that both x and y are bigints, though | |
3317 | x might be able to fit into a fixnum. */ | |
3318 | static SCM | |
3319 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
3320 | { | |
3321 | SCM q, r, min_r; | |
3322 | ||
3323 | /* Note that x might be small enough to fit into a | |
3324 | fixnum, so we must not let it escape into the wild */ | |
3325 | q = scm_i_mkbig (); | |
3326 | r = scm_i_mkbig (); | |
3327 | ||
3328 | /* min_r will eventually become -abs(y)/2 */ | |
3329 | min_r = scm_i_mkbig (); | |
3330 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3331 | SCM_I_BIG_MPZ (y), 1); | |
3332 | ||
3333 | /* Arrange for rr to initially be non-positive, | |
3334 | because that simplifies the test to see | |
3335 | if it is within the needed bounds. */ | |
3336 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3337 | { | |
3338 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3339 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3340 | scm_remember_upto_here_2 (x, y); | |
3341 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3342 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3343 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3344 | SCM_I_BIG_MPZ (q), 1); | |
3345 | } | |
3346 | else | |
3347 | { | |
3348 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3349 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3350 | scm_remember_upto_here_2 (x, y); | |
3351 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3352 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3353 | SCM_I_BIG_MPZ (q), 1); | |
3354 | } | |
3355 | scm_remember_upto_here_2 (r, min_r); | |
3356 | return scm_i_normbig (q); | |
3357 | } | |
3358 | ||
3359 | static SCM | |
3360 | scm_i_exact_rational_centered_quotient (SCM x, SCM y) | |
3361 | { | |
3362 | return scm_centered_quotient | |
3363 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
3364 | scm_product (scm_numerator (y), scm_denominator (x))); | |
3365 | } | |
3366 | ||
3367 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
3368 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
3369 | static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y); | |
3370 | ||
3371 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
3372 | (SCM x, SCM y), | |
3373 | "Return the real number @var{r} such that\n" | |
3374 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
3375 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
3376 | "for some integer @var{q}.\n" | |
3377 | "@lisp\n" | |
3378 | "(centered-remainder 123 10) @result{} 3\n" | |
3379 | "(centered-remainder 123 -10) @result{} 3\n" | |
3380 | "(centered-remainder -123 10) @result{} -3\n" | |
3381 | "(centered-remainder -123 -10) @result{} -3\n" | |
3382 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
3383 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
3384 | "@end lisp") | |
3385 | #define FUNC_NAME s_scm_centered_remainder | |
3386 | { | |
3387 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3388 | { | |
3389 | scm_t_inum xx = SCM_I_INUM (x); | |
3390 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3391 | { | |
3392 | scm_t_inum yy = SCM_I_INUM (y); | |
3393 | if (SCM_UNLIKELY (yy == 0)) | |
3394 | scm_num_overflow (s_scm_centered_remainder); | |
3395 | else | |
3396 | { | |
3397 | scm_t_inum rr = xx % yy; | |
3398 | if (SCM_LIKELY (xx > 0)) | |
3399 | { | |
3400 | if (SCM_LIKELY (yy > 0)) | |
3401 | { | |
3402 | if (rr >= (yy + 1) / 2) | |
3403 | rr -= yy; | |
3404 | } | |
3405 | else | |
3406 | { | |
3407 | if (rr >= (1 - yy) / 2) | |
3408 | rr += yy; | |
3409 | } | |
3410 | } | |
3411 | else | |
3412 | { | |
3413 | if (SCM_LIKELY (yy > 0)) | |
3414 | { | |
3415 | if (rr < -yy / 2) | |
3416 | rr += yy; | |
3417 | } | |
3418 | else | |
3419 | { | |
3420 | if (rr < yy / 2) | |
3421 | rr -= yy; | |
3422 | } | |
3423 | } | |
3424 | return SCM_I_MAKINUM (rr); | |
3425 | } | |
3426 | } | |
3427 | else if (SCM_BIGP (y)) | |
3428 | { | |
3429 | /* Pass a denormalized bignum version of x (even though it | |
3430 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
3431 | return scm_i_bigint_centered_remainder (scm_i_long2big (xx), y); | |
3432 | } | |
3433 | else if (SCM_REALP (y)) | |
3434 | return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y)); | |
3435 | else if (SCM_FRACTIONP (y)) | |
3436 | return scm_i_exact_rational_centered_remainder (x, y); | |
3437 | else | |
3438 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
3439 | s_scm_centered_remainder); | |
3440 | } | |
3441 | else if (SCM_BIGP (x)) | |
3442 | { | |
3443 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3444 | { | |
3445 | scm_t_inum yy = SCM_I_INUM (y); | |
3446 | if (SCM_UNLIKELY (yy == 0)) | |
3447 | scm_num_overflow (s_scm_centered_remainder); | |
3448 | else | |
3449 | { | |
3450 | scm_t_inum rr; | |
3451 | /* Arrange for rr to initially be non-positive, | |
3452 | because that simplifies the test to see | |
3453 | if it is within the needed bounds. */ | |
3454 | if (yy > 0) | |
3455 | { | |
3456 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
3457 | scm_remember_upto_here_1 (x); | |
3458 | if (rr < -yy / 2) | |
3459 | rr += yy; | |
3460 | } | |
3461 | else | |
3462 | { | |
3463 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
3464 | scm_remember_upto_here_1 (x); | |
3465 | if (rr < yy / 2) | |
3466 | rr -= yy; | |
3467 | } | |
3468 | return SCM_I_MAKINUM (rr); | |
3469 | } | |
3470 | } | |
3471 | else if (SCM_BIGP (y)) | |
3472 | return scm_i_bigint_centered_remainder (x, y); | |
3473 | else if (SCM_REALP (y)) | |
3474 | return scm_i_inexact_centered_remainder | |
3475 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
3476 | else if (SCM_FRACTIONP (y)) | |
3477 | return scm_i_exact_rational_centered_remainder (x, y); | |
3478 | else | |
3479 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
3480 | s_scm_centered_remainder); | |
3481 | } | |
3482 | else if (SCM_REALP (x)) | |
3483 | { | |
3484 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3485 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3486 | return scm_i_inexact_centered_remainder | |
3487 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
3488 | else | |
3489 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
3490 | s_scm_centered_remainder); | |
3491 | } | |
3492 | else if (SCM_FRACTIONP (x)) | |
3493 | { | |
3494 | if (SCM_REALP (y)) | |
3495 | return scm_i_inexact_centered_remainder | |
3496 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
3497 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3498 | return scm_i_exact_rational_centered_remainder (x, y); | |
3499 | else | |
3500 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
3501 | s_scm_centered_remainder); | |
3502 | } | |
3503 | else | |
3504 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
3505 | s_scm_centered_remainder); | |
3506 | } | |
3507 | #undef FUNC_NAME | |
3508 | ||
3509 | static SCM | |
3510 | scm_i_inexact_centered_remainder (double x, double y) | |
3511 | { | |
3512 | double q; | |
3513 | ||
3514 | /* Although it would be more efficient to use fmod here, we can't | |
3515 | because it would in some cases produce results inconsistent with | |
3516 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
3517 | close). In particular, when x-y/2 is very close to a multiple of | |
3518 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
3519 | two cases must correspond to different choices of q. If quotient | |
3520 | chooses one and remainder chooses the other, it would be bad. */ | |
3521 | if (SCM_LIKELY (y > 0)) | |
3522 | q = floor (x/y + 0.5); | |
3523 | else if (SCM_LIKELY (y < 0)) | |
3524 | q = ceil (x/y - 0.5); | |
3525 | else if (y == 0) | |
3526 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
3527 | else | |
3528 | return scm_nan (); | |
3529 | return scm_from_double (x - q * y); | |
3530 | } | |
3531 | ||
3532 | /* Assumes that both x and y are bigints, though | |
3533 | x might be able to fit into a fixnum. */ | |
3534 | static SCM | |
3535 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
3536 | { | |
3537 | SCM r, min_r; | |
3538 | ||
3539 | /* Note that x might be small enough to fit into a | |
3540 | fixnum, so we must not let it escape into the wild */ | |
3541 | r = scm_i_mkbig (); | |
3542 | ||
3543 | /* min_r will eventually become -abs(y)/2 */ | |
3544 | min_r = scm_i_mkbig (); | |
3545 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3546 | SCM_I_BIG_MPZ (y), 1); | |
3547 | ||
3548 | /* Arrange for rr to initially be non-positive, | |
3549 | because that simplifies the test to see | |
3550 | if it is within the needed bounds. */ | |
3551 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3552 | { | |
3553 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
3554 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3555 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3556 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3557 | mpz_add (SCM_I_BIG_MPZ (r), | |
3558 | SCM_I_BIG_MPZ (r), | |
3559 | SCM_I_BIG_MPZ (y)); | |
3560 | } | |
3561 | else | |
3562 | { | |
3563 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
3564 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3565 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3566 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3567 | SCM_I_BIG_MPZ (r), | |
3568 | SCM_I_BIG_MPZ (y)); | |
3569 | } | |
3570 | scm_remember_upto_here_2 (x, y); | |
3571 | return scm_i_normbig (r); | |
3572 | } | |
3573 | ||
3574 | static SCM | |
3575 | scm_i_exact_rational_centered_remainder (SCM x, SCM y) | |
3576 | { | |
3577 | SCM xd = scm_denominator (x); | |
3578 | SCM yd = scm_denominator (y); | |
3579 | SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd), | |
3580 | scm_product (scm_numerator (y), xd)); | |
3581 | return scm_divide (r1, scm_product (xd, yd)); | |
3582 | } | |
3583 | ||
3584 | ||
3585 | static void scm_i_inexact_centered_divide (double x, double y, | |
3586 | SCM *qp, SCM *rp); | |
3587 | static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3588 | static void scm_i_exact_rational_centered_divide (SCM x, SCM y, | |
3589 | SCM *qp, SCM *rp); | |
3590 | ||
3591 | SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0, | |
3592 | (SCM x, SCM y), | |
3593 | "Return the integer @var{q} and the real number @var{r}\n" | |
3594 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
3595 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
3596 | "@lisp\n" | |
3597 | "(centered/ 123 10) @result{} 12 and 3\n" | |
3598 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
3599 | "(centered/ -123 10) @result{} -12 and -3\n" | |
3600 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
3601 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3602 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
3603 | "@end lisp") | |
3604 | #define FUNC_NAME s_scm_i_centered_divide | |
3605 | { | |
3606 | SCM q, r; | |
3607 | ||
3608 | scm_centered_divide(x, y, &q, &r); | |
3609 | return scm_values (scm_list_2 (q, r)); | |
3610 | } | |
3611 | #undef FUNC_NAME | |
3612 | ||
3613 | #define s_scm_centered_divide s_scm_i_centered_divide | |
3614 | #define g_scm_centered_divide g_scm_i_centered_divide | |
3615 | ||
3616 | void | |
3617 | scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3618 | { | |
3619 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3620 | { | |
3621 | scm_t_inum xx = SCM_I_INUM (x); | |
3622 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3623 | { | |
3624 | scm_t_inum yy = SCM_I_INUM (y); | |
3625 | if (SCM_UNLIKELY (yy == 0)) | |
3626 | scm_num_overflow (s_scm_centered_divide); | |
3627 | else | |
3628 | { | |
3629 | scm_t_inum qq = xx / yy; | |
3630 | scm_t_inum rr = xx % yy; | |
3631 | if (SCM_LIKELY (xx > 0)) | |
3632 | { | |
3633 | if (SCM_LIKELY (yy > 0)) | |
3634 | { | |
3635 | if (rr >= (yy + 1) / 2) | |
3636 | { qq++; rr -= yy; } | |
3637 | } | |
3638 | else | |
3639 | { | |
3640 | if (rr >= (1 - yy) / 2) | |
3641 | { qq--; rr += yy; } | |
3642 | } | |
3643 | } | |
3644 | else | |
3645 | { | |
3646 | if (SCM_LIKELY (yy > 0)) | |
3647 | { | |
3648 | if (rr < -yy / 2) | |
3649 | { qq--; rr += yy; } | |
3650 | } | |
3651 | else | |
3652 | { | |
3653 | if (rr < yy / 2) | |
3654 | { qq++; rr -= yy; } | |
3655 | } | |
3656 | } | |
3657 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
3658 | *qp = SCM_I_MAKINUM (qq); | |
3659 | else | |
3660 | *qp = scm_i_inum2big (qq); | |
3661 | *rp = SCM_I_MAKINUM (rr); | |
3662 | } | |
3663 | return; | |
3664 | } | |
3665 | else if (SCM_BIGP (y)) | |
3666 | { | |
3667 | /* Pass a denormalized bignum version of x (even though it | |
3668 | can fit in a fixnum) to scm_i_bigint_centered_divide */ | |
3669 | return scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp); | |
3670 | } | |
3671 | else if (SCM_REALP (y)) | |
3672 | return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
3673 | else if (SCM_FRACTIONP (y)) | |
3674 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3675 | else | |
3676 | return two_valued_wta_dispatch_2 | |
3677 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3678 | s_scm_centered_divide, qp, rp); | |
3679 | } | |
3680 | else if (SCM_BIGP (x)) | |
3681 | { | |
3682 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3683 | { | |
3684 | scm_t_inum yy = SCM_I_INUM (y); | |
3685 | if (SCM_UNLIKELY (yy == 0)) | |
3686 | scm_num_overflow (s_scm_centered_divide); | |
3687 | else | |
3688 | { | |
3689 | SCM q = scm_i_mkbig (); | |
3690 | scm_t_inum rr; | |
3691 | /* Arrange for rr to initially be non-positive, | |
3692 | because that simplifies the test to see | |
3693 | if it is within the needed bounds. */ | |
3694 | if (yy > 0) | |
3695 | { | |
3696 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3697 | SCM_I_BIG_MPZ (x), yy); | |
3698 | scm_remember_upto_here_1 (x); | |
3699 | if (rr < -yy / 2) | |
3700 | { | |
3701 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3702 | SCM_I_BIG_MPZ (q), 1); | |
3703 | rr += yy; | |
3704 | } | |
3705 | } | |
3706 | else | |
3707 | { | |
3708 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3709 | SCM_I_BIG_MPZ (x), -yy); | |
3710 | scm_remember_upto_here_1 (x); | |
3711 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
3712 | if (rr < yy / 2) | |
3713 | { | |
3714 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3715 | SCM_I_BIG_MPZ (q), 1); | |
3716 | rr -= yy; | |
3717 | } | |
3718 | } | |
3719 | *qp = scm_i_normbig (q); | |
3720 | *rp = SCM_I_MAKINUM (rr); | |
3721 | } | |
3722 | return; | |
3723 | } | |
3724 | else if (SCM_BIGP (y)) | |
3725 | return scm_i_bigint_centered_divide (x, y, qp, rp); | |
3726 | else if (SCM_REALP (y)) | |
3727 | return scm_i_inexact_centered_divide | |
3728 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
3729 | else if (SCM_FRACTIONP (y)) | |
3730 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3731 | else | |
3732 | return two_valued_wta_dispatch_2 | |
3733 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3734 | s_scm_centered_divide, qp, rp); | |
3735 | } | |
3736 | else if (SCM_REALP (x)) | |
3737 | { | |
3738 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3739 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3740 | return scm_i_inexact_centered_divide | |
3741 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
3742 | else | |
3743 | return two_valued_wta_dispatch_2 | |
3744 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3745 | s_scm_centered_divide, qp, rp); | |
3746 | } | |
3747 | else if (SCM_FRACTIONP (x)) | |
3748 | { | |
3749 | if (SCM_REALP (y)) | |
3750 | return scm_i_inexact_centered_divide | |
3751 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
3752 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3753 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3754 | else | |
3755 | return two_valued_wta_dispatch_2 | |
3756 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3757 | s_scm_centered_divide, qp, rp); | |
3758 | } | |
3759 | else | |
3760 | return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1, | |
3761 | s_scm_centered_divide, qp, rp); | |
3762 | } | |
3763 | ||
3764 | static void | |
3765 | scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp) | |
3766 | { | |
3767 | double q, r; | |
3768 | ||
3769 | if (SCM_LIKELY (y > 0)) | |
3770 | q = floor (x/y + 0.5); | |
3771 | else if (SCM_LIKELY (y < 0)) | |
3772 | q = ceil (x/y - 0.5); | |
3773 | else if (y == 0) | |
3774 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ | |
3775 | else | |
3776 | q = guile_NaN; | |
3777 | r = x - q * y; | |
3778 | *qp = scm_from_double (q); | |
3779 | *rp = scm_from_double (r); | |
3780 | } | |
3781 | ||
3782 | /* Assumes that both x and y are bigints, though | |
3783 | x might be able to fit into a fixnum. */ | |
3784 | static void | |
3785 | scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3786 | { | |
3787 | SCM q, r, min_r; | |
3788 | ||
3789 | /* Note that x might be small enough to fit into a | |
3790 | fixnum, so we must not let it escape into the wild */ | |
3791 | q = scm_i_mkbig (); | |
3792 | r = scm_i_mkbig (); | |
3793 | ||
3794 | /* min_r will eventually become -abs(y/2) */ | |
3795 | min_r = scm_i_mkbig (); | |
3796 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3797 | SCM_I_BIG_MPZ (y), 1); | |
3798 | ||
3799 | /* Arrange for rr to initially be non-positive, | |
3800 | because that simplifies the test to see | |
3801 | if it is within the needed bounds. */ | |
3802 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3803 | { | |
3804 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3805 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3806 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3807 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3808 | { | |
3809 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3810 | SCM_I_BIG_MPZ (q), 1); | |
3811 | mpz_add (SCM_I_BIG_MPZ (r), | |
3812 | SCM_I_BIG_MPZ (r), | |
3813 | SCM_I_BIG_MPZ (y)); | |
3814 | } | |
3815 | } | |
3816 | else | |
3817 | { | |
3818 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3819 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3820 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3821 | { | |
3822 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3823 | SCM_I_BIG_MPZ (q), 1); | |
3824 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3825 | SCM_I_BIG_MPZ (r), | |
3826 | SCM_I_BIG_MPZ (y)); | |
3827 | } | |
3828 | } | |
3829 | scm_remember_upto_here_2 (x, y); | |
3830 | *qp = scm_i_normbig (q); | |
3831 | *rp = scm_i_normbig (r); | |
3832 | } | |
3833 | ||
3834 | static void | |
3835 | scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3836 | { | |
3837 | SCM r1; | |
3838 | SCM xd = scm_denominator (x); | |
3839 | SCM yd = scm_denominator (y); | |
3840 | ||
3841 | scm_centered_divide (scm_product (scm_numerator (x), yd), | |
3842 | scm_product (scm_numerator (y), xd), | |
3843 | qp, &r1); | |
3844 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
3845 | } | |
3846 | ||
3847 | static SCM scm_i_inexact_round_quotient (double x, double y); | |
3848 | static SCM scm_i_bigint_round_quotient (SCM x, SCM y); | |
3849 | static SCM scm_i_exact_rational_round_quotient (SCM x, SCM y); | |
3850 | ||
3851 | SCM_PRIMITIVE_GENERIC (scm_round_quotient, "round-quotient", 2, 0, 0, | |
ff62c168 | 3852 | (SCM x, SCM y), |
8f9da340 MW |
3853 | "Return @math{@var{x} / @var{y}} to the nearest integer,\n" |
3854 | "with ties going to the nearest even integer.\n" | |
ff62c168 | 3855 | "@lisp\n" |
8f9da340 MW |
3856 | "(round-quotient 123 10) @result{} 12\n" |
3857 | "(round-quotient 123 -10) @result{} -12\n" | |
3858 | "(round-quotient -123 10) @result{} -12\n" | |
3859 | "(round-quotient -123 -10) @result{} 12\n" | |
3860 | "(round-quotient 125 10) @result{} 12\n" | |
3861 | "(round-quotient 127 10) @result{} 13\n" | |
3862 | "(round-quotient 135 10) @result{} 14\n" | |
3863 | "(round-quotient -123.2 -63.5) @result{} 2.0\n" | |
3864 | "(round-quotient 16/3 -10/7) @result{} -4\n" | |
ff62c168 | 3865 | "@end lisp") |
8f9da340 | 3866 | #define FUNC_NAME s_scm_round_quotient |
ff62c168 MW |
3867 | { |
3868 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3869 | { | |
4a46bc2a | 3870 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3871 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3872 | { | |
3873 | scm_t_inum yy = SCM_I_INUM (y); | |
3874 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3875 | scm_num_overflow (s_scm_round_quotient); |
ff62c168 MW |
3876 | else |
3877 | { | |
ff62c168 | 3878 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3879 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3880 | scm_t_inum ay = yy; |
3881 | scm_t_inum r2 = 2 * rr; | |
3882 | ||
3883 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3884 | { |
8f9da340 MW |
3885 | ay = -ay; |
3886 | r2 = -r2; | |
3887 | } | |
3888 | ||
3889 | if (qq & 1L) | |
3890 | { | |
3891 | if (r2 >= ay) | |
3892 | qq++; | |
3893 | else if (r2 <= -ay) | |
3894 | qq--; | |
ff62c168 MW |
3895 | } |
3896 | else | |
3897 | { | |
8f9da340 MW |
3898 | if (r2 > ay) |
3899 | qq++; | |
3900 | else if (r2 < -ay) | |
3901 | qq--; | |
ff62c168 | 3902 | } |
4a46bc2a MW |
3903 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
3904 | return SCM_I_MAKINUM (qq); | |
3905 | else | |
3906 | return scm_i_inum2big (qq); | |
ff62c168 MW |
3907 | } |
3908 | } | |
3909 | else if (SCM_BIGP (y)) | |
3910 | { | |
3911 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3912 | can fit in a fixnum) to scm_i_bigint_round_quotient */ |
3913 | return scm_i_bigint_round_quotient (scm_i_long2big (xx), y); | |
ff62c168 MW |
3914 | } |
3915 | else if (SCM_REALP (y)) | |
8f9da340 | 3916 | return scm_i_inexact_round_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3917 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3918 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3919 | else |
8f9da340 MW |
3920 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3921 | s_scm_round_quotient); | |
ff62c168 MW |
3922 | } |
3923 | else if (SCM_BIGP (x)) | |
3924 | { | |
3925 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3926 | { | |
3927 | scm_t_inum yy = SCM_I_INUM (y); | |
3928 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3929 | scm_num_overflow (s_scm_round_quotient); |
4a46bc2a MW |
3930 | else if (SCM_UNLIKELY (yy == 1)) |
3931 | return x; | |
ff62c168 MW |
3932 | else |
3933 | { | |
3934 | SCM q = scm_i_mkbig (); | |
3935 | scm_t_inum rr; | |
8f9da340 MW |
3936 | int needs_adjustment; |
3937 | ||
ff62c168 MW |
3938 | if (yy > 0) |
3939 | { | |
8f9da340 MW |
3940 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3941 | SCM_I_BIG_MPZ (x), yy); | |
3942 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3943 | needs_adjustment = (2*rr >= yy); | |
3944 | else | |
3945 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3946 | } |
3947 | else | |
3948 | { | |
3949 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3950 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3951 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3952 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3953 | needs_adjustment = (2*rr <= yy); | |
3954 | else | |
3955 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3956 | } |
8f9da340 MW |
3957 | scm_remember_upto_here_1 (x); |
3958 | if (needs_adjustment) | |
3959 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
ff62c168 MW |
3960 | return scm_i_normbig (q); |
3961 | } | |
3962 | } | |
3963 | else if (SCM_BIGP (y)) | |
8f9da340 | 3964 | return scm_i_bigint_round_quotient (x, y); |
ff62c168 | 3965 | else if (SCM_REALP (y)) |
8f9da340 | 3966 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3967 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3968 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3969 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3970 | else |
8f9da340 MW |
3971 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3972 | s_scm_round_quotient); | |
ff62c168 MW |
3973 | } |
3974 | else if (SCM_REALP (x)) | |
3975 | { | |
3976 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3977 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3978 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3979 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3980 | else | |
8f9da340 MW |
3981 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3982 | s_scm_round_quotient); | |
ff62c168 MW |
3983 | } |
3984 | else if (SCM_FRACTIONP (x)) | |
3985 | { | |
3986 | if (SCM_REALP (y)) | |
8f9da340 | 3987 | return scm_i_inexact_round_quotient |
ff62c168 | 3988 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3989 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3990 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3991 | else |
8f9da340 MW |
3992 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3993 | s_scm_round_quotient); | |
ff62c168 MW |
3994 | } |
3995 | else | |
8f9da340 MW |
3996 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG1, |
3997 | s_scm_round_quotient); | |
ff62c168 MW |
3998 | } |
3999 | #undef FUNC_NAME | |
4000 | ||
4001 | static SCM | |
8f9da340 | 4002 | scm_i_inexact_round_quotient (double x, double y) |
ff62c168 | 4003 | { |
8f9da340 MW |
4004 | if (SCM_UNLIKELY (y == 0)) |
4005 | scm_num_overflow (s_scm_round_quotient); /* or return a NaN? */ | |
ff62c168 | 4006 | else |
8f9da340 | 4007 | return scm_from_double (scm_c_round (x / y)); |
ff62c168 MW |
4008 | } |
4009 | ||
4010 | /* Assumes that both x and y are bigints, though | |
4011 | x might be able to fit into a fixnum. */ | |
4012 | static SCM | |
8f9da340 | 4013 | scm_i_bigint_round_quotient (SCM x, SCM y) |
ff62c168 | 4014 | { |
8f9da340 MW |
4015 | SCM q, r, r2; |
4016 | int cmp, needs_adjustment; | |
ff62c168 MW |
4017 | |
4018 | /* Note that x might be small enough to fit into a | |
4019 | fixnum, so we must not let it escape into the wild */ | |
4020 | q = scm_i_mkbig (); | |
4021 | r = scm_i_mkbig (); | |
8f9da340 | 4022 | r2 = scm_i_mkbig (); |
ff62c168 | 4023 | |
8f9da340 MW |
4024 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
4025 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4026 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
4027 | scm_remember_upto_here_2 (x, r); | |
ff62c168 | 4028 | |
8f9da340 MW |
4029 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
4030 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
4031 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 4032 | else |
8f9da340 MW |
4033 | needs_adjustment = (cmp > 0); |
4034 | scm_remember_upto_here_2 (r2, y); | |
4035 | ||
4036 | if (needs_adjustment) | |
4037 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
4038 | ||
ff62c168 MW |
4039 | return scm_i_normbig (q); |
4040 | } | |
4041 | ||
ff62c168 | 4042 | static SCM |
8f9da340 | 4043 | scm_i_exact_rational_round_quotient (SCM x, SCM y) |
ff62c168 | 4044 | { |
8f9da340 | 4045 | return scm_round_quotient |
03ddd15b MW |
4046 | (scm_product (scm_numerator (x), scm_denominator (y)), |
4047 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
4048 | } |
4049 | ||
8f9da340 MW |
4050 | static SCM scm_i_inexact_round_remainder (double x, double y); |
4051 | static SCM scm_i_bigint_round_remainder (SCM x, SCM y); | |
4052 | static SCM scm_i_exact_rational_round_remainder (SCM x, SCM y); | |
ff62c168 | 4053 | |
8f9da340 | 4054 | SCM_PRIMITIVE_GENERIC (scm_round_remainder, "round-remainder", 2, 0, 0, |
ff62c168 MW |
4055 | (SCM x, SCM y), |
4056 | "Return the real number @var{r} such that\n" | |
8f9da340 MW |
4057 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}, where\n" |
4058 | "@var{q} is @math{@var{x} / @var{y}} rounded to the\n" | |
4059 | "nearest integer, with ties going to the nearest\n" | |
4060 | "even integer.\n" | |
ff62c168 | 4061 | "@lisp\n" |
8f9da340 MW |
4062 | "(round-remainder 123 10) @result{} 3\n" |
4063 | "(round-remainder 123 -10) @result{} 3\n" | |
4064 | "(round-remainder -123 10) @result{} -3\n" | |
4065 | "(round-remainder -123 -10) @result{} -3\n" | |
4066 | "(round-remainder 125 10) @result{} 5\n" | |
4067 | "(round-remainder 127 10) @result{} -3\n" | |
4068 | "(round-remainder 135 10) @result{} -5\n" | |
4069 | "(round-remainder -123.2 -63.5) @result{} 3.8\n" | |
4070 | "(round-remainder 16/3 -10/7) @result{} -8/21\n" | |
ff62c168 | 4071 | "@end lisp") |
8f9da340 | 4072 | #define FUNC_NAME s_scm_round_remainder |
ff62c168 MW |
4073 | { |
4074 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
4075 | { | |
4a46bc2a | 4076 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
4077 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
4078 | { | |
4079 | scm_t_inum yy = SCM_I_INUM (y); | |
4080 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 4081 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
4082 | else |
4083 | { | |
8f9da340 | 4084 | scm_t_inum qq = xx / yy; |
ff62c168 | 4085 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
4086 | scm_t_inum ay = yy; |
4087 | scm_t_inum r2 = 2 * rr; | |
4088 | ||
4089 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 4090 | { |
8f9da340 MW |
4091 | ay = -ay; |
4092 | r2 = -r2; | |
4093 | } | |
4094 | ||
4095 | if (qq & 1L) | |
4096 | { | |
4097 | if (r2 >= ay) | |
4098 | rr -= yy; | |
4099 | else if (r2 <= -ay) | |
4100 | rr += yy; | |
ff62c168 MW |
4101 | } |
4102 | else | |
4103 | { | |
8f9da340 MW |
4104 | if (r2 > ay) |
4105 | rr -= yy; | |
4106 | else if (r2 < -ay) | |
4107 | rr += yy; | |
ff62c168 MW |
4108 | } |
4109 | return SCM_I_MAKINUM (rr); | |
4110 | } | |
4111 | } | |
4112 | else if (SCM_BIGP (y)) | |
4113 | { | |
4114 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
4115 | can fit in a fixnum) to scm_i_bigint_round_remainder */ |
4116 | return scm_i_bigint_round_remainder | |
4117 | (scm_i_long2big (xx), y); | |
ff62c168 MW |
4118 | } |
4119 | else if (SCM_REALP (y)) | |
8f9da340 | 4120 | return scm_i_inexact_round_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 4121 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 4122 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 4123 | else |
8f9da340 MW |
4124 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
4125 | s_scm_round_remainder); | |
ff62c168 MW |
4126 | } |
4127 | else if (SCM_BIGP (x)) | |
4128 | { | |
4129 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
4130 | { | |
4131 | scm_t_inum yy = SCM_I_INUM (y); | |
4132 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 4133 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
4134 | else |
4135 | { | |
8f9da340 | 4136 | SCM q = scm_i_mkbig (); |
ff62c168 | 4137 | scm_t_inum rr; |
8f9da340 MW |
4138 | int needs_adjustment; |
4139 | ||
ff62c168 MW |
4140 | if (yy > 0) |
4141 | { | |
8f9da340 MW |
4142 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
4143 | SCM_I_BIG_MPZ (x), yy); | |
4144 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
4145 | needs_adjustment = (2*rr >= yy); | |
4146 | else | |
4147 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
4148 | } |
4149 | else | |
4150 | { | |
8f9da340 MW |
4151 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
4152 | SCM_I_BIG_MPZ (x), -yy); | |
4153 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
4154 | needs_adjustment = (2*rr <= yy); | |
4155 | else | |
4156 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 4157 | } |
8f9da340 MW |
4158 | scm_remember_upto_here_2 (x, q); |
4159 | if (needs_adjustment) | |
4160 | rr -= yy; | |
ff62c168 MW |
4161 | return SCM_I_MAKINUM (rr); |
4162 | } | |
4163 | } | |
4164 | else if (SCM_BIGP (y)) | |
8f9da340 | 4165 | return scm_i_bigint_round_remainder (x, y); |
ff62c168 | 4166 | else if (SCM_REALP (y)) |
8f9da340 | 4167 | return scm_i_inexact_round_remainder |
ff62c168 MW |
4168 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
4169 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 4170 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 4171 | else |
8f9da340 MW |
4172 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
4173 | s_scm_round_remainder); | |
ff62c168 MW |
4174 | } |
4175 | else if (SCM_REALP (x)) | |
4176 | { | |
4177 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
4178 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 4179 | return scm_i_inexact_round_remainder |
ff62c168 MW |
4180 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
4181 | else | |
8f9da340 MW |
4182 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
4183 | s_scm_round_remainder); | |
ff62c168 MW |
4184 | } |
4185 | else if (SCM_FRACTIONP (x)) | |
4186 | { | |
4187 | if (SCM_REALP (y)) | |
8f9da340 | 4188 | return scm_i_inexact_round_remainder |
ff62c168 | 4189 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 4190 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 4191 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 4192 | else |
8f9da340 MW |
4193 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
4194 | s_scm_round_remainder); | |
ff62c168 MW |
4195 | } |
4196 | else | |
8f9da340 MW |
4197 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG1, |
4198 | s_scm_round_remainder); | |
ff62c168 MW |
4199 | } |
4200 | #undef FUNC_NAME | |
4201 | ||
4202 | static SCM | |
8f9da340 | 4203 | scm_i_inexact_round_remainder (double x, double y) |
ff62c168 | 4204 | { |
ff62c168 MW |
4205 | /* Although it would be more efficient to use fmod here, we can't |
4206 | because it would in some cases produce results inconsistent with | |
8f9da340 | 4207 | scm_i_inexact_round_quotient, such that x != r + q * y (not even |
ff62c168 | 4208 | close). In particular, when x-y/2 is very close to a multiple of |
8f9da340 MW |
4209 | y, then r might be either -abs(y/2) or abs(y/2), but those two |
4210 | cases must correspond to different choices of q. If quotient | |
ff62c168 | 4211 | chooses one and remainder chooses the other, it would be bad. */ |
8f9da340 MW |
4212 | |
4213 | if (SCM_UNLIKELY (y == 0)) | |
4214 | scm_num_overflow (s_scm_round_remainder); /* or return a NaN? */ | |
ff62c168 | 4215 | else |
8f9da340 MW |
4216 | { |
4217 | double q = scm_c_round (x / y); | |
4218 | return scm_from_double (x - q * y); | |
4219 | } | |
ff62c168 MW |
4220 | } |
4221 | ||
4222 | /* Assumes that both x and y are bigints, though | |
4223 | x might be able to fit into a fixnum. */ | |
4224 | static SCM | |
8f9da340 | 4225 | scm_i_bigint_round_remainder (SCM x, SCM y) |
ff62c168 | 4226 | { |
8f9da340 MW |
4227 | SCM q, r, r2; |
4228 | int cmp, needs_adjustment; | |
ff62c168 MW |
4229 | |
4230 | /* Note that x might be small enough to fit into a | |
4231 | fixnum, so we must not let it escape into the wild */ | |
8f9da340 | 4232 | q = scm_i_mkbig (); |
ff62c168 | 4233 | r = scm_i_mkbig (); |
8f9da340 | 4234 | r2 = scm_i_mkbig (); |
ff62c168 | 4235 | |
8f9da340 MW |
4236 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
4237 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4238 | scm_remember_upto_here_1 (x); | |
4239 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 4240 | |
8f9da340 MW |
4241 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
4242 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
4243 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 4244 | else |
8f9da340 MW |
4245 | needs_adjustment = (cmp > 0); |
4246 | scm_remember_upto_here_2 (q, r2); | |
4247 | ||
4248 | if (needs_adjustment) | |
4249 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
4250 | ||
4251 | scm_remember_upto_here_1 (y); | |
ff62c168 MW |
4252 | return scm_i_normbig (r); |
4253 | } | |
4254 | ||
ff62c168 | 4255 | static SCM |
8f9da340 | 4256 | scm_i_exact_rational_round_remainder (SCM x, SCM y) |
ff62c168 | 4257 | { |
03ddd15b MW |
4258 | SCM xd = scm_denominator (x); |
4259 | SCM yd = scm_denominator (y); | |
8f9da340 MW |
4260 | SCM r1 = scm_round_remainder (scm_product (scm_numerator (x), yd), |
4261 | scm_product (scm_numerator (y), xd)); | |
03ddd15b | 4262 | return scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
4263 | } |
4264 | ||
4265 | ||
8f9da340 MW |
4266 | static void scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp); |
4267 | static void scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
4268 | static void scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
ff62c168 | 4269 | |
8f9da340 | 4270 | SCM_PRIMITIVE_GENERIC (scm_i_round_divide, "round/", 2, 0, 0, |
ff62c168 MW |
4271 | (SCM x, SCM y), |
4272 | "Return the integer @var{q} and the real number @var{r}\n" | |
4273 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
8f9da340 MW |
4274 | "and @var{q} is @math{@var{x} / @var{y}} rounded to the\n" |
4275 | "nearest integer, with ties going to the nearest even integer.\n" | |
ff62c168 | 4276 | "@lisp\n" |
8f9da340 MW |
4277 | "(round/ 123 10) @result{} 12 and 3\n" |
4278 | "(round/ 123 -10) @result{} -12 and 3\n" | |
4279 | "(round/ -123 10) @result{} -12 and -3\n" | |
4280 | "(round/ -123 -10) @result{} 12 and -3\n" | |
4281 | "(round/ 125 10) @result{} 12 and 5\n" | |
4282 | "(round/ 127 10) @result{} 13 and -3\n" | |
4283 | "(round/ 135 10) @result{} 14 and -5\n" | |
4284 | "(round/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
4285 | "(round/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
ff62c168 | 4286 | "@end lisp") |
8f9da340 | 4287 | #define FUNC_NAME s_scm_i_round_divide |
5fbf680b MW |
4288 | { |
4289 | SCM q, r; | |
4290 | ||
8f9da340 | 4291 | scm_round_divide(x, y, &q, &r); |
5fbf680b MW |
4292 | return scm_values (scm_list_2 (q, r)); |
4293 | } | |
4294 | #undef FUNC_NAME | |
4295 | ||
8f9da340 MW |
4296 | #define s_scm_round_divide s_scm_i_round_divide |
4297 | #define g_scm_round_divide g_scm_i_round_divide | |
5fbf680b MW |
4298 | |
4299 | void | |
8f9da340 | 4300 | scm_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 MW |
4301 | { |
4302 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
4303 | { | |
4a46bc2a | 4304 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
4305 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
4306 | { | |
4307 | scm_t_inum yy = SCM_I_INUM (y); | |
4308 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 4309 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
4310 | else |
4311 | { | |
ff62c168 | 4312 | scm_t_inum qq = xx / yy; |
4a46bc2a | 4313 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
4314 | scm_t_inum ay = yy; |
4315 | scm_t_inum r2 = 2 * rr; | |
4316 | ||
4317 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 4318 | { |
8f9da340 MW |
4319 | ay = -ay; |
4320 | r2 = -r2; | |
4321 | } | |
4322 | ||
4323 | if (qq & 1L) | |
4324 | { | |
4325 | if (r2 >= ay) | |
4326 | { qq++; rr -= yy; } | |
4327 | else if (r2 <= -ay) | |
4328 | { qq--; rr += yy; } | |
ff62c168 MW |
4329 | } |
4330 | else | |
4331 | { | |
8f9da340 MW |
4332 | if (r2 > ay) |
4333 | { qq++; rr -= yy; } | |
4334 | else if (r2 < -ay) | |
4335 | { qq--; rr += yy; } | |
ff62c168 | 4336 | } |
4a46bc2a | 4337 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 4338 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 4339 | else |
5fbf680b MW |
4340 | *qp = scm_i_inum2big (qq); |
4341 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 4342 | } |
5fbf680b | 4343 | return; |
ff62c168 MW |
4344 | } |
4345 | else if (SCM_BIGP (y)) | |
4346 | { | |
4347 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
4348 | can fit in a fixnum) to scm_i_bigint_round_divide */ |
4349 | return scm_i_bigint_round_divide | |
4350 | (scm_i_long2big (SCM_I_INUM (x)), y, qp, rp); | |
ff62c168 MW |
4351 | } |
4352 | else if (SCM_REALP (y)) | |
8f9da340 | 4353 | return scm_i_inexact_round_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 4354 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 4355 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 4356 | else |
8f9da340 MW |
4357 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
4358 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
4359 | } |
4360 | else if (SCM_BIGP (x)) | |
4361 | { | |
4362 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
4363 | { | |
4364 | scm_t_inum yy = SCM_I_INUM (y); | |
4365 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 4366 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
4367 | else |
4368 | { | |
4369 | SCM q = scm_i_mkbig (); | |
4370 | scm_t_inum rr; | |
8f9da340 MW |
4371 | int needs_adjustment; |
4372 | ||
ff62c168 MW |
4373 | if (yy > 0) |
4374 | { | |
8f9da340 MW |
4375 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
4376 | SCM_I_BIG_MPZ (x), yy); | |
4377 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
4378 | needs_adjustment = (2*rr >= yy); | |
4379 | else | |
4380 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
4381 | } |
4382 | else | |
4383 | { | |
4384 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
4385 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 4386 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
4387 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
4388 | needs_adjustment = (2*rr <= yy); | |
4389 | else | |
4390 | needs_adjustment = (2*rr < yy); | |
4391 | } | |
4392 | scm_remember_upto_here_1 (x); | |
4393 | if (needs_adjustment) | |
4394 | { | |
4395 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
4396 | rr -= yy; | |
ff62c168 | 4397 | } |
5fbf680b MW |
4398 | *qp = scm_i_normbig (q); |
4399 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 4400 | } |
5fbf680b | 4401 | return; |
ff62c168 MW |
4402 | } |
4403 | else if (SCM_BIGP (y)) | |
8f9da340 | 4404 | return scm_i_bigint_round_divide (x, y, qp, rp); |
ff62c168 | 4405 | else if (SCM_REALP (y)) |
8f9da340 | 4406 | return scm_i_inexact_round_divide |
5fbf680b | 4407 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 4408 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 4409 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 4410 | else |
8f9da340 MW |
4411 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
4412 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
4413 | } |
4414 | else if (SCM_REALP (x)) | |
4415 | { | |
4416 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
4417 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 4418 | return scm_i_inexact_round_divide |
5fbf680b | 4419 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
03ddd15b | 4420 | else |
8f9da340 MW |
4421 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
4422 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
4423 | } |
4424 | else if (SCM_FRACTIONP (x)) | |
4425 | { | |
4426 | if (SCM_REALP (y)) | |
8f9da340 | 4427 | return scm_i_inexact_round_divide |
5fbf680b | 4428 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b | 4429 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 4430 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 4431 | else |
8f9da340 MW |
4432 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
4433 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
4434 | } |
4435 | else | |
8f9da340 MW |
4436 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG1, |
4437 | s_scm_round_divide, qp, rp); | |
ff62c168 | 4438 | } |
ff62c168 | 4439 | |
5fbf680b | 4440 | static void |
8f9da340 | 4441 | scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp) |
ff62c168 | 4442 | { |
8f9da340 MW |
4443 | if (SCM_UNLIKELY (y == 0)) |
4444 | scm_num_overflow (s_scm_round_divide); /* or return a NaN? */ | |
ff62c168 | 4445 | else |
8f9da340 MW |
4446 | { |
4447 | double q = scm_c_round (x / y); | |
4448 | double r = x - q * y; | |
4449 | *qp = scm_from_double (q); | |
4450 | *rp = scm_from_double (r); | |
4451 | } | |
ff62c168 MW |
4452 | } |
4453 | ||
4454 | /* Assumes that both x and y are bigints, though | |
4455 | x might be able to fit into a fixnum. */ | |
5fbf680b | 4456 | static void |
8f9da340 | 4457 | scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 4458 | { |
8f9da340 MW |
4459 | SCM q, r, r2; |
4460 | int cmp, needs_adjustment; | |
ff62c168 MW |
4461 | |
4462 | /* Note that x might be small enough to fit into a | |
4463 | fixnum, so we must not let it escape into the wild */ | |
4464 | q = scm_i_mkbig (); | |
4465 | r = scm_i_mkbig (); | |
8f9da340 | 4466 | r2 = scm_i_mkbig (); |
ff62c168 | 4467 | |
8f9da340 MW |
4468 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
4469 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4470 | scm_remember_upto_here_1 (x); | |
4471 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 4472 | |
8f9da340 MW |
4473 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
4474 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
4475 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 4476 | else |
8f9da340 MW |
4477 | needs_adjustment = (cmp > 0); |
4478 | ||
4479 | if (needs_adjustment) | |
ff62c168 | 4480 | { |
8f9da340 MW |
4481 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
4482 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
ff62c168 | 4483 | } |
8f9da340 MW |
4484 | |
4485 | scm_remember_upto_here_2 (r2, y); | |
5fbf680b MW |
4486 | *qp = scm_i_normbig (q); |
4487 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
4488 | } |
4489 | ||
5fbf680b | 4490 | static void |
8f9da340 | 4491 | scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 4492 | { |
03ddd15b MW |
4493 | SCM r1; |
4494 | SCM xd = scm_denominator (x); | |
4495 | SCM yd = scm_denominator (y); | |
4496 | ||
8f9da340 MW |
4497 | scm_round_divide (scm_product (scm_numerator (x), yd), |
4498 | scm_product (scm_numerator (y), xd), | |
4499 | qp, &r1); | |
03ddd15b | 4500 | *rp = scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
4501 | } |
4502 | ||
4503 | ||
78d3deb1 AW |
4504 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
4505 | (SCM x, SCM y, SCM rest), | |
4506 | "Return the greatest common divisor of all parameter values.\n" | |
4507 | "If called without arguments, 0 is returned.") | |
4508 | #define FUNC_NAME s_scm_i_gcd | |
4509 | { | |
4510 | while (!scm_is_null (rest)) | |
4511 | { x = scm_gcd (x, y); | |
4512 | y = scm_car (rest); | |
4513 | rest = scm_cdr (rest); | |
4514 | } | |
4515 | return scm_gcd (x, y); | |
4516 | } | |
4517 | #undef FUNC_NAME | |
4518 | ||
4519 | #define s_gcd s_scm_i_gcd | |
4520 | #define g_gcd g_scm_i_gcd | |
4521 | ||
0f2d19dd | 4522 | SCM |
6e8d25a6 | 4523 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 4524 | { |
ca46fb90 | 4525 | if (SCM_UNBNDP (y)) |
1dd79792 | 4526 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 4527 | |
e11e83f3 | 4528 | if (SCM_I_INUMP (x)) |
ca46fb90 | 4529 | { |
e11e83f3 | 4530 | if (SCM_I_INUMP (y)) |
ca46fb90 | 4531 | { |
e25f3727 AW |
4532 | scm_t_inum xx = SCM_I_INUM (x); |
4533 | scm_t_inum yy = SCM_I_INUM (y); | |
4534 | scm_t_inum u = xx < 0 ? -xx : xx; | |
4535 | scm_t_inum v = yy < 0 ? -yy : yy; | |
4536 | scm_t_inum result; | |
0aacf84e MD |
4537 | if (xx == 0) |
4538 | result = v; | |
4539 | else if (yy == 0) | |
4540 | result = u; | |
4541 | else | |
4542 | { | |
e25f3727 AW |
4543 | scm_t_inum k = 1; |
4544 | scm_t_inum t; | |
0aacf84e MD |
4545 | /* Determine a common factor 2^k */ |
4546 | while (!(1 & (u | v))) | |
4547 | { | |
4548 | k <<= 1; | |
4549 | u >>= 1; | |
4550 | v >>= 1; | |
4551 | } | |
4552 | /* Now, any factor 2^n can be eliminated */ | |
4553 | if (u & 1) | |
4554 | t = -v; | |
4555 | else | |
4556 | { | |
4557 | t = u; | |
4558 | b3: | |
4559 | t = SCM_SRS (t, 1); | |
4560 | } | |
4561 | if (!(1 & t)) | |
4562 | goto b3; | |
4563 | if (t > 0) | |
4564 | u = t; | |
4565 | else | |
4566 | v = -t; | |
4567 | t = u - v; | |
4568 | if (t != 0) | |
4569 | goto b3; | |
4570 | result = u * k; | |
4571 | } | |
4572 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 4573 | ? SCM_I_MAKINUM (result) |
e25f3727 | 4574 | : scm_i_inum2big (result)); |
ca46fb90 RB |
4575 | } |
4576 | else if (SCM_BIGP (y)) | |
4577 | { | |
0bff4dce KR |
4578 | SCM_SWAP (x, y); |
4579 | goto big_inum; | |
ca46fb90 RB |
4580 | } |
4581 | else | |
4582 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 4583 | } |
ca46fb90 RB |
4584 | else if (SCM_BIGP (x)) |
4585 | { | |
e11e83f3 | 4586 | if (SCM_I_INUMP (y)) |
ca46fb90 | 4587 | { |
e25f3727 AW |
4588 | scm_t_bits result; |
4589 | scm_t_inum yy; | |
0bff4dce | 4590 | big_inum: |
e11e83f3 | 4591 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
4592 | if (yy == 0) |
4593 | return scm_abs (x); | |
0aacf84e MD |
4594 | if (yy < 0) |
4595 | yy = -yy; | |
ca46fb90 RB |
4596 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
4597 | scm_remember_upto_here_1 (x); | |
0aacf84e | 4598 | return (SCM_POSFIXABLE (result) |
d956fa6f | 4599 | ? SCM_I_MAKINUM (result) |
e25f3727 | 4600 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
4601 | } |
4602 | else if (SCM_BIGP (y)) | |
4603 | { | |
4604 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
4605 | mpz_gcd (SCM_I_BIG_MPZ (result), |
4606 | SCM_I_BIG_MPZ (x), | |
4607 | SCM_I_BIG_MPZ (y)); | |
4608 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
4609 | return scm_i_normbig (result); |
4610 | } | |
4611 | else | |
4612 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 4613 | } |
ca46fb90 | 4614 | else |
09fb7599 | 4615 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
4616 | } |
4617 | ||
78d3deb1 AW |
4618 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
4619 | (SCM x, SCM y, SCM rest), | |
4620 | "Return the least common multiple of the arguments.\n" | |
4621 | "If called without arguments, 1 is returned.") | |
4622 | #define FUNC_NAME s_scm_i_lcm | |
4623 | { | |
4624 | while (!scm_is_null (rest)) | |
4625 | { x = scm_lcm (x, y); | |
4626 | y = scm_car (rest); | |
4627 | rest = scm_cdr (rest); | |
4628 | } | |
4629 | return scm_lcm (x, y); | |
4630 | } | |
4631 | #undef FUNC_NAME | |
4632 | ||
4633 | #define s_lcm s_scm_i_lcm | |
4634 | #define g_lcm g_scm_i_lcm | |
4635 | ||
0f2d19dd | 4636 | SCM |
6e8d25a6 | 4637 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 4638 | { |
ca46fb90 RB |
4639 | if (SCM_UNBNDP (n2)) |
4640 | { | |
4641 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
4642 | return SCM_I_MAKINUM (1L); |
4643 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 4644 | } |
09fb7599 | 4645 | |
e11e83f3 | 4646 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 4647 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 4648 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 4649 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 4650 | |
e11e83f3 | 4651 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 4652 | { |
e11e83f3 | 4653 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4654 | { |
4655 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 4656 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
4657 | return d; |
4658 | else | |
4659 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
4660 | } | |
4661 | else | |
4662 | { | |
4663 | /* inum n1, big n2 */ | |
4664 | inumbig: | |
4665 | { | |
4666 | SCM result = scm_i_mkbig (); | |
e25f3727 | 4667 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
4668 | if (nn1 == 0) return SCM_INUM0; |
4669 | if (nn1 < 0) nn1 = - nn1; | |
4670 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
4671 | scm_remember_upto_here_1 (n2); | |
4672 | return result; | |
4673 | } | |
4674 | } | |
4675 | } | |
4676 | else | |
4677 | { | |
4678 | /* big n1 */ | |
e11e83f3 | 4679 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4680 | { |
4681 | SCM_SWAP (n1, n2); | |
4682 | goto inumbig; | |
4683 | } | |
4684 | else | |
4685 | { | |
4686 | SCM result = scm_i_mkbig (); | |
4687 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
4688 | SCM_I_BIG_MPZ (n1), | |
4689 | SCM_I_BIG_MPZ (n2)); | |
4690 | scm_remember_upto_here_2(n1, n2); | |
4691 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
4692 | return result; | |
4693 | } | |
f872b822 | 4694 | } |
0f2d19dd JB |
4695 | } |
4696 | ||
8a525303 GB |
4697 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
4698 | ||
4699 | Logand: | |
4700 | X Y Result Method: | |
4701 | (len) | |
4702 | + + + x (map digit:logand X Y) | |
4703 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
4704 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
4705 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
4706 | ||
4707 | Logior: | |
4708 | X Y Result Method: | |
4709 | ||
4710 | + + + (map digit:logior X Y) | |
4711 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
4712 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
4713 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
4714 | ||
4715 | Logxor: | |
4716 | X Y Result Method: | |
4717 | ||
4718 | + + + (map digit:logxor X Y) | |
4719 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
4720 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
4721 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
4722 | ||
4723 | Logtest: | |
4724 | X Y Result | |
4725 | ||
4726 | + + (any digit:logand X Y) | |
4727 | + - (any digit:logand X (lognot (+ -1 Y))) | |
4728 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
4729 | - - #t | |
4730 | ||
4731 | */ | |
4732 | ||
78d3deb1 AW |
4733 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
4734 | (SCM x, SCM y, SCM rest), | |
4735 | "Return the bitwise AND of the integer arguments.\n\n" | |
4736 | "@lisp\n" | |
4737 | "(logand) @result{} -1\n" | |
4738 | "(logand 7) @result{} 7\n" | |
4739 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
4740 | "@end lisp") | |
4741 | #define FUNC_NAME s_scm_i_logand | |
4742 | { | |
4743 | while (!scm_is_null (rest)) | |
4744 | { x = scm_logand (x, y); | |
4745 | y = scm_car (rest); | |
4746 | rest = scm_cdr (rest); | |
4747 | } | |
4748 | return scm_logand (x, y); | |
4749 | } | |
4750 | #undef FUNC_NAME | |
4751 | ||
4752 | #define s_scm_logand s_scm_i_logand | |
4753 | ||
4754 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 4755 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 4756 | { |
e25f3727 | 4757 | scm_t_inum nn1; |
9a00c9fc | 4758 | |
0aacf84e MD |
4759 | if (SCM_UNBNDP (n2)) |
4760 | { | |
4761 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 4762 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
4763 | else if (!SCM_NUMBERP (n1)) |
4764 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
4765 | else if (SCM_NUMBERP (n1)) | |
4766 | return n1; | |
4767 | else | |
4768 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4769 | } |
09fb7599 | 4770 | |
e11e83f3 | 4771 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4772 | { |
e11e83f3 MV |
4773 | nn1 = SCM_I_INUM (n1); |
4774 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4775 | { |
e25f3727 | 4776 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4777 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
4778 | } |
4779 | else if SCM_BIGP (n2) | |
4780 | { | |
4781 | intbig: | |
4782 | if (n1 == 0) | |
4783 | return SCM_INUM0; | |
4784 | { | |
4785 | SCM result_z = scm_i_mkbig (); | |
4786 | mpz_t nn1_z; | |
4787 | mpz_init_set_si (nn1_z, nn1); | |
4788 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4789 | scm_remember_upto_here_1 (n2); | |
4790 | mpz_clear (nn1_z); | |
4791 | return scm_i_normbig (result_z); | |
4792 | } | |
4793 | } | |
4794 | else | |
4795 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4796 | } | |
4797 | else if (SCM_BIGP (n1)) | |
4798 | { | |
e11e83f3 | 4799 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4800 | { |
4801 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4802 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4803 | goto intbig; |
4804 | } | |
4805 | else if (SCM_BIGP (n2)) | |
4806 | { | |
4807 | SCM result_z = scm_i_mkbig (); | |
4808 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
4809 | SCM_I_BIG_MPZ (n1), | |
4810 | SCM_I_BIG_MPZ (n2)); | |
4811 | scm_remember_upto_here_2 (n1, n2); | |
4812 | return scm_i_normbig (result_z); | |
4813 | } | |
4814 | else | |
4815 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4816 | } |
0aacf84e | 4817 | else |
09fb7599 | 4818 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4819 | } |
1bbd0b84 | 4820 | #undef FUNC_NAME |
0f2d19dd | 4821 | |
09fb7599 | 4822 | |
78d3deb1 AW |
4823 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
4824 | (SCM x, SCM y, SCM rest), | |
4825 | "Return the bitwise OR of the integer arguments.\n\n" | |
4826 | "@lisp\n" | |
4827 | "(logior) @result{} 0\n" | |
4828 | "(logior 7) @result{} 7\n" | |
4829 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
4830 | "@end lisp") | |
4831 | #define FUNC_NAME s_scm_i_logior | |
4832 | { | |
4833 | while (!scm_is_null (rest)) | |
4834 | { x = scm_logior (x, y); | |
4835 | y = scm_car (rest); | |
4836 | rest = scm_cdr (rest); | |
4837 | } | |
4838 | return scm_logior (x, y); | |
4839 | } | |
4840 | #undef FUNC_NAME | |
4841 | ||
4842 | #define s_scm_logior s_scm_i_logior | |
4843 | ||
4844 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 4845 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 4846 | { |
e25f3727 | 4847 | scm_t_inum nn1; |
9a00c9fc | 4848 | |
0aacf84e MD |
4849 | if (SCM_UNBNDP (n2)) |
4850 | { | |
4851 | if (SCM_UNBNDP (n1)) | |
4852 | return SCM_INUM0; | |
4853 | else if (SCM_NUMBERP (n1)) | |
4854 | return n1; | |
4855 | else | |
4856 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4857 | } |
09fb7599 | 4858 | |
e11e83f3 | 4859 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4860 | { |
e11e83f3 MV |
4861 | nn1 = SCM_I_INUM (n1); |
4862 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4863 | { |
e11e83f3 | 4864 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 4865 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
4866 | } |
4867 | else if (SCM_BIGP (n2)) | |
4868 | { | |
4869 | intbig: | |
4870 | if (nn1 == 0) | |
4871 | return n2; | |
4872 | { | |
4873 | SCM result_z = scm_i_mkbig (); | |
4874 | mpz_t nn1_z; | |
4875 | mpz_init_set_si (nn1_z, nn1); | |
4876 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4877 | scm_remember_upto_here_1 (n2); | |
4878 | mpz_clear (nn1_z); | |
9806de0d | 4879 | return scm_i_normbig (result_z); |
0aacf84e MD |
4880 | } |
4881 | } | |
4882 | else | |
4883 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4884 | } | |
4885 | else if (SCM_BIGP (n1)) | |
4886 | { | |
e11e83f3 | 4887 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4888 | { |
4889 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4890 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4891 | goto intbig; |
4892 | } | |
4893 | else if (SCM_BIGP (n2)) | |
4894 | { | |
4895 | SCM result_z = scm_i_mkbig (); | |
4896 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
4897 | SCM_I_BIG_MPZ (n1), | |
4898 | SCM_I_BIG_MPZ (n2)); | |
4899 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 4900 | return scm_i_normbig (result_z); |
0aacf84e MD |
4901 | } |
4902 | else | |
4903 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4904 | } |
0aacf84e | 4905 | else |
09fb7599 | 4906 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4907 | } |
1bbd0b84 | 4908 | #undef FUNC_NAME |
0f2d19dd | 4909 | |
09fb7599 | 4910 | |
78d3deb1 AW |
4911 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
4912 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
4913 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
4914 | "set in the result if it is set in an odd number of arguments.\n" | |
4915 | "@lisp\n" | |
4916 | "(logxor) @result{} 0\n" | |
4917 | "(logxor 7) @result{} 7\n" | |
4918 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
4919 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 4920 | "@end lisp") |
78d3deb1 AW |
4921 | #define FUNC_NAME s_scm_i_logxor |
4922 | { | |
4923 | while (!scm_is_null (rest)) | |
4924 | { x = scm_logxor (x, y); | |
4925 | y = scm_car (rest); | |
4926 | rest = scm_cdr (rest); | |
4927 | } | |
4928 | return scm_logxor (x, y); | |
4929 | } | |
4930 | #undef FUNC_NAME | |
4931 | ||
4932 | #define s_scm_logxor s_scm_i_logxor | |
4933 | ||
4934 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 4935 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 4936 | { |
e25f3727 | 4937 | scm_t_inum nn1; |
9a00c9fc | 4938 | |
0aacf84e MD |
4939 | if (SCM_UNBNDP (n2)) |
4940 | { | |
4941 | if (SCM_UNBNDP (n1)) | |
4942 | return SCM_INUM0; | |
4943 | else if (SCM_NUMBERP (n1)) | |
4944 | return n1; | |
4945 | else | |
4946 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4947 | } |
09fb7599 | 4948 | |
e11e83f3 | 4949 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4950 | { |
e11e83f3 MV |
4951 | nn1 = SCM_I_INUM (n1); |
4952 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4953 | { |
e25f3727 | 4954 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4955 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
4956 | } |
4957 | else if (SCM_BIGP (n2)) | |
4958 | { | |
4959 | intbig: | |
4960 | { | |
4961 | SCM result_z = scm_i_mkbig (); | |
4962 | mpz_t nn1_z; | |
4963 | mpz_init_set_si (nn1_z, nn1); | |
4964 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4965 | scm_remember_upto_here_1 (n2); | |
4966 | mpz_clear (nn1_z); | |
4967 | return scm_i_normbig (result_z); | |
4968 | } | |
4969 | } | |
4970 | else | |
4971 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4972 | } | |
4973 | else if (SCM_BIGP (n1)) | |
4974 | { | |
e11e83f3 | 4975 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4976 | { |
4977 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4978 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4979 | goto intbig; |
4980 | } | |
4981 | else if (SCM_BIGP (n2)) | |
4982 | { | |
4983 | SCM result_z = scm_i_mkbig (); | |
4984 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
4985 | SCM_I_BIG_MPZ (n1), | |
4986 | SCM_I_BIG_MPZ (n2)); | |
4987 | scm_remember_upto_here_2 (n1, n2); | |
4988 | return scm_i_normbig (result_z); | |
4989 | } | |
4990 | else | |
4991 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4992 | } |
0aacf84e | 4993 | else |
09fb7599 | 4994 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4995 | } |
1bbd0b84 | 4996 | #undef FUNC_NAME |
0f2d19dd | 4997 | |
09fb7599 | 4998 | |
a1ec6916 | 4999 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 5000 | (SCM j, SCM k), |
ba6e7231 KR |
5001 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
5002 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
5003 | "without actually calculating the @code{logand}, just testing\n" | |
5004 | "for non-zero.\n" | |
5005 | "\n" | |
1e6808ea | 5006 | "@lisp\n" |
b380b885 MD |
5007 | "(logtest #b0100 #b1011) @result{} #f\n" |
5008 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 5009 | "@end lisp") |
1bbd0b84 | 5010 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 5011 | { |
e25f3727 | 5012 | scm_t_inum nj; |
9a00c9fc | 5013 | |
e11e83f3 | 5014 | if (SCM_I_INUMP (j)) |
0aacf84e | 5015 | { |
e11e83f3 MV |
5016 | nj = SCM_I_INUM (j); |
5017 | if (SCM_I_INUMP (k)) | |
0aacf84e | 5018 | { |
e25f3727 | 5019 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 5020 | return scm_from_bool (nj & nk); |
0aacf84e MD |
5021 | } |
5022 | else if (SCM_BIGP (k)) | |
5023 | { | |
5024 | intbig: | |
5025 | if (nj == 0) | |
5026 | return SCM_BOOL_F; | |
5027 | { | |
5028 | SCM result; | |
5029 | mpz_t nj_z; | |
5030 | mpz_init_set_si (nj_z, nj); | |
5031 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
5032 | scm_remember_upto_here_1 (k); | |
73e4de09 | 5033 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
5034 | mpz_clear (nj_z); |
5035 | return result; | |
5036 | } | |
5037 | } | |
5038 | else | |
5039 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
5040 | } | |
5041 | else if (SCM_BIGP (j)) | |
5042 | { | |
e11e83f3 | 5043 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
5044 | { |
5045 | SCM_SWAP (j, k); | |
e11e83f3 | 5046 | nj = SCM_I_INUM (j); |
0aacf84e MD |
5047 | goto intbig; |
5048 | } | |
5049 | else if (SCM_BIGP (k)) | |
5050 | { | |
5051 | SCM result; | |
5052 | mpz_t result_z; | |
5053 | mpz_init (result_z); | |
5054 | mpz_and (result_z, | |
5055 | SCM_I_BIG_MPZ (j), | |
5056 | SCM_I_BIG_MPZ (k)); | |
5057 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 5058 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
5059 | mpz_clear (result_z); |
5060 | return result; | |
5061 | } | |
5062 | else | |
5063 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
5064 | } | |
5065 | else | |
5066 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 5067 | } |
1bbd0b84 | 5068 | #undef FUNC_NAME |
0f2d19dd | 5069 | |
c1bfcf60 | 5070 | |
a1ec6916 | 5071 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 5072 | (SCM index, SCM j), |
ba6e7231 KR |
5073 | "Test whether bit number @var{index} in @var{j} is set.\n" |
5074 | "@var{index} starts from 0 for the least significant bit.\n" | |
5075 | "\n" | |
1e6808ea | 5076 | "@lisp\n" |
b380b885 MD |
5077 | "(logbit? 0 #b1101) @result{} #t\n" |
5078 | "(logbit? 1 #b1101) @result{} #f\n" | |
5079 | "(logbit? 2 #b1101) @result{} #t\n" | |
5080 | "(logbit? 3 #b1101) @result{} #t\n" | |
5081 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 5082 | "@end lisp") |
1bbd0b84 | 5083 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 5084 | { |
78166ad5 | 5085 | unsigned long int iindex; |
5efd3c7d | 5086 | iindex = scm_to_ulong (index); |
78166ad5 | 5087 | |
e11e83f3 | 5088 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
5089 | { |
5090 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 5091 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 5092 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 5093 | } |
0aacf84e MD |
5094 | else if (SCM_BIGP (j)) |
5095 | { | |
5096 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
5097 | scm_remember_upto_here_1 (j); | |
73e4de09 | 5098 | return scm_from_bool (val); |
0aacf84e MD |
5099 | } |
5100 | else | |
78166ad5 | 5101 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 5102 | } |
1bbd0b84 | 5103 | #undef FUNC_NAME |
0f2d19dd | 5104 | |
78166ad5 | 5105 | |
a1ec6916 | 5106 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 5107 | (SCM n), |
4d814788 | 5108 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
5109 | "argument.\n" |
5110 | "\n" | |
b380b885 MD |
5111 | "@lisp\n" |
5112 | "(number->string (lognot #b10000000) 2)\n" | |
5113 | " @result{} \"-10000001\"\n" | |
5114 | "(number->string (lognot #b0) 2)\n" | |
5115 | " @result{} \"-1\"\n" | |
1e6808ea | 5116 | "@end lisp") |
1bbd0b84 | 5117 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 5118 | { |
e11e83f3 | 5119 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
5120 | /* No overflow here, just need to toggle all the bits making up the inum. |
5121 | Enhancement: No need to strip the tag and add it back, could just xor | |
5122 | a block of 1 bits, if that worked with the various debug versions of | |
5123 | the SCM typedef. */ | |
e11e83f3 | 5124 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
5125 | |
5126 | } else if (SCM_BIGP (n)) { | |
5127 | SCM result = scm_i_mkbig (); | |
5128 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
5129 | scm_remember_upto_here_1 (n); | |
5130 | return result; | |
5131 | ||
5132 | } else { | |
5133 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
5134 | } | |
0f2d19dd | 5135 | } |
1bbd0b84 | 5136 | #undef FUNC_NAME |
0f2d19dd | 5137 | |
518b7508 KR |
5138 | /* returns 0 if IN is not an integer. OUT must already be |
5139 | initialized. */ | |
5140 | static int | |
5141 | coerce_to_big (SCM in, mpz_t out) | |
5142 | { | |
5143 | if (SCM_BIGP (in)) | |
5144 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
5145 | else if (SCM_I_INUMP (in)) |
5146 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
5147 | else |
5148 | return 0; | |
5149 | ||
5150 | return 1; | |
5151 | } | |
5152 | ||
d885e204 | 5153 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
5154 | (SCM n, SCM k, SCM m), |
5155 | "Return @var{n} raised to the integer exponent\n" | |
5156 | "@var{k}, modulo @var{m}.\n" | |
5157 | "\n" | |
5158 | "@lisp\n" | |
5159 | "(modulo-expt 2 3 5)\n" | |
5160 | " @result{} 3\n" | |
5161 | "@end lisp") | |
d885e204 | 5162 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
5163 | { |
5164 | mpz_t n_tmp; | |
5165 | mpz_t k_tmp; | |
5166 | mpz_t m_tmp; | |
5167 | ||
5168 | /* There are two classes of error we might encounter -- | |
5169 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
5170 | and | |
5171 | 2) wrong-type errors, which of course we'll report by calling | |
5172 | SCM_WRONG_TYPE_ARG. | |
5173 | We don't report those errors immediately, however; instead we do | |
5174 | some cleanup first. These variables tell us which error (if | |
5175 | any) we should report after cleaning up. | |
5176 | */ | |
5177 | int report_overflow = 0; | |
5178 | ||
5179 | int position_of_wrong_type = 0; | |
5180 | SCM value_of_wrong_type = SCM_INUM0; | |
5181 | ||
5182 | SCM result = SCM_UNDEFINED; | |
5183 | ||
5184 | mpz_init (n_tmp); | |
5185 | mpz_init (k_tmp); | |
5186 | mpz_init (m_tmp); | |
5187 | ||
bc36d050 | 5188 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
5189 | { |
5190 | report_overflow = 1; | |
5191 | goto cleanup; | |
5192 | } | |
5193 | ||
5194 | if (!coerce_to_big (n, n_tmp)) | |
5195 | { | |
5196 | value_of_wrong_type = n; | |
5197 | position_of_wrong_type = 1; | |
5198 | goto cleanup; | |
5199 | } | |
5200 | ||
5201 | if (!coerce_to_big (k, k_tmp)) | |
5202 | { | |
5203 | value_of_wrong_type = k; | |
5204 | position_of_wrong_type = 2; | |
5205 | goto cleanup; | |
5206 | } | |
5207 | ||
5208 | if (!coerce_to_big (m, m_tmp)) | |
5209 | { | |
5210 | value_of_wrong_type = m; | |
5211 | position_of_wrong_type = 3; | |
5212 | goto cleanup; | |
5213 | } | |
5214 | ||
5215 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
5216 | will get a divide-by-zero exception when an inverse 1/n mod m | |
5217 | doesn't exist (or is not unique). Since exceptions are hard to | |
5218 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
5219 | a simple failure code, which is easy to handle. */ | |
5220 | ||
5221 | if (-1 == mpz_sgn (k_tmp)) | |
5222 | { | |
5223 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
5224 | { | |
5225 | report_overflow = 1; | |
5226 | goto cleanup; | |
5227 | } | |
5228 | mpz_neg (k_tmp, k_tmp); | |
5229 | } | |
5230 | ||
5231 | result = scm_i_mkbig (); | |
5232 | mpz_powm (SCM_I_BIG_MPZ (result), | |
5233 | n_tmp, | |
5234 | k_tmp, | |
5235 | m_tmp); | |
b7b8c575 KR |
5236 | |
5237 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
5238 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
5239 | ||
518b7508 KR |
5240 | cleanup: |
5241 | mpz_clear (m_tmp); | |
5242 | mpz_clear (k_tmp); | |
5243 | mpz_clear (n_tmp); | |
5244 | ||
5245 | if (report_overflow) | |
5246 | scm_num_overflow (FUNC_NAME); | |
5247 | ||
5248 | if (position_of_wrong_type) | |
5249 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
5250 | value_of_wrong_type); | |
5251 | ||
5252 | return scm_i_normbig (result); | |
5253 | } | |
5254 | #undef FUNC_NAME | |
5255 | ||
a1ec6916 | 5256 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 5257 | (SCM n, SCM k), |
ba6e7231 KR |
5258 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
5259 | "exact integer, @var{n} can be any number.\n" | |
5260 | "\n" | |
2519490c MW |
5261 | "Negative @var{k} is supported, and results in\n" |
5262 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
5263 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 5264 | "includes @math{0^0} is 1.\n" |
1e6808ea | 5265 | "\n" |
b380b885 | 5266 | "@lisp\n" |
ba6e7231 KR |
5267 | "(integer-expt 2 5) @result{} 32\n" |
5268 | "(integer-expt -3 3) @result{} -27\n" | |
5269 | "(integer-expt 5 -3) @result{} 1/125\n" | |
5270 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 5271 | "@end lisp") |
1bbd0b84 | 5272 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 5273 | { |
e25f3727 | 5274 | scm_t_inum i2 = 0; |
1c35cb19 RB |
5275 | SCM z_i2 = SCM_BOOL_F; |
5276 | int i2_is_big = 0; | |
d956fa6f | 5277 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 5278 | |
bfe1f03a MW |
5279 | /* Specifically refrain from checking the type of the first argument. |
5280 | This allows us to exponentiate any object that can be multiplied. | |
5281 | If we must raise to a negative power, we must also be able to | |
5282 | take its reciprocal. */ | |
5283 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 5284 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 5285 | |
bfe1f03a MW |
5286 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
5287 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
5288 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
5289 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
5290 | /* The next check is necessary only because R6RS specifies different | |
5291 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
5292 | we simply skip this case and move on. */ | |
5293 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
5294 | { | |
5295 | /* k cannot be 0 at this point, because we | |
5296 | have already checked for that case above */ | |
5297 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
5298 | return n; |
5299 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
5300 | return scm_nan (); | |
5301 | } | |
ca46fb90 | 5302 | |
e11e83f3 MV |
5303 | if (SCM_I_INUMP (k)) |
5304 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
5305 | else if (SCM_BIGP (k)) |
5306 | { | |
5307 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
5308 | scm_remember_upto_here_1 (k); |
5309 | i2_is_big = 1; | |
5310 | } | |
2830fd91 | 5311 | else |
ca46fb90 RB |
5312 | SCM_WRONG_TYPE_ARG (2, k); |
5313 | ||
5314 | if (i2_is_big) | |
f872b822 | 5315 | { |
ca46fb90 RB |
5316 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
5317 | { | |
5318 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
5319 | n = scm_divide (n, SCM_UNDEFINED); | |
5320 | } | |
5321 | while (1) | |
5322 | { | |
5323 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
5324 | { | |
ca46fb90 RB |
5325 | return acc; |
5326 | } | |
5327 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
5328 | { | |
ca46fb90 RB |
5329 | return scm_product (acc, n); |
5330 | } | |
5331 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
5332 | acc = scm_product (acc, n); | |
5333 | n = scm_product (n, n); | |
5334 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
5335 | } | |
f872b822 | 5336 | } |
ca46fb90 | 5337 | else |
f872b822 | 5338 | { |
ca46fb90 RB |
5339 | if (i2 < 0) |
5340 | { | |
5341 | i2 = -i2; | |
5342 | n = scm_divide (n, SCM_UNDEFINED); | |
5343 | } | |
5344 | while (1) | |
5345 | { | |
5346 | if (0 == i2) | |
5347 | return acc; | |
5348 | if (1 == i2) | |
5349 | return scm_product (acc, n); | |
5350 | if (i2 & 1) | |
5351 | acc = scm_product (acc, n); | |
5352 | n = scm_product (n, n); | |
5353 | i2 >>= 1; | |
5354 | } | |
f872b822 | 5355 | } |
0f2d19dd | 5356 | } |
1bbd0b84 | 5357 | #undef FUNC_NAME |
0f2d19dd | 5358 | |
a1ec6916 | 5359 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 5360 | (SCM n, SCM cnt), |
32f19569 KR |
5361 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
5362 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 5363 | "\n" |
e7644cb2 | 5364 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
5365 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
5366 | "infinity. (Note that this is not the same rounding as\n" | |
5367 | "@code{quotient} does.)\n" | |
5368 | "\n" | |
5369 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
5370 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
5371 | "shift dropping bits.\n" | |
1e6808ea | 5372 | "\n" |
b380b885 | 5373 | "@lisp\n" |
1e6808ea MG |
5374 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
5375 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
5376 | "\n" |
5377 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
5378 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 5379 | "@end lisp") |
1bbd0b84 | 5380 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 5381 | { |
3ab9f56e | 5382 | long bits_to_shift; |
5efd3c7d | 5383 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 5384 | |
788aca27 KR |
5385 | if (SCM_I_INUMP (n)) |
5386 | { | |
e25f3727 | 5387 | scm_t_inum nn = SCM_I_INUM (n); |
788aca27 KR |
5388 | |
5389 | if (bits_to_shift > 0) | |
5390 | { | |
5391 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
5392 | overflow a non-zero fixnum. For smaller shifts we check the | |
5393 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
5394 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
5395 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
5396 | bits_to_shift)". */ | |
5397 | ||
5398 | if (nn == 0) | |
5399 | return n; | |
5400 | ||
5401 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 5402 | && ((scm_t_bits) |
788aca27 KR |
5403 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) |
5404 | <= 1)) | |
5405 | { | |
5406 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
5407 | } | |
5408 | else | |
5409 | { | |
e25f3727 | 5410 | SCM result = scm_i_inum2big (nn); |
788aca27 KR |
5411 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
5412 | bits_to_shift); | |
5413 | return result; | |
5414 | } | |
5415 | } | |
5416 | else | |
5417 | { | |
5418 | bits_to_shift = -bits_to_shift; | |
5419 | if (bits_to_shift >= SCM_LONG_BIT) | |
cff5fa33 | 5420 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1)); |
788aca27 KR |
5421 | else |
5422 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
5423 | } | |
5424 | ||
5425 | } | |
5426 | else if (SCM_BIGP (n)) | |
ca46fb90 | 5427 | { |
788aca27 KR |
5428 | SCM result; |
5429 | ||
5430 | if (bits_to_shift == 0) | |
5431 | return n; | |
5432 | ||
5433 | result = scm_i_mkbig (); | |
5434 | if (bits_to_shift >= 0) | |
5435 | { | |
5436 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
5437 | bits_to_shift); | |
5438 | return result; | |
5439 | } | |
ca46fb90 | 5440 | else |
788aca27 KR |
5441 | { |
5442 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
5443 | we have to allocate a bignum even if the result is going to be a | |
5444 | fixnum. */ | |
5445 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
5446 | -bits_to_shift); | |
5447 | return scm_i_normbig (result); | |
5448 | } | |
5449 | ||
ca46fb90 RB |
5450 | } |
5451 | else | |
788aca27 KR |
5452 | { |
5453 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
5454 | } | |
0f2d19dd | 5455 | } |
1bbd0b84 | 5456 | #undef FUNC_NAME |
0f2d19dd | 5457 | |
3c9f20f8 | 5458 | |
a1ec6916 | 5459 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 5460 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
5461 | "Return the integer composed of the @var{start} (inclusive)\n" |
5462 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
5463 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
5464 | "\n" | |
b380b885 MD |
5465 | "@lisp\n" |
5466 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
5467 | " @result{} \"1010\"\n" | |
5468 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
5469 | " @result{} \"10110\"\n" | |
5470 | "@end lisp") | |
1bbd0b84 | 5471 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 5472 | { |
7f848242 | 5473 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
5474 | istart = scm_to_ulong (start); |
5475 | iend = scm_to_ulong (end); | |
c1bfcf60 | 5476 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 5477 | |
7f848242 KR |
5478 | /* how many bits to keep */ |
5479 | bits = iend - istart; | |
5480 | ||
e11e83f3 | 5481 | if (SCM_I_INUMP (n)) |
0aacf84e | 5482 | { |
e25f3727 | 5483 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
5484 | |
5485 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 5486 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 5487 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 5488 | |
0aacf84e MD |
5489 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
5490 | { | |
5491 | /* Since we emulate two's complement encoded numbers, this | |
5492 | * special case requires us to produce a result that has | |
7f848242 | 5493 | * more bits than can be stored in a fixnum. |
0aacf84e | 5494 | */ |
e25f3727 | 5495 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
5496 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
5497 | bits); | |
5498 | return result; | |
0aacf84e | 5499 | } |
ac0c002c | 5500 | |
7f848242 | 5501 | /* mask down to requisite bits */ |
857ae6af | 5502 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 5503 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
5504 | } |
5505 | else if (SCM_BIGP (n)) | |
ac0c002c | 5506 | { |
7f848242 KR |
5507 | SCM result; |
5508 | if (bits == 1) | |
5509 | { | |
d956fa6f | 5510 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
5511 | } |
5512 | else | |
5513 | { | |
5514 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
5515 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
5516 | such bits into a ulong. */ | |
5517 | result = scm_i_mkbig (); | |
5518 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
5519 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
5520 | result = scm_i_normbig (result); | |
5521 | } | |
5522 | scm_remember_upto_here_1 (n); | |
5523 | return result; | |
ac0c002c | 5524 | } |
0aacf84e | 5525 | else |
78166ad5 | 5526 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 5527 | } |
1bbd0b84 | 5528 | #undef FUNC_NAME |
0f2d19dd | 5529 | |
7f848242 | 5530 | |
e4755e5c JB |
5531 | static const char scm_logtab[] = { |
5532 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
5533 | }; | |
1cc91f1b | 5534 | |
a1ec6916 | 5535 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 5536 | (SCM n), |
1e6808ea MG |
5537 | "Return the number of bits in integer @var{n}. If integer is\n" |
5538 | "positive, the 1-bits in its binary representation are counted.\n" | |
5539 | "If negative, the 0-bits in its two's-complement binary\n" | |
5540 | "representation are counted. If 0, 0 is returned.\n" | |
5541 | "\n" | |
b380b885 MD |
5542 | "@lisp\n" |
5543 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
5544 | " @result{} 4\n" |
5545 | "(logcount 0)\n" | |
5546 | " @result{} 0\n" | |
5547 | "(logcount -2)\n" | |
5548 | " @result{} 1\n" | |
5549 | "@end lisp") | |
5550 | #define FUNC_NAME s_scm_logcount | |
5551 | { | |
e11e83f3 | 5552 | if (SCM_I_INUMP (n)) |
f872b822 | 5553 | { |
e25f3727 AW |
5554 | unsigned long c = 0; |
5555 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
5556 | if (nn < 0) |
5557 | nn = -1 - nn; | |
5558 | while (nn) | |
5559 | { | |
5560 | c += scm_logtab[15 & nn]; | |
5561 | nn >>= 4; | |
5562 | } | |
d956fa6f | 5563 | return SCM_I_MAKINUM (c); |
f872b822 | 5564 | } |
ca46fb90 | 5565 | else if (SCM_BIGP (n)) |
f872b822 | 5566 | { |
ca46fb90 | 5567 | unsigned long count; |
713a4259 KR |
5568 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
5569 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 5570 | else |
713a4259 KR |
5571 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
5572 | scm_remember_upto_here_1 (n); | |
d956fa6f | 5573 | return SCM_I_MAKINUM (count); |
f872b822 | 5574 | } |
ca46fb90 RB |
5575 | else |
5576 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 5577 | } |
ca46fb90 | 5578 | #undef FUNC_NAME |
0f2d19dd JB |
5579 | |
5580 | ||
ca46fb90 RB |
5581 | static const char scm_ilentab[] = { |
5582 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
5583 | }; | |
5584 | ||
0f2d19dd | 5585 | |
ca46fb90 RB |
5586 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
5587 | (SCM n), | |
5588 | "Return the number of bits necessary to represent @var{n}.\n" | |
5589 | "\n" | |
5590 | "@lisp\n" | |
5591 | "(integer-length #b10101010)\n" | |
5592 | " @result{} 8\n" | |
5593 | "(integer-length 0)\n" | |
5594 | " @result{} 0\n" | |
5595 | "(integer-length #b1111)\n" | |
5596 | " @result{} 4\n" | |
5597 | "@end lisp") | |
5598 | #define FUNC_NAME s_scm_integer_length | |
5599 | { | |
e11e83f3 | 5600 | if (SCM_I_INUMP (n)) |
0aacf84e | 5601 | { |
e25f3727 | 5602 | unsigned long c = 0; |
0aacf84e | 5603 | unsigned int l = 4; |
e25f3727 | 5604 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
5605 | if (nn < 0) |
5606 | nn = -1 - nn; | |
5607 | while (nn) | |
5608 | { | |
5609 | c += 4; | |
5610 | l = scm_ilentab [15 & nn]; | |
5611 | nn >>= 4; | |
5612 | } | |
d956fa6f | 5613 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
5614 | } |
5615 | else if (SCM_BIGP (n)) | |
5616 | { | |
5617 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
5618 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
5619 | 1 too big, so check for that and adjust. */ | |
5620 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
5621 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
5622 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
5623 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
5624 | size--; | |
5625 | scm_remember_upto_here_1 (n); | |
d956fa6f | 5626 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
5627 | } |
5628 | else | |
ca46fb90 | 5629 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
5630 | } |
5631 | #undef FUNC_NAME | |
0f2d19dd JB |
5632 | |
5633 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
5634 | #define SCM_MAX_DBL_PREC 60 |
5635 | #define SCM_MAX_DBL_RADIX 36 | |
5636 | ||
5637 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
5638 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
5639 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
5640 | ||
5641 | static | |
5642 | void init_dblprec(int *prec, int radix) { | |
5643 | /* determine floating point precision by adding successively | |
5644 | smaller increments to 1.0 until it is considered == 1.0 */ | |
5645 | double f = ((double)1.0)/radix; | |
5646 | double fsum = 1.0 + f; | |
5647 | ||
5648 | *prec = 0; | |
5649 | while (fsum != 1.0) | |
5650 | { | |
5651 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
5652 | fsum = 1.0; | |
5653 | else | |
5654 | { | |
5655 | f /= radix; | |
5656 | fsum = f + 1.0; | |
5657 | } | |
5658 | } | |
5659 | (*prec) -= 1; | |
5660 | } | |
5661 | ||
5662 | static | |
5663 | void init_fx_radix(double *fx_list, int radix) | |
5664 | { | |
5665 | /* initialize a per-radix list of tolerances. When added | |
5666 | to a number < 1.0, we can determine if we should raund | |
5667 | up and quit converting a number to a string. */ | |
5668 | int i; | |
5669 | fx_list[0] = 0.0; | |
5670 | fx_list[1] = 0.5; | |
5671 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
5672 | fx_list[i] = (fx_list[i-1] / radix); | |
5673 | } | |
5674 | ||
5675 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 5676 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 5677 | |
1be6b49c | 5678 | static size_t |
0b799eea | 5679 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 5680 | { |
0b799eea MV |
5681 | int efmt, dpt, d, i, wp; |
5682 | double *fx; | |
5683 | #ifdef DBL_MIN_10_EXP | |
5684 | double f_cpy; | |
5685 | int exp_cpy; | |
5686 | #endif /* DBL_MIN_10_EXP */ | |
5687 | size_t ch = 0; | |
5688 | int exp = 0; | |
5689 | ||
5690 | if(radix < 2 || | |
5691 | radix > SCM_MAX_DBL_RADIX) | |
5692 | { | |
5693 | /* revert to existing behavior */ | |
5694 | radix = 10; | |
5695 | } | |
5696 | ||
5697 | wp = scm_dblprec[radix-2]; | |
5698 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 5699 | |
f872b822 | 5700 | if (f == 0.0) |
abb7e44d MV |
5701 | { |
5702 | #ifdef HAVE_COPYSIGN | |
5703 | double sgn = copysign (1.0, f); | |
5704 | ||
5705 | if (sgn < 0.0) | |
5706 | a[ch++] = '-'; | |
5707 | #endif | |
abb7e44d MV |
5708 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
5709 | } | |
7351e207 | 5710 | |
2e65b52f | 5711 | if (isinf (f)) |
7351e207 MV |
5712 | { |
5713 | if (f < 0) | |
5714 | strcpy (a, "-inf.0"); | |
5715 | else | |
5716 | strcpy (a, "+inf.0"); | |
5717 | return ch+6; | |
5718 | } | |
2e65b52f | 5719 | else if (isnan (f)) |
7351e207 MV |
5720 | { |
5721 | strcpy (a, "+nan.0"); | |
5722 | return ch+6; | |
5723 | } | |
5724 | ||
f872b822 MD |
5725 | if (f < 0.0) |
5726 | { | |
5727 | f = -f; | |
5728 | a[ch++] = '-'; | |
5729 | } | |
7351e207 | 5730 | |
f872b822 MD |
5731 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
5732 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
5733 | /* just do the checking...if it passes, we do the conversion for our |
5734 | radix again below */ | |
5735 | f_cpy = f; | |
5736 | exp_cpy = exp; | |
5737 | ||
5738 | while (f_cpy < 1.0) | |
f872b822 | 5739 | { |
0b799eea MV |
5740 | f_cpy *= 10.0; |
5741 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
5742 | { |
5743 | a[ch++] = '#'; | |
5744 | a[ch++] = '.'; | |
5745 | a[ch++] = '#'; | |
5746 | return ch; | |
5747 | } | |
f872b822 | 5748 | } |
0b799eea | 5749 | while (f_cpy > 10.0) |
f872b822 | 5750 | { |
0b799eea MV |
5751 | f_cpy *= 0.10; |
5752 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
5753 | { |
5754 | a[ch++] = '#'; | |
5755 | a[ch++] = '.'; | |
5756 | a[ch++] = '#'; | |
5757 | return ch; | |
5758 | } | |
f872b822 | 5759 | } |
0b799eea MV |
5760 | #endif |
5761 | ||
f872b822 MD |
5762 | while (f < 1.0) |
5763 | { | |
0b799eea | 5764 | f *= radix; |
f872b822 MD |
5765 | exp--; |
5766 | } | |
0b799eea | 5767 | while (f > radix) |
f872b822 | 5768 | { |
0b799eea | 5769 | f /= radix; |
f872b822 MD |
5770 | exp++; |
5771 | } | |
0b799eea MV |
5772 | |
5773 | if (f + fx[wp] >= radix) | |
f872b822 MD |
5774 | { |
5775 | f = 1.0; | |
5776 | exp++; | |
5777 | } | |
0f2d19dd | 5778 | zero: |
0b799eea MV |
5779 | #ifdef ENGNOT |
5780 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 5781 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
5782 | exp -= dpt++; |
5783 | efmt = 1; | |
f872b822 MD |
5784 | #else |
5785 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 5786 | if (!efmt) |
cda139a7 MD |
5787 | { |
5788 | if (exp < 0) | |
5789 | { | |
5790 | a[ch++] = '0'; | |
5791 | a[ch++] = '.'; | |
5792 | dpt = exp; | |
f872b822 MD |
5793 | while (++dpt) |
5794 | a[ch++] = '0'; | |
cda139a7 MD |
5795 | } |
5796 | else | |
f872b822 | 5797 | dpt = exp + 1; |
cda139a7 | 5798 | } |
0f2d19dd JB |
5799 | else |
5800 | dpt = 1; | |
f872b822 MD |
5801 | #endif |
5802 | ||
5803 | do | |
5804 | { | |
5805 | d = f; | |
5806 | f -= d; | |
0b799eea | 5807 | a[ch++] = number_chars[d]; |
f872b822 MD |
5808 | if (f < fx[wp]) |
5809 | break; | |
5810 | if (f + fx[wp] >= 1.0) | |
5811 | { | |
0b799eea | 5812 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
5813 | break; |
5814 | } | |
0b799eea | 5815 | f *= radix; |
f872b822 MD |
5816 | if (!(--dpt)) |
5817 | a[ch++] = '.'; | |
0f2d19dd | 5818 | } |
f872b822 | 5819 | while (wp--); |
0f2d19dd JB |
5820 | |
5821 | if (dpt > 0) | |
cda139a7 | 5822 | { |
f872b822 | 5823 | #ifndef ENGNOT |
cda139a7 MD |
5824 | if ((dpt > 4) && (exp > 6)) |
5825 | { | |
f872b822 | 5826 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 5827 | for (i = ch++; i > d; i--) |
f872b822 | 5828 | a[i] = a[i - 1]; |
cda139a7 MD |
5829 | a[d] = '.'; |
5830 | efmt = 1; | |
5831 | } | |
5832 | else | |
f872b822 | 5833 | #endif |
cda139a7 | 5834 | { |
f872b822 MD |
5835 | while (--dpt) |
5836 | a[ch++] = '0'; | |
cda139a7 MD |
5837 | a[ch++] = '.'; |
5838 | } | |
5839 | } | |
f872b822 MD |
5840 | if (a[ch - 1] == '.') |
5841 | a[ch++] = '0'; /* trailing zero */ | |
5842 | if (efmt && exp) | |
5843 | { | |
5844 | a[ch++] = 'e'; | |
5845 | if (exp < 0) | |
5846 | { | |
5847 | exp = -exp; | |
5848 | a[ch++] = '-'; | |
5849 | } | |
0b799eea MV |
5850 | for (i = radix; i <= exp; i *= radix); |
5851 | for (i /= radix; i; i /= radix) | |
f872b822 | 5852 | { |
0b799eea | 5853 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
5854 | exp %= i; |
5855 | } | |
0f2d19dd | 5856 | } |
0f2d19dd JB |
5857 | return ch; |
5858 | } | |
5859 | ||
7a1aba42 MV |
5860 | |
5861 | static size_t | |
5862 | icmplx2str (double real, double imag, char *str, int radix) | |
5863 | { | |
5864 | size_t i; | |
c7218482 | 5865 | double sgn; |
7a1aba42 MV |
5866 | |
5867 | i = idbl2str (real, str, radix); | |
c7218482 MW |
5868 | #ifdef HAVE_COPYSIGN |
5869 | sgn = copysign (1.0, imag); | |
5870 | #else | |
5871 | sgn = imag; | |
5872 | #endif | |
5873 | /* Don't output a '+' for negative numbers or for Inf and | |
5874 | NaN. They will provide their own sign. */ | |
5875 | if (sgn >= 0 && DOUBLE_IS_FINITE (imag)) | |
5876 | str[i++] = '+'; | |
5877 | i += idbl2str (imag, &str[i], radix); | |
5878 | str[i++] = 'i'; | |
7a1aba42 MV |
5879 | return i; |
5880 | } | |
5881 | ||
1be6b49c | 5882 | static size_t |
0b799eea | 5883 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 5884 | { |
1be6b49c | 5885 | size_t i; |
3c9a524f | 5886 | if (SCM_REALP (flt)) |
0b799eea | 5887 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 5888 | else |
7a1aba42 MV |
5889 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
5890 | str, radix); | |
0f2d19dd JB |
5891 | return i; |
5892 | } | |
0f2d19dd | 5893 | |
2881e77b | 5894 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
5895 | characters in the result. |
5896 | rad is output base | |
5897 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 5898 | size_t |
2881e77b MV |
5899 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
5900 | { | |
5901 | if (num < 0) | |
5902 | { | |
5903 | *p++ = '-'; | |
5904 | return scm_iuint2str (-num, rad, p) + 1; | |
5905 | } | |
5906 | else | |
5907 | return scm_iuint2str (num, rad, p); | |
5908 | } | |
5909 | ||
5910 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
5911 | characters in the result. | |
5912 | rad is output base | |
5913 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
5914 | size_t | |
5915 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 5916 | { |
1be6b49c ML |
5917 | size_t j = 1; |
5918 | size_t i; | |
2881e77b | 5919 | scm_t_uintmax n = num; |
5c11cc9d | 5920 | |
a6f3af16 AW |
5921 | if (rad < 2 || rad > 36) |
5922 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
5923 | ||
f872b822 | 5924 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
5925 | j++; |
5926 | ||
5927 | i = j; | |
2881e77b | 5928 | n = num; |
f872b822 MD |
5929 | while (i--) |
5930 | { | |
5c11cc9d GH |
5931 | int d = n % rad; |
5932 | ||
f872b822 | 5933 | n /= rad; |
a6f3af16 | 5934 | p[i] = number_chars[d]; |
f872b822 | 5935 | } |
0f2d19dd JB |
5936 | return j; |
5937 | } | |
5938 | ||
a1ec6916 | 5939 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
5940 | (SCM n, SCM radix), |
5941 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
5942 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
5943 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 5944 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 5945 | { |
1bbd0b84 | 5946 | int base; |
98cb6e75 | 5947 | |
0aacf84e | 5948 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 5949 | base = 10; |
0aacf84e | 5950 | else |
5efd3c7d | 5951 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 5952 | |
e11e83f3 | 5953 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
5954 | { |
5955 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 5956 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 5957 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
5958 | } |
5959 | else if (SCM_BIGP (n)) | |
5960 | { | |
5961 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
5962 | scm_remember_upto_here_1 (n); | |
cc95e00a | 5963 | return scm_take_locale_string (str); |
0aacf84e | 5964 | } |
f92e85f7 MV |
5965 | else if (SCM_FRACTIONP (n)) |
5966 | { | |
f92e85f7 | 5967 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 5968 | scm_from_locale_string ("/"), |
f92e85f7 MV |
5969 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
5970 | } | |
0aacf84e MD |
5971 | else if (SCM_INEXACTP (n)) |
5972 | { | |
5973 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 5974 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
5975 | } |
5976 | else | |
bb628794 | 5977 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 5978 | } |
1bbd0b84 | 5979 | #undef FUNC_NAME |
0f2d19dd JB |
5980 | |
5981 | ||
ca46fb90 RB |
5982 | /* These print routines used to be stubbed here so that scm_repl.c |
5983 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 5984 | |
0f2d19dd | 5985 | int |
e81d98ec | 5986 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5987 | { |
56e55ac7 | 5988 | char num_buf[FLOBUFLEN]; |
0b799eea | 5989 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
5990 | return !0; |
5991 | } | |
5992 | ||
b479fe9a MV |
5993 | void |
5994 | scm_i_print_double (double val, SCM port) | |
5995 | { | |
5996 | char num_buf[FLOBUFLEN]; | |
5997 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
5998 | } | |
5999 | ||
f3ae5d60 | 6000 | int |
e81d98ec | 6001 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 6002 | |
f3ae5d60 | 6003 | { |
56e55ac7 | 6004 | char num_buf[FLOBUFLEN]; |
0b799eea | 6005 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
6006 | return !0; |
6007 | } | |
1cc91f1b | 6008 | |
7a1aba42 MV |
6009 | void |
6010 | scm_i_print_complex (double real, double imag, SCM port) | |
6011 | { | |
6012 | char num_buf[FLOBUFLEN]; | |
6013 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
6014 | } | |
6015 | ||
f92e85f7 MV |
6016 | int |
6017 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
6018 | { | |
6019 | SCM str; | |
f92e85f7 | 6020 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 6021 | scm_display (str, port); |
f92e85f7 MV |
6022 | scm_remember_upto_here_1 (str); |
6023 | return !0; | |
6024 | } | |
6025 | ||
0f2d19dd | 6026 | int |
e81d98ec | 6027 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 6028 | { |
ca46fb90 RB |
6029 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
6030 | scm_remember_upto_here_1 (exp); | |
6031 | scm_lfwrite (str, (size_t) strlen (str), port); | |
6032 | free (str); | |
0f2d19dd JB |
6033 | return !0; |
6034 | } | |
6035 | /*** END nums->strs ***/ | |
6036 | ||
3c9a524f | 6037 | |
0f2d19dd | 6038 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 6039 | |
3c9a524f DH |
6040 | /* The following functions implement the conversion from strings to numbers. |
6041 | * The implementation somehow follows the grammar for numbers as it is given | |
6042 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
6043 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
6044 | * points should be noted about the implementation: | |
bc3d34f5 | 6045 | * |
3c9a524f DH |
6046 | * * Each function keeps a local index variable 'idx' that points at the |
6047 | * current position within the parsed string. The global index is only | |
6048 | * updated if the function could parse the corresponding syntactic unit | |
6049 | * successfully. | |
bc3d34f5 | 6050 | * |
3c9a524f | 6051 | * * Similarly, the functions keep track of indicators of inexactness ('#', |
bc3d34f5 MW |
6052 | * '.' or exponents) using local variables ('hash_seen', 'x'). |
6053 | * | |
3c9a524f DH |
6054 | * * Sequences of digits are parsed into temporary variables holding fixnums. |
6055 | * Only if these fixnums would overflow, the result variables are updated | |
6056 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
6057 | * the temporary variables holding the fixnums are cleared, and the process | |
6058 | * starts over again. If for example fixnums were able to store five decimal | |
6059 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
6060 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
6061 | * only every five digits two bignum operations were performed. | |
bc3d34f5 MW |
6062 | * |
6063 | * Notes on the handling of exactness specifiers: | |
6064 | * | |
6065 | * When parsing non-real complex numbers, we apply exactness specifiers on | |
6066 | * per-component basis, as is done in PLT Scheme. For complex numbers | |
6067 | * written in rectangular form, exactness specifiers are applied to the | |
6068 | * real and imaginary parts before calling scm_make_rectangular. For | |
6069 | * complex numbers written in polar form, exactness specifiers are applied | |
6070 | * to the magnitude and angle before calling scm_make_polar. | |
6071 | * | |
6072 | * There are two kinds of exactness specifiers: forced and implicit. A | |
6073 | * forced exactness specifier is a "#e" or "#i" prefix at the beginning of | |
6074 | * the entire number, and applies to both components of a complex number. | |
6075 | * "#e" causes each component to be made exact, and "#i" causes each | |
6076 | * component to be made inexact. If no forced exactness specifier is | |
6077 | * present, then the exactness of each component is determined | |
6078 | * independently by the presence or absence of a decimal point or hash mark | |
6079 | * within that component. If a decimal point or hash mark is present, the | |
6080 | * component is made inexact, otherwise it is made exact. | |
6081 | * | |
6082 | * After the exactness specifiers have been applied to each component, they | |
6083 | * are passed to either scm_make_rectangular or scm_make_polar to produce | |
6084 | * the final result. Note that this will result in a real number if the | |
6085 | * imaginary part, magnitude, or angle is an exact 0. | |
6086 | * | |
6087 | * For example, (string->number "#i5.0+0i") does the equivalent of: | |
6088 | * | |
6089 | * (make-rectangular (exact->inexact 5) (exact->inexact 0)) | |
3c9a524f DH |
6090 | */ |
6091 | ||
6092 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
6093 | ||
6094 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
6095 | ||
a6f3af16 AW |
6096 | /* Caller is responsible for checking that the return value is in range |
6097 | for the given radix, which should be <= 36. */ | |
6098 | static unsigned int | |
6099 | char_decimal_value (scm_t_uint32 c) | |
6100 | { | |
6101 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
6102 | that's certainly above any valid decimal, so we take advantage of | |
6103 | that to elide some tests. */ | |
6104 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
6105 | ||
6106 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
6107 | hexadecimals. */ | |
6108 | if (d >= 10U) | |
6109 | { | |
6110 | c = uc_tolower (c); | |
6111 | if (c >= (scm_t_uint32) 'a') | |
6112 | d = c - (scm_t_uint32)'a' + 10U; | |
6113 | } | |
6114 | return d; | |
6115 | } | |
3c9a524f | 6116 | |
2a8fecee | 6117 | static SCM |
3f47e526 | 6118 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 6119 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 6120 | { |
3c9a524f DH |
6121 | unsigned int idx = *p_idx; |
6122 | unsigned int hash_seen = 0; | |
6123 | scm_t_bits shift = 1; | |
6124 | scm_t_bits add = 0; | |
6125 | unsigned int digit_value; | |
6126 | SCM result; | |
6127 | char c; | |
3f47e526 | 6128 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6129 | |
6130 | if (idx == len) | |
6131 | return SCM_BOOL_F; | |
2a8fecee | 6132 | |
3f47e526 | 6133 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 6134 | digit_value = char_decimal_value (c); |
3c9a524f DH |
6135 | if (digit_value >= radix) |
6136 | return SCM_BOOL_F; | |
6137 | ||
6138 | idx++; | |
d956fa6f | 6139 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 6140 | while (idx != len) |
f872b822 | 6141 | { |
3f47e526 | 6142 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 6143 | if (c == '#') |
3c9a524f DH |
6144 | { |
6145 | hash_seen = 1; | |
6146 | digit_value = 0; | |
6147 | } | |
a6f3af16 AW |
6148 | else if (hash_seen) |
6149 | break; | |
3c9a524f | 6150 | else |
a6f3af16 AW |
6151 | { |
6152 | digit_value = char_decimal_value (c); | |
6153 | /* This check catches non-decimals in addition to out-of-range | |
6154 | decimals. */ | |
6155 | if (digit_value >= radix) | |
6156 | break; | |
6157 | } | |
3c9a524f DH |
6158 | |
6159 | idx++; | |
6160 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
6161 | { | |
d956fa6f | 6162 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 6163 | if (add > 0) |
d956fa6f | 6164 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
6165 | |
6166 | shift = radix; | |
6167 | add = digit_value; | |
6168 | } | |
6169 | else | |
6170 | { | |
6171 | shift = shift * radix; | |
6172 | add = add * radix + digit_value; | |
6173 | } | |
6174 | }; | |
6175 | ||
6176 | if (shift > 1) | |
d956fa6f | 6177 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 6178 | if (add > 0) |
d956fa6f | 6179 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
6180 | |
6181 | *p_idx = idx; | |
6182 | if (hash_seen) | |
6183 | *p_exactness = INEXACT; | |
6184 | ||
6185 | return result; | |
2a8fecee JB |
6186 | } |
6187 | ||
6188 | ||
3c9a524f DH |
6189 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
6190 | * covers the parts of the rules that start at a potential point. The value | |
6191 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
6192 | * in variable result. The content of *p_exactness indicates, whether a hash |
6193 | * has already been seen in the digits before the point. | |
3c9a524f | 6194 | */ |
1cc91f1b | 6195 | |
3f47e526 | 6196 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
6197 | |
6198 | static SCM | |
3f47e526 | 6199 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 6200 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 6201 | { |
3c9a524f DH |
6202 | unsigned int idx = *p_idx; |
6203 | enum t_exactness x = *p_exactness; | |
3f47e526 | 6204 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6205 | |
6206 | if (idx == len) | |
79d34f68 | 6207 | return result; |
3c9a524f | 6208 | |
3f47e526 | 6209 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
6210 | { |
6211 | scm_t_bits shift = 1; | |
6212 | scm_t_bits add = 0; | |
6213 | unsigned int digit_value; | |
cff5fa33 | 6214 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
6215 | |
6216 | idx++; | |
6217 | while (idx != len) | |
6218 | { | |
3f47e526 MG |
6219 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
6220 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
6221 | { |
6222 | if (x == INEXACT) | |
6223 | return SCM_BOOL_F; | |
6224 | else | |
6225 | digit_value = DIGIT2UINT (c); | |
6226 | } | |
6227 | else if (c == '#') | |
6228 | { | |
6229 | x = INEXACT; | |
6230 | digit_value = 0; | |
6231 | } | |
6232 | else | |
6233 | break; | |
6234 | ||
6235 | idx++; | |
6236 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
6237 | { | |
d956fa6f MV |
6238 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
6239 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 6240 | if (add > 0) |
d956fa6f | 6241 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
6242 | |
6243 | shift = 10; | |
6244 | add = digit_value; | |
6245 | } | |
6246 | else | |
6247 | { | |
6248 | shift = shift * 10; | |
6249 | add = add * 10 + digit_value; | |
6250 | } | |
6251 | }; | |
6252 | ||
6253 | if (add > 0) | |
6254 | { | |
d956fa6f MV |
6255 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
6256 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
6257 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
6258 | } |
6259 | ||
d8592269 | 6260 | result = scm_divide (result, big_shift); |
79d34f68 | 6261 | |
3c9a524f DH |
6262 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
6263 | x = INEXACT; | |
f872b822 | 6264 | } |
3c9a524f | 6265 | |
3c9a524f | 6266 | if (idx != len) |
f872b822 | 6267 | { |
3c9a524f DH |
6268 | int sign = 1; |
6269 | unsigned int start; | |
3f47e526 | 6270 | scm_t_wchar c; |
3c9a524f DH |
6271 | int exponent; |
6272 | SCM e; | |
6273 | ||
6274 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
6275 | ||
3f47e526 | 6276 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 6277 | { |
3c9a524f DH |
6278 | case 'd': case 'D': |
6279 | case 'e': case 'E': | |
6280 | case 'f': case 'F': | |
6281 | case 'l': case 'L': | |
6282 | case 's': case 'S': | |
6283 | idx++; | |
ee0ddd21 AW |
6284 | if (idx == len) |
6285 | return SCM_BOOL_F; | |
6286 | ||
3c9a524f | 6287 | start = idx; |
3f47e526 | 6288 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6289 | if (c == '-') |
6290 | { | |
6291 | idx++; | |
ee0ddd21 AW |
6292 | if (idx == len) |
6293 | return SCM_BOOL_F; | |
6294 | ||
3c9a524f | 6295 | sign = -1; |
3f47e526 | 6296 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6297 | } |
6298 | else if (c == '+') | |
6299 | { | |
6300 | idx++; | |
ee0ddd21 AW |
6301 | if (idx == len) |
6302 | return SCM_BOOL_F; | |
6303 | ||
3c9a524f | 6304 | sign = 1; |
3f47e526 | 6305 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6306 | } |
6307 | else | |
6308 | sign = 1; | |
6309 | ||
3f47e526 | 6310 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
6311 | return SCM_BOOL_F; |
6312 | ||
6313 | idx++; | |
6314 | exponent = DIGIT2UINT (c); | |
6315 | while (idx != len) | |
f872b822 | 6316 | { |
3f47e526 MG |
6317 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
6318 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
6319 | { |
6320 | idx++; | |
6321 | if (exponent <= SCM_MAXEXP) | |
6322 | exponent = exponent * 10 + DIGIT2UINT (c); | |
6323 | } | |
6324 | else | |
6325 | break; | |
f872b822 | 6326 | } |
3c9a524f DH |
6327 | |
6328 | if (exponent > SCM_MAXEXP) | |
f872b822 | 6329 | { |
3c9a524f | 6330 | size_t exp_len = idx - start; |
3f47e526 | 6331 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
6332 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
6333 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 6334 | } |
3c9a524f | 6335 | |
d956fa6f | 6336 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
6337 | if (sign == 1) |
6338 | result = scm_product (result, e); | |
6339 | else | |
f92e85f7 | 6340 | result = scm_divide2real (result, e); |
3c9a524f DH |
6341 | |
6342 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
6343 | x = INEXACT; | |
6344 | ||
f872b822 | 6345 | break; |
3c9a524f | 6346 | |
f872b822 | 6347 | default: |
3c9a524f | 6348 | break; |
f872b822 | 6349 | } |
0f2d19dd | 6350 | } |
3c9a524f DH |
6351 | |
6352 | *p_idx = idx; | |
6353 | if (x == INEXACT) | |
6354 | *p_exactness = x; | |
6355 | ||
6356 | return result; | |
0f2d19dd | 6357 | } |
0f2d19dd | 6358 | |
3c9a524f DH |
6359 | |
6360 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
6361 | ||
6362 | static SCM | |
3f47e526 | 6363 | mem2ureal (SCM mem, unsigned int *p_idx, |
9d427b2c | 6364 | unsigned int radix, enum t_exactness forced_x) |
0f2d19dd | 6365 | { |
3c9a524f | 6366 | unsigned int idx = *p_idx; |
164d2481 | 6367 | SCM result; |
3f47e526 | 6368 | size_t len = scm_i_string_length (mem); |
3c9a524f | 6369 | |
40f89215 NJ |
6370 | /* Start off believing that the number will be exact. This changes |
6371 | to INEXACT if we see a decimal point or a hash. */ | |
9d427b2c | 6372 | enum t_exactness implicit_x = EXACT; |
40f89215 | 6373 | |
3c9a524f DH |
6374 | if (idx == len) |
6375 | return SCM_BOOL_F; | |
6376 | ||
3f47e526 | 6377 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
6378 | { |
6379 | *p_idx = idx+5; | |
6380 | return scm_inf (); | |
6381 | } | |
6382 | ||
3f47e526 | 6383 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 6384 | { |
d8592269 MV |
6385 | /* Cobble up the fractional part. We might want to set the |
6386 | NaN's mantissa from it. */ | |
7351e207 | 6387 | idx += 4; |
9d427b2c | 6388 | mem2uinteger (mem, &idx, 10, &implicit_x); |
7351e207 MV |
6389 | *p_idx = idx; |
6390 | return scm_nan (); | |
6391 | } | |
6392 | ||
3f47e526 | 6393 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
6394 | { |
6395 | if (radix != 10) | |
6396 | return SCM_BOOL_F; | |
6397 | else if (idx + 1 == len) | |
6398 | return SCM_BOOL_F; | |
3f47e526 | 6399 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
6400 | return SCM_BOOL_F; |
6401 | else | |
cff5fa33 | 6402 | result = mem2decimal_from_point (SCM_INUM0, mem, |
9d427b2c | 6403 | p_idx, &implicit_x); |
f872b822 | 6404 | } |
3c9a524f DH |
6405 | else |
6406 | { | |
3c9a524f | 6407 | SCM uinteger; |
3c9a524f | 6408 | |
9d427b2c | 6409 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 6410 | if (scm_is_false (uinteger)) |
3c9a524f DH |
6411 | return SCM_BOOL_F; |
6412 | ||
6413 | if (idx == len) | |
6414 | result = uinteger; | |
3f47e526 | 6415 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 6416 | { |
3c9a524f DH |
6417 | SCM divisor; |
6418 | ||
6419 | idx++; | |
ee0ddd21 AW |
6420 | if (idx == len) |
6421 | return SCM_BOOL_F; | |
3c9a524f | 6422 | |
9d427b2c | 6423 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 6424 | if (scm_is_false (divisor)) |
3c9a524f DH |
6425 | return SCM_BOOL_F; |
6426 | ||
f92e85f7 | 6427 | /* both are int/big here, I assume */ |
cba42c93 | 6428 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 6429 | } |
3c9a524f DH |
6430 | else if (radix == 10) |
6431 | { | |
9d427b2c | 6432 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
73e4de09 | 6433 | if (scm_is_false (result)) |
3c9a524f DH |
6434 | return SCM_BOOL_F; |
6435 | } | |
6436 | else | |
6437 | result = uinteger; | |
6438 | ||
6439 | *p_idx = idx; | |
f872b822 | 6440 | } |
164d2481 | 6441 | |
9d427b2c MW |
6442 | switch (forced_x) |
6443 | { | |
6444 | case EXACT: | |
6445 | if (SCM_INEXACTP (result)) | |
6446 | return scm_inexact_to_exact (result); | |
6447 | else | |
6448 | return result; | |
6449 | case INEXACT: | |
6450 | if (SCM_INEXACTP (result)) | |
6451 | return result; | |
6452 | else | |
6453 | return scm_exact_to_inexact (result); | |
6454 | case NO_EXACTNESS: | |
6455 | if (implicit_x == INEXACT) | |
6456 | { | |
6457 | if (SCM_INEXACTP (result)) | |
6458 | return result; | |
6459 | else | |
6460 | return scm_exact_to_inexact (result); | |
6461 | } | |
6462 | else | |
6463 | return result; | |
6464 | } | |
164d2481 | 6465 | |
9d427b2c MW |
6466 | /* We should never get here */ |
6467 | scm_syserror ("mem2ureal"); | |
3c9a524f | 6468 | } |
0f2d19dd | 6469 | |
0f2d19dd | 6470 | |
3c9a524f | 6471 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 6472 | |
3c9a524f | 6473 | static SCM |
3f47e526 | 6474 | mem2complex (SCM mem, unsigned int idx, |
9d427b2c | 6475 | unsigned int radix, enum t_exactness forced_x) |
3c9a524f | 6476 | { |
3f47e526 | 6477 | scm_t_wchar c; |
3c9a524f DH |
6478 | int sign = 0; |
6479 | SCM ureal; | |
3f47e526 | 6480 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6481 | |
6482 | if (idx == len) | |
6483 | return SCM_BOOL_F; | |
6484 | ||
3f47e526 | 6485 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6486 | if (c == '+') |
6487 | { | |
6488 | idx++; | |
6489 | sign = 1; | |
6490 | } | |
6491 | else if (c == '-') | |
6492 | { | |
6493 | idx++; | |
6494 | sign = -1; | |
0f2d19dd | 6495 | } |
0f2d19dd | 6496 | |
3c9a524f DH |
6497 | if (idx == len) |
6498 | return SCM_BOOL_F; | |
6499 | ||
9d427b2c | 6500 | ureal = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 6501 | if (scm_is_false (ureal)) |
f872b822 | 6502 | { |
3c9a524f DH |
6503 | /* input must be either +i or -i */ |
6504 | ||
6505 | if (sign == 0) | |
6506 | return SCM_BOOL_F; | |
6507 | ||
3f47e526 MG |
6508 | if (scm_i_string_ref (mem, idx) == 'i' |
6509 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 6510 | { |
3c9a524f DH |
6511 | idx++; |
6512 | if (idx != len) | |
6513 | return SCM_BOOL_F; | |
6514 | ||
cff5fa33 | 6515 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 6516 | } |
3c9a524f DH |
6517 | else |
6518 | return SCM_BOOL_F; | |
0f2d19dd | 6519 | } |
3c9a524f DH |
6520 | else |
6521 | { | |
73e4de09 | 6522 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 6523 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 6524 | |
3c9a524f DH |
6525 | if (idx == len) |
6526 | return ureal; | |
6527 | ||
3f47e526 | 6528 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 6529 | switch (c) |
f872b822 | 6530 | { |
3c9a524f DH |
6531 | case 'i': case 'I': |
6532 | /* either +<ureal>i or -<ureal>i */ | |
6533 | ||
6534 | idx++; | |
6535 | if (sign == 0) | |
6536 | return SCM_BOOL_F; | |
6537 | if (idx != len) | |
6538 | return SCM_BOOL_F; | |
cff5fa33 | 6539 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
6540 | |
6541 | case '@': | |
6542 | /* polar input: <real>@<real>. */ | |
6543 | ||
6544 | idx++; | |
6545 | if (idx == len) | |
6546 | return SCM_BOOL_F; | |
6547 | else | |
f872b822 | 6548 | { |
3c9a524f DH |
6549 | int sign; |
6550 | SCM angle; | |
6551 | SCM result; | |
6552 | ||
3f47e526 | 6553 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
6554 | if (c == '+') |
6555 | { | |
6556 | idx++; | |
ee0ddd21 AW |
6557 | if (idx == len) |
6558 | return SCM_BOOL_F; | |
3c9a524f DH |
6559 | sign = 1; |
6560 | } | |
6561 | else if (c == '-') | |
6562 | { | |
6563 | idx++; | |
ee0ddd21 AW |
6564 | if (idx == len) |
6565 | return SCM_BOOL_F; | |
3c9a524f DH |
6566 | sign = -1; |
6567 | } | |
6568 | else | |
6569 | sign = 1; | |
6570 | ||
9d427b2c | 6571 | angle = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 6572 | if (scm_is_false (angle)) |
3c9a524f DH |
6573 | return SCM_BOOL_F; |
6574 | if (idx != len) | |
6575 | return SCM_BOOL_F; | |
6576 | ||
73e4de09 | 6577 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
6578 | angle = scm_difference (angle, SCM_UNDEFINED); |
6579 | ||
6580 | result = scm_make_polar (ureal, angle); | |
6581 | return result; | |
f872b822 | 6582 | } |
3c9a524f DH |
6583 | case '+': |
6584 | case '-': | |
6585 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 6586 | |
3c9a524f DH |
6587 | idx++; |
6588 | if (idx == len) | |
6589 | return SCM_BOOL_F; | |
6590 | else | |
6591 | { | |
6592 | int sign = (c == '+') ? 1 : -1; | |
9d427b2c | 6593 | SCM imag = mem2ureal (mem, &idx, radix, forced_x); |
0f2d19dd | 6594 | |
73e4de09 | 6595 | if (scm_is_false (imag)) |
d956fa6f | 6596 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 6597 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 6598 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 6599 | |
3c9a524f DH |
6600 | if (idx == len) |
6601 | return SCM_BOOL_F; | |
3f47e526 MG |
6602 | if (scm_i_string_ref (mem, idx) != 'i' |
6603 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 6604 | return SCM_BOOL_F; |
0f2d19dd | 6605 | |
3c9a524f DH |
6606 | idx++; |
6607 | if (idx != len) | |
6608 | return SCM_BOOL_F; | |
0f2d19dd | 6609 | |
1fe5e088 | 6610 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
6611 | } |
6612 | default: | |
6613 | return SCM_BOOL_F; | |
6614 | } | |
6615 | } | |
0f2d19dd | 6616 | } |
0f2d19dd JB |
6617 | |
6618 | ||
3c9a524f DH |
6619 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
6620 | ||
6621 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 6622 | |
0f2d19dd | 6623 | SCM |
3f47e526 | 6624 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 6625 | { |
3c9a524f DH |
6626 | unsigned int idx = 0; |
6627 | unsigned int radix = NO_RADIX; | |
6628 | enum t_exactness forced_x = NO_EXACTNESS; | |
3f47e526 | 6629 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
6630 | |
6631 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 6632 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 6633 | { |
3f47e526 | 6634 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
6635 | { |
6636 | case 'b': case 'B': | |
6637 | if (radix != NO_RADIX) | |
6638 | return SCM_BOOL_F; | |
6639 | radix = DUAL; | |
6640 | break; | |
6641 | case 'd': case 'D': | |
6642 | if (radix != NO_RADIX) | |
6643 | return SCM_BOOL_F; | |
6644 | radix = DEC; | |
6645 | break; | |
6646 | case 'i': case 'I': | |
6647 | if (forced_x != NO_EXACTNESS) | |
6648 | return SCM_BOOL_F; | |
6649 | forced_x = INEXACT; | |
6650 | break; | |
6651 | case 'e': case 'E': | |
6652 | if (forced_x != NO_EXACTNESS) | |
6653 | return SCM_BOOL_F; | |
6654 | forced_x = EXACT; | |
6655 | break; | |
6656 | case 'o': case 'O': | |
6657 | if (radix != NO_RADIX) | |
6658 | return SCM_BOOL_F; | |
6659 | radix = OCT; | |
6660 | break; | |
6661 | case 'x': case 'X': | |
6662 | if (radix != NO_RADIX) | |
6663 | return SCM_BOOL_F; | |
6664 | radix = HEX; | |
6665 | break; | |
6666 | default: | |
f872b822 | 6667 | return SCM_BOOL_F; |
3c9a524f DH |
6668 | } |
6669 | idx += 2; | |
6670 | } | |
6671 | ||
6672 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
6673 | if (radix == NO_RADIX) | |
9d427b2c | 6674 | radix = default_radix; |
f872b822 | 6675 | |
9d427b2c | 6676 | return mem2complex (mem, idx, radix, forced_x); |
0f2d19dd JB |
6677 | } |
6678 | ||
3f47e526 MG |
6679 | SCM |
6680 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
6681 | unsigned int default_radix) | |
6682 | { | |
6683 | SCM str = scm_from_locale_stringn (mem, len); | |
6684 | ||
6685 | return scm_i_string_to_number (str, default_radix); | |
6686 | } | |
6687 | ||
0f2d19dd | 6688 | |
a1ec6916 | 6689 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 6690 | (SCM string, SCM radix), |
1e6808ea | 6691 | "Return a number of the maximally precise representation\n" |
942e5b91 | 6692 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
6693 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
6694 | "is a default radix that may be overridden by an explicit radix\n" | |
6695 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
6696 | "supplied, then the default radix is 10. If string is not a\n" | |
6697 | "syntactically valid notation for a number, then\n" | |
6698 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 6699 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
6700 | { |
6701 | SCM answer; | |
5efd3c7d | 6702 | unsigned int base; |
a6d9e5ab | 6703 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
6704 | |
6705 | if (SCM_UNBNDP (radix)) | |
6706 | base = 10; | |
6707 | else | |
6708 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
6709 | ||
3f47e526 | 6710 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
6711 | scm_remember_upto_here_1 (string); |
6712 | return answer; | |
0f2d19dd | 6713 | } |
1bbd0b84 | 6714 | #undef FUNC_NAME |
3c9a524f DH |
6715 | |
6716 | ||
0f2d19dd JB |
6717 | /*** END strs->nums ***/ |
6718 | ||
5986c47d | 6719 | |
8507ec80 MV |
6720 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
6721 | (SCM x), | |
6722 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
6723 | "otherwise.") | |
6724 | #define FUNC_NAME s_scm_number_p | |
6725 | { | |
6726 | return scm_from_bool (SCM_NUMBERP (x)); | |
6727 | } | |
6728 | #undef FUNC_NAME | |
6729 | ||
6730 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 6731 | (SCM x), |
942e5b91 | 6732 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 6733 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
6734 | "values form subsets of the set of complex numbers, i. e. the\n" |
6735 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
6736 | "rational or integer number.") | |
8507ec80 | 6737 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 6738 | { |
8507ec80 MV |
6739 | /* all numbers are complex. */ |
6740 | return scm_number_p (x); | |
0f2d19dd | 6741 | } |
1bbd0b84 | 6742 | #undef FUNC_NAME |
0f2d19dd | 6743 | |
f92e85f7 MV |
6744 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
6745 | (SCM x), | |
6746 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
6747 | "otherwise. Note that the set of integer values forms a subset of\n" | |
6748 | "the set of real numbers, i. e. the predicate will also be\n" | |
6749 | "fulfilled if @var{x} is an integer number.") | |
6750 | #define FUNC_NAME s_scm_real_p | |
6751 | { | |
c960e556 MW |
6752 | return scm_from_bool |
6753 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
6754 | } |
6755 | #undef FUNC_NAME | |
6756 | ||
6757 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 6758 | (SCM x), |
942e5b91 | 6759 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 6760 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 6761 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
6762 | "fulfilled if @var{x} is an integer number.") |
6763 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 6764 | { |
c960e556 | 6765 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
6766 | return SCM_BOOL_T; |
6767 | else if (SCM_REALP (x)) | |
c960e556 MW |
6768 | /* due to their limited precision, finite floating point numbers are |
6769 | rational as well. (finite means neither infinity nor a NaN) */ | |
6770 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 6771 | else |
bb628794 | 6772 | return SCM_BOOL_F; |
0f2d19dd | 6773 | } |
1bbd0b84 | 6774 | #undef FUNC_NAME |
0f2d19dd | 6775 | |
a1ec6916 | 6776 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 6777 | (SCM x), |
942e5b91 MG |
6778 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
6779 | "else.") | |
1bbd0b84 | 6780 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 6781 | { |
c960e556 | 6782 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 6783 | return SCM_BOOL_T; |
c960e556 MW |
6784 | else if (SCM_REALP (x)) |
6785 | { | |
6786 | double val = SCM_REAL_VALUE (x); | |
6787 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
6788 | } | |
6789 | else | |
8e43ed5d | 6790 | return SCM_BOOL_F; |
0f2d19dd | 6791 | } |
1bbd0b84 | 6792 | #undef FUNC_NAME |
0f2d19dd JB |
6793 | |
6794 | ||
8a1f4f98 AW |
6795 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
6796 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
6797 | (SCM x, SCM y, SCM rest), | |
6798 | "Return @code{#t} if all parameters are numerically equal.") | |
6799 | #define FUNC_NAME s_scm_i_num_eq_p | |
6800 | { | |
6801 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6802 | return SCM_BOOL_T; | |
6803 | while (!scm_is_null (rest)) | |
6804 | { | |
6805 | if (scm_is_false (scm_num_eq_p (x, y))) | |
6806 | return SCM_BOOL_F; | |
6807 | x = y; | |
6808 | y = scm_car (rest); | |
6809 | rest = scm_cdr (rest); | |
6810 | } | |
6811 | return scm_num_eq_p (x, y); | |
6812 | } | |
6813 | #undef FUNC_NAME | |
0f2d19dd | 6814 | SCM |
6e8d25a6 | 6815 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 6816 | { |
d8b95e27 | 6817 | again: |
e11e83f3 | 6818 | if (SCM_I_INUMP (x)) |
0aacf84e | 6819 | { |
e25f3727 | 6820 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 6821 | if (SCM_I_INUMP (y)) |
0aacf84e | 6822 | { |
e25f3727 | 6823 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 6824 | return scm_from_bool (xx == yy); |
0aacf84e MD |
6825 | } |
6826 | else if (SCM_BIGP (y)) | |
6827 | return SCM_BOOL_F; | |
6828 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
6829 | { |
6830 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
6831 | to a double and compare. | |
6832 | ||
6833 | But on a 64-bit system an inum is bigger than a double and | |
6834 | casting it to a double (call that dxx) will round. dxx is at | |
6835 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
6836 | an integer and fits a long. So we cast yy to a long and | |
6837 | compare with plain xx. | |
6838 | ||
6839 | An alternative (for any size system actually) would be to check | |
6840 | yy is an integer (with floor) and is in range of an inum | |
6841 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
6842 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
6843 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
6844 | |
6845 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
6846 | return scm_from_bool ((double) xx == yy |
6847 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6848 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 6849 | } |
0aacf84e | 6850 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6851 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6852 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
6853 | else if (SCM_FRACTIONP (y)) |
6854 | return SCM_BOOL_F; | |
0aacf84e | 6855 | else |
8a1f4f98 | 6856 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6857 | } |
0aacf84e MD |
6858 | else if (SCM_BIGP (x)) |
6859 | { | |
e11e83f3 | 6860 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6861 | return SCM_BOOL_F; |
6862 | else if (SCM_BIGP (y)) | |
6863 | { | |
6864 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6865 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6866 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6867 | } |
6868 | else if (SCM_REALP (y)) | |
6869 | { | |
6870 | int cmp; | |
2e65b52f | 6871 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6872 | return SCM_BOOL_F; |
6873 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6874 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6875 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6876 | } |
6877 | else if (SCM_COMPLEXP (y)) | |
6878 | { | |
6879 | int cmp; | |
6880 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
6881 | return SCM_BOOL_F; | |
2e65b52f | 6882 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
6883 | return SCM_BOOL_F; |
6884 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
6885 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6886 | return scm_from_bool (0 == cmp); |
0aacf84e | 6887 | } |
f92e85f7 MV |
6888 | else if (SCM_FRACTIONP (y)) |
6889 | return SCM_BOOL_F; | |
0aacf84e | 6890 | else |
8a1f4f98 | 6891 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6892 | } |
0aacf84e MD |
6893 | else if (SCM_REALP (x)) |
6894 | { | |
e8c5b1f2 | 6895 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 6896 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
6897 | { |
6898 | /* see comments with inum/real above */ | |
e25f3727 | 6899 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
6900 | return scm_from_bool (xx == (double) yy |
6901 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6902 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 6903 | } |
0aacf84e MD |
6904 | else if (SCM_BIGP (y)) |
6905 | { | |
6906 | int cmp; | |
2e65b52f | 6907 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6908 | return SCM_BOOL_F; |
6909 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6910 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6911 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6912 | } |
6913 | else if (SCM_REALP (y)) | |
73e4de09 | 6914 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 6915 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6916 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6917 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6918 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6919 | { |
6920 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6921 | if (isnan (xx)) |
d8b95e27 | 6922 | return SCM_BOOL_F; |
2e65b52f | 6923 | if (isinf (xx)) |
73e4de09 | 6924 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6925 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6926 | goto again; | |
6927 | } | |
0aacf84e | 6928 | else |
8a1f4f98 | 6929 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6930 | } |
0aacf84e MD |
6931 | else if (SCM_COMPLEXP (x)) |
6932 | { | |
e11e83f3 MV |
6933 | if (SCM_I_INUMP (y)) |
6934 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
6935 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6936 | else if (SCM_BIGP (y)) | |
6937 | { | |
6938 | int cmp; | |
6939 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
6940 | return SCM_BOOL_F; | |
2e65b52f | 6941 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
6942 | return SCM_BOOL_F; |
6943 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
6944 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6945 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6946 | } |
6947 | else if (SCM_REALP (y)) | |
73e4de09 | 6948 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
6949 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6950 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 6951 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6952 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6953 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6954 | { |
6955 | double xx; | |
6956 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
6957 | return SCM_BOOL_F; | |
6958 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 6959 | if (isnan (xx)) |
d8b95e27 | 6960 | return SCM_BOOL_F; |
2e65b52f | 6961 | if (isinf (xx)) |
73e4de09 | 6962 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6963 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6964 | goto again; | |
6965 | } | |
f92e85f7 | 6966 | else |
8a1f4f98 | 6967 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
6968 | } |
6969 | else if (SCM_FRACTIONP (x)) | |
6970 | { | |
e11e83f3 | 6971 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
6972 | return SCM_BOOL_F; |
6973 | else if (SCM_BIGP (y)) | |
6974 | return SCM_BOOL_F; | |
6975 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
6976 | { |
6977 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6978 | if (isnan (yy)) |
d8b95e27 | 6979 | return SCM_BOOL_F; |
2e65b52f | 6980 | if (isinf (yy)) |
73e4de09 | 6981 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6982 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6983 | goto again; | |
6984 | } | |
f92e85f7 | 6985 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
6986 | { |
6987 | double yy; | |
6988 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
6989 | return SCM_BOOL_F; | |
6990 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 6991 | if (isnan (yy)) |
d8b95e27 | 6992 | return SCM_BOOL_F; |
2e65b52f | 6993 | if (isinf (yy)) |
73e4de09 | 6994 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6995 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6996 | goto again; | |
6997 | } | |
f92e85f7 MV |
6998 | else if (SCM_FRACTIONP (y)) |
6999 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 7000 | else |
8a1f4f98 | 7001 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 7002 | } |
0aacf84e | 7003 | else |
8a1f4f98 | 7004 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
7005 | } |
7006 | ||
7007 | ||
a5f0b599 KR |
7008 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
7009 | done are good for inums, but for bignums an answer can almost always be | |
7010 | had by just examining a few high bits of the operands, as done by GMP in | |
7011 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
7012 | of the float exponent to take into account. */ | |
7013 | ||
8c93b597 | 7014 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
7015 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
7016 | (SCM x, SCM y, SCM rest), | |
7017 | "Return @code{#t} if the list of parameters is monotonically\n" | |
7018 | "increasing.") | |
7019 | #define FUNC_NAME s_scm_i_num_less_p | |
7020 | { | |
7021 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
7022 | return SCM_BOOL_T; | |
7023 | while (!scm_is_null (rest)) | |
7024 | { | |
7025 | if (scm_is_false (scm_less_p (x, y))) | |
7026 | return SCM_BOOL_F; | |
7027 | x = y; | |
7028 | y = scm_car (rest); | |
7029 | rest = scm_cdr (rest); | |
7030 | } | |
7031 | return scm_less_p (x, y); | |
7032 | } | |
7033 | #undef FUNC_NAME | |
0f2d19dd | 7034 | SCM |
6e8d25a6 | 7035 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 7036 | { |
a5f0b599 | 7037 | again: |
e11e83f3 | 7038 | if (SCM_I_INUMP (x)) |
0aacf84e | 7039 | { |
e25f3727 | 7040 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 7041 | if (SCM_I_INUMP (y)) |
0aacf84e | 7042 | { |
e25f3727 | 7043 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 7044 | return scm_from_bool (xx < yy); |
0aacf84e MD |
7045 | } |
7046 | else if (SCM_BIGP (y)) | |
7047 | { | |
7048 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7049 | scm_remember_upto_here_1 (y); | |
73e4de09 | 7050 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
7051 | } |
7052 | else if (SCM_REALP (y)) | |
73e4de09 | 7053 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 7054 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
7055 | { |
7056 | /* "x < a/b" becomes "x*b < a" */ | |
7057 | int_frac: | |
7058 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
7059 | y = SCM_FRACTION_NUMERATOR (y); | |
7060 | goto again; | |
7061 | } | |
0aacf84e | 7062 | else |
8a1f4f98 | 7063 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 7064 | } |
0aacf84e MD |
7065 | else if (SCM_BIGP (x)) |
7066 | { | |
e11e83f3 | 7067 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7068 | { |
7069 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7070 | scm_remember_upto_here_1 (x); | |
73e4de09 | 7071 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
7072 | } |
7073 | else if (SCM_BIGP (y)) | |
7074 | { | |
7075 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
7076 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 7077 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
7078 | } |
7079 | else if (SCM_REALP (y)) | |
7080 | { | |
7081 | int cmp; | |
2e65b52f | 7082 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
7083 | return SCM_BOOL_F; |
7084 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
7085 | scm_remember_upto_here_1 (x); | |
73e4de09 | 7086 | return scm_from_bool (cmp < 0); |
0aacf84e | 7087 | } |
f92e85f7 | 7088 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 7089 | goto int_frac; |
0aacf84e | 7090 | else |
8a1f4f98 | 7091 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 7092 | } |
0aacf84e MD |
7093 | else if (SCM_REALP (x)) |
7094 | { | |
e11e83f3 MV |
7095 | if (SCM_I_INUMP (y)) |
7096 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
7097 | else if (SCM_BIGP (y)) |
7098 | { | |
7099 | int cmp; | |
2e65b52f | 7100 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
7101 | return SCM_BOOL_F; |
7102 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
7103 | scm_remember_upto_here_1 (y); | |
73e4de09 | 7104 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
7105 | } |
7106 | else if (SCM_REALP (y)) | |
73e4de09 | 7107 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 7108 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
7109 | { |
7110 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 7111 | if (isnan (xx)) |
a5f0b599 | 7112 | return SCM_BOOL_F; |
2e65b52f | 7113 | if (isinf (xx)) |
73e4de09 | 7114 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
7115 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
7116 | goto again; | |
7117 | } | |
f92e85f7 | 7118 | else |
8a1f4f98 | 7119 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
7120 | } |
7121 | else if (SCM_FRACTIONP (x)) | |
7122 | { | |
e11e83f3 | 7123 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
7124 | { |
7125 | /* "a/b < y" becomes "a < y*b" */ | |
7126 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
7127 | x = SCM_FRACTION_NUMERATOR (x); | |
7128 | goto again; | |
7129 | } | |
f92e85f7 | 7130 | else if (SCM_REALP (y)) |
a5f0b599 KR |
7131 | { |
7132 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 7133 | if (isnan (yy)) |
a5f0b599 | 7134 | return SCM_BOOL_F; |
2e65b52f | 7135 | if (isinf (yy)) |
73e4de09 | 7136 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
7137 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
7138 | goto again; | |
7139 | } | |
f92e85f7 | 7140 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
7141 | { |
7142 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
7143 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
7144 | SCM_FRACTION_DENOMINATOR (y)); | |
7145 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
7146 | SCM_FRACTION_DENOMINATOR (x)); | |
7147 | x = new_x; | |
7148 | y = new_y; | |
7149 | goto again; | |
7150 | } | |
0aacf84e | 7151 | else |
8a1f4f98 | 7152 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 7153 | } |
0aacf84e | 7154 | else |
8a1f4f98 | 7155 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
7156 | } |
7157 | ||
7158 | ||
8a1f4f98 AW |
7159 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
7160 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
7161 | (SCM x, SCM y, SCM rest), | |
7162 | "Return @code{#t} if the list of parameters is monotonically\n" | |
7163 | "decreasing.") | |
7164 | #define FUNC_NAME s_scm_i_num_gr_p | |
7165 | { | |
7166 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
7167 | return SCM_BOOL_T; | |
7168 | while (!scm_is_null (rest)) | |
7169 | { | |
7170 | if (scm_is_false (scm_gr_p (x, y))) | |
7171 | return SCM_BOOL_F; | |
7172 | x = y; | |
7173 | y = scm_car (rest); | |
7174 | rest = scm_cdr (rest); | |
7175 | } | |
7176 | return scm_gr_p (x, y); | |
7177 | } | |
7178 | #undef FUNC_NAME | |
7179 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
7180 | SCM |
7181 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 7182 | { |
c76b1eaf | 7183 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 7184 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 7185 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 7186 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
7187 | else |
7188 | return scm_less_p (y, x); | |
0f2d19dd | 7189 | } |
1bbd0b84 | 7190 | #undef FUNC_NAME |
0f2d19dd JB |
7191 | |
7192 | ||
8a1f4f98 AW |
7193 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
7194 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
7195 | (SCM x, SCM y, SCM rest), | |
7196 | "Return @code{#t} if the list of parameters is monotonically\n" | |
7197 | "non-decreasing.") | |
7198 | #define FUNC_NAME s_scm_i_num_leq_p | |
7199 | { | |
7200 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
7201 | return SCM_BOOL_T; | |
7202 | while (!scm_is_null (rest)) | |
7203 | { | |
7204 | if (scm_is_false (scm_leq_p (x, y))) | |
7205 | return SCM_BOOL_F; | |
7206 | x = y; | |
7207 | y = scm_car (rest); | |
7208 | rest = scm_cdr (rest); | |
7209 | } | |
7210 | return scm_leq_p (x, y); | |
7211 | } | |
7212 | #undef FUNC_NAME | |
7213 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
7214 | SCM |
7215 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 7216 | { |
c76b1eaf | 7217 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 7218 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 7219 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 7220 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 7221 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 7222 | return SCM_BOOL_F; |
c76b1eaf | 7223 | else |
73e4de09 | 7224 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 7225 | } |
1bbd0b84 | 7226 | #undef FUNC_NAME |
0f2d19dd JB |
7227 | |
7228 | ||
8a1f4f98 AW |
7229 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
7230 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
7231 | (SCM x, SCM y, SCM rest), | |
7232 | "Return @code{#t} if the list of parameters is monotonically\n" | |
7233 | "non-increasing.") | |
7234 | #define FUNC_NAME s_scm_i_num_geq_p | |
7235 | { | |
7236 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
7237 | return SCM_BOOL_T; | |
7238 | while (!scm_is_null (rest)) | |
7239 | { | |
7240 | if (scm_is_false (scm_geq_p (x, y))) | |
7241 | return SCM_BOOL_F; | |
7242 | x = y; | |
7243 | y = scm_car (rest); | |
7244 | rest = scm_cdr (rest); | |
7245 | } | |
7246 | return scm_geq_p (x, y); | |
7247 | } | |
7248 | #undef FUNC_NAME | |
7249 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
7250 | SCM |
7251 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 7252 | { |
c76b1eaf | 7253 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 7254 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 7255 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 7256 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 7257 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 7258 | return SCM_BOOL_F; |
c76b1eaf | 7259 | else |
73e4de09 | 7260 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 7261 | } |
1bbd0b84 | 7262 | #undef FUNC_NAME |
0f2d19dd JB |
7263 | |
7264 | ||
2519490c MW |
7265 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
7266 | (SCM z), | |
7267 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
7268 | "zero.") | |
7269 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 7270 | { |
e11e83f3 | 7271 | if (SCM_I_INUMP (z)) |
bc36d050 | 7272 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 7273 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 7274 | return SCM_BOOL_F; |
0aacf84e | 7275 | else if (SCM_REALP (z)) |
73e4de09 | 7276 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 7277 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 7278 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 7279 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
7280 | else if (SCM_FRACTIONP (z)) |
7281 | return SCM_BOOL_F; | |
0aacf84e | 7282 | else |
2519490c | 7283 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 7284 | } |
2519490c | 7285 | #undef FUNC_NAME |
0f2d19dd JB |
7286 | |
7287 | ||
2519490c MW |
7288 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
7289 | (SCM x), | |
7290 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
7291 | "zero.") | |
7292 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 7293 | { |
e11e83f3 MV |
7294 | if (SCM_I_INUMP (x)) |
7295 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
7296 | else if (SCM_BIGP (x)) |
7297 | { | |
7298 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7299 | scm_remember_upto_here_1 (x); | |
73e4de09 | 7300 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
7301 | } |
7302 | else if (SCM_REALP (x)) | |
73e4de09 | 7303 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
7304 | else if (SCM_FRACTIONP (x)) |
7305 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 7306 | else |
2519490c | 7307 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 7308 | } |
2519490c | 7309 | #undef FUNC_NAME |
0f2d19dd JB |
7310 | |
7311 | ||
2519490c MW |
7312 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
7313 | (SCM x), | |
7314 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
7315 | "zero.") | |
7316 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 7317 | { |
e11e83f3 MV |
7318 | if (SCM_I_INUMP (x)) |
7319 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
7320 | else if (SCM_BIGP (x)) |
7321 | { | |
7322 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7323 | scm_remember_upto_here_1 (x); | |
73e4de09 | 7324 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
7325 | } |
7326 | else if (SCM_REALP (x)) | |
73e4de09 | 7327 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
7328 | else if (SCM_FRACTIONP (x)) |
7329 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 7330 | else |
2519490c | 7331 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 7332 | } |
2519490c | 7333 | #undef FUNC_NAME |
0f2d19dd JB |
7334 | |
7335 | ||
2a06f791 KR |
7336 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
7337 | required by r5rs. On that basis, for exact/inexact combinations the | |
7338 | exact is converted to inexact to compare and possibly return. This is | |
7339 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
7340 | its test, such trouble is not required for min and max. */ | |
7341 | ||
78d3deb1 AW |
7342 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
7343 | (SCM x, SCM y, SCM rest), | |
7344 | "Return the maximum of all parameter values.") | |
7345 | #define FUNC_NAME s_scm_i_max | |
7346 | { | |
7347 | while (!scm_is_null (rest)) | |
7348 | { x = scm_max (x, y); | |
7349 | y = scm_car (rest); | |
7350 | rest = scm_cdr (rest); | |
7351 | } | |
7352 | return scm_max (x, y); | |
7353 | } | |
7354 | #undef FUNC_NAME | |
7355 | ||
7356 | #define s_max s_scm_i_max | |
7357 | #define g_max g_scm_i_max | |
7358 | ||
0f2d19dd | 7359 | SCM |
6e8d25a6 | 7360 | scm_max (SCM x, SCM y) |
0f2d19dd | 7361 | { |
0aacf84e MD |
7362 | if (SCM_UNBNDP (y)) |
7363 | { | |
7364 | if (SCM_UNBNDP (x)) | |
7365 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 7366 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
7367 | return x; |
7368 | else | |
7369 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 7370 | } |
f4c627b3 | 7371 | |
e11e83f3 | 7372 | if (SCM_I_INUMP (x)) |
0aacf84e | 7373 | { |
e25f3727 | 7374 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 7375 | if (SCM_I_INUMP (y)) |
0aacf84e | 7376 | { |
e25f3727 | 7377 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7378 | return (xx < yy) ? y : x; |
7379 | } | |
7380 | else if (SCM_BIGP (y)) | |
7381 | { | |
7382 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7383 | scm_remember_upto_here_1 (y); | |
7384 | return (sgn < 0) ? x : y; | |
7385 | } | |
7386 | else if (SCM_REALP (y)) | |
7387 | { | |
2e274311 MW |
7388 | double xxd = xx; |
7389 | double yyd = SCM_REAL_VALUE (y); | |
7390 | ||
7391 | if (xxd > yyd) | |
7392 | return scm_from_double (xxd); | |
7393 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
7394 | else if (SCM_LIKELY (!(xxd == yyd))) | |
7395 | return y; | |
7396 | /* Handle signed zeroes properly */ | |
7397 | else if (xx == 0) | |
7398 | return flo0; | |
7399 | else | |
7400 | return y; | |
0aacf84e | 7401 | } |
f92e85f7 MV |
7402 | else if (SCM_FRACTIONP (y)) |
7403 | { | |
e4bc5d6c | 7404 | use_less: |
73e4de09 | 7405 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 7406 | } |
0aacf84e MD |
7407 | else |
7408 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 7409 | } |
0aacf84e MD |
7410 | else if (SCM_BIGP (x)) |
7411 | { | |
e11e83f3 | 7412 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7413 | { |
7414 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7415 | scm_remember_upto_here_1 (x); | |
7416 | return (sgn < 0) ? y : x; | |
7417 | } | |
7418 | else if (SCM_BIGP (y)) | |
7419 | { | |
7420 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
7421 | scm_remember_upto_here_2 (x, y); | |
7422 | return (cmp > 0) ? x : y; | |
7423 | } | |
7424 | else if (SCM_REALP (y)) | |
7425 | { | |
2a06f791 KR |
7426 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
7427 | double xx, yy; | |
7428 | big_real: | |
7429 | xx = scm_i_big2dbl (x); | |
7430 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 7431 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 7432 | } |
f92e85f7 MV |
7433 | else if (SCM_FRACTIONP (y)) |
7434 | { | |
e4bc5d6c | 7435 | goto use_less; |
f92e85f7 | 7436 | } |
0aacf84e MD |
7437 | else |
7438 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 7439 | } |
0aacf84e MD |
7440 | else if (SCM_REALP (x)) |
7441 | { | |
e11e83f3 | 7442 | if (SCM_I_INUMP (y)) |
0aacf84e | 7443 | { |
2e274311 MW |
7444 | scm_t_inum yy = SCM_I_INUM (y); |
7445 | double xxd = SCM_REAL_VALUE (x); | |
7446 | double yyd = yy; | |
7447 | ||
7448 | if (yyd > xxd) | |
7449 | return scm_from_double (yyd); | |
7450 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
7451 | else if (SCM_LIKELY (!(xxd == yyd))) | |
7452 | return x; | |
7453 | /* Handle signed zeroes properly */ | |
7454 | else if (yy == 0) | |
7455 | return flo0; | |
7456 | else | |
7457 | return x; | |
0aacf84e MD |
7458 | } |
7459 | else if (SCM_BIGP (y)) | |
7460 | { | |
b6f8f763 | 7461 | SCM_SWAP (x, y); |
2a06f791 | 7462 | goto big_real; |
0aacf84e MD |
7463 | } |
7464 | else if (SCM_REALP (y)) | |
7465 | { | |
0aacf84e | 7466 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
7467 | double yy = SCM_REAL_VALUE (y); |
7468 | ||
7469 | /* For purposes of max: +inf.0 > nan > everything else, per R6RS */ | |
7470 | if (xx > yy) | |
7471 | return x; | |
7472 | else if (SCM_LIKELY (xx < yy)) | |
7473 | return y; | |
7474 | /* If neither (xx > yy) nor (xx < yy), then | |
7475 | either they're equal or one is a NaN */ | |
7476 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 7477 | return DOUBLE_IS_POSITIVE_INFINITY (yy) ? y : x; |
2e274311 | 7478 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 7479 | return DOUBLE_IS_POSITIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
7480 | /* xx == yy, but handle signed zeroes properly */ |
7481 | else if (double_is_non_negative_zero (yy)) | |
7482 | return y; | |
7483 | else | |
7484 | return x; | |
0aacf84e | 7485 | } |
f92e85f7 MV |
7486 | else if (SCM_FRACTIONP (y)) |
7487 | { | |
7488 | double yy = scm_i_fraction2double (y); | |
7489 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 7490 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
7491 | } |
7492 | else | |
7493 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
7494 | } | |
7495 | else if (SCM_FRACTIONP (x)) | |
7496 | { | |
e11e83f3 | 7497 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7498 | { |
e4bc5d6c | 7499 | goto use_less; |
f92e85f7 MV |
7500 | } |
7501 | else if (SCM_BIGP (y)) | |
7502 | { | |
e4bc5d6c | 7503 | goto use_less; |
f92e85f7 MV |
7504 | } |
7505 | else if (SCM_REALP (y)) | |
7506 | { | |
7507 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7508 | /* if y==NaN then ">" is false, so we return the NaN y */ |
7509 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7510 | } |
7511 | else if (SCM_FRACTIONP (y)) | |
7512 | { | |
e4bc5d6c | 7513 | goto use_less; |
f92e85f7 | 7514 | } |
0aacf84e MD |
7515 | else |
7516 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 7517 | } |
0aacf84e | 7518 | else |
f4c627b3 | 7519 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
7520 | } |
7521 | ||
7522 | ||
78d3deb1 AW |
7523 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
7524 | (SCM x, SCM y, SCM rest), | |
7525 | "Return the minimum of all parameter values.") | |
7526 | #define FUNC_NAME s_scm_i_min | |
7527 | { | |
7528 | while (!scm_is_null (rest)) | |
7529 | { x = scm_min (x, y); | |
7530 | y = scm_car (rest); | |
7531 | rest = scm_cdr (rest); | |
7532 | } | |
7533 | return scm_min (x, y); | |
7534 | } | |
7535 | #undef FUNC_NAME | |
7536 | ||
7537 | #define s_min s_scm_i_min | |
7538 | #define g_min g_scm_i_min | |
7539 | ||
0f2d19dd | 7540 | SCM |
6e8d25a6 | 7541 | scm_min (SCM x, SCM y) |
0f2d19dd | 7542 | { |
0aacf84e MD |
7543 | if (SCM_UNBNDP (y)) |
7544 | { | |
7545 | if (SCM_UNBNDP (x)) | |
7546 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 7547 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
7548 | return x; |
7549 | else | |
7550 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 7551 | } |
f4c627b3 | 7552 | |
e11e83f3 | 7553 | if (SCM_I_INUMP (x)) |
0aacf84e | 7554 | { |
e25f3727 | 7555 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 7556 | if (SCM_I_INUMP (y)) |
0aacf84e | 7557 | { |
e25f3727 | 7558 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7559 | return (xx < yy) ? x : y; |
7560 | } | |
7561 | else if (SCM_BIGP (y)) | |
7562 | { | |
7563 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7564 | scm_remember_upto_here_1 (y); | |
7565 | return (sgn < 0) ? y : x; | |
7566 | } | |
7567 | else if (SCM_REALP (y)) | |
7568 | { | |
7569 | double z = xx; | |
7570 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 7571 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 7572 | } |
f92e85f7 MV |
7573 | else if (SCM_FRACTIONP (y)) |
7574 | { | |
e4bc5d6c | 7575 | use_less: |
73e4de09 | 7576 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 7577 | } |
0aacf84e MD |
7578 | else |
7579 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 7580 | } |
0aacf84e MD |
7581 | else if (SCM_BIGP (x)) |
7582 | { | |
e11e83f3 | 7583 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7584 | { |
7585 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7586 | scm_remember_upto_here_1 (x); | |
7587 | return (sgn < 0) ? x : y; | |
7588 | } | |
7589 | else if (SCM_BIGP (y)) | |
7590 | { | |
7591 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
7592 | scm_remember_upto_here_2 (x, y); | |
7593 | return (cmp > 0) ? y : x; | |
7594 | } | |
7595 | else if (SCM_REALP (y)) | |
7596 | { | |
2a06f791 KR |
7597 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
7598 | double xx, yy; | |
7599 | big_real: | |
7600 | xx = scm_i_big2dbl (x); | |
7601 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 7602 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 7603 | } |
f92e85f7 MV |
7604 | else if (SCM_FRACTIONP (y)) |
7605 | { | |
e4bc5d6c | 7606 | goto use_less; |
f92e85f7 | 7607 | } |
0aacf84e MD |
7608 | else |
7609 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 7610 | } |
0aacf84e MD |
7611 | else if (SCM_REALP (x)) |
7612 | { | |
e11e83f3 | 7613 | if (SCM_I_INUMP (y)) |
0aacf84e | 7614 | { |
e11e83f3 | 7615 | double z = SCM_I_INUM (y); |
0aacf84e | 7616 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 7617 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
7618 | } |
7619 | else if (SCM_BIGP (y)) | |
7620 | { | |
b6f8f763 | 7621 | SCM_SWAP (x, y); |
2a06f791 | 7622 | goto big_real; |
0aacf84e MD |
7623 | } |
7624 | else if (SCM_REALP (y)) | |
7625 | { | |
0aacf84e | 7626 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
7627 | double yy = SCM_REAL_VALUE (y); |
7628 | ||
7629 | /* For purposes of min: -inf.0 < nan < everything else, per R6RS */ | |
7630 | if (xx < yy) | |
7631 | return x; | |
7632 | else if (SCM_LIKELY (xx > yy)) | |
7633 | return y; | |
7634 | /* If neither (xx < yy) nor (xx > yy), then | |
7635 | either they're equal or one is a NaN */ | |
7636 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 7637 | return DOUBLE_IS_NEGATIVE_INFINITY (yy) ? y : x; |
2e274311 | 7638 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 7639 | return DOUBLE_IS_NEGATIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
7640 | /* xx == yy, but handle signed zeroes properly */ |
7641 | else if (double_is_non_negative_zero (xx)) | |
7642 | return y; | |
7643 | else | |
7644 | return x; | |
0aacf84e | 7645 | } |
f92e85f7 MV |
7646 | else if (SCM_FRACTIONP (y)) |
7647 | { | |
7648 | double yy = scm_i_fraction2double (y); | |
7649 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 7650 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 7651 | } |
0aacf84e MD |
7652 | else |
7653 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 7654 | } |
f92e85f7 MV |
7655 | else if (SCM_FRACTIONP (x)) |
7656 | { | |
e11e83f3 | 7657 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7658 | { |
e4bc5d6c | 7659 | goto use_less; |
f92e85f7 MV |
7660 | } |
7661 | else if (SCM_BIGP (y)) | |
7662 | { | |
e4bc5d6c | 7663 | goto use_less; |
f92e85f7 MV |
7664 | } |
7665 | else if (SCM_REALP (y)) | |
7666 | { | |
7667 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7668 | /* if y==NaN then "<" is false, so we return the NaN y */ |
7669 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7670 | } |
7671 | else if (SCM_FRACTIONP (y)) | |
7672 | { | |
e4bc5d6c | 7673 | goto use_less; |
f92e85f7 MV |
7674 | } |
7675 | else | |
78d3deb1 | 7676 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 7677 | } |
0aacf84e | 7678 | else |
f4c627b3 | 7679 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
7680 | } |
7681 | ||
7682 | ||
8ccd24f7 AW |
7683 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
7684 | (SCM x, SCM y, SCM rest), | |
7685 | "Return the sum of all parameter values. Return 0 if called without\n" | |
7686 | "any parameters." ) | |
7687 | #define FUNC_NAME s_scm_i_sum | |
7688 | { | |
7689 | while (!scm_is_null (rest)) | |
7690 | { x = scm_sum (x, y); | |
7691 | y = scm_car (rest); | |
7692 | rest = scm_cdr (rest); | |
7693 | } | |
7694 | return scm_sum (x, y); | |
7695 | } | |
7696 | #undef FUNC_NAME | |
7697 | ||
7698 | #define s_sum s_scm_i_sum | |
7699 | #define g_sum g_scm_i_sum | |
7700 | ||
0f2d19dd | 7701 | SCM |
6e8d25a6 | 7702 | scm_sum (SCM x, SCM y) |
0f2d19dd | 7703 | { |
9cc37597 | 7704 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7705 | { |
7706 | if (SCM_NUMBERP (x)) return x; | |
7707 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 7708 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 7709 | } |
c209c88e | 7710 | |
9cc37597 | 7711 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 7712 | { |
9cc37597 | 7713 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 7714 | { |
e25f3727 AW |
7715 | scm_t_inum xx = SCM_I_INUM (x); |
7716 | scm_t_inum yy = SCM_I_INUM (y); | |
7717 | scm_t_inum z = xx + yy; | |
7718 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
7719 | } |
7720 | else if (SCM_BIGP (y)) | |
7721 | { | |
7722 | SCM_SWAP (x, y); | |
7723 | goto add_big_inum; | |
7724 | } | |
7725 | else if (SCM_REALP (y)) | |
7726 | { | |
e25f3727 | 7727 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 7728 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
7729 | } |
7730 | else if (SCM_COMPLEXP (y)) | |
7731 | { | |
e25f3727 | 7732 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 7733 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
7734 | SCM_COMPLEX_IMAG (y)); |
7735 | } | |
f92e85f7 | 7736 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7737 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7738 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7739 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
7740 | else |
7741 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
7742 | } else if (SCM_BIGP (x)) |
7743 | { | |
e11e83f3 | 7744 | if (SCM_I_INUMP (y)) |
0aacf84e | 7745 | { |
e25f3727 | 7746 | scm_t_inum inum; |
0aacf84e MD |
7747 | int bigsgn; |
7748 | add_big_inum: | |
e11e83f3 | 7749 | inum = SCM_I_INUM (y); |
0aacf84e MD |
7750 | if (inum == 0) |
7751 | return x; | |
7752 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7753 | if (inum < 0) | |
7754 | { | |
7755 | SCM result = scm_i_mkbig (); | |
7756 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
7757 | scm_remember_upto_here_1 (x); | |
7758 | /* we know the result will have to be a bignum */ | |
7759 | if (bigsgn == -1) | |
7760 | return result; | |
7761 | return scm_i_normbig (result); | |
7762 | } | |
7763 | else | |
7764 | { | |
7765 | SCM result = scm_i_mkbig (); | |
7766 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
7767 | scm_remember_upto_here_1 (x); | |
7768 | /* we know the result will have to be a bignum */ | |
7769 | if (bigsgn == 1) | |
7770 | return result; | |
7771 | return scm_i_normbig (result); | |
7772 | } | |
7773 | } | |
7774 | else if (SCM_BIGP (y)) | |
7775 | { | |
7776 | SCM result = scm_i_mkbig (); | |
7777 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7778 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7779 | mpz_add (SCM_I_BIG_MPZ (result), | |
7780 | SCM_I_BIG_MPZ (x), | |
7781 | SCM_I_BIG_MPZ (y)); | |
7782 | scm_remember_upto_here_2 (x, y); | |
7783 | /* we know the result will have to be a bignum */ | |
7784 | if (sgn_x == sgn_y) | |
7785 | return result; | |
7786 | return scm_i_normbig (result); | |
7787 | } | |
7788 | else if (SCM_REALP (y)) | |
7789 | { | |
7790 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
7791 | scm_remember_upto_here_1 (x); | |
55f26379 | 7792 | return scm_from_double (result); |
0aacf84e MD |
7793 | } |
7794 | else if (SCM_COMPLEXP (y)) | |
7795 | { | |
7796 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7797 | + SCM_COMPLEX_REAL (y)); | |
7798 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7799 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7800 | } |
f92e85f7 | 7801 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7802 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7803 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7804 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7805 | else |
7806 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 7807 | } |
0aacf84e MD |
7808 | else if (SCM_REALP (x)) |
7809 | { | |
e11e83f3 | 7810 | if (SCM_I_INUMP (y)) |
55f26379 | 7811 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
7812 | else if (SCM_BIGP (y)) |
7813 | { | |
7814 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
7815 | scm_remember_upto_here_1 (y); | |
55f26379 | 7816 | return scm_from_double (result); |
0aacf84e MD |
7817 | } |
7818 | else if (SCM_REALP (y)) | |
55f26379 | 7819 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 7820 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7821 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7822 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7823 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7824 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
7825 | else |
7826 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 7827 | } |
0aacf84e MD |
7828 | else if (SCM_COMPLEXP (x)) |
7829 | { | |
e11e83f3 | 7830 | if (SCM_I_INUMP (y)) |
8507ec80 | 7831 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
7832 | SCM_COMPLEX_IMAG (x)); |
7833 | else if (SCM_BIGP (y)) | |
7834 | { | |
7835 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
7836 | + SCM_COMPLEX_REAL (x)); | |
7837 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7838 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7839 | } |
7840 | else if (SCM_REALP (y)) | |
8507ec80 | 7841 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
7842 | SCM_COMPLEX_IMAG (x)); |
7843 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7844 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7845 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7846 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7847 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
7848 | SCM_COMPLEX_IMAG (x)); |
7849 | else | |
7850 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
7851 | } | |
7852 | else if (SCM_FRACTIONP (x)) | |
7853 | { | |
e11e83f3 | 7854 | if (SCM_I_INUMP (y)) |
cba42c93 | 7855 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7856 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7857 | SCM_FRACTION_DENOMINATOR (x)); | |
7858 | else if (SCM_BIGP (y)) | |
cba42c93 | 7859 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7860 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7861 | SCM_FRACTION_DENOMINATOR (x)); | |
7862 | else if (SCM_REALP (y)) | |
55f26379 | 7863 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 7864 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7865 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
7866 | SCM_COMPLEX_IMAG (y)); |
7867 | else if (SCM_FRACTIONP (y)) | |
7868 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 7869 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7870 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7871 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7872 | else |
7873 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 7874 | } |
0aacf84e | 7875 | else |
98cb6e75 | 7876 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
7877 | } |
7878 | ||
7879 | ||
40882e3d KR |
7880 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
7881 | (SCM x), | |
7882 | "Return @math{@var{x}+1}.") | |
7883 | #define FUNC_NAME s_scm_oneplus | |
7884 | { | |
cff5fa33 | 7885 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
7886 | } |
7887 | #undef FUNC_NAME | |
7888 | ||
7889 | ||
78d3deb1 AW |
7890 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
7891 | (SCM x, SCM y, SCM rest), | |
7892 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
7893 | "the sum of all but the first argument are subtracted from the first\n" | |
7894 | "argument.") | |
7895 | #define FUNC_NAME s_scm_i_difference | |
7896 | { | |
7897 | while (!scm_is_null (rest)) | |
7898 | { x = scm_difference (x, y); | |
7899 | y = scm_car (rest); | |
7900 | rest = scm_cdr (rest); | |
7901 | } | |
7902 | return scm_difference (x, y); | |
7903 | } | |
7904 | #undef FUNC_NAME | |
7905 | ||
7906 | #define s_difference s_scm_i_difference | |
7907 | #define g_difference g_scm_i_difference | |
7908 | ||
0f2d19dd | 7909 | SCM |
6e8d25a6 | 7910 | scm_difference (SCM x, SCM y) |
78d3deb1 | 7911 | #define FUNC_NAME s_difference |
0f2d19dd | 7912 | { |
9cc37597 | 7913 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7914 | { |
7915 | if (SCM_UNBNDP (x)) | |
7916 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
7917 | else | |
e11e83f3 | 7918 | if (SCM_I_INUMP (x)) |
ca46fb90 | 7919 | { |
e25f3727 | 7920 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 7921 | if (SCM_FIXABLE (xx)) |
d956fa6f | 7922 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 7923 | else |
e25f3727 | 7924 | return scm_i_inum2big (xx); |
ca46fb90 RB |
7925 | } |
7926 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
7927 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
7928 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
7929 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
7930 | else if (SCM_REALP (x)) | |
55f26379 | 7931 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 7932 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 7933 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 7934 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 7935 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 7936 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 7937 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
7938 | else |
7939 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 7940 | } |
ca46fb90 | 7941 | |
9cc37597 | 7942 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7943 | { |
9cc37597 | 7944 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7945 | { |
e25f3727 AW |
7946 | scm_t_inum xx = SCM_I_INUM (x); |
7947 | scm_t_inum yy = SCM_I_INUM (y); | |
7948 | scm_t_inum z = xx - yy; | |
0aacf84e | 7949 | if (SCM_FIXABLE (z)) |
d956fa6f | 7950 | return SCM_I_MAKINUM (z); |
0aacf84e | 7951 | else |
e25f3727 | 7952 | return scm_i_inum2big (z); |
0aacf84e MD |
7953 | } |
7954 | else if (SCM_BIGP (y)) | |
7955 | { | |
7956 | /* inum-x - big-y */ | |
e25f3727 | 7957 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 7958 | |
0aacf84e | 7959 | if (xx == 0) |
b5c40589 MW |
7960 | { |
7961 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
7962 | bignum, but negating that gives a fixnum. */ | |
7963 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
7964 | } | |
0aacf84e MD |
7965 | else |
7966 | { | |
7967 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7968 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7969 | |
0aacf84e MD |
7970 | if (xx >= 0) |
7971 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
7972 | else | |
7973 | { | |
7974 | /* x - y == -(y + -x) */ | |
7975 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
7976 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7977 | } | |
7978 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 7979 | |
0aacf84e MD |
7980 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
7981 | /* we know the result will have to be a bignum */ | |
7982 | return result; | |
7983 | else | |
7984 | return scm_i_normbig (result); | |
7985 | } | |
7986 | } | |
7987 | else if (SCM_REALP (y)) | |
7988 | { | |
e25f3727 | 7989 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7990 | |
7991 | /* | |
7992 | * We need to handle x == exact 0 | |
7993 | * specially because R6RS states that: | |
7994 | * (- 0.0) ==> -0.0 and | |
7995 | * (- 0.0 0.0) ==> 0.0 | |
7996 | * and the scheme compiler changes | |
7997 | * (- 0.0) into (- 0 0.0) | |
7998 | * So we need to treat (- 0 0.0) like (- 0.0). | |
7999 | * At the C level, (-x) is different than (0.0 - x). | |
8000 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
8001 | */ | |
8002 | if (xx == 0) | |
8003 | return scm_from_double (- SCM_REAL_VALUE (y)); | |
8004 | else | |
8005 | return scm_from_double (xx - SCM_REAL_VALUE (y)); | |
0aacf84e MD |
8006 | } |
8007 | else if (SCM_COMPLEXP (y)) | |
8008 | { | |
e25f3727 | 8009 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
8010 | |
8011 | /* We need to handle x == exact 0 specially. | |
8012 | See the comment above (for SCM_REALP (y)) */ | |
8013 | if (xx == 0) | |
8014 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
8015 | - SCM_COMPLEX_IMAG (y)); | |
8016 | else | |
8017 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
8018 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 8019 | } |
f92e85f7 MV |
8020 | else if (SCM_FRACTIONP (y)) |
8021 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 8022 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
8023 | SCM_FRACTION_NUMERATOR (y)), |
8024 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
8025 | else |
8026 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 8027 | } |
0aacf84e MD |
8028 | else if (SCM_BIGP (x)) |
8029 | { | |
e11e83f3 | 8030 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
8031 | { |
8032 | /* big-x - inum-y */ | |
e25f3727 | 8033 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 8034 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 8035 | |
0aacf84e MD |
8036 | scm_remember_upto_here_1 (x); |
8037 | if (sgn_x == 0) | |
c71b0706 | 8038 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 8039 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
8040 | else |
8041 | { | |
8042 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 8043 | |
708f22c6 KR |
8044 | if (yy >= 0) |
8045 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
8046 | else | |
8047 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 8048 | scm_remember_upto_here_1 (x); |
ca46fb90 | 8049 | |
0aacf84e MD |
8050 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
8051 | /* we know the result will have to be a bignum */ | |
8052 | return result; | |
8053 | else | |
8054 | return scm_i_normbig (result); | |
8055 | } | |
8056 | } | |
8057 | else if (SCM_BIGP (y)) | |
8058 | { | |
8059 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
8060 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
8061 | SCM result = scm_i_mkbig (); | |
8062 | mpz_sub (SCM_I_BIG_MPZ (result), | |
8063 | SCM_I_BIG_MPZ (x), | |
8064 | SCM_I_BIG_MPZ (y)); | |
8065 | scm_remember_upto_here_2 (x, y); | |
8066 | /* we know the result will have to be a bignum */ | |
8067 | if ((sgn_x == 1) && (sgn_y == -1)) | |
8068 | return result; | |
8069 | if ((sgn_x == -1) && (sgn_y == 1)) | |
8070 | return result; | |
8071 | return scm_i_normbig (result); | |
8072 | } | |
8073 | else if (SCM_REALP (y)) | |
8074 | { | |
8075 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
8076 | scm_remember_upto_here_1 (x); | |
55f26379 | 8077 | return scm_from_double (result); |
0aacf84e MD |
8078 | } |
8079 | else if (SCM_COMPLEXP (y)) | |
8080 | { | |
8081 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
8082 | - SCM_COMPLEX_REAL (y)); | |
8083 | scm_remember_upto_here_1 (x); | |
8507ec80 | 8084 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 8085 | } |
f92e85f7 | 8086 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8087 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
8088 | SCM_FRACTION_NUMERATOR (y)), |
8089 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 8090 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 8091 | } |
0aacf84e MD |
8092 | else if (SCM_REALP (x)) |
8093 | { | |
e11e83f3 | 8094 | if (SCM_I_INUMP (y)) |
55f26379 | 8095 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
8096 | else if (SCM_BIGP (y)) |
8097 | { | |
8098 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8099 | scm_remember_upto_here_1 (x); | |
55f26379 | 8100 | return scm_from_double (result); |
0aacf84e MD |
8101 | } |
8102 | else if (SCM_REALP (y)) | |
55f26379 | 8103 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 8104 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 8105 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 8106 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 8107 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8108 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
8109 | else |
8110 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 8111 | } |
0aacf84e MD |
8112 | else if (SCM_COMPLEXP (x)) |
8113 | { | |
e11e83f3 | 8114 | if (SCM_I_INUMP (y)) |
8507ec80 | 8115 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
8116 | SCM_COMPLEX_IMAG (x)); |
8117 | else if (SCM_BIGP (y)) | |
8118 | { | |
8119 | double real_part = (SCM_COMPLEX_REAL (x) | |
8120 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
8121 | scm_remember_upto_here_1 (x); | |
8507ec80 | 8122 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
8123 | } |
8124 | else if (SCM_REALP (y)) | |
8507ec80 | 8125 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
8126 | SCM_COMPLEX_IMAG (x)); |
8127 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 8128 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 8129 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 8130 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 8131 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
8132 | SCM_COMPLEX_IMAG (x)); |
8133 | else | |
8134 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
8135 | } | |
8136 | else if (SCM_FRACTIONP (x)) | |
8137 | { | |
e11e83f3 | 8138 | if (SCM_I_INUMP (y)) |
f92e85f7 | 8139 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 8140 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8141 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
8142 | SCM_FRACTION_DENOMINATOR (x)); | |
8143 | else if (SCM_BIGP (y)) | |
cba42c93 | 8144 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8145 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
8146 | SCM_FRACTION_DENOMINATOR (x)); | |
8147 | else if (SCM_REALP (y)) | |
55f26379 | 8148 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 8149 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 8150 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
8151 | -SCM_COMPLEX_IMAG (y)); |
8152 | else if (SCM_FRACTIONP (y)) | |
8153 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 8154 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
8155 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
8156 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
8157 | else |
8158 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 8159 | } |
0aacf84e | 8160 | else |
98cb6e75 | 8161 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 8162 | } |
c05e97b7 | 8163 | #undef FUNC_NAME |
0f2d19dd | 8164 | |
ca46fb90 | 8165 | |
40882e3d KR |
8166 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
8167 | (SCM x), | |
8168 | "Return @math{@var{x}-1}.") | |
8169 | #define FUNC_NAME s_scm_oneminus | |
8170 | { | |
cff5fa33 | 8171 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
8172 | } |
8173 | #undef FUNC_NAME | |
8174 | ||
8175 | ||
78d3deb1 AW |
8176 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
8177 | (SCM x, SCM y, SCM rest), | |
8178 | "Return the product of all arguments. If called without arguments,\n" | |
8179 | "1 is returned.") | |
8180 | #define FUNC_NAME s_scm_i_product | |
8181 | { | |
8182 | while (!scm_is_null (rest)) | |
8183 | { x = scm_product (x, y); | |
8184 | y = scm_car (rest); | |
8185 | rest = scm_cdr (rest); | |
8186 | } | |
8187 | return scm_product (x, y); | |
8188 | } | |
8189 | #undef FUNC_NAME | |
8190 | ||
8191 | #define s_product s_scm_i_product | |
8192 | #define g_product g_scm_i_product | |
8193 | ||
0f2d19dd | 8194 | SCM |
6e8d25a6 | 8195 | scm_product (SCM x, SCM y) |
0f2d19dd | 8196 | { |
9cc37597 | 8197 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
8198 | { |
8199 | if (SCM_UNBNDP (x)) | |
d956fa6f | 8200 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
8201 | else if (SCM_NUMBERP (x)) |
8202 | return x; | |
8203 | else | |
8204 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 8205 | } |
ca46fb90 | 8206 | |
9cc37597 | 8207 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 8208 | { |
e25f3727 | 8209 | scm_t_inum xx; |
f4c627b3 | 8210 | |
5e791807 | 8211 | xinum: |
e11e83f3 | 8212 | xx = SCM_I_INUM (x); |
f4c627b3 | 8213 | |
0aacf84e MD |
8214 | switch (xx) |
8215 | { | |
5e791807 MW |
8216 | case 1: |
8217 | /* exact1 is the universal multiplicative identity */ | |
8218 | return y; | |
8219 | break; | |
8220 | case 0: | |
8221 | /* exact0 times a fixnum is exact0: optimize this case */ | |
8222 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
8223 | return SCM_INUM0; | |
8224 | /* if the other argument is inexact, the result is inexact, | |
8225 | and we must do the multiplication in order to handle | |
8226 | infinities and NaNs properly. */ | |
8227 | else if (SCM_REALP (y)) | |
8228 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
8229 | else if (SCM_COMPLEXP (y)) | |
8230 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
8231 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
8232 | /* we've already handled inexact numbers, | |
8233 | so y must be exact, and we return exact0 */ | |
8234 | else if (SCM_NUMP (y)) | |
8235 | return SCM_INUM0; | |
8236 | else | |
8237 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
8238 | break; | |
8239 | case -1: | |
b5c40589 | 8240 | /* |
5e791807 MW |
8241 | * This case is important for more than just optimization. |
8242 | * It handles the case of negating | |
b5c40589 MW |
8243 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
8244 | * which is a bignum that must be changed back into a fixnum. | |
8245 | * Failure to do so will cause the following to return #f: | |
8246 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
8247 | */ | |
b5c40589 MW |
8248 | return scm_difference(y, SCM_UNDEFINED); |
8249 | break; | |
0aacf84e | 8250 | } |
f4c627b3 | 8251 | |
9cc37597 | 8252 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 8253 | { |
e25f3727 AW |
8254 | scm_t_inum yy = SCM_I_INUM (y); |
8255 | scm_t_inum kk = xx * yy; | |
d956fa6f | 8256 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 8257 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
8258 | return k; |
8259 | else | |
8260 | { | |
e25f3727 | 8261 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
8262 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
8263 | return scm_i_normbig (result); | |
8264 | } | |
8265 | } | |
8266 | else if (SCM_BIGP (y)) | |
8267 | { | |
8268 | SCM result = scm_i_mkbig (); | |
8269 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
8270 | scm_remember_upto_here_1 (y); | |
8271 | return result; | |
8272 | } | |
8273 | else if (SCM_REALP (y)) | |
55f26379 | 8274 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 8275 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 8276 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 8277 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 8278 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8279 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 8280 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
8281 | else |
8282 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 8283 | } |
0aacf84e MD |
8284 | else if (SCM_BIGP (x)) |
8285 | { | |
e11e83f3 | 8286 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
8287 | { |
8288 | SCM_SWAP (x, y); | |
5e791807 | 8289 | goto xinum; |
0aacf84e MD |
8290 | } |
8291 | else if (SCM_BIGP (y)) | |
8292 | { | |
8293 | SCM result = scm_i_mkbig (); | |
8294 | mpz_mul (SCM_I_BIG_MPZ (result), | |
8295 | SCM_I_BIG_MPZ (x), | |
8296 | SCM_I_BIG_MPZ (y)); | |
8297 | scm_remember_upto_here_2 (x, y); | |
8298 | return result; | |
8299 | } | |
8300 | else if (SCM_REALP (y)) | |
8301 | { | |
8302 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
8303 | scm_remember_upto_here_1 (x); | |
55f26379 | 8304 | return scm_from_double (result); |
0aacf84e MD |
8305 | } |
8306 | else if (SCM_COMPLEXP (y)) | |
8307 | { | |
8308 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
8309 | scm_remember_upto_here_1 (x); | |
8507ec80 | 8310 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
8311 | z * SCM_COMPLEX_IMAG (y)); |
8312 | } | |
f92e85f7 | 8313 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8314 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 8315 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
8316 | else |
8317 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 8318 | } |
0aacf84e MD |
8319 | else if (SCM_REALP (x)) |
8320 | { | |
e11e83f3 | 8321 | if (SCM_I_INUMP (y)) |
5e791807 MW |
8322 | { |
8323 | SCM_SWAP (x, y); | |
8324 | goto xinum; | |
8325 | } | |
0aacf84e MD |
8326 | else if (SCM_BIGP (y)) |
8327 | { | |
8328 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
8329 | scm_remember_upto_here_1 (y); | |
55f26379 | 8330 | return scm_from_double (result); |
0aacf84e MD |
8331 | } |
8332 | else if (SCM_REALP (y)) | |
55f26379 | 8333 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 8334 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 8335 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 8336 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 8337 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8338 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
8339 | else |
8340 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 8341 | } |
0aacf84e MD |
8342 | else if (SCM_COMPLEXP (x)) |
8343 | { | |
e11e83f3 | 8344 | if (SCM_I_INUMP (y)) |
5e791807 MW |
8345 | { |
8346 | SCM_SWAP (x, y); | |
8347 | goto xinum; | |
8348 | } | |
0aacf84e MD |
8349 | else if (SCM_BIGP (y)) |
8350 | { | |
8351 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8352 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8353 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 8354 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
8355 | } |
8356 | else if (SCM_REALP (y)) | |
8507ec80 | 8357 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
8358 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
8359 | else if (SCM_COMPLEXP (y)) | |
8360 | { | |
8507ec80 | 8361 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
8362 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
8363 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
8364 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
8365 | } | |
f92e85f7 MV |
8366 | else if (SCM_FRACTIONP (y)) |
8367 | { | |
8368 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 8369 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
8370 | yy * SCM_COMPLEX_IMAG (x)); |
8371 | } | |
8372 | else | |
8373 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
8374 | } | |
8375 | else if (SCM_FRACTIONP (x)) | |
8376 | { | |
e11e83f3 | 8377 | if (SCM_I_INUMP (y)) |
cba42c93 | 8378 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
8379 | SCM_FRACTION_DENOMINATOR (x)); |
8380 | else if (SCM_BIGP (y)) | |
cba42c93 | 8381 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
8382 | SCM_FRACTION_DENOMINATOR (x)); |
8383 | else if (SCM_REALP (y)) | |
55f26379 | 8384 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
8385 | else if (SCM_COMPLEXP (y)) |
8386 | { | |
8387 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 8388 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
8389 | xx * SCM_COMPLEX_IMAG (y)); |
8390 | } | |
8391 | else if (SCM_FRACTIONP (y)) | |
8392 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 8393 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8394 | SCM_FRACTION_NUMERATOR (y)), |
8395 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
8396 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
8397 | else |
8398 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 8399 | } |
0aacf84e | 8400 | else |
f4c627b3 | 8401 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
8402 | } |
8403 | ||
7351e207 MV |
8404 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
8405 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
8406 | #define ALLOW_DIVIDE_BY_ZERO | |
8407 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
8408 | #endif | |
0f2d19dd | 8409 | |
ba74ef4e MV |
8410 | /* The code below for complex division is adapted from the GNU |
8411 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
8412 | this copyright: */ | |
8413 | ||
8414 | /**************************************************************** | |
8415 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
8416 | ||
8417 | Permission to use, copy, modify, and distribute this software | |
8418 | and its documentation for any purpose and without fee is hereby | |
8419 | granted, provided that the above copyright notice appear in all | |
8420 | copies and that both that the copyright notice and this | |
8421 | permission notice and warranty disclaimer appear in supporting | |
8422 | documentation, and that the names of AT&T Bell Laboratories or | |
8423 | Bellcore or any of their entities not be used in advertising or | |
8424 | publicity pertaining to distribution of the software without | |
8425 | specific, written prior permission. | |
8426 | ||
8427 | AT&T and Bellcore disclaim all warranties with regard to this | |
8428 | software, including all implied warranties of merchantability | |
8429 | and fitness. In no event shall AT&T or Bellcore be liable for | |
8430 | any special, indirect or consequential damages or any damages | |
8431 | whatsoever resulting from loss of use, data or profits, whether | |
8432 | in an action of contract, negligence or other tortious action, | |
8433 | arising out of or in connection with the use or performance of | |
8434 | this software. | |
8435 | ****************************************************************/ | |
8436 | ||
78d3deb1 AW |
8437 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
8438 | (SCM x, SCM y, SCM rest), | |
8439 | "Divide the first argument by the product of the remaining\n" | |
8440 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
8441 | "returned.") | |
8442 | #define FUNC_NAME s_scm_i_divide | |
8443 | { | |
8444 | while (!scm_is_null (rest)) | |
8445 | { x = scm_divide (x, y); | |
8446 | y = scm_car (rest); | |
8447 | rest = scm_cdr (rest); | |
8448 | } | |
8449 | return scm_divide (x, y); | |
8450 | } | |
8451 | #undef FUNC_NAME | |
8452 | ||
8453 | #define s_divide s_scm_i_divide | |
8454 | #define g_divide g_scm_i_divide | |
8455 | ||
f92e85f7 | 8456 | static SCM |
78d3deb1 AW |
8457 | do_divide (SCM x, SCM y, int inexact) |
8458 | #define FUNC_NAME s_divide | |
0f2d19dd | 8459 | { |
f8de44c1 DH |
8460 | double a; |
8461 | ||
9cc37597 | 8462 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
8463 | { |
8464 | if (SCM_UNBNDP (x)) | |
8465 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 8466 | else if (SCM_I_INUMP (x)) |
0aacf84e | 8467 | { |
e25f3727 | 8468 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
8469 | if (xx == 1 || xx == -1) |
8470 | return x; | |
7351e207 | 8471 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8472 | else if (xx == 0) |
8473 | scm_num_overflow (s_divide); | |
7351e207 | 8474 | #endif |
0aacf84e | 8475 | else |
f92e85f7 MV |
8476 | { |
8477 | if (inexact) | |
55f26379 | 8478 | return scm_from_double (1.0 / (double) xx); |
cff5fa33 | 8479 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 8480 | } |
0aacf84e MD |
8481 | } |
8482 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
8483 | { |
8484 | if (inexact) | |
55f26379 | 8485 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cff5fa33 | 8486 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 8487 | } |
0aacf84e MD |
8488 | else if (SCM_REALP (x)) |
8489 | { | |
8490 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 8491 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8492 | if (xx == 0.0) |
8493 | scm_num_overflow (s_divide); | |
8494 | else | |
7351e207 | 8495 | #endif |
55f26379 | 8496 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
8497 | } |
8498 | else if (SCM_COMPLEXP (x)) | |
8499 | { | |
8500 | double r = SCM_COMPLEX_REAL (x); | |
8501 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 8502 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
8503 | { |
8504 | double t = r / i; | |
8505 | double d = i * (1.0 + t * t); | |
8507ec80 | 8506 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
8507 | } |
8508 | else | |
8509 | { | |
8510 | double t = i / r; | |
8511 | double d = r * (1.0 + t * t); | |
8507ec80 | 8512 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
8513 | } |
8514 | } | |
f92e85f7 | 8515 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 8516 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 8517 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
8518 | else |
8519 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 8520 | } |
f8de44c1 | 8521 | |
9cc37597 | 8522 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 8523 | { |
e25f3727 | 8524 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 8525 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 8526 | { |
e25f3727 | 8527 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
8528 | if (yy == 0) |
8529 | { | |
7351e207 | 8530 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 8531 | scm_num_overflow (s_divide); |
7351e207 | 8532 | #else |
55f26379 | 8533 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 8534 | #endif |
0aacf84e MD |
8535 | } |
8536 | else if (xx % yy != 0) | |
f92e85f7 MV |
8537 | { |
8538 | if (inexact) | |
55f26379 | 8539 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 8540 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 8541 | } |
0aacf84e MD |
8542 | else |
8543 | { | |
e25f3727 | 8544 | scm_t_inum z = xx / yy; |
0aacf84e | 8545 | if (SCM_FIXABLE (z)) |
d956fa6f | 8546 | return SCM_I_MAKINUM (z); |
0aacf84e | 8547 | else |
e25f3727 | 8548 | return scm_i_inum2big (z); |
0aacf84e | 8549 | } |
f872b822 | 8550 | } |
0aacf84e | 8551 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
8552 | { |
8553 | if (inexact) | |
55f26379 | 8554 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 8555 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 8556 | } |
0aacf84e MD |
8557 | else if (SCM_REALP (y)) |
8558 | { | |
8559 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8560 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8561 | if (yy == 0.0) |
8562 | scm_num_overflow (s_divide); | |
8563 | else | |
7351e207 | 8564 | #endif |
55f26379 | 8565 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 8566 | } |
0aacf84e MD |
8567 | else if (SCM_COMPLEXP (y)) |
8568 | { | |
8569 | a = xx; | |
8570 | complex_div: /* y _must_ be a complex number */ | |
8571 | { | |
8572 | double r = SCM_COMPLEX_REAL (y); | |
8573 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8574 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
8575 | { |
8576 | double t = r / i; | |
8577 | double d = i * (1.0 + t * t); | |
8507ec80 | 8578 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
8579 | } |
8580 | else | |
8581 | { | |
8582 | double t = i / r; | |
8583 | double d = r * (1.0 + t * t); | |
8507ec80 | 8584 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
8585 | } |
8586 | } | |
8587 | } | |
f92e85f7 MV |
8588 | else if (SCM_FRACTIONP (y)) |
8589 | /* a / b/c = ac / b */ | |
cba42c93 | 8590 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 8591 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
8592 | else |
8593 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 8594 | } |
0aacf84e MD |
8595 | else if (SCM_BIGP (x)) |
8596 | { | |
e11e83f3 | 8597 | if (SCM_I_INUMP (y)) |
0aacf84e | 8598 | { |
e25f3727 | 8599 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
8600 | if (yy == 0) |
8601 | { | |
7351e207 | 8602 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 8603 | scm_num_overflow (s_divide); |
7351e207 | 8604 | #else |
0aacf84e MD |
8605 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
8606 | scm_remember_upto_here_1 (x); | |
8607 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 8608 | #endif |
0aacf84e MD |
8609 | } |
8610 | else if (yy == 1) | |
8611 | return x; | |
8612 | else | |
8613 | { | |
8614 | /* FIXME: HMM, what are the relative performance issues here? | |
8615 | We need to test. Is it faster on average to test | |
8616 | divisible_p, then perform whichever operation, or is it | |
8617 | faster to perform the integer div opportunistically and | |
8618 | switch to real if there's a remainder? For now we take the | |
8619 | middle ground: test, then if divisible, use the faster div | |
8620 | func. */ | |
8621 | ||
e25f3727 | 8622 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
8623 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
8624 | ||
8625 | if (divisible_p) | |
8626 | { | |
8627 | SCM result = scm_i_mkbig (); | |
8628 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
8629 | scm_remember_upto_here_1 (x); | |
8630 | if (yy < 0) | |
8631 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
8632 | return scm_i_normbig (result); | |
8633 | } | |
8634 | else | |
f92e85f7 MV |
8635 | { |
8636 | if (inexact) | |
55f26379 | 8637 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 8638 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 8639 | } |
0aacf84e MD |
8640 | } |
8641 | } | |
8642 | else if (SCM_BIGP (y)) | |
8643 | { | |
a4955a04 MW |
8644 | /* big_x / big_y */ |
8645 | if (inexact) | |
0aacf84e | 8646 | { |
a4955a04 MW |
8647 | /* It's easily possible for the ratio x/y to fit a double |
8648 | but one or both x and y be too big to fit a double, | |
8649 | hence the use of mpq_get_d rather than converting and | |
8650 | dividing. */ | |
8651 | mpq_t q; | |
8652 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
8653 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
8654 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
8655 | } |
8656 | else | |
8657 | { | |
a4955a04 MW |
8658 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
8659 | SCM_I_BIG_MPZ (y)); | |
8660 | if (divisible_p) | |
8661 | { | |
8662 | SCM result = scm_i_mkbig (); | |
8663 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
8664 | SCM_I_BIG_MPZ (x), | |
8665 | SCM_I_BIG_MPZ (y)); | |
8666 | scm_remember_upto_here_2 (x, y); | |
8667 | return scm_i_normbig (result); | |
8668 | } | |
8669 | else | |
8670 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
8671 | } |
8672 | } | |
8673 | else if (SCM_REALP (y)) | |
8674 | { | |
8675 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8676 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8677 | if (yy == 0.0) |
8678 | scm_num_overflow (s_divide); | |
8679 | else | |
7351e207 | 8680 | #endif |
55f26379 | 8681 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
8682 | } |
8683 | else if (SCM_COMPLEXP (y)) | |
8684 | { | |
8685 | a = scm_i_big2dbl (x); | |
8686 | goto complex_div; | |
8687 | } | |
f92e85f7 | 8688 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8689 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 8690 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
8691 | else |
8692 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8693 | } |
0aacf84e MD |
8694 | else if (SCM_REALP (x)) |
8695 | { | |
8696 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 8697 | if (SCM_I_INUMP (y)) |
0aacf84e | 8698 | { |
e25f3727 | 8699 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8700 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8701 | if (yy == 0) |
8702 | scm_num_overflow (s_divide); | |
8703 | else | |
7351e207 | 8704 | #endif |
55f26379 | 8705 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
8706 | } |
8707 | else if (SCM_BIGP (y)) | |
8708 | { | |
8709 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8710 | scm_remember_upto_here_1 (y); | |
55f26379 | 8711 | return scm_from_double (rx / dby); |
0aacf84e MD |
8712 | } |
8713 | else if (SCM_REALP (y)) | |
8714 | { | |
8715 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8716 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8717 | if (yy == 0.0) |
8718 | scm_num_overflow (s_divide); | |
8719 | else | |
7351e207 | 8720 | #endif |
55f26379 | 8721 | return scm_from_double (rx / yy); |
0aacf84e MD |
8722 | } |
8723 | else if (SCM_COMPLEXP (y)) | |
8724 | { | |
8725 | a = rx; | |
8726 | goto complex_div; | |
8727 | } | |
f92e85f7 | 8728 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8729 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
8730 | else |
8731 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8732 | } |
0aacf84e MD |
8733 | else if (SCM_COMPLEXP (x)) |
8734 | { | |
8735 | double rx = SCM_COMPLEX_REAL (x); | |
8736 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 8737 | if (SCM_I_INUMP (y)) |
0aacf84e | 8738 | { |
e25f3727 | 8739 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8740 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8741 | if (yy == 0) |
8742 | scm_num_overflow (s_divide); | |
8743 | else | |
7351e207 | 8744 | #endif |
0aacf84e MD |
8745 | { |
8746 | double d = yy; | |
8507ec80 | 8747 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
8748 | } |
8749 | } | |
8750 | else if (SCM_BIGP (y)) | |
8751 | { | |
8752 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8753 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8754 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
8755 | } |
8756 | else if (SCM_REALP (y)) | |
8757 | { | |
8758 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8759 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8760 | if (yy == 0.0) |
8761 | scm_num_overflow (s_divide); | |
8762 | else | |
7351e207 | 8763 | #endif |
8507ec80 | 8764 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
8765 | } |
8766 | else if (SCM_COMPLEXP (y)) | |
8767 | { | |
8768 | double ry = SCM_COMPLEX_REAL (y); | |
8769 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8770 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
8771 | { |
8772 | double t = ry / iy; | |
8773 | double d = iy * (1.0 + t * t); | |
8507ec80 | 8774 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
8775 | } |
8776 | else | |
8777 | { | |
8778 | double t = iy / ry; | |
8779 | double d = ry * (1.0 + t * t); | |
8507ec80 | 8780 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
8781 | } |
8782 | } | |
f92e85f7 MV |
8783 | else if (SCM_FRACTIONP (y)) |
8784 | { | |
8785 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 8786 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 8787 | } |
0aacf84e MD |
8788 | else |
8789 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 8790 | } |
f92e85f7 MV |
8791 | else if (SCM_FRACTIONP (x)) |
8792 | { | |
e11e83f3 | 8793 | if (SCM_I_INUMP (y)) |
f92e85f7 | 8794 | { |
e25f3727 | 8795 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
8796 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
8797 | if (yy == 0) | |
8798 | scm_num_overflow (s_divide); | |
8799 | else | |
8800 | #endif | |
cba42c93 | 8801 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8802 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8803 | } | |
8804 | else if (SCM_BIGP (y)) | |
8805 | { | |
cba42c93 | 8806 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8807 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8808 | } | |
8809 | else if (SCM_REALP (y)) | |
8810 | { | |
8811 | double yy = SCM_REAL_VALUE (y); | |
8812 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8813 | if (yy == 0.0) | |
8814 | scm_num_overflow (s_divide); | |
8815 | else | |
8816 | #endif | |
55f26379 | 8817 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
8818 | } |
8819 | else if (SCM_COMPLEXP (y)) | |
8820 | { | |
8821 | a = scm_i_fraction2double (x); | |
8822 | goto complex_div; | |
8823 | } | |
8824 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 8825 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
8826 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
8827 | else | |
8828 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
8829 | } | |
0aacf84e | 8830 | else |
f8de44c1 | 8831 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 8832 | } |
f92e85f7 MV |
8833 | |
8834 | SCM | |
8835 | scm_divide (SCM x, SCM y) | |
8836 | { | |
78d3deb1 | 8837 | return do_divide (x, y, 0); |
f92e85f7 MV |
8838 | } |
8839 | ||
8840 | static SCM scm_divide2real (SCM x, SCM y) | |
8841 | { | |
78d3deb1 | 8842 | return do_divide (x, y, 1); |
f92e85f7 | 8843 | } |
c05e97b7 | 8844 | #undef FUNC_NAME |
0f2d19dd | 8845 | |
fa605590 | 8846 | |
0f2d19dd | 8847 | double |
3101f40f | 8848 | scm_c_truncate (double x) |
0f2d19dd | 8849 | { |
fa605590 KR |
8850 | #if HAVE_TRUNC |
8851 | return trunc (x); | |
8852 | #else | |
f872b822 MD |
8853 | if (x < 0.0) |
8854 | return -floor (-x); | |
8855 | return floor (x); | |
fa605590 | 8856 | #endif |
0f2d19dd | 8857 | } |
0f2d19dd | 8858 | |
3101f40f MV |
8859 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
8860 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
8861 | Then half-way cases are identified and adjusted down if the | |
8862 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
8863 | |
8864 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
8865 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
8866 | ||
8867 | An odd "result" value is identified with result/2 != floor(result/2). | |
8868 | This is done with plus_half, since that value is ready for use sooner in | |
8869 | a pipelined cpu, and we're already requiring plus_half == result. | |
8870 | ||
8871 | Note however that we need to be careful when x is big and already an | |
8872 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
8873 | us to return such a value, incorrectly. For instance if the hardware is | |
8874 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
8875 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
8876 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
8877 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
8878 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
8879 | ||
8880 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
8881 | x is already an integer. If it is then clearly that's the desired result | |
8882 | already. And if it's not then the exponent must be small enough to allow | |
8883 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
8884 | ||
0f2d19dd | 8885 | double |
3101f40f | 8886 | scm_c_round (double x) |
0f2d19dd | 8887 | { |
6187f48b KR |
8888 | double plus_half, result; |
8889 | ||
8890 | if (x == floor (x)) | |
8891 | return x; | |
8892 | ||
8893 | plus_half = x + 0.5; | |
8894 | result = floor (plus_half); | |
3101f40f | 8895 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
8896 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
8897 | ? result - 1 | |
8898 | : result); | |
0f2d19dd JB |
8899 | } |
8900 | ||
f92e85f7 MV |
8901 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
8902 | (SCM x), | |
8903 | "Round the number @var{x} towards zero.") | |
8904 | #define FUNC_NAME s_scm_truncate_number | |
8905 | { | |
73e4de09 | 8906 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
8907 | return scm_floor (x); |
8908 | else | |
8909 | return scm_ceiling (x); | |
8910 | } | |
8911 | #undef FUNC_NAME | |
8912 | ||
f92e85f7 MV |
8913 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, |
8914 | (SCM x), | |
8915 | "Round the number @var{x} towards the nearest integer. " | |
8916 | "When it is exactly halfway between two integers, " | |
8917 | "round towards the even one.") | |
8918 | #define FUNC_NAME s_scm_round_number | |
8919 | { | |
e11e83f3 | 8920 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
8921 | return x; |
8922 | else if (SCM_REALP (x)) | |
3101f40f | 8923 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 8924 | else |
bae30667 KR |
8925 | { |
8926 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
8927 | single quotient+remainder division then examining to see which way | |
8928 | the rounding should go. */ | |
8929 | SCM plus_half = scm_sum (x, exactly_one_half); | |
8930 | SCM result = scm_floor (plus_half); | |
3101f40f | 8931 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
8932 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
8933 | && scm_is_true (scm_odd_p (result))) | |
cff5fa33 | 8934 | return scm_difference (result, SCM_INUM1); |
bae30667 KR |
8935 | else |
8936 | return result; | |
8937 | } | |
f92e85f7 MV |
8938 | } |
8939 | #undef FUNC_NAME | |
8940 | ||
8941 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
8942 | (SCM x), | |
8943 | "Round the number @var{x} towards minus infinity.") | |
8944 | #define FUNC_NAME s_scm_floor | |
8945 | { | |
e11e83f3 | 8946 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8947 | return x; |
8948 | else if (SCM_REALP (x)) | |
55f26379 | 8949 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
8950 | else if (SCM_FRACTIONP (x)) |
8951 | { | |
8952 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
8953 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 8954 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
8955 | { |
8956 | /* For positive x, rounding towards zero is correct. */ | |
8957 | return q; | |
8958 | } | |
8959 | else | |
8960 | { | |
8961 | /* For negative x, we need to return q-1 unless x is an | |
8962 | integer. But fractions are never integer, per our | |
8963 | assumptions. */ | |
cff5fa33 | 8964 | return scm_difference (q, SCM_INUM1); |
f92e85f7 MV |
8965 | } |
8966 | } | |
8967 | else | |
8968 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
8969 | } | |
8970 | #undef FUNC_NAME | |
8971 | ||
8972 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
8973 | (SCM x), | |
8974 | "Round the number @var{x} towards infinity.") | |
8975 | #define FUNC_NAME s_scm_ceiling | |
8976 | { | |
e11e83f3 | 8977 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8978 | return x; |
8979 | else if (SCM_REALP (x)) | |
55f26379 | 8980 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
8981 | else if (SCM_FRACTIONP (x)) |
8982 | { | |
8983 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
8984 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 8985 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
8986 | { |
8987 | /* For negative x, rounding towards zero is correct. */ | |
8988 | return q; | |
8989 | } | |
8990 | else | |
8991 | { | |
8992 | /* For positive x, we need to return q+1 unless x is an | |
8993 | integer. But fractions are never integer, per our | |
8994 | assumptions. */ | |
cff5fa33 | 8995 | return scm_sum (q, SCM_INUM1); |
f92e85f7 MV |
8996 | } |
8997 | } | |
8998 | else | |
8999 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
9000 | } | |
9001 | #undef FUNC_NAME | |
0f2d19dd | 9002 | |
2519490c MW |
9003 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
9004 | (SCM x, SCM y), | |
9005 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 9006 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 9007 | { |
01c7284a MW |
9008 | if (scm_is_integer (y)) |
9009 | { | |
9010 | if (scm_is_true (scm_exact_p (y))) | |
9011 | return scm_integer_expt (x, y); | |
9012 | else | |
9013 | { | |
9014 | /* Here we handle the case where the exponent is an inexact | |
9015 | integer. We make the exponent exact in order to use | |
9016 | scm_integer_expt, and thus avoid the spurious imaginary | |
9017 | parts that may result from round-off errors in the general | |
9018 | e^(y log x) method below (for example when squaring a large | |
9019 | negative number). In this case, we must return an inexact | |
9020 | result for correctness. We also make the base inexact so | |
9021 | that scm_integer_expt will use fast inexact arithmetic | |
9022 | internally. Note that making the base inexact is not | |
9023 | sufficient to guarantee an inexact result, because | |
9024 | scm_integer_expt will return an exact 1 when the exponent | |
9025 | is 0, even if the base is inexact. */ | |
9026 | return scm_exact_to_inexact | |
9027 | (scm_integer_expt (scm_exact_to_inexact (x), | |
9028 | scm_inexact_to_exact (y))); | |
9029 | } | |
9030 | } | |
6fc4d012 AW |
9031 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
9032 | { | |
9033 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
9034 | } | |
2519490c | 9035 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 9036 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c MW |
9037 | else if (scm_is_complex (x)) |
9038 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); | |
9039 | else | |
9040 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); | |
0f2d19dd | 9041 | } |
1bbd0b84 | 9042 | #undef FUNC_NAME |
0f2d19dd | 9043 | |
7f41099e MW |
9044 | /* sin/cos/tan/asin/acos/atan |
9045 | sinh/cosh/tanh/asinh/acosh/atanh | |
9046 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
9047 | Written by Jerry D. Hedden, (C) FSF. | |
9048 | See the file `COPYING' for terms applying to this program. */ | |
9049 | ||
ad79736c AW |
9050 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
9051 | (SCM z), | |
9052 | "Compute the sine of @var{z}.") | |
9053 | #define FUNC_NAME s_scm_sin | |
9054 | { | |
8deddc94 MW |
9055 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9056 | return z; /* sin(exact0) = exact0 */ | |
9057 | else if (scm_is_real (z)) | |
ad79736c AW |
9058 | return scm_from_double (sin (scm_to_double (z))); |
9059 | else if (SCM_COMPLEXP (z)) | |
9060 | { double x, y; | |
9061 | x = SCM_COMPLEX_REAL (z); | |
9062 | y = SCM_COMPLEX_IMAG (z); | |
9063 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
9064 | cos (x) * sinh (y)); | |
9065 | } | |
9066 | else | |
9067 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
9068 | } | |
9069 | #undef FUNC_NAME | |
0f2d19dd | 9070 | |
ad79736c AW |
9071 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
9072 | (SCM z), | |
9073 | "Compute the cosine of @var{z}.") | |
9074 | #define FUNC_NAME s_scm_cos | |
9075 | { | |
8deddc94 MW |
9076 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9077 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
9078 | else if (scm_is_real (z)) | |
ad79736c AW |
9079 | return scm_from_double (cos (scm_to_double (z))); |
9080 | else if (SCM_COMPLEXP (z)) | |
9081 | { double x, y; | |
9082 | x = SCM_COMPLEX_REAL (z); | |
9083 | y = SCM_COMPLEX_IMAG (z); | |
9084 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
9085 | -sin (x) * sinh (y)); | |
9086 | } | |
9087 | else | |
9088 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
9089 | } | |
9090 | #undef FUNC_NAME | |
9091 | ||
9092 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
9093 | (SCM z), | |
9094 | "Compute the tangent of @var{z}.") | |
9095 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 9096 | { |
8deddc94 MW |
9097 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9098 | return z; /* tan(exact0) = exact0 */ | |
9099 | else if (scm_is_real (z)) | |
ad79736c AW |
9100 | return scm_from_double (tan (scm_to_double (z))); |
9101 | else if (SCM_COMPLEXP (z)) | |
9102 | { double x, y, w; | |
9103 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
9104 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
9105 | w = cos (x) + cosh (y); | |
9106 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
9107 | if (w == 0.0) | |
9108 | scm_num_overflow (s_scm_tan); | |
9109 | #endif | |
9110 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
9111 | } | |
9112 | else | |
9113 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
9114 | } | |
9115 | #undef FUNC_NAME | |
9116 | ||
9117 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
9118 | (SCM z), | |
9119 | "Compute the hyperbolic sine of @var{z}.") | |
9120 | #define FUNC_NAME s_scm_sinh | |
9121 | { | |
8deddc94 MW |
9122 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9123 | return z; /* sinh(exact0) = exact0 */ | |
9124 | else if (scm_is_real (z)) | |
ad79736c AW |
9125 | return scm_from_double (sinh (scm_to_double (z))); |
9126 | else if (SCM_COMPLEXP (z)) | |
9127 | { double x, y; | |
9128 | x = SCM_COMPLEX_REAL (z); | |
9129 | y = SCM_COMPLEX_IMAG (z); | |
9130 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
9131 | cosh (x) * sin (y)); | |
9132 | } | |
9133 | else | |
9134 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
9135 | } | |
9136 | #undef FUNC_NAME | |
9137 | ||
9138 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
9139 | (SCM z), | |
9140 | "Compute the hyperbolic cosine of @var{z}.") | |
9141 | #define FUNC_NAME s_scm_cosh | |
9142 | { | |
8deddc94 MW |
9143 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9144 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
9145 | else if (scm_is_real (z)) | |
ad79736c AW |
9146 | return scm_from_double (cosh (scm_to_double (z))); |
9147 | else if (SCM_COMPLEXP (z)) | |
9148 | { double x, y; | |
9149 | x = SCM_COMPLEX_REAL (z); | |
9150 | y = SCM_COMPLEX_IMAG (z); | |
9151 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
9152 | sinh (x) * sin (y)); | |
9153 | } | |
9154 | else | |
9155 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
9156 | } | |
9157 | #undef FUNC_NAME | |
9158 | ||
9159 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
9160 | (SCM z), | |
9161 | "Compute the hyperbolic tangent of @var{z}.") | |
9162 | #define FUNC_NAME s_scm_tanh | |
9163 | { | |
8deddc94 MW |
9164 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9165 | return z; /* tanh(exact0) = exact0 */ | |
9166 | else if (scm_is_real (z)) | |
ad79736c AW |
9167 | return scm_from_double (tanh (scm_to_double (z))); |
9168 | else if (SCM_COMPLEXP (z)) | |
9169 | { double x, y, w; | |
9170 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
9171 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
9172 | w = cosh (x) + cos (y); | |
9173 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
9174 | if (w == 0.0) | |
9175 | scm_num_overflow (s_scm_tanh); | |
9176 | #endif | |
9177 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
9178 | } | |
9179 | else | |
9180 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
9181 | } | |
9182 | #undef FUNC_NAME | |
9183 | ||
9184 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
9185 | (SCM z), | |
9186 | "Compute the arc sine of @var{z}.") | |
9187 | #define FUNC_NAME s_scm_asin | |
9188 | { | |
8deddc94 MW |
9189 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9190 | return z; /* asin(exact0) = exact0 */ | |
9191 | else if (scm_is_real (z)) | |
ad79736c AW |
9192 | { |
9193 | double w = scm_to_double (z); | |
9194 | if (w >= -1.0 && w <= 1.0) | |
9195 | return scm_from_double (asin (w)); | |
9196 | else | |
9197 | return scm_product (scm_c_make_rectangular (0, -1), | |
9198 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
9199 | } | |
9200 | else if (SCM_COMPLEXP (z)) | |
9201 | { double x, y; | |
9202 | x = SCM_COMPLEX_REAL (z); | |
9203 | y = SCM_COMPLEX_IMAG (z); | |
9204 | return scm_product (scm_c_make_rectangular (0, -1), | |
9205 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
9206 | } | |
9207 | else | |
9208 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
9209 | } | |
9210 | #undef FUNC_NAME | |
9211 | ||
9212 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
9213 | (SCM z), | |
9214 | "Compute the arc cosine of @var{z}.") | |
9215 | #define FUNC_NAME s_scm_acos | |
9216 | { | |
8deddc94 MW |
9217 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
9218 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
9219 | else if (scm_is_real (z)) | |
ad79736c AW |
9220 | { |
9221 | double w = scm_to_double (z); | |
9222 | if (w >= -1.0 && w <= 1.0) | |
9223 | return scm_from_double (acos (w)); | |
9224 | else | |
9225 | return scm_sum (scm_from_double (acos (0.0)), | |
9226 | scm_product (scm_c_make_rectangular (0, 1), | |
9227 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
9228 | } | |
9229 | else if (SCM_COMPLEXP (z)) | |
9230 | { double x, y; | |
9231 | x = SCM_COMPLEX_REAL (z); | |
9232 | y = SCM_COMPLEX_IMAG (z); | |
9233 | return scm_sum (scm_from_double (acos (0.0)), | |
9234 | scm_product (scm_c_make_rectangular (0, 1), | |
9235 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
9236 | } | |
9237 | else | |
9238 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
9239 | } | |
9240 | #undef FUNC_NAME | |
9241 | ||
9242 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
9243 | (SCM z, SCM y), | |
9244 | "With one argument, compute the arc tangent of @var{z}.\n" | |
9245 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
9246 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
9247 | #define FUNC_NAME s_scm_atan | |
9248 | { | |
9249 | if (SCM_UNBNDP (y)) | |
9250 | { | |
8deddc94 MW |
9251 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9252 | return z; /* atan(exact0) = exact0 */ | |
9253 | else if (scm_is_real (z)) | |
ad79736c AW |
9254 | return scm_from_double (atan (scm_to_double (z))); |
9255 | else if (SCM_COMPLEXP (z)) | |
9256 | { | |
9257 | double v, w; | |
9258 | v = SCM_COMPLEX_REAL (z); | |
9259 | w = SCM_COMPLEX_IMAG (z); | |
9260 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
9261 | scm_c_make_rectangular (v, w + 1.0))), | |
9262 | scm_c_make_rectangular (0, 2)); | |
9263 | } | |
9264 | else | |
18104cac | 9265 | SCM_WTA_DISPATCH_1 (g_scm_atan, z, SCM_ARG1, s_scm_atan); |
ad79736c AW |
9266 | } |
9267 | else if (scm_is_real (z)) | |
9268 | { | |
9269 | if (scm_is_real (y)) | |
9270 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
9271 | else | |
9272 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
9273 | } | |
9274 | else | |
9275 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
9276 | } | |
9277 | #undef FUNC_NAME | |
9278 | ||
9279 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
9280 | (SCM z), | |
9281 | "Compute the inverse hyperbolic sine of @var{z}.") | |
9282 | #define FUNC_NAME s_scm_sys_asinh | |
9283 | { | |
8deddc94 MW |
9284 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9285 | return z; /* asinh(exact0) = exact0 */ | |
9286 | else if (scm_is_real (z)) | |
ad79736c AW |
9287 | return scm_from_double (asinh (scm_to_double (z))); |
9288 | else if (scm_is_number (z)) | |
9289 | return scm_log (scm_sum (z, | |
9290 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 9291 | SCM_INUM1)))); |
ad79736c AW |
9292 | else |
9293 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
9294 | } | |
9295 | #undef FUNC_NAME | |
9296 | ||
9297 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
9298 | (SCM z), | |
9299 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
9300 | #define FUNC_NAME s_scm_sys_acosh | |
9301 | { | |
8deddc94 MW |
9302 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
9303 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
9304 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
9305 | return scm_from_double (acosh (scm_to_double (z))); |
9306 | else if (scm_is_number (z)) | |
9307 | return scm_log (scm_sum (z, | |
9308 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 9309 | SCM_INUM1)))); |
ad79736c AW |
9310 | else |
9311 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
9312 | } | |
9313 | #undef FUNC_NAME | |
9314 | ||
9315 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
9316 | (SCM z), | |
9317 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
9318 | #define FUNC_NAME s_scm_sys_atanh | |
9319 | { | |
8deddc94 MW |
9320 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
9321 | return z; /* atanh(exact0) = exact0 */ | |
9322 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
9323 | return scm_from_double (atanh (scm_to_double (z))); |
9324 | else if (scm_is_number (z)) | |
cff5fa33 MW |
9325 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
9326 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
9327 | SCM_I_MAKINUM (2)); |
9328 | else | |
9329 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 9330 | } |
1bbd0b84 | 9331 | #undef FUNC_NAME |
0f2d19dd | 9332 | |
8507ec80 MV |
9333 | SCM |
9334 | scm_c_make_rectangular (double re, double im) | |
9335 | { | |
c7218482 | 9336 | SCM z; |
03604fcf | 9337 | |
c7218482 MW |
9338 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
9339 | "complex")); | |
9340 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); | |
9341 | SCM_COMPLEX_REAL (z) = re; | |
9342 | SCM_COMPLEX_IMAG (z) = im; | |
9343 | return z; | |
8507ec80 | 9344 | } |
0f2d19dd | 9345 | |
a1ec6916 | 9346 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
9347 | (SCM real_part, SCM imaginary_part), |
9348 | "Return a complex number constructed of the given @var{real-part} " | |
9349 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 9350 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 9351 | { |
ad79736c AW |
9352 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
9353 | SCM_ARG1, FUNC_NAME, "real"); | |
9354 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
9355 | SCM_ARG2, FUNC_NAME, "real"); | |
c7218482 MW |
9356 | |
9357 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ | |
9358 | if (scm_is_eq (imaginary_part, SCM_INUM0)) | |
9359 | return real_part; | |
9360 | else | |
9361 | return scm_c_make_rectangular (scm_to_double (real_part), | |
9362 | scm_to_double (imaginary_part)); | |
0f2d19dd | 9363 | } |
1bbd0b84 | 9364 | #undef FUNC_NAME |
0f2d19dd | 9365 | |
8507ec80 MV |
9366 | SCM |
9367 | scm_c_make_polar (double mag, double ang) | |
9368 | { | |
9369 | double s, c; | |
5e647d08 LC |
9370 | |
9371 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
9372 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
9373 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
9374 | details. */ | |
9375 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
9376 | sincos (ang, &s, &c); |
9377 | #else | |
9378 | s = sin (ang); | |
9379 | c = cos (ang); | |
9380 | #endif | |
9d427b2c MW |
9381 | |
9382 | /* If s and c are NaNs, this indicates that the angle is a NaN, | |
9383 | infinite, or perhaps simply too large to determine its value | |
9384 | mod 2*pi. However, we know something that the floating-point | |
9385 | implementation doesn't know: We know that s and c are finite. | |
9386 | Therefore, if the magnitude is zero, return a complex zero. | |
9387 | ||
9388 | The reason we check for the NaNs instead of using this case | |
9389 | whenever mag == 0.0 is because when the angle is known, we'd | |
9390 | like to return the correct kind of non-real complex zero: | |
9391 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending | |
9392 | on which quadrant the angle is in. | |
9393 | */ | |
9394 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) | |
9395 | return scm_c_make_rectangular (0.0, 0.0); | |
9396 | else | |
9397 | return scm_c_make_rectangular (mag * c, mag * s); | |
8507ec80 | 9398 | } |
0f2d19dd | 9399 | |
a1ec6916 | 9400 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
c7218482 MW |
9401 | (SCM mag, SCM ang), |
9402 | "Return the complex number @var{mag} * e^(i * @var{ang}).") | |
1bbd0b84 | 9403 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 9404 | { |
c7218482 MW |
9405 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
9406 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); | |
9407 | ||
9408 | /* If mag is exact0, return exact0 */ | |
9409 | if (scm_is_eq (mag, SCM_INUM0)) | |
9410 | return SCM_INUM0; | |
9411 | /* Return a real if ang is exact0 */ | |
9412 | else if (scm_is_eq (ang, SCM_INUM0)) | |
9413 | return mag; | |
9414 | else | |
9415 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); | |
0f2d19dd | 9416 | } |
1bbd0b84 | 9417 | #undef FUNC_NAME |
0f2d19dd JB |
9418 | |
9419 | ||
2519490c MW |
9420 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
9421 | (SCM z), | |
9422 | "Return the real part of the number @var{z}.") | |
9423 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 9424 | { |
2519490c | 9425 | if (SCM_COMPLEXP (z)) |
55f26379 | 9426 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 9427 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 9428 | return z; |
0aacf84e | 9429 | else |
2519490c | 9430 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 9431 | } |
2519490c | 9432 | #undef FUNC_NAME |
0f2d19dd JB |
9433 | |
9434 | ||
2519490c MW |
9435 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
9436 | (SCM z), | |
9437 | "Return the imaginary part of the number @var{z}.") | |
9438 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 9439 | { |
2519490c MW |
9440 | if (SCM_COMPLEXP (z)) |
9441 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
c7218482 | 9442 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 9443 | return SCM_INUM0; |
0aacf84e | 9444 | else |
2519490c | 9445 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 9446 | } |
2519490c | 9447 | #undef FUNC_NAME |
0f2d19dd | 9448 | |
2519490c MW |
9449 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
9450 | (SCM z), | |
9451 | "Return the numerator of the number @var{z}.") | |
9452 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 9453 | { |
2519490c | 9454 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
9455 | return z; |
9456 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 9457 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
9458 | else if (SCM_REALP (z)) |
9459 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
9460 | else | |
2519490c | 9461 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 9462 | } |
2519490c | 9463 | #undef FUNC_NAME |
f92e85f7 MV |
9464 | |
9465 | ||
2519490c MW |
9466 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
9467 | (SCM z), | |
9468 | "Return the denominator of the number @var{z}.") | |
9469 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 9470 | { |
2519490c | 9471 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 9472 | return SCM_INUM1; |
f92e85f7 | 9473 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 9474 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
9475 | else if (SCM_REALP (z)) |
9476 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
9477 | else | |
2519490c | 9478 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
f92e85f7 | 9479 | } |
2519490c | 9480 | #undef FUNC_NAME |
0f2d19dd | 9481 | |
2519490c MW |
9482 | |
9483 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
9484 | (SCM z), | |
9485 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
9486 | "@code{abs} for real arguments, but also allows complex numbers.") | |
9487 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 9488 | { |
e11e83f3 | 9489 | if (SCM_I_INUMP (z)) |
0aacf84e | 9490 | { |
e25f3727 | 9491 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
9492 | if (zz >= 0) |
9493 | return z; | |
9494 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 9495 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 9496 | else |
e25f3727 | 9497 | return scm_i_inum2big (-zz); |
5986c47d | 9498 | } |
0aacf84e MD |
9499 | else if (SCM_BIGP (z)) |
9500 | { | |
9501 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
9502 | scm_remember_upto_here_1 (z); | |
9503 | if (sgn < 0) | |
9504 | return scm_i_clonebig (z, 0); | |
9505 | else | |
9506 | return z; | |
5986c47d | 9507 | } |
0aacf84e | 9508 | else if (SCM_REALP (z)) |
55f26379 | 9509 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 9510 | else if (SCM_COMPLEXP (z)) |
55f26379 | 9511 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
9512 | else if (SCM_FRACTIONP (z)) |
9513 | { | |
73e4de09 | 9514 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 9515 | return z; |
cba42c93 | 9516 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
9517 | SCM_FRACTION_DENOMINATOR (z)); |
9518 | } | |
0aacf84e | 9519 | else |
2519490c | 9520 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
0f2d19dd | 9521 | } |
2519490c | 9522 | #undef FUNC_NAME |
0f2d19dd JB |
9523 | |
9524 | ||
2519490c MW |
9525 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
9526 | (SCM z), | |
9527 | "Return the angle of the complex number @var{z}.") | |
9528 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 9529 | { |
c8ae173e | 9530 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 9531 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
9532 | But if atan2 follows the floating point rounding mode, then the value |
9533 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 9534 | if (SCM_I_INUMP (z)) |
0aacf84e | 9535 | { |
e11e83f3 | 9536 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 9537 | return flo0; |
0aacf84e | 9538 | else |
55f26379 | 9539 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 9540 | } |
0aacf84e MD |
9541 | else if (SCM_BIGP (z)) |
9542 | { | |
9543 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
9544 | scm_remember_upto_here_1 (z); | |
9545 | if (sgn < 0) | |
55f26379 | 9546 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 9547 | else |
e7efe8e7 | 9548 | return flo0; |
0f2d19dd | 9549 | } |
0aacf84e | 9550 | else if (SCM_REALP (z)) |
c8ae173e KR |
9551 | { |
9552 | if (SCM_REAL_VALUE (z) >= 0) | |
e7efe8e7 | 9553 | return flo0; |
c8ae173e | 9554 | else |
55f26379 | 9555 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 9556 | } |
0aacf84e | 9557 | else if (SCM_COMPLEXP (z)) |
55f26379 | 9558 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
9559 | else if (SCM_FRACTIONP (z)) |
9560 | { | |
73e4de09 | 9561 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 9562 | return flo0; |
55f26379 | 9563 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 9564 | } |
0aacf84e | 9565 | else |
2519490c | 9566 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 9567 | } |
2519490c | 9568 | #undef FUNC_NAME |
0f2d19dd JB |
9569 | |
9570 | ||
2519490c MW |
9571 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
9572 | (SCM z), | |
9573 | "Convert the number @var{z} to its inexact representation.\n") | |
9574 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 9575 | { |
e11e83f3 | 9576 | if (SCM_I_INUMP (z)) |
55f26379 | 9577 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 9578 | else if (SCM_BIGP (z)) |
55f26379 | 9579 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 9580 | else if (SCM_FRACTIONP (z)) |
55f26379 | 9581 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
9582 | else if (SCM_INEXACTP (z)) |
9583 | return z; | |
9584 | else | |
2519490c | 9585 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
3c9a524f | 9586 | } |
2519490c | 9587 | #undef FUNC_NAME |
3c9a524f DH |
9588 | |
9589 | ||
2519490c MW |
9590 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
9591 | (SCM z), | |
9592 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 9593 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 9594 | { |
c7218482 | 9595 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f872b822 | 9596 | return z; |
c7218482 | 9597 | else |
0aacf84e | 9598 | { |
c7218482 MW |
9599 | double val; |
9600 | ||
9601 | if (SCM_REALP (z)) | |
9602 | val = SCM_REAL_VALUE (z); | |
9603 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) | |
9604 | val = SCM_COMPLEX_REAL (z); | |
9605 | else | |
9606 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); | |
9607 | ||
9608 | if (!SCM_LIKELY (DOUBLE_IS_FINITE (val))) | |
f92e85f7 | 9609 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 9610 | else |
f92e85f7 MV |
9611 | { |
9612 | mpq_t frac; | |
9613 | SCM q; | |
9614 | ||
9615 | mpq_init (frac); | |
c7218482 | 9616 | mpq_set_d (frac, val); |
cba42c93 | 9617 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
c7218482 | 9618 | scm_i_mpz2num (mpq_denref (frac))); |
f92e85f7 | 9619 | |
cba42c93 | 9620 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
9621 | for frac... |
9622 | */ | |
9623 | mpq_clear (frac); | |
9624 | return q; | |
9625 | } | |
c2ff8ab0 | 9626 | } |
0f2d19dd | 9627 | } |
1bbd0b84 | 9628 | #undef FUNC_NAME |
0f2d19dd | 9629 | |
f92e85f7 | 9630 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
9631 | (SCM x, SCM eps), |
9632 | "Returns the @emph{simplest} rational number differing\n" | |
9633 | "from @var{x} by no more than @var{eps}.\n" | |
9634 | "\n" | |
9635 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
9636 | "exact result when both its arguments are exact. Thus, you might need\n" | |
9637 | "to use @code{inexact->exact} on the arguments.\n" | |
9638 | "\n" | |
9639 | "@lisp\n" | |
9640 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
9641 | "@result{} 6/5\n" | |
9642 | "@end lisp") | |
f92e85f7 MV |
9643 | #define FUNC_NAME s_scm_rationalize |
9644 | { | |
605f6980 MW |
9645 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
9646 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
9647 | eps = scm_abs (eps); | |
9648 | if (scm_is_false (scm_positive_p (eps))) | |
9649 | { | |
9650 | /* eps is either zero or a NaN */ | |
9651 | if (scm_is_true (scm_nan_p (eps))) | |
9652 | return scm_nan (); | |
9653 | else if (SCM_INEXACTP (eps)) | |
9654 | return scm_exact_to_inexact (x); | |
9655 | else | |
9656 | return x; | |
9657 | } | |
9658 | else if (scm_is_false (scm_finite_p (eps))) | |
9659 | { | |
9660 | if (scm_is_true (scm_finite_p (x))) | |
9661 | return flo0; | |
9662 | else | |
9663 | return scm_nan (); | |
9664 | } | |
9665 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 9666 | return x; |
605f6980 MW |
9667 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
9668 | scm_ceiling (scm_difference (x, eps))))) | |
9669 | { | |
9670 | /* There's an integer within range; we want the one closest to zero */ | |
9671 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
9672 | { | |
9673 | /* zero is within range */ | |
9674 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
9675 | return flo0; | |
9676 | else | |
9677 | return SCM_INUM0; | |
9678 | } | |
9679 | else if (scm_is_true (scm_positive_p (x))) | |
9680 | return scm_ceiling (scm_difference (x, eps)); | |
9681 | else | |
9682 | return scm_floor (scm_sum (x, eps)); | |
9683 | } | |
9684 | else | |
f92e85f7 MV |
9685 | { |
9686 | /* Use continued fractions to find closest ratio. All | |
9687 | arithmetic is done with exact numbers. | |
9688 | */ | |
9689 | ||
9690 | SCM ex = scm_inexact_to_exact (x); | |
9691 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
9692 | SCM tt = SCM_INUM1; |
9693 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
9694 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
9695 | SCM rx; |
9696 | int i = 0; | |
9697 | ||
f92e85f7 MV |
9698 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
9699 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
9700 | ||
9701 | /* We stop after a million iterations just to be absolutely sure | |
9702 | that we don't go into an infinite loop. The process normally | |
9703 | converges after less than a dozen iterations. | |
9704 | */ | |
9705 | ||
f92e85f7 MV |
9706 | while (++i < 1000000) |
9707 | { | |
9708 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
9709 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
9710 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
9711 | scm_is_false | |
f92e85f7 | 9712 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 9713 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
9714 | { |
9715 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 9716 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
9717 | return scm_exact_to_inexact (res); |
9718 | else | |
9719 | return res; | |
9720 | } | |
f92e85f7 MV |
9721 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
9722 | SCM_UNDEFINED); | |
9723 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
9724 | a2 = a1; | |
9725 | b2 = b1; | |
9726 | a1 = a; | |
9727 | b1 = b; | |
9728 | } | |
9729 | scm_num_overflow (s_scm_rationalize); | |
9730 | } | |
f92e85f7 MV |
9731 | } |
9732 | #undef FUNC_NAME | |
9733 | ||
73e4de09 MV |
9734 | /* conversion functions */ |
9735 | ||
9736 | int | |
9737 | scm_is_integer (SCM val) | |
9738 | { | |
9739 | return scm_is_true (scm_integer_p (val)); | |
9740 | } | |
9741 | ||
9742 | int | |
9743 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
9744 | { | |
e11e83f3 | 9745 | if (SCM_I_INUMP (val)) |
73e4de09 | 9746 | { |
e11e83f3 | 9747 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9748 | return n >= min && n <= max; |
9749 | } | |
9750 | else if (SCM_BIGP (val)) | |
9751 | { | |
9752 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
9753 | return 0; | |
9754 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
9755 | { |
9756 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
9757 | { | |
9758 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
9759 | return n >= min && n <= max; | |
9760 | } | |
9761 | else | |
9762 | return 0; | |
9763 | } | |
73e4de09 MV |
9764 | else |
9765 | { | |
d956fa6f MV |
9766 | scm_t_intmax n; |
9767 | size_t count; | |
73e4de09 | 9768 | |
d956fa6f MV |
9769 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9770 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
9771 | return 0; | |
9772 | ||
9773 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9774 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9775 | |
d956fa6f | 9776 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 9777 | { |
d956fa6f MV |
9778 | if (n < 0) |
9779 | return 0; | |
73e4de09 | 9780 | } |
73e4de09 MV |
9781 | else |
9782 | { | |
d956fa6f MV |
9783 | n = -n; |
9784 | if (n >= 0) | |
9785 | return 0; | |
73e4de09 | 9786 | } |
d956fa6f MV |
9787 | |
9788 | return n >= min && n <= max; | |
73e4de09 MV |
9789 | } |
9790 | } | |
73e4de09 MV |
9791 | else |
9792 | return 0; | |
9793 | } | |
9794 | ||
9795 | int | |
9796 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
9797 | { | |
e11e83f3 | 9798 | if (SCM_I_INUMP (val)) |
73e4de09 | 9799 | { |
e11e83f3 | 9800 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9801 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
9802 | } | |
9803 | else if (SCM_BIGP (val)) | |
9804 | { | |
9805 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
9806 | return 0; | |
9807 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
9808 | { |
9809 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
9810 | { | |
9811 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
9812 | return n >= min && n <= max; | |
9813 | } | |
9814 | else | |
9815 | return 0; | |
9816 | } | |
73e4de09 MV |
9817 | else |
9818 | { | |
d956fa6f MV |
9819 | scm_t_uintmax n; |
9820 | size_t count; | |
73e4de09 | 9821 | |
d956fa6f MV |
9822 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
9823 | return 0; | |
73e4de09 | 9824 | |
d956fa6f MV |
9825 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9826 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 9827 | return 0; |
d956fa6f MV |
9828 | |
9829 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9830 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9831 | |
d956fa6f | 9832 | return n >= min && n <= max; |
73e4de09 MV |
9833 | } |
9834 | } | |
73e4de09 MV |
9835 | else |
9836 | return 0; | |
9837 | } | |
9838 | ||
1713d319 MV |
9839 | static void |
9840 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
9841 | { | |
9842 | scm_error (scm_out_of_range_key, | |
9843 | NULL, | |
9844 | "Value out of range ~S to ~S: ~S", | |
9845 | scm_list_3 (min, max, bad_val), | |
9846 | scm_list_1 (bad_val)); | |
9847 | } | |
9848 | ||
bfd7932e MV |
9849 | #define TYPE scm_t_intmax |
9850 | #define TYPE_MIN min | |
9851 | #define TYPE_MAX max | |
9852 | #define SIZEOF_TYPE 0 | |
9853 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
9854 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
9855 | #include "libguile/conv-integer.i.c" | |
9856 | ||
9857 | #define TYPE scm_t_uintmax | |
9858 | #define TYPE_MIN min | |
9859 | #define TYPE_MAX max | |
9860 | #define SIZEOF_TYPE 0 | |
9861 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
9862 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
9863 | #include "libguile/conv-uinteger.i.c" | |
9864 | ||
9865 | #define TYPE scm_t_int8 | |
9866 | #define TYPE_MIN SCM_T_INT8_MIN | |
9867 | #define TYPE_MAX SCM_T_INT8_MAX | |
9868 | #define SIZEOF_TYPE 1 | |
9869 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
9870 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
9871 | #include "libguile/conv-integer.i.c" | |
9872 | ||
9873 | #define TYPE scm_t_uint8 | |
9874 | #define TYPE_MIN 0 | |
9875 | #define TYPE_MAX SCM_T_UINT8_MAX | |
9876 | #define SIZEOF_TYPE 1 | |
9877 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
9878 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
9879 | #include "libguile/conv-uinteger.i.c" | |
9880 | ||
9881 | #define TYPE scm_t_int16 | |
9882 | #define TYPE_MIN SCM_T_INT16_MIN | |
9883 | #define TYPE_MAX SCM_T_INT16_MAX | |
9884 | #define SIZEOF_TYPE 2 | |
9885 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
9886 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
9887 | #include "libguile/conv-integer.i.c" | |
9888 | ||
9889 | #define TYPE scm_t_uint16 | |
9890 | #define TYPE_MIN 0 | |
9891 | #define TYPE_MAX SCM_T_UINT16_MAX | |
9892 | #define SIZEOF_TYPE 2 | |
9893 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
9894 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
9895 | #include "libguile/conv-uinteger.i.c" | |
9896 | ||
9897 | #define TYPE scm_t_int32 | |
9898 | #define TYPE_MIN SCM_T_INT32_MIN | |
9899 | #define TYPE_MAX SCM_T_INT32_MAX | |
9900 | #define SIZEOF_TYPE 4 | |
9901 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
9902 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
9903 | #include "libguile/conv-integer.i.c" | |
9904 | ||
9905 | #define TYPE scm_t_uint32 | |
9906 | #define TYPE_MIN 0 | |
9907 | #define TYPE_MAX SCM_T_UINT32_MAX | |
9908 | #define SIZEOF_TYPE 4 | |
9909 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
9910 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
9911 | #include "libguile/conv-uinteger.i.c" | |
9912 | ||
904a78f1 MG |
9913 | #define TYPE scm_t_wchar |
9914 | #define TYPE_MIN (scm_t_int32)-1 | |
9915 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
9916 | #define SIZEOF_TYPE 4 | |
9917 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
9918 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
9919 | #include "libguile/conv-integer.i.c" | |
9920 | ||
bfd7932e MV |
9921 | #define TYPE scm_t_int64 |
9922 | #define TYPE_MIN SCM_T_INT64_MIN | |
9923 | #define TYPE_MAX SCM_T_INT64_MAX | |
9924 | #define SIZEOF_TYPE 8 | |
9925 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
9926 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
9927 | #include "libguile/conv-integer.i.c" | |
9928 | ||
9929 | #define TYPE scm_t_uint64 | |
9930 | #define TYPE_MIN 0 | |
9931 | #define TYPE_MAX SCM_T_UINT64_MAX | |
9932 | #define SIZEOF_TYPE 8 | |
9933 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
9934 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
9935 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 9936 | |
cd036260 MV |
9937 | void |
9938 | scm_to_mpz (SCM val, mpz_t rop) | |
9939 | { | |
9940 | if (SCM_I_INUMP (val)) | |
9941 | mpz_set_si (rop, SCM_I_INUM (val)); | |
9942 | else if (SCM_BIGP (val)) | |
9943 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
9944 | else | |
9945 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
9946 | } | |
9947 | ||
9948 | SCM | |
9949 | scm_from_mpz (mpz_t val) | |
9950 | { | |
9951 | return scm_i_mpz2num (val); | |
9952 | } | |
9953 | ||
73e4de09 MV |
9954 | int |
9955 | scm_is_real (SCM val) | |
9956 | { | |
9957 | return scm_is_true (scm_real_p (val)); | |
9958 | } | |
9959 | ||
55f26379 MV |
9960 | int |
9961 | scm_is_rational (SCM val) | |
9962 | { | |
9963 | return scm_is_true (scm_rational_p (val)); | |
9964 | } | |
9965 | ||
73e4de09 MV |
9966 | double |
9967 | scm_to_double (SCM val) | |
9968 | { | |
55f26379 MV |
9969 | if (SCM_I_INUMP (val)) |
9970 | return SCM_I_INUM (val); | |
9971 | else if (SCM_BIGP (val)) | |
9972 | return scm_i_big2dbl (val); | |
9973 | else if (SCM_FRACTIONP (val)) | |
9974 | return scm_i_fraction2double (val); | |
9975 | else if (SCM_REALP (val)) | |
9976 | return SCM_REAL_VALUE (val); | |
9977 | else | |
7a1aba42 | 9978 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
9979 | } |
9980 | ||
9981 | SCM | |
9982 | scm_from_double (double val) | |
9983 | { | |
978c52d1 LC |
9984 | SCM z; |
9985 | ||
9986 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
9987 | ||
9988 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 9989 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 9990 | |
55f26379 | 9991 | return z; |
73e4de09 MV |
9992 | } |
9993 | ||
220058a8 | 9994 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
9995 | |
9996 | float | |
e25f3727 | 9997 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9998 | { |
220058a8 AW |
9999 | scm_c_issue_deprecation_warning |
10000 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
10001 | ||
55f26379 MV |
10002 | if (SCM_BIGP (num)) |
10003 | { | |
10004 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 10005 | if (!isinf (res)) |
55f26379 MV |
10006 | return res; |
10007 | else | |
10008 | scm_out_of_range (NULL, num); | |
10009 | } | |
10010 | else | |
10011 | return scm_to_double (num); | |
10012 | } | |
10013 | ||
10014 | double | |
e25f3727 | 10015 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 10016 | { |
220058a8 AW |
10017 | scm_c_issue_deprecation_warning |
10018 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
10019 | ||
55f26379 MV |
10020 | if (SCM_BIGP (num)) |
10021 | { | |
10022 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 10023 | if (!isinf (res)) |
55f26379 MV |
10024 | return res; |
10025 | else | |
10026 | scm_out_of_range (NULL, num); | |
10027 | } | |
10028 | else | |
10029 | return scm_to_double (num); | |
10030 | } | |
10031 | ||
10032 | #endif | |
10033 | ||
8507ec80 MV |
10034 | int |
10035 | scm_is_complex (SCM val) | |
10036 | { | |
10037 | return scm_is_true (scm_complex_p (val)); | |
10038 | } | |
10039 | ||
10040 | double | |
10041 | scm_c_real_part (SCM z) | |
10042 | { | |
10043 | if (SCM_COMPLEXP (z)) | |
10044 | return SCM_COMPLEX_REAL (z); | |
10045 | else | |
10046 | { | |
10047 | /* Use the scm_real_part to get proper error checking and | |
10048 | dispatching. | |
10049 | */ | |
10050 | return scm_to_double (scm_real_part (z)); | |
10051 | } | |
10052 | } | |
10053 | ||
10054 | double | |
10055 | scm_c_imag_part (SCM z) | |
10056 | { | |
10057 | if (SCM_COMPLEXP (z)) | |
10058 | return SCM_COMPLEX_IMAG (z); | |
10059 | else | |
10060 | { | |
10061 | /* Use the scm_imag_part to get proper error checking and | |
10062 | dispatching. The result will almost always be 0.0, but not | |
10063 | always. | |
10064 | */ | |
10065 | return scm_to_double (scm_imag_part (z)); | |
10066 | } | |
10067 | } | |
10068 | ||
10069 | double | |
10070 | scm_c_magnitude (SCM z) | |
10071 | { | |
10072 | return scm_to_double (scm_magnitude (z)); | |
10073 | } | |
10074 | ||
10075 | double | |
10076 | scm_c_angle (SCM z) | |
10077 | { | |
10078 | return scm_to_double (scm_angle (z)); | |
10079 | } | |
10080 | ||
10081 | int | |
10082 | scm_is_number (SCM z) | |
10083 | { | |
10084 | return scm_is_true (scm_number_p (z)); | |
10085 | } | |
10086 | ||
8ab3d8a0 KR |
10087 | |
10088 | /* In the following functions we dispatch to the real-arg funcs like log() | |
10089 | when we know the arg is real, instead of just handing everything to | |
10090 | clog() for instance. This is in case clog() doesn't optimize for a | |
10091 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
10092 | well use it to go straight to the applicable C func. */ | |
10093 | ||
2519490c MW |
10094 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
10095 | (SCM z), | |
10096 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
10097 | #define FUNC_NAME s_scm_log |
10098 | { | |
10099 | if (SCM_COMPLEXP (z)) | |
10100 | { | |
4b26c03e | 10101 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
10102 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
10103 | #else | |
10104 | double re = SCM_COMPLEX_REAL (z); | |
10105 | double im = SCM_COMPLEX_IMAG (z); | |
10106 | return scm_c_make_rectangular (log (hypot (re, im)), | |
10107 | atan2 (im, re)); | |
10108 | #endif | |
10109 | } | |
2519490c | 10110 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
10111 | { |
10112 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
10113 | although the value itself overflows. */ | |
10114 | double re = scm_to_double (z); | |
10115 | double l = log (fabs (re)); | |
10116 | if (re >= 0.0) | |
10117 | return scm_from_double (l); | |
10118 | else | |
10119 | return scm_c_make_rectangular (l, M_PI); | |
10120 | } | |
2519490c MW |
10121 | else |
10122 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); | |
8ab3d8a0 KR |
10123 | } |
10124 | #undef FUNC_NAME | |
10125 | ||
10126 | ||
2519490c MW |
10127 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
10128 | (SCM z), | |
10129 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
10130 | #define FUNC_NAME s_scm_log10 |
10131 | { | |
10132 | if (SCM_COMPLEXP (z)) | |
10133 | { | |
10134 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
10135 | clog() and a multiply by M_LOG10E, rather than the fallback | |
10136 | log10+hypot+atan2.) */ | |
f328f862 LC |
10137 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
10138 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
10139 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
10140 | #else | |
10141 | double re = SCM_COMPLEX_REAL (z); | |
10142 | double im = SCM_COMPLEX_IMAG (z); | |
10143 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
10144 | M_LOG10E * atan2 (im, re)); | |
10145 | #endif | |
10146 | } | |
2519490c | 10147 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
10148 | { |
10149 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
10150 | although the value itself overflows. */ | |
10151 | double re = scm_to_double (z); | |
10152 | double l = log10 (fabs (re)); | |
10153 | if (re >= 0.0) | |
10154 | return scm_from_double (l); | |
10155 | else | |
10156 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
10157 | } | |
2519490c MW |
10158 | else |
10159 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); | |
8ab3d8a0 KR |
10160 | } |
10161 | #undef FUNC_NAME | |
10162 | ||
10163 | ||
2519490c MW |
10164 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
10165 | (SCM z), | |
10166 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
10167 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
10168 | #define FUNC_NAME s_scm_exp |
10169 | { | |
10170 | if (SCM_COMPLEXP (z)) | |
10171 | { | |
4b26c03e | 10172 | #if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
10173 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
10174 | #else | |
10175 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
10176 | SCM_COMPLEX_IMAG (z)); | |
10177 | #endif | |
10178 | } | |
2519490c | 10179 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
10180 | { |
10181 | /* When z is a negative bignum the conversion to double overflows, | |
10182 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
10183 | return scm_from_double (exp (scm_to_double (z))); | |
10184 | } | |
2519490c MW |
10185 | else |
10186 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); | |
8ab3d8a0 KR |
10187 | } |
10188 | #undef FUNC_NAME | |
10189 | ||
10190 | ||
2519490c MW |
10191 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
10192 | (SCM z), | |
10193 | "Return the square root of @var{z}. Of the two possible roots\n" | |
ffb62a43 | 10194 | "(positive and negative), the one with positive real part\n" |
2519490c MW |
10195 | "is returned, or if that's zero then a positive imaginary part.\n" |
10196 | "Thus,\n" | |
10197 | "\n" | |
10198 | "@example\n" | |
10199 | "(sqrt 9.0) @result{} 3.0\n" | |
10200 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
10201 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
10202 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
10203 | "@end example") | |
8ab3d8a0 KR |
10204 | #define FUNC_NAME s_scm_sqrt |
10205 | { | |
2519490c | 10206 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 10207 | { |
f328f862 LC |
10208 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
10209 | && defined SCM_COMPLEX_VALUE | |
2519490c | 10210 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 10211 | #else |
2519490c MW |
10212 | double re = SCM_COMPLEX_REAL (z); |
10213 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
10214 | return scm_c_make_polar (sqrt (hypot (re, im)), |
10215 | 0.5 * atan2 (im, re)); | |
10216 | #endif | |
10217 | } | |
2519490c | 10218 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 10219 | { |
2519490c | 10220 | double xx = scm_to_double (z); |
8ab3d8a0 KR |
10221 | if (xx < 0) |
10222 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
10223 | else | |
10224 | return scm_from_double (sqrt (xx)); | |
10225 | } | |
2519490c MW |
10226 | else |
10227 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); | |
8ab3d8a0 KR |
10228 | } |
10229 | #undef FUNC_NAME | |
10230 | ||
10231 | ||
10232 | ||
0f2d19dd JB |
10233 | void |
10234 | scm_init_numbers () | |
0f2d19dd | 10235 | { |
0b799eea MV |
10236 | int i; |
10237 | ||
713a4259 KR |
10238 | mpz_init_set_si (z_negative_one, -1); |
10239 | ||
a261c0e9 DH |
10240 | /* It may be possible to tune the performance of some algorithms by using |
10241 | * the following constants to avoid the creation of bignums. Please, before | |
10242 | * using these values, remember the two rules of program optimization: | |
10243 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 10244 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 10245 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 10246 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 10247 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 10248 | |
f3ae5d60 MD |
10249 | scm_add_feature ("complex"); |
10250 | scm_add_feature ("inexact"); | |
e7efe8e7 | 10251 | flo0 = scm_from_double (0.0); |
0b799eea MV |
10252 | |
10253 | /* determine floating point precision */ | |
55f26379 | 10254 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
10255 | { |
10256 | init_dblprec(&scm_dblprec[i-2],i); | |
10257 | init_fx_radix(fx_per_radix[i-2],i); | |
10258 | } | |
f872b822 | 10259 | #ifdef DBL_DIG |
0b799eea | 10260 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 10261 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 10262 | #endif |
1be6b49c | 10263 | |
cff5fa33 | 10264 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 10265 | #include "libguile/numbers.x" |
0f2d19dd | 10266 | } |
89e00824 ML |
10267 | |
10268 | /* | |
10269 | Local Variables: | |
10270 | c-file-style: "gnu" | |
10271 | End: | |
10272 | */ |