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 | ||
bbec4602 LC |
48 | #include <verify.h> |
49 | ||
0f2d19dd | 50 | #include <math.h> |
fc194577 | 51 | #include <string.h> |
3f47e526 MG |
52 | #include <unicase.h> |
53 | #include <unictype.h> | |
f92e85f7 | 54 | |
8ab3d8a0 KR |
55 | #if HAVE_COMPLEX_H |
56 | #include <complex.h> | |
57 | #endif | |
58 | ||
a0599745 | 59 | #include "libguile/_scm.h" |
a0599745 MD |
60 | #include "libguile/feature.h" |
61 | #include "libguile/ports.h" | |
62 | #include "libguile/root.h" | |
63 | #include "libguile/smob.h" | |
64 | #include "libguile/strings.h" | |
864e7d42 | 65 | #include "libguile/bdw-gc.h" |
a0599745 MD |
66 | |
67 | #include "libguile/validate.h" | |
68 | #include "libguile/numbers.h" | |
1be6b49c | 69 | #include "libguile/deprecation.h" |
f4c627b3 | 70 | |
f92e85f7 MV |
71 | #include "libguile/eq.h" |
72 | ||
8ab3d8a0 KR |
73 | /* values per glibc, if not already defined */ |
74 | #ifndef M_LOG10E | |
75 | #define M_LOG10E 0.43429448190325182765 | |
76 | #endif | |
85bdb6ac MW |
77 | #ifndef M_LN2 |
78 | #define M_LN2 0.69314718055994530942 | |
79 | #endif | |
8ab3d8a0 KR |
80 | #ifndef M_PI |
81 | #define M_PI 3.14159265358979323846 | |
82 | #endif | |
83 | ||
e25f3727 AW |
84 | typedef scm_t_signed_bits scm_t_inum; |
85 | #define scm_from_inum(x) (scm_from_signed_integer (x)) | |
86 | ||
7112615f MW |
87 | /* Tests to see if a C double is neither infinite nor a NaN. |
88 | TODO: if it's available, use C99's isfinite(x) instead */ | |
89 | #define DOUBLE_IS_FINITE(x) (!isinf(x) && !isnan(x)) | |
90 | ||
041fccf6 MW |
91 | /* On some platforms, isinf(x) returns 0, 1 or -1, indicating the sign |
92 | of the infinity, but other platforms return a boolean only. */ | |
93 | #define DOUBLE_IS_POSITIVE_INFINITY(x) (isinf(x) && ((x) > 0)) | |
94 | #define DOUBLE_IS_NEGATIVE_INFINITY(x) (isinf(x) && ((x) < 0)) | |
95 | ||
0f2d19dd | 96 | \f |
f4c627b3 | 97 | |
ca46fb90 RB |
98 | /* |
99 | Wonder if this might be faster for some of our code? A switch on | |
100 | the numtag would jump directly to the right case, and the | |
101 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
102 | ||
103 | #define SCM_I_NUMTAG_NOTNUM 0 | |
104 | #define SCM_I_NUMTAG_INUM 1 | |
105 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
106 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
107 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
108 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 109 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 110 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 111 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
112 | : SCM_I_NUMTAG_NOTNUM))) |
113 | */ | |
f92e85f7 | 114 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
115 | |
116 | ||
e7efe8e7 | 117 | static SCM flo0; |
ff62c168 | 118 | static SCM exactly_one_half; |
a5f6b751 | 119 | static SCM flo_log10e; |
e7efe8e7 | 120 | |
34d19ef6 | 121 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 122 | |
56e55ac7 | 123 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
124 | * printed or scm_string representation of an inexact number. |
125 | */ | |
0b799eea | 126 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 127 | |
b127c712 | 128 | |
ad79736c AW |
129 | #if !defined (HAVE_ASINH) |
130 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } | |
131 | #endif | |
132 | #if !defined (HAVE_ACOSH) | |
133 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } | |
134 | #endif | |
135 | #if !defined (HAVE_ATANH) | |
136 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } | |
137 | #endif | |
138 | ||
18d78c5e MW |
139 | /* mpz_cmp_d in GMP before 4.2 didn't recognise infinities, so |
140 | xmpz_cmp_d uses an explicit check. Starting with GMP 4.2 (released | |
141 | in March 2006), mpz_cmp_d now handles infinities properly. */ | |
f8a8200b | 142 | #if 1 |
b127c712 | 143 | #define xmpz_cmp_d(z, d) \ |
2e65b52f | 144 | (isinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) |
b127c712 KR |
145 | #else |
146 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
147 | #endif | |
148 | ||
f92e85f7 | 149 | |
4b26c03e | 150 | #if defined (GUILE_I) |
03976fee | 151 | #if defined HAVE_COMPLEX_DOUBLE |
8ab3d8a0 KR |
152 | |
153 | /* For an SCM object Z which is a complex number (ie. satisfies | |
154 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
155 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 156 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 157 | |
7a35784c | 158 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
8ab3d8a0 KR |
159 | |
160 | /* Convert a C "complex double" to an SCM value. */ | |
7a35784c | 161 | static inline SCM |
8ab3d8a0 KR |
162 | scm_from_complex_double (complex double z) |
163 | { | |
164 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
165 | } | |
bca69a9f | 166 | |
8ab3d8a0 | 167 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 168 | #endif /* GUILE_I */ |
8ab3d8a0 | 169 | |
0f2d19dd JB |
170 | \f |
171 | ||
713a4259 | 172 | static mpz_t z_negative_one; |
ac0c002c DH |
173 | |
174 | \f | |
864e7d42 LC |
175 | /* Clear the `mpz_t' embedded in bignum PTR. */ |
176 | static void | |
177 | finalize_bignum (GC_PTR ptr, GC_PTR data) | |
178 | { | |
179 | SCM bignum; | |
180 | ||
21041372 | 181 | bignum = SCM_PACK_POINTER (ptr); |
864e7d42 LC |
182 | mpz_clear (SCM_I_BIG_MPZ (bignum)); |
183 | } | |
184 | ||
d017fcdf LC |
185 | /* Return a new uninitialized bignum. */ |
186 | static inline SCM | |
187 | make_bignum (void) | |
188 | { | |
189 | scm_t_bits *p; | |
864e7d42 LC |
190 | GC_finalization_proc prev_finalizer; |
191 | GC_PTR prev_finalizer_data; | |
d017fcdf LC |
192 | |
193 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ | |
194 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), | |
195 | "bignum"); | |
196 | p[0] = scm_tc16_big; | |
197 | ||
864e7d42 LC |
198 | GC_REGISTER_FINALIZER_NO_ORDER (p, finalize_bignum, NULL, |
199 | &prev_finalizer, | |
200 | &prev_finalizer_data); | |
201 | ||
d017fcdf LC |
202 | return SCM_PACK (p); |
203 | } | |
ac0c002c | 204 | |
864e7d42 | 205 | |
189171c5 | 206 | SCM |
ca46fb90 RB |
207 | scm_i_mkbig () |
208 | { | |
209 | /* Return a newly created bignum. */ | |
d017fcdf | 210 | SCM z = make_bignum (); |
ca46fb90 RB |
211 | mpz_init (SCM_I_BIG_MPZ (z)); |
212 | return z; | |
213 | } | |
214 | ||
e25f3727 AW |
215 | static SCM |
216 | scm_i_inum2big (scm_t_inum x) | |
217 | { | |
218 | /* Return a newly created bignum initialized to X. */ | |
219 | SCM z = make_bignum (); | |
220 | #if SIZEOF_VOID_P == SIZEOF_LONG | |
221 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
222 | #else | |
223 | /* Note that in this case, you'll also have to check all mpz_*_ui and | |
224 | mpz_*_si invocations in Guile. */ | |
225 | #error creation of mpz not implemented for this inum size | |
226 | #endif | |
227 | return z; | |
228 | } | |
229 | ||
189171c5 | 230 | SCM |
c71b0706 MV |
231 | scm_i_long2big (long x) |
232 | { | |
233 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 234 | SCM z = make_bignum (); |
c71b0706 MV |
235 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
236 | return z; | |
237 | } | |
238 | ||
189171c5 | 239 | SCM |
c71b0706 MV |
240 | scm_i_ulong2big (unsigned long x) |
241 | { | |
242 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 243 | SCM z = make_bignum (); |
c71b0706 MV |
244 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
245 | return z; | |
246 | } | |
247 | ||
189171c5 | 248 | SCM |
ca46fb90 RB |
249 | scm_i_clonebig (SCM src_big, int same_sign_p) |
250 | { | |
251 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
d017fcdf | 252 | SCM z = make_bignum (); |
ca46fb90 | 253 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
0aacf84e MD |
254 | if (!same_sign_p) |
255 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
256 | return z; |
257 | } | |
258 | ||
189171c5 | 259 | int |
ca46fb90 RB |
260 | scm_i_bigcmp (SCM x, SCM y) |
261 | { | |
262 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
263 | /* presume we already know x and y are bignums */ | |
264 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
265 | scm_remember_upto_here_2 (x, y); | |
266 | return result; | |
267 | } | |
268 | ||
189171c5 | 269 | SCM |
ca46fb90 RB |
270 | scm_i_dbl2big (double d) |
271 | { | |
272 | /* results are only defined if d is an integer */ | |
d017fcdf | 273 | SCM z = make_bignum (); |
ca46fb90 RB |
274 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
275 | return z; | |
276 | } | |
277 | ||
f92e85f7 MV |
278 | /* Convert a integer in double representation to a SCM number. */ |
279 | ||
189171c5 | 280 | SCM |
f92e85f7 MV |
281 | scm_i_dbl2num (double u) |
282 | { | |
283 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
284 | powers of 2, so there's no rounding when making "double" values | |
285 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
286 | get rounded on a 64-bit machine, hence the "+1". | |
287 | ||
288 | The use of floor() to force to an integer value ensures we get a | |
289 | "numerically closest" value without depending on how a | |
290 | double->long cast or how mpz_set_d will round. For reference, | |
291 | double->long probably follows the hardware rounding mode, | |
292 | mpz_set_d truncates towards zero. */ | |
293 | ||
294 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
295 | representable as a double? */ | |
296 | ||
297 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
298 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
e25f3727 | 299 | return SCM_I_MAKINUM ((scm_t_inum) u); |
f92e85f7 MV |
300 | else |
301 | return scm_i_dbl2big (u); | |
302 | } | |
303 | ||
089c9a59 KR |
304 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
305 | with R5RS exact->inexact. | |
306 | ||
307 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
308 | (ie. truncate towards zero), then adjust to get the closest double by |
309 | examining the next lower bit and adding 1 (to the absolute value) if | |
310 | necessary. | |
311 | ||
312 | Bignums exactly half way between representable doubles are rounded to the | |
313 | next higher absolute value (ie. away from zero). This seems like an | |
314 | adequate interpretation of R5RS "numerically closest", and it's easier | |
315 | and faster than a full "nearest-even" style. | |
316 | ||
317 | The bit test must be done on the absolute value of the mpz_t, which means | |
318 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
319 | negatives as twos complement. | |
320 | ||
18d78c5e MW |
321 | In GMP before 4.2, mpz_get_d rounding was unspecified. It ended up |
322 | following the hardware rounding mode, but applied to the absolute | |
323 | value of the mpz_t operand. This is not what we want so we put the | |
324 | high DBL_MANT_DIG bits into a temporary. Starting with GMP 4.2 | |
325 | (released in March 2006) mpz_get_d now always truncates towards zero. | |
f8a8200b | 326 | |
18d78c5e MW |
327 | ENHANCE-ME: The temporary init+clear to force the rounding in GMP |
328 | before 4.2 is a slowdown. It'd be faster to pick out the relevant | |
329 | high bits with mpz_getlimbn. */ | |
089c9a59 KR |
330 | |
331 | double | |
ca46fb90 RB |
332 | scm_i_big2dbl (SCM b) |
333 | { | |
089c9a59 KR |
334 | double result; |
335 | size_t bits; | |
336 | ||
337 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
338 | ||
f8a8200b | 339 | #if 1 |
089c9a59 | 340 | { |
18d78c5e MW |
341 | /* For GMP earlier than 4.2, force truncation towards zero */ |
342 | ||
343 | /* FIXME: DBL_MANT_DIG is the number of base-`FLT_RADIX' digits, | |
344 | _not_ the number of bits, so this code will break badly on a | |
345 | system with non-binary doubles. */ | |
346 | ||
089c9a59 KR |
347 | mpz_t tmp; |
348 | if (bits > DBL_MANT_DIG) | |
349 | { | |
350 | size_t shift = bits - DBL_MANT_DIG; | |
351 | mpz_init2 (tmp, DBL_MANT_DIG); | |
352 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
353 | result = ldexp (mpz_get_d (tmp), shift); | |
354 | mpz_clear (tmp); | |
355 | } | |
356 | else | |
357 | { | |
358 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
359 | } | |
360 | } | |
361 | #else | |
18d78c5e | 362 | /* GMP 4.2 or later */ |
089c9a59 KR |
363 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
364 | #endif | |
365 | ||
366 | if (bits > DBL_MANT_DIG) | |
367 | { | |
368 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
369 | /* test bit number "pos" in absolute value */ | |
370 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
371 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
372 | { | |
373 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
374 | } | |
375 | } | |
376 | ||
ca46fb90 RB |
377 | scm_remember_upto_here_1 (b); |
378 | return result; | |
379 | } | |
380 | ||
189171c5 | 381 | SCM |
ca46fb90 RB |
382 | scm_i_normbig (SCM b) |
383 | { | |
384 | /* convert a big back to a fixnum if it'll fit */ | |
385 | /* presume b is a bignum */ | |
386 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
387 | { | |
e25f3727 | 388 | scm_t_inum val = mpz_get_si (SCM_I_BIG_MPZ (b)); |
ca46fb90 | 389 | if (SCM_FIXABLE (val)) |
d956fa6f | 390 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
391 | } |
392 | return b; | |
393 | } | |
f872b822 | 394 | |
f92e85f7 MV |
395 | static SCM_C_INLINE_KEYWORD SCM |
396 | scm_i_mpz2num (mpz_t b) | |
397 | { | |
398 | /* convert a mpz number to a SCM number. */ | |
399 | if (mpz_fits_slong_p (b)) | |
400 | { | |
e25f3727 | 401 | scm_t_inum val = mpz_get_si (b); |
f92e85f7 | 402 | if (SCM_FIXABLE (val)) |
d956fa6f | 403 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
404 | } |
405 | ||
406 | { | |
d017fcdf | 407 | SCM z = make_bignum (); |
f92e85f7 MV |
408 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
409 | return z; | |
410 | } | |
411 | } | |
412 | ||
413 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
414 | static SCM scm_divide2real (SCM x, SCM y); | |
415 | ||
cba42c93 MV |
416 | static SCM |
417 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 418 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 419 | { |
c60e130c MV |
420 | /* First make sure the arguments are proper. |
421 | */ | |
e11e83f3 | 422 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 423 | { |
bc36d050 | 424 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 425 | scm_num_overflow ("make-ratio"); |
cff5fa33 | 426 | if (scm_is_eq (denominator, SCM_INUM1)) |
f92e85f7 MV |
427 | return numerator; |
428 | } | |
429 | else | |
430 | { | |
431 | if (!(SCM_BIGP(denominator))) | |
432 | SCM_WRONG_TYPE_ARG (2, denominator); | |
433 | } | |
e11e83f3 | 434 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
435 | SCM_WRONG_TYPE_ARG (1, numerator); |
436 | ||
437 | /* Then flip signs so that the denominator is positive. | |
438 | */ | |
73e4de09 | 439 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
440 | { |
441 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
442 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
443 | } | |
444 | ||
445 | /* Now consider for each of the four fixnum/bignum combinations | |
446 | whether the rational number is really an integer. | |
447 | */ | |
e11e83f3 | 448 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 449 | { |
e25f3727 | 450 | scm_t_inum x = SCM_I_INUM (numerator); |
bc36d050 | 451 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 452 | return SCM_INUM0; |
e11e83f3 | 453 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 454 | { |
e25f3727 | 455 | scm_t_inum y; |
e11e83f3 | 456 | y = SCM_I_INUM (denominator); |
f92e85f7 | 457 | if (x == y) |
cff5fa33 | 458 | return SCM_INUM1; |
f92e85f7 | 459 | if ((x % y) == 0) |
d956fa6f | 460 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 461 | } |
dd5130ca KR |
462 | else |
463 | { | |
464 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
465 | of that value for the denominator, as a bignum. Apart from |
466 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
467 | integer. */ | |
468 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
469 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
470 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 471 | return SCM_I_MAKINUM(-1); |
dd5130ca | 472 | } |
f92e85f7 | 473 | } |
c60e130c | 474 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 475 | { |
e11e83f3 | 476 | if (SCM_I_INUMP (denominator)) |
c60e130c | 477 | { |
e25f3727 | 478 | scm_t_inum yy = SCM_I_INUM (denominator); |
c60e130c MV |
479 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
480 | return scm_divide (numerator, denominator); | |
481 | } | |
482 | else | |
f92e85f7 | 483 | { |
bc36d050 | 484 | if (scm_is_eq (numerator, denominator)) |
cff5fa33 | 485 | return SCM_INUM1; |
c60e130c MV |
486 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
487 | SCM_I_BIG_MPZ (denominator))) | |
488 | return scm_divide(numerator, denominator); | |
f92e85f7 | 489 | } |
f92e85f7 | 490 | } |
c60e130c MV |
491 | |
492 | /* No, it's a proper fraction. | |
493 | */ | |
e2bf3b19 HWN |
494 | { |
495 | SCM divisor = scm_gcd (numerator, denominator); | |
cff5fa33 | 496 | if (!(scm_is_eq (divisor, SCM_INUM1))) |
e2bf3b19 HWN |
497 | { |
498 | numerator = scm_divide (numerator, divisor); | |
499 | denominator = scm_divide (denominator, divisor); | |
500 | } | |
501 | ||
502 | return scm_double_cell (scm_tc16_fraction, | |
503 | SCM_UNPACK (numerator), | |
504 | SCM_UNPACK (denominator), 0); | |
505 | } | |
f92e85f7 | 506 | } |
c60e130c | 507 | #undef FUNC_NAME |
f92e85f7 | 508 | |
f92e85f7 MV |
509 | double |
510 | scm_i_fraction2double (SCM z) | |
511 | { | |
55f26379 MV |
512 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
513 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
514 | } |
515 | ||
2e274311 MW |
516 | static int |
517 | double_is_non_negative_zero (double x) | |
518 | { | |
519 | static double zero = 0.0; | |
520 | ||
521 | return !memcmp (&x, &zero, sizeof(double)); | |
522 | } | |
523 | ||
2519490c MW |
524 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
525 | (SCM x), | |
942e5b91 MG |
526 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
527 | "otherwise.") | |
1bbd0b84 | 528 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 529 | { |
41df63cf MW |
530 | if (SCM_INEXACTP (x)) |
531 | return SCM_BOOL_F; | |
532 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 533 | return SCM_BOOL_T; |
41df63cf | 534 | else |
fa075d40 | 535 | return scm_wta_dispatch_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
536 | } |
537 | #undef FUNC_NAME | |
538 | ||
022dda69 MG |
539 | int |
540 | scm_is_exact (SCM val) | |
541 | { | |
542 | return scm_is_true (scm_exact_p (val)); | |
543 | } | |
41df63cf | 544 | |
2519490c | 545 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
546 | (SCM x), |
547 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
548 | "else.") | |
549 | #define FUNC_NAME s_scm_inexact_p | |
550 | { | |
551 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 552 | return SCM_BOOL_T; |
41df63cf | 553 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 554 | return SCM_BOOL_F; |
41df63cf | 555 | else |
fa075d40 | 556 | return scm_wta_dispatch_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 557 | } |
1bbd0b84 | 558 | #undef FUNC_NAME |
0f2d19dd | 559 | |
022dda69 MG |
560 | int |
561 | scm_is_inexact (SCM val) | |
562 | { | |
563 | return scm_is_true (scm_inexact_p (val)); | |
564 | } | |
4219f20d | 565 | |
2519490c | 566 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 567 | (SCM n), |
942e5b91 MG |
568 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
569 | "otherwise.") | |
1bbd0b84 | 570 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 571 | { |
e11e83f3 | 572 | if (SCM_I_INUMP (n)) |
0aacf84e | 573 | { |
e25f3727 | 574 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 575 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
576 | } |
577 | else if (SCM_BIGP (n)) | |
578 | { | |
579 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
580 | scm_remember_upto_here_1 (n); | |
73e4de09 | 581 | return scm_from_bool (odd_p); |
0aacf84e | 582 | } |
f92e85f7 MV |
583 | else if (SCM_REALP (n)) |
584 | { | |
2519490c MW |
585 | double val = SCM_REAL_VALUE (n); |
586 | if (DOUBLE_IS_FINITE (val)) | |
587 | { | |
588 | double rem = fabs (fmod (val, 2.0)); | |
589 | if (rem == 1.0) | |
590 | return SCM_BOOL_T; | |
591 | else if (rem == 0.0) | |
592 | return SCM_BOOL_F; | |
593 | } | |
f92e85f7 | 594 | } |
fa075d40 | 595 | return scm_wta_dispatch_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 596 | } |
1bbd0b84 | 597 | #undef FUNC_NAME |
0f2d19dd | 598 | |
4219f20d | 599 | |
2519490c | 600 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 601 | (SCM n), |
942e5b91 MG |
602 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
603 | "otherwise.") | |
1bbd0b84 | 604 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 605 | { |
e11e83f3 | 606 | if (SCM_I_INUMP (n)) |
0aacf84e | 607 | { |
e25f3727 | 608 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 609 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
610 | } |
611 | else if (SCM_BIGP (n)) | |
612 | { | |
613 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
614 | scm_remember_upto_here_1 (n); | |
73e4de09 | 615 | return scm_from_bool (even_p); |
0aacf84e | 616 | } |
f92e85f7 MV |
617 | else if (SCM_REALP (n)) |
618 | { | |
2519490c MW |
619 | double val = SCM_REAL_VALUE (n); |
620 | if (DOUBLE_IS_FINITE (val)) | |
621 | { | |
622 | double rem = fabs (fmod (val, 2.0)); | |
623 | if (rem == 1.0) | |
624 | return SCM_BOOL_F; | |
625 | else if (rem == 0.0) | |
626 | return SCM_BOOL_T; | |
627 | } | |
f92e85f7 | 628 | } |
fa075d40 | 629 | return scm_wta_dispatch_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 630 | } |
1bbd0b84 | 631 | #undef FUNC_NAME |
0f2d19dd | 632 | |
2519490c MW |
633 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
634 | (SCM x), | |
10391e06 AW |
635 | "Return @code{#t} if the real number @var{x} is neither\n" |
636 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
637 | #define FUNC_NAME s_scm_finite_p |
638 | { | |
639 | if (SCM_REALP (x)) | |
640 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 641 | else if (scm_is_real (x)) |
7112615f MW |
642 | return SCM_BOOL_T; |
643 | else | |
fa075d40 | 644 | return scm_wta_dispatch_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
645 | } |
646 | #undef FUNC_NAME | |
647 | ||
2519490c MW |
648 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
649 | (SCM x), | |
650 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
651 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
652 | #define FUNC_NAME s_scm_inf_p |
653 | { | |
b1092b3a | 654 | if (SCM_REALP (x)) |
2e65b52f | 655 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 656 | else if (scm_is_real (x)) |
7351e207 | 657 | return SCM_BOOL_F; |
10391e06 | 658 | else |
fa075d40 | 659 | return scm_wta_dispatch_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
660 | } |
661 | #undef FUNC_NAME | |
662 | ||
2519490c MW |
663 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
664 | (SCM x), | |
10391e06 AW |
665 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
666 | "or @code{#f} otherwise.") | |
7351e207 MV |
667 | #define FUNC_NAME s_scm_nan_p |
668 | { | |
10391e06 AW |
669 | if (SCM_REALP (x)) |
670 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
671 | else if (scm_is_real (x)) | |
7351e207 | 672 | return SCM_BOOL_F; |
10391e06 | 673 | else |
fa075d40 | 674 | return scm_wta_dispatch_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
675 | } |
676 | #undef FUNC_NAME | |
677 | ||
678 | /* Guile's idea of infinity. */ | |
679 | static double guile_Inf; | |
680 | ||
681 | /* Guile's idea of not a number. */ | |
682 | static double guile_NaN; | |
683 | ||
684 | static void | |
685 | guile_ieee_init (void) | |
686 | { | |
7351e207 MV |
687 | /* Some version of gcc on some old version of Linux used to crash when |
688 | trying to make Inf and NaN. */ | |
689 | ||
240a27d2 KR |
690 | #ifdef INFINITY |
691 | /* C99 INFINITY, when available. | |
692 | FIXME: The standard allows for INFINITY to be something that overflows | |
693 | at compile time. We ought to have a configure test to check for that | |
694 | before trying to use it. (But in practice we believe this is not a | |
695 | problem on any system guile is likely to target.) */ | |
696 | guile_Inf = INFINITY; | |
56a3dcd4 | 697 | #elif defined HAVE_DINFINITY |
240a27d2 | 698 | /* OSF */ |
7351e207 | 699 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 700 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
701 | #else |
702 | double tmp = 1e+10; | |
703 | guile_Inf = tmp; | |
704 | for (;;) | |
705 | { | |
706 | guile_Inf *= 1e+10; | |
707 | if (guile_Inf == tmp) | |
708 | break; | |
709 | tmp = guile_Inf; | |
710 | } | |
711 | #endif | |
712 | ||
240a27d2 KR |
713 | #ifdef NAN |
714 | /* C99 NAN, when available */ | |
715 | guile_NaN = NAN; | |
56a3dcd4 | 716 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
717 | { |
718 | /* OSF */ | |
719 | extern unsigned int DQNAN[2]; | |
720 | guile_NaN = (*((double *)(DQNAN))); | |
721 | } | |
7351e207 MV |
722 | #else |
723 | guile_NaN = guile_Inf / guile_Inf; | |
724 | #endif | |
7351e207 MV |
725 | } |
726 | ||
727 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
728 | (void), | |
729 | "Return Inf.") | |
730 | #define FUNC_NAME s_scm_inf | |
731 | { | |
732 | static int initialized = 0; | |
733 | if (! initialized) | |
734 | { | |
735 | guile_ieee_init (); | |
736 | initialized = 1; | |
737 | } | |
55f26379 | 738 | return scm_from_double (guile_Inf); |
7351e207 MV |
739 | } |
740 | #undef FUNC_NAME | |
741 | ||
742 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
743 | (void), | |
744 | "Return NaN.") | |
745 | #define FUNC_NAME s_scm_nan | |
746 | { | |
747 | static int initialized = 0; | |
0aacf84e | 748 | if (!initialized) |
7351e207 MV |
749 | { |
750 | guile_ieee_init (); | |
751 | initialized = 1; | |
752 | } | |
55f26379 | 753 | return scm_from_double (guile_NaN); |
7351e207 MV |
754 | } |
755 | #undef FUNC_NAME | |
756 | ||
4219f20d | 757 | |
a48d60b1 MD |
758 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
759 | (SCM x), | |
760 | "Return the absolute value of @var{x}.") | |
2519490c | 761 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 762 | { |
e11e83f3 | 763 | if (SCM_I_INUMP (x)) |
0aacf84e | 764 | { |
e25f3727 | 765 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
766 | if (xx >= 0) |
767 | return x; | |
768 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 769 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 770 | else |
e25f3727 | 771 | return scm_i_inum2big (-xx); |
4219f20d | 772 | } |
9b9ef10c MW |
773 | else if (SCM_LIKELY (SCM_REALP (x))) |
774 | { | |
775 | double xx = SCM_REAL_VALUE (x); | |
776 | /* If x is a NaN then xx<0 is false so we return x unchanged */ | |
777 | if (xx < 0.0) | |
778 | return scm_from_double (-xx); | |
779 | /* Handle signed zeroes properly */ | |
780 | else if (SCM_UNLIKELY (xx == 0.0)) | |
781 | return flo0; | |
782 | else | |
783 | return x; | |
784 | } | |
0aacf84e MD |
785 | else if (SCM_BIGP (x)) |
786 | { | |
787 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
788 | if (sgn < 0) | |
789 | return scm_i_clonebig (x, 0); | |
790 | else | |
791 | return x; | |
4219f20d | 792 | } |
f92e85f7 MV |
793 | else if (SCM_FRACTIONP (x)) |
794 | { | |
73e4de09 | 795 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 796 | return x; |
cba42c93 | 797 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
798 | SCM_FRACTION_DENOMINATOR (x)); |
799 | } | |
0aacf84e | 800 | else |
fa075d40 | 801 | return scm_wta_dispatch_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 802 | } |
a48d60b1 | 803 | #undef FUNC_NAME |
0f2d19dd | 804 | |
4219f20d | 805 | |
2519490c MW |
806 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
807 | (SCM x, SCM y), | |
808 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
809 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 810 | { |
495a39c4 | 811 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 812 | { |
495a39c4 | 813 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 814 | return scm_truncate_quotient (x, y); |
0aacf84e | 815 | else |
fa075d40 | 816 | return scm_wta_dispatch_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 817 | } |
0aacf84e | 818 | else |
fa075d40 | 819 | return scm_wta_dispatch_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 820 | } |
2519490c | 821 | #undef FUNC_NAME |
0f2d19dd | 822 | |
2519490c MW |
823 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
824 | (SCM x, SCM y), | |
825 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
826 | "@lisp\n" | |
827 | "(remainder 13 4) @result{} 1\n" | |
828 | "(remainder -13 4) @result{} -1\n" | |
829 | "@end lisp") | |
830 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 831 | { |
495a39c4 | 832 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 833 | { |
495a39c4 | 834 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 835 | return scm_truncate_remainder (x, y); |
0aacf84e | 836 | else |
fa075d40 | 837 | return scm_wta_dispatch_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 838 | } |
0aacf84e | 839 | else |
fa075d40 | 840 | return scm_wta_dispatch_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 841 | } |
2519490c | 842 | #undef FUNC_NAME |
0f2d19dd | 843 | |
89a7e495 | 844 | |
2519490c MW |
845 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
846 | (SCM x, SCM y), | |
847 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
848 | "@lisp\n" | |
849 | "(modulo 13 4) @result{} 1\n" | |
850 | "(modulo -13 4) @result{} 3\n" | |
851 | "@end lisp") | |
852 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 853 | { |
495a39c4 | 854 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 855 | { |
495a39c4 | 856 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 857 | return scm_floor_remainder (x, y); |
0aacf84e | 858 | else |
fa075d40 | 859 | return scm_wta_dispatch_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 860 | } |
0aacf84e | 861 | else |
fa075d40 | 862 | return scm_wta_dispatch_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 863 | } |
2519490c | 864 | #undef FUNC_NAME |
0f2d19dd | 865 | |
5fbf680b MW |
866 | /* two_valued_wta_dispatch_2 is a version of SCM_WTA_DISPATCH_2 for |
867 | two-valued functions. It is called from primitive generics that take | |
868 | two arguments and return two values, when the core procedure is | |
869 | unable to handle the given argument types. If there are GOOPS | |
870 | methods for this primitive generic, it dispatches to GOOPS and, if | |
871 | successful, expects two values to be returned, which are placed in | |
872 | *rp1 and *rp2. If there are no GOOPS methods, it throws a | |
873 | wrong-type-arg exception. | |
874 | ||
875 | FIXME: This obviously belongs somewhere else, but until we decide on | |
876 | the right API, it is here as a static function, because it is needed | |
877 | by the *_divide functions below. | |
878 | */ | |
879 | static void | |
880 | two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos, | |
881 | const char *subr, SCM *rp1, SCM *rp2) | |
882 | { | |
fa075d40 AW |
883 | SCM vals = scm_wta_dispatch_2 (gf, a1, a2, pos, subr); |
884 | ||
885 | scm_i_extract_values_2 (vals, rp1, rp2); | |
5fbf680b MW |
886 | } |
887 | ||
a8da6d93 MW |
888 | SCM_DEFINE (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, |
889 | (SCM x, SCM y), | |
890 | "Return the integer @var{q} such that\n" | |
891 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
892 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
893 | "@lisp\n" | |
894 | "(euclidean-quotient 123 10) @result{} 12\n" | |
895 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
896 | "(euclidean-quotient -123 10) @result{} -13\n" | |
897 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
898 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
899 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
900 | "@end lisp") | |
ff62c168 MW |
901 | #define FUNC_NAME s_scm_euclidean_quotient |
902 | { | |
a8da6d93 MW |
903 | if (scm_is_false (scm_negative_p (y))) |
904 | return scm_floor_quotient (x, y); | |
ff62c168 | 905 | else |
a8da6d93 | 906 | return scm_ceiling_quotient (x, y); |
ff62c168 MW |
907 | } |
908 | #undef FUNC_NAME | |
909 | ||
a8da6d93 MW |
910 | SCM_DEFINE (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, |
911 | (SCM x, SCM y), | |
912 | "Return the real number @var{r} such that\n" | |
913 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
914 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
915 | "for some integer @var{q}.\n" | |
916 | "@lisp\n" | |
917 | "(euclidean-remainder 123 10) @result{} 3\n" | |
918 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
919 | "(euclidean-remainder -123 10) @result{} 7\n" | |
920 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
921 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
922 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
923 | "@end lisp") | |
ff62c168 MW |
924 | #define FUNC_NAME s_scm_euclidean_remainder |
925 | { | |
a8da6d93 MW |
926 | if (scm_is_false (scm_negative_p (y))) |
927 | return scm_floor_remainder (x, y); | |
ff62c168 | 928 | else |
a8da6d93 | 929 | return scm_ceiling_remainder (x, y); |
ff62c168 MW |
930 | } |
931 | #undef FUNC_NAME | |
932 | ||
a8da6d93 MW |
933 | SCM_DEFINE (scm_i_euclidean_divide, "euclidean/", 2, 0, 0, |
934 | (SCM x, SCM y), | |
935 | "Return the integer @var{q} and the real number @var{r}\n" | |
936 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
937 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
938 | "@lisp\n" | |
939 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
940 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
941 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
942 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
943 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
944 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
945 | "@end lisp") | |
5fbf680b MW |
946 | #define FUNC_NAME s_scm_i_euclidean_divide |
947 | { | |
a8da6d93 MW |
948 | if (scm_is_false (scm_negative_p (y))) |
949 | return scm_i_floor_divide (x, y); | |
950 | else | |
951 | return scm_i_ceiling_divide (x, y); | |
5fbf680b MW |
952 | } |
953 | #undef FUNC_NAME | |
954 | ||
5fbf680b MW |
955 | void |
956 | scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 | 957 | { |
a8da6d93 MW |
958 | if (scm_is_false (scm_negative_p (y))) |
959 | return scm_floor_divide (x, y, qp, rp); | |
ff62c168 | 960 | else |
a8da6d93 | 961 | return scm_ceiling_divide (x, y, qp, rp); |
ff62c168 MW |
962 | } |
963 | ||
8f9da340 MW |
964 | static SCM scm_i_inexact_floor_quotient (double x, double y); |
965 | static SCM scm_i_exact_rational_floor_quotient (SCM x, SCM y); | |
966 | ||
967 | SCM_PRIMITIVE_GENERIC (scm_floor_quotient, "floor-quotient", 2, 0, 0, | |
968 | (SCM x, SCM y), | |
969 | "Return the floor of @math{@var{x} / @var{y}}.\n" | |
970 | "@lisp\n" | |
971 | "(floor-quotient 123 10) @result{} 12\n" | |
972 | "(floor-quotient 123 -10) @result{} -13\n" | |
973 | "(floor-quotient -123 10) @result{} -13\n" | |
974 | "(floor-quotient -123 -10) @result{} 12\n" | |
975 | "(floor-quotient -123.2 -63.5) @result{} 1.0\n" | |
976 | "(floor-quotient 16/3 -10/7) @result{} -4\n" | |
977 | "@end lisp") | |
978 | #define FUNC_NAME s_scm_floor_quotient | |
979 | { | |
980 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
981 | { | |
982 | scm_t_inum xx = SCM_I_INUM (x); | |
983 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
984 | { | |
985 | scm_t_inum yy = SCM_I_INUM (y); | |
986 | scm_t_inum xx1 = xx; | |
987 | scm_t_inum qq; | |
988 | if (SCM_LIKELY (yy > 0)) | |
989 | { | |
990 | if (SCM_UNLIKELY (xx < 0)) | |
991 | xx1 = xx - yy + 1; | |
992 | } | |
993 | else if (SCM_UNLIKELY (yy == 0)) | |
994 | scm_num_overflow (s_scm_floor_quotient); | |
995 | else if (xx > 0) | |
996 | xx1 = xx - yy - 1; | |
997 | qq = xx1 / yy; | |
998 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
999 | return SCM_I_MAKINUM (qq); | |
1000 | else | |
1001 | return scm_i_inum2big (qq); | |
1002 | } | |
1003 | else if (SCM_BIGP (y)) | |
1004 | { | |
1005 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1006 | scm_remember_upto_here_1 (y); | |
1007 | if (sign > 0) | |
1008 | return SCM_I_MAKINUM ((xx < 0) ? -1 : 0); | |
1009 | else | |
1010 | return SCM_I_MAKINUM ((xx > 0) ? -1 : 0); | |
1011 | } | |
1012 | else if (SCM_REALP (y)) | |
1013 | return scm_i_inexact_floor_quotient (xx, SCM_REAL_VALUE (y)); | |
1014 | else if (SCM_FRACTIONP (y)) | |
1015 | return scm_i_exact_rational_floor_quotient (x, y); | |
1016 | else | |
fa075d40 AW |
1017 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
1018 | s_scm_floor_quotient); | |
8f9da340 MW |
1019 | } |
1020 | else if (SCM_BIGP (x)) | |
1021 | { | |
1022 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1023 | { | |
1024 | scm_t_inum yy = SCM_I_INUM (y); | |
1025 | if (SCM_UNLIKELY (yy == 0)) | |
1026 | scm_num_overflow (s_scm_floor_quotient); | |
1027 | else if (SCM_UNLIKELY (yy == 1)) | |
1028 | return x; | |
1029 | else | |
1030 | { | |
1031 | SCM q = scm_i_mkbig (); | |
1032 | if (yy > 0) | |
1033 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1034 | else | |
1035 | { | |
1036 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1037 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1038 | } | |
1039 | scm_remember_upto_here_1 (x); | |
1040 | return scm_i_normbig (q); | |
1041 | } | |
1042 | } | |
1043 | else if (SCM_BIGP (y)) | |
1044 | { | |
1045 | SCM q = scm_i_mkbig (); | |
1046 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1047 | SCM_I_BIG_MPZ (x), | |
1048 | SCM_I_BIG_MPZ (y)); | |
1049 | scm_remember_upto_here_2 (x, y); | |
1050 | return scm_i_normbig (q); | |
1051 | } | |
1052 | else if (SCM_REALP (y)) | |
1053 | return scm_i_inexact_floor_quotient | |
1054 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1055 | else if (SCM_FRACTIONP (y)) | |
1056 | return scm_i_exact_rational_floor_quotient (x, y); | |
1057 | else | |
fa075d40 AW |
1058 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
1059 | s_scm_floor_quotient); | |
8f9da340 MW |
1060 | } |
1061 | else if (SCM_REALP (x)) | |
1062 | { | |
1063 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1064 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1065 | return scm_i_inexact_floor_quotient | |
1066 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1067 | else | |
fa075d40 AW |
1068 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
1069 | s_scm_floor_quotient); | |
8f9da340 MW |
1070 | } |
1071 | else if (SCM_FRACTIONP (x)) | |
1072 | { | |
1073 | if (SCM_REALP (y)) | |
1074 | return scm_i_inexact_floor_quotient | |
1075 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1076 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1077 | return scm_i_exact_rational_floor_quotient (x, y); | |
1078 | else | |
fa075d40 AW |
1079 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG2, |
1080 | s_scm_floor_quotient); | |
8f9da340 MW |
1081 | } |
1082 | else | |
fa075d40 AW |
1083 | return scm_wta_dispatch_2 (g_scm_floor_quotient, x, y, SCM_ARG1, |
1084 | s_scm_floor_quotient); | |
8f9da340 MW |
1085 | } |
1086 | #undef FUNC_NAME | |
1087 | ||
1088 | static SCM | |
1089 | scm_i_inexact_floor_quotient (double x, double y) | |
1090 | { | |
1091 | if (SCM_UNLIKELY (y == 0)) | |
1092 | scm_num_overflow (s_scm_floor_quotient); /* or return a NaN? */ | |
1093 | else | |
1094 | return scm_from_double (floor (x / y)); | |
1095 | } | |
1096 | ||
1097 | static SCM | |
1098 | scm_i_exact_rational_floor_quotient (SCM x, SCM y) | |
1099 | { | |
1100 | return scm_floor_quotient | |
1101 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1102 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1103 | } | |
1104 | ||
1105 | static SCM scm_i_inexact_floor_remainder (double x, double y); | |
1106 | static SCM scm_i_exact_rational_floor_remainder (SCM x, SCM y); | |
1107 | ||
1108 | SCM_PRIMITIVE_GENERIC (scm_floor_remainder, "floor-remainder", 2, 0, 0, | |
1109 | (SCM x, SCM y), | |
1110 | "Return the real number @var{r} such that\n" | |
1111 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1112 | "where @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1113 | "@lisp\n" | |
1114 | "(floor-remainder 123 10) @result{} 3\n" | |
1115 | "(floor-remainder 123 -10) @result{} -7\n" | |
1116 | "(floor-remainder -123 10) @result{} 7\n" | |
1117 | "(floor-remainder -123 -10) @result{} -3\n" | |
1118 | "(floor-remainder -123.2 -63.5) @result{} -59.7\n" | |
1119 | "(floor-remainder 16/3 -10/7) @result{} -8/21\n" | |
1120 | "@end lisp") | |
1121 | #define FUNC_NAME s_scm_floor_remainder | |
1122 | { | |
1123 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1124 | { | |
1125 | scm_t_inum xx = SCM_I_INUM (x); | |
1126 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1127 | { | |
1128 | scm_t_inum yy = SCM_I_INUM (y); | |
1129 | if (SCM_UNLIKELY (yy == 0)) | |
1130 | scm_num_overflow (s_scm_floor_remainder); | |
1131 | else | |
1132 | { | |
1133 | scm_t_inum rr = xx % yy; | |
1134 | int needs_adjustment; | |
1135 | ||
1136 | if (SCM_LIKELY (yy > 0)) | |
1137 | needs_adjustment = (rr < 0); | |
1138 | else | |
1139 | needs_adjustment = (rr > 0); | |
1140 | ||
1141 | if (needs_adjustment) | |
1142 | rr += yy; | |
1143 | return SCM_I_MAKINUM (rr); | |
1144 | } | |
1145 | } | |
1146 | else if (SCM_BIGP (y)) | |
1147 | { | |
1148 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1149 | scm_remember_upto_here_1 (y); | |
1150 | if (sign > 0) | |
1151 | { | |
1152 | if (xx < 0) | |
1153 | { | |
1154 | SCM r = scm_i_mkbig (); | |
1155 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1156 | scm_remember_upto_here_1 (y); | |
1157 | return scm_i_normbig (r); | |
1158 | } | |
1159 | else | |
1160 | return x; | |
1161 | } | |
1162 | else if (xx <= 0) | |
1163 | return x; | |
1164 | else | |
1165 | { | |
1166 | SCM r = scm_i_mkbig (); | |
1167 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1168 | scm_remember_upto_here_1 (y); | |
1169 | return scm_i_normbig (r); | |
1170 | } | |
1171 | } | |
1172 | else if (SCM_REALP (y)) | |
1173 | return scm_i_inexact_floor_remainder (xx, SCM_REAL_VALUE (y)); | |
1174 | else if (SCM_FRACTIONP (y)) | |
1175 | return scm_i_exact_rational_floor_remainder (x, y); | |
1176 | else | |
fa075d40 AW |
1177 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
1178 | s_scm_floor_remainder); | |
8f9da340 MW |
1179 | } |
1180 | else if (SCM_BIGP (x)) | |
1181 | { | |
1182 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1183 | { | |
1184 | scm_t_inum yy = SCM_I_INUM (y); | |
1185 | if (SCM_UNLIKELY (yy == 0)) | |
1186 | scm_num_overflow (s_scm_floor_remainder); | |
1187 | else | |
1188 | { | |
1189 | scm_t_inum rr; | |
1190 | if (yy > 0) | |
1191 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1192 | else | |
1193 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1194 | scm_remember_upto_here_1 (x); | |
1195 | return SCM_I_MAKINUM (rr); | |
1196 | } | |
1197 | } | |
1198 | else if (SCM_BIGP (y)) | |
1199 | { | |
1200 | SCM r = scm_i_mkbig (); | |
1201 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
1202 | SCM_I_BIG_MPZ (x), | |
1203 | SCM_I_BIG_MPZ (y)); | |
1204 | scm_remember_upto_here_2 (x, y); | |
1205 | return scm_i_normbig (r); | |
1206 | } | |
1207 | else if (SCM_REALP (y)) | |
1208 | return scm_i_inexact_floor_remainder | |
1209 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1210 | else if (SCM_FRACTIONP (y)) | |
1211 | return scm_i_exact_rational_floor_remainder (x, y); | |
1212 | else | |
fa075d40 AW |
1213 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
1214 | s_scm_floor_remainder); | |
8f9da340 MW |
1215 | } |
1216 | else if (SCM_REALP (x)) | |
1217 | { | |
1218 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1219 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1220 | return scm_i_inexact_floor_remainder | |
1221 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1222 | else | |
fa075d40 AW |
1223 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
1224 | s_scm_floor_remainder); | |
8f9da340 MW |
1225 | } |
1226 | else if (SCM_FRACTIONP (x)) | |
1227 | { | |
1228 | if (SCM_REALP (y)) | |
1229 | return scm_i_inexact_floor_remainder | |
1230 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1231 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1232 | return scm_i_exact_rational_floor_remainder (x, y); | |
1233 | else | |
fa075d40 AW |
1234 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG2, |
1235 | s_scm_floor_remainder); | |
8f9da340 MW |
1236 | } |
1237 | else | |
fa075d40 AW |
1238 | return scm_wta_dispatch_2 (g_scm_floor_remainder, x, y, SCM_ARG1, |
1239 | s_scm_floor_remainder); | |
8f9da340 MW |
1240 | } |
1241 | #undef FUNC_NAME | |
1242 | ||
1243 | static SCM | |
1244 | scm_i_inexact_floor_remainder (double x, double y) | |
1245 | { | |
1246 | /* Although it would be more efficient to use fmod here, we can't | |
1247 | because it would in some cases produce results inconsistent with | |
1248 | scm_i_inexact_floor_quotient, such that x != q * y + r (not even | |
1249 | close). In particular, when x is very close to a multiple of y, | |
1250 | then r might be either 0.0 or y, but those two cases must | |
1251 | correspond to different choices of q. If r = 0.0 then q must be | |
1252 | x/y, and if r = y then q must be x/y-1. If quotient chooses one | |
1253 | and remainder chooses the other, it would be bad. */ | |
1254 | if (SCM_UNLIKELY (y == 0)) | |
1255 | scm_num_overflow (s_scm_floor_remainder); /* or return a NaN? */ | |
1256 | else | |
1257 | return scm_from_double (x - y * floor (x / y)); | |
1258 | } | |
1259 | ||
1260 | static SCM | |
1261 | scm_i_exact_rational_floor_remainder (SCM x, SCM y) | |
1262 | { | |
1263 | SCM xd = scm_denominator (x); | |
1264 | SCM yd = scm_denominator (y); | |
1265 | SCM r1 = scm_floor_remainder (scm_product (scm_numerator (x), yd), | |
1266 | scm_product (scm_numerator (y), xd)); | |
1267 | return scm_divide (r1, scm_product (xd, yd)); | |
1268 | } | |
1269 | ||
1270 | ||
1271 | static void scm_i_inexact_floor_divide (double x, double y, | |
1272 | SCM *qp, SCM *rp); | |
1273 | static void scm_i_exact_rational_floor_divide (SCM x, SCM y, | |
1274 | SCM *qp, SCM *rp); | |
1275 | ||
1276 | SCM_PRIMITIVE_GENERIC (scm_i_floor_divide, "floor/", 2, 0, 0, | |
1277 | (SCM x, SCM y), | |
1278 | "Return the integer @var{q} and the real number @var{r}\n" | |
1279 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1280 | "and @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1281 | "@lisp\n" | |
1282 | "(floor/ 123 10) @result{} 12 and 3\n" | |
1283 | "(floor/ 123 -10) @result{} -13 and -7\n" | |
1284 | "(floor/ -123 10) @result{} -13 and 7\n" | |
1285 | "(floor/ -123 -10) @result{} 12 and -3\n" | |
1286 | "(floor/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
1287 | "(floor/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
1288 | "@end lisp") | |
1289 | #define FUNC_NAME s_scm_i_floor_divide | |
1290 | { | |
1291 | SCM q, r; | |
1292 | ||
1293 | scm_floor_divide(x, y, &q, &r); | |
1294 | return scm_values (scm_list_2 (q, r)); | |
1295 | } | |
1296 | #undef FUNC_NAME | |
1297 | ||
1298 | #define s_scm_floor_divide s_scm_i_floor_divide | |
1299 | #define g_scm_floor_divide g_scm_i_floor_divide | |
1300 | ||
1301 | void | |
1302 | scm_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1303 | { | |
1304 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1305 | { | |
1306 | scm_t_inum xx = SCM_I_INUM (x); | |
1307 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1308 | { | |
1309 | scm_t_inum yy = SCM_I_INUM (y); | |
1310 | if (SCM_UNLIKELY (yy == 0)) | |
1311 | scm_num_overflow (s_scm_floor_divide); | |
1312 | else | |
1313 | { | |
1314 | scm_t_inum qq = xx / yy; | |
1315 | scm_t_inum rr = xx % yy; | |
1316 | int needs_adjustment; | |
1317 | ||
1318 | if (SCM_LIKELY (yy > 0)) | |
1319 | needs_adjustment = (rr < 0); | |
1320 | else | |
1321 | needs_adjustment = (rr > 0); | |
1322 | ||
1323 | if (needs_adjustment) | |
1324 | { | |
1325 | rr += yy; | |
1326 | qq--; | |
1327 | } | |
1328 | ||
1329 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1330 | *qp = SCM_I_MAKINUM (qq); | |
1331 | else | |
1332 | *qp = scm_i_inum2big (qq); | |
1333 | *rp = SCM_I_MAKINUM (rr); | |
1334 | } | |
1335 | return; | |
1336 | } | |
1337 | else if (SCM_BIGP (y)) | |
1338 | { | |
1339 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1340 | scm_remember_upto_here_1 (y); | |
1341 | if (sign > 0) | |
1342 | { | |
1343 | if (xx < 0) | |
1344 | { | |
1345 | SCM r = scm_i_mkbig (); | |
1346 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1347 | scm_remember_upto_here_1 (y); | |
1348 | *qp = SCM_I_MAKINUM (-1); | |
1349 | *rp = scm_i_normbig (r); | |
1350 | } | |
1351 | else | |
1352 | { | |
1353 | *qp = SCM_INUM0; | |
1354 | *rp = x; | |
1355 | } | |
1356 | } | |
1357 | else if (xx <= 0) | |
1358 | { | |
1359 | *qp = SCM_INUM0; | |
1360 | *rp = x; | |
1361 | } | |
1362 | else | |
1363 | { | |
1364 | SCM r = scm_i_mkbig (); | |
1365 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1366 | scm_remember_upto_here_1 (y); | |
1367 | *qp = SCM_I_MAKINUM (-1); | |
1368 | *rp = scm_i_normbig (r); | |
1369 | } | |
1370 | return; | |
1371 | } | |
1372 | else if (SCM_REALP (y)) | |
1373 | return scm_i_inexact_floor_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1374 | else if (SCM_FRACTIONP (y)) | |
1375 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1376 | else | |
1377 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1378 | s_scm_floor_divide, qp, rp); | |
1379 | } | |
1380 | else if (SCM_BIGP (x)) | |
1381 | { | |
1382 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1383 | { | |
1384 | scm_t_inum yy = SCM_I_INUM (y); | |
1385 | if (SCM_UNLIKELY (yy == 0)) | |
1386 | scm_num_overflow (s_scm_floor_divide); | |
1387 | else | |
1388 | { | |
1389 | SCM q = scm_i_mkbig (); | |
1390 | SCM r = scm_i_mkbig (); | |
1391 | if (yy > 0) | |
1392 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1393 | SCM_I_BIG_MPZ (x), yy); | |
1394 | else | |
1395 | { | |
1396 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1397 | SCM_I_BIG_MPZ (x), -yy); | |
1398 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1399 | } | |
1400 | scm_remember_upto_here_1 (x); | |
1401 | *qp = scm_i_normbig (q); | |
1402 | *rp = scm_i_normbig (r); | |
1403 | } | |
1404 | return; | |
1405 | } | |
1406 | else if (SCM_BIGP (y)) | |
1407 | { | |
1408 | SCM q = scm_i_mkbig (); | |
1409 | SCM r = scm_i_mkbig (); | |
1410 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1411 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1412 | scm_remember_upto_here_2 (x, y); | |
1413 | *qp = scm_i_normbig (q); | |
1414 | *rp = scm_i_normbig (r); | |
1415 | return; | |
1416 | } | |
1417 | else if (SCM_REALP (y)) | |
1418 | return scm_i_inexact_floor_divide | |
1419 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1420 | else if (SCM_FRACTIONP (y)) | |
1421 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1422 | else | |
1423 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1424 | s_scm_floor_divide, qp, rp); | |
1425 | } | |
1426 | else if (SCM_REALP (x)) | |
1427 | { | |
1428 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1429 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1430 | return scm_i_inexact_floor_divide | |
1431 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
1432 | else | |
1433 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1434 | s_scm_floor_divide, qp, rp); | |
1435 | } | |
1436 | else if (SCM_FRACTIONP (x)) | |
1437 | { | |
1438 | if (SCM_REALP (y)) | |
1439 | return scm_i_inexact_floor_divide | |
1440 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
1441 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1442 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1443 | else | |
1444 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1445 | s_scm_floor_divide, qp, rp); | |
1446 | } | |
1447 | else | |
1448 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG1, | |
1449 | s_scm_floor_divide, qp, rp); | |
1450 | } | |
1451 | ||
1452 | static void | |
1453 | scm_i_inexact_floor_divide (double x, double y, SCM *qp, SCM *rp) | |
1454 | { | |
1455 | if (SCM_UNLIKELY (y == 0)) | |
1456 | scm_num_overflow (s_scm_floor_divide); /* or return a NaN? */ | |
1457 | else | |
1458 | { | |
1459 | double q = floor (x / y); | |
1460 | double r = x - q * y; | |
1461 | *qp = scm_from_double (q); | |
1462 | *rp = scm_from_double (r); | |
1463 | } | |
1464 | } | |
1465 | ||
1466 | static void | |
1467 | scm_i_exact_rational_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1468 | { | |
1469 | SCM r1; | |
1470 | SCM xd = scm_denominator (x); | |
1471 | SCM yd = scm_denominator (y); | |
1472 | ||
1473 | scm_floor_divide (scm_product (scm_numerator (x), yd), | |
1474 | scm_product (scm_numerator (y), xd), | |
1475 | qp, &r1); | |
1476 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
1477 | } | |
1478 | ||
1479 | static SCM scm_i_inexact_ceiling_quotient (double x, double y); | |
1480 | static SCM scm_i_exact_rational_ceiling_quotient (SCM x, SCM y); | |
1481 | ||
1482 | SCM_PRIMITIVE_GENERIC (scm_ceiling_quotient, "ceiling-quotient", 2, 0, 0, | |
1483 | (SCM x, SCM y), | |
1484 | "Return the ceiling of @math{@var{x} / @var{y}}.\n" | |
1485 | "@lisp\n" | |
1486 | "(ceiling-quotient 123 10) @result{} 13\n" | |
1487 | "(ceiling-quotient 123 -10) @result{} -12\n" | |
1488 | "(ceiling-quotient -123 10) @result{} -12\n" | |
1489 | "(ceiling-quotient -123 -10) @result{} 13\n" | |
1490 | "(ceiling-quotient -123.2 -63.5) @result{} 2.0\n" | |
1491 | "(ceiling-quotient 16/3 -10/7) @result{} -3\n" | |
1492 | "@end lisp") | |
1493 | #define FUNC_NAME s_scm_ceiling_quotient | |
1494 | { | |
1495 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1496 | { | |
1497 | scm_t_inum xx = SCM_I_INUM (x); | |
1498 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1499 | { | |
1500 | scm_t_inum yy = SCM_I_INUM (y); | |
1501 | if (SCM_UNLIKELY (yy == 0)) | |
1502 | scm_num_overflow (s_scm_ceiling_quotient); | |
1503 | else | |
1504 | { | |
1505 | scm_t_inum xx1 = xx; | |
1506 | scm_t_inum qq; | |
1507 | if (SCM_LIKELY (yy > 0)) | |
1508 | { | |
1509 | if (SCM_LIKELY (xx >= 0)) | |
1510 | xx1 = xx + yy - 1; | |
1511 | } | |
8f9da340 MW |
1512 | else if (xx < 0) |
1513 | xx1 = xx + yy + 1; | |
1514 | qq = xx1 / yy; | |
1515 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1516 | return SCM_I_MAKINUM (qq); | |
1517 | else | |
1518 | return scm_i_inum2big (qq); | |
1519 | } | |
1520 | } | |
1521 | else if (SCM_BIGP (y)) | |
1522 | { | |
1523 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1524 | scm_remember_upto_here_1 (y); | |
1525 | if (SCM_LIKELY (sign > 0)) | |
1526 | { | |
1527 | if (SCM_LIKELY (xx > 0)) | |
1528 | return SCM_INUM1; | |
1529 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1530 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1531 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1532 | { | |
1533 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1534 | scm_remember_upto_here_1 (y); | |
1535 | return SCM_I_MAKINUM (-1); | |
1536 | } | |
1537 | else | |
1538 | return SCM_INUM0; | |
1539 | } | |
1540 | else if (xx >= 0) | |
1541 | return SCM_INUM0; | |
1542 | else | |
1543 | return SCM_INUM1; | |
1544 | } | |
1545 | else if (SCM_REALP (y)) | |
1546 | return scm_i_inexact_ceiling_quotient (xx, SCM_REAL_VALUE (y)); | |
1547 | else if (SCM_FRACTIONP (y)) | |
1548 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1549 | else | |
fa075d40 AW |
1550 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
1551 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1552 | } |
1553 | else if (SCM_BIGP (x)) | |
1554 | { | |
1555 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1556 | { | |
1557 | scm_t_inum yy = SCM_I_INUM (y); | |
1558 | if (SCM_UNLIKELY (yy == 0)) | |
1559 | scm_num_overflow (s_scm_ceiling_quotient); | |
1560 | else if (SCM_UNLIKELY (yy == 1)) | |
1561 | return x; | |
1562 | else | |
1563 | { | |
1564 | SCM q = scm_i_mkbig (); | |
1565 | if (yy > 0) | |
1566 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1567 | else | |
1568 | { | |
1569 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1570 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1571 | } | |
1572 | scm_remember_upto_here_1 (x); | |
1573 | return scm_i_normbig (q); | |
1574 | } | |
1575 | } | |
1576 | else if (SCM_BIGP (y)) | |
1577 | { | |
1578 | SCM q = scm_i_mkbig (); | |
1579 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1580 | SCM_I_BIG_MPZ (x), | |
1581 | SCM_I_BIG_MPZ (y)); | |
1582 | scm_remember_upto_here_2 (x, y); | |
1583 | return scm_i_normbig (q); | |
1584 | } | |
1585 | else if (SCM_REALP (y)) | |
1586 | return scm_i_inexact_ceiling_quotient | |
1587 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1588 | else if (SCM_FRACTIONP (y)) | |
1589 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1590 | else | |
fa075d40 AW |
1591 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
1592 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1593 | } |
1594 | else if (SCM_REALP (x)) | |
1595 | { | |
1596 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1597 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1598 | return scm_i_inexact_ceiling_quotient | |
1599 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1600 | else | |
fa075d40 AW |
1601 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
1602 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1603 | } |
1604 | else if (SCM_FRACTIONP (x)) | |
1605 | { | |
1606 | if (SCM_REALP (y)) | |
1607 | return scm_i_inexact_ceiling_quotient | |
1608 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1609 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1610 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1611 | else | |
fa075d40 AW |
1612 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, |
1613 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1614 | } |
1615 | else | |
fa075d40 AW |
1616 | return scm_wta_dispatch_2 (g_scm_ceiling_quotient, x, y, SCM_ARG1, |
1617 | s_scm_ceiling_quotient); | |
8f9da340 MW |
1618 | } |
1619 | #undef FUNC_NAME | |
1620 | ||
1621 | static SCM | |
1622 | scm_i_inexact_ceiling_quotient (double x, double y) | |
1623 | { | |
1624 | if (SCM_UNLIKELY (y == 0)) | |
1625 | scm_num_overflow (s_scm_ceiling_quotient); /* or return a NaN? */ | |
1626 | else | |
1627 | return scm_from_double (ceil (x / y)); | |
1628 | } | |
1629 | ||
1630 | static SCM | |
1631 | scm_i_exact_rational_ceiling_quotient (SCM x, SCM y) | |
1632 | { | |
1633 | return scm_ceiling_quotient | |
1634 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1635 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1636 | } | |
1637 | ||
1638 | static SCM scm_i_inexact_ceiling_remainder (double x, double y); | |
1639 | static SCM scm_i_exact_rational_ceiling_remainder (SCM x, SCM y); | |
1640 | ||
1641 | SCM_PRIMITIVE_GENERIC (scm_ceiling_remainder, "ceiling-remainder", 2, 0, 0, | |
1642 | (SCM x, SCM y), | |
1643 | "Return the real number @var{r} such that\n" | |
1644 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1645 | "where @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1646 | "@lisp\n" | |
1647 | "(ceiling-remainder 123 10) @result{} -7\n" | |
1648 | "(ceiling-remainder 123 -10) @result{} 3\n" | |
1649 | "(ceiling-remainder -123 10) @result{} -3\n" | |
1650 | "(ceiling-remainder -123 -10) @result{} 7\n" | |
1651 | "(ceiling-remainder -123.2 -63.5) @result{} 3.8\n" | |
1652 | "(ceiling-remainder 16/3 -10/7) @result{} 22/21\n" | |
1653 | "@end lisp") | |
1654 | #define FUNC_NAME s_scm_ceiling_remainder | |
1655 | { | |
1656 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1657 | { | |
1658 | scm_t_inum xx = SCM_I_INUM (x); | |
1659 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1660 | { | |
1661 | scm_t_inum yy = SCM_I_INUM (y); | |
1662 | if (SCM_UNLIKELY (yy == 0)) | |
1663 | scm_num_overflow (s_scm_ceiling_remainder); | |
1664 | else | |
1665 | { | |
1666 | scm_t_inum rr = xx % yy; | |
1667 | int needs_adjustment; | |
1668 | ||
1669 | if (SCM_LIKELY (yy > 0)) | |
1670 | needs_adjustment = (rr > 0); | |
1671 | else | |
1672 | needs_adjustment = (rr < 0); | |
1673 | ||
1674 | if (needs_adjustment) | |
1675 | rr -= yy; | |
1676 | return SCM_I_MAKINUM (rr); | |
1677 | } | |
1678 | } | |
1679 | else if (SCM_BIGP (y)) | |
1680 | { | |
1681 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1682 | scm_remember_upto_here_1 (y); | |
1683 | if (SCM_LIKELY (sign > 0)) | |
1684 | { | |
1685 | if (SCM_LIKELY (xx > 0)) | |
1686 | { | |
1687 | SCM r = scm_i_mkbig (); | |
1688 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1689 | scm_remember_upto_here_1 (y); | |
1690 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1691 | return scm_i_normbig (r); | |
1692 | } | |
1693 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1694 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1695 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1696 | { | |
1697 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1698 | scm_remember_upto_here_1 (y); | |
1699 | return SCM_INUM0; | |
1700 | } | |
1701 | else | |
1702 | return x; | |
1703 | } | |
1704 | else if (xx >= 0) | |
1705 | return x; | |
1706 | else | |
1707 | { | |
1708 | SCM r = scm_i_mkbig (); | |
1709 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1710 | scm_remember_upto_here_1 (y); | |
1711 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1712 | return scm_i_normbig (r); | |
1713 | } | |
1714 | } | |
1715 | else if (SCM_REALP (y)) | |
1716 | return scm_i_inexact_ceiling_remainder (xx, SCM_REAL_VALUE (y)); | |
1717 | else if (SCM_FRACTIONP (y)) | |
1718 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1719 | else | |
fa075d40 AW |
1720 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
1721 | s_scm_ceiling_remainder); | |
8f9da340 MW |
1722 | } |
1723 | else if (SCM_BIGP (x)) | |
1724 | { | |
1725 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1726 | { | |
1727 | scm_t_inum yy = SCM_I_INUM (y); | |
1728 | if (SCM_UNLIKELY (yy == 0)) | |
1729 | scm_num_overflow (s_scm_ceiling_remainder); | |
1730 | else | |
1731 | { | |
1732 | scm_t_inum rr; | |
1733 | if (yy > 0) | |
1734 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1735 | else | |
1736 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1737 | scm_remember_upto_here_1 (x); | |
1738 | return SCM_I_MAKINUM (rr); | |
1739 | } | |
1740 | } | |
1741 | else if (SCM_BIGP (y)) | |
1742 | { | |
1743 | SCM r = scm_i_mkbig (); | |
1744 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
1745 | SCM_I_BIG_MPZ (x), | |
1746 | SCM_I_BIG_MPZ (y)); | |
1747 | scm_remember_upto_here_2 (x, y); | |
1748 | return scm_i_normbig (r); | |
1749 | } | |
1750 | else if (SCM_REALP (y)) | |
1751 | return scm_i_inexact_ceiling_remainder | |
1752 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1753 | else if (SCM_FRACTIONP (y)) | |
1754 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1755 | else | |
fa075d40 AW |
1756 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
1757 | s_scm_ceiling_remainder); | |
8f9da340 MW |
1758 | } |
1759 | else if (SCM_REALP (x)) | |
1760 | { | |
1761 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1762 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1763 | return scm_i_inexact_ceiling_remainder | |
1764 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1765 | else | |
fa075d40 AW |
1766 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
1767 | s_scm_ceiling_remainder); | |
8f9da340 MW |
1768 | } |
1769 | else if (SCM_FRACTIONP (x)) | |
1770 | { | |
1771 | if (SCM_REALP (y)) | |
1772 | return scm_i_inexact_ceiling_remainder | |
1773 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1774 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1775 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1776 | else | |
fa075d40 AW |
1777 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, |
1778 | s_scm_ceiling_remainder); | |
8f9da340 MW |
1779 | } |
1780 | else | |
fa075d40 AW |
1781 | return scm_wta_dispatch_2 (g_scm_ceiling_remainder, x, y, SCM_ARG1, |
1782 | s_scm_ceiling_remainder); | |
8f9da340 MW |
1783 | } |
1784 | #undef FUNC_NAME | |
1785 | ||
1786 | static SCM | |
1787 | scm_i_inexact_ceiling_remainder (double x, double y) | |
1788 | { | |
1789 | /* Although it would be more efficient to use fmod here, we can't | |
1790 | because it would in some cases produce results inconsistent with | |
1791 | scm_i_inexact_ceiling_quotient, such that x != q * y + r (not even | |
1792 | close). In particular, when x is very close to a multiple of y, | |
1793 | then r might be either 0.0 or -y, but those two cases must | |
1794 | correspond to different choices of q. If r = 0.0 then q must be | |
1795 | x/y, and if r = -y then q must be x/y+1. If quotient chooses one | |
1796 | and remainder chooses the other, it would be bad. */ | |
1797 | if (SCM_UNLIKELY (y == 0)) | |
1798 | scm_num_overflow (s_scm_ceiling_remainder); /* or return a NaN? */ | |
1799 | else | |
1800 | return scm_from_double (x - y * ceil (x / y)); | |
1801 | } | |
1802 | ||
1803 | static SCM | |
1804 | scm_i_exact_rational_ceiling_remainder (SCM x, SCM y) | |
1805 | { | |
1806 | SCM xd = scm_denominator (x); | |
1807 | SCM yd = scm_denominator (y); | |
1808 | SCM r1 = scm_ceiling_remainder (scm_product (scm_numerator (x), yd), | |
1809 | scm_product (scm_numerator (y), xd)); | |
1810 | return scm_divide (r1, scm_product (xd, yd)); | |
1811 | } | |
1812 | ||
1813 | static void scm_i_inexact_ceiling_divide (double x, double y, | |
1814 | SCM *qp, SCM *rp); | |
1815 | static void scm_i_exact_rational_ceiling_divide (SCM x, SCM y, | |
1816 | SCM *qp, SCM *rp); | |
1817 | ||
1818 | SCM_PRIMITIVE_GENERIC (scm_i_ceiling_divide, "ceiling/", 2, 0, 0, | |
1819 | (SCM x, SCM y), | |
1820 | "Return the integer @var{q} and the real number @var{r}\n" | |
1821 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1822 | "and @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1823 | "@lisp\n" | |
1824 | "(ceiling/ 123 10) @result{} 13 and -7\n" | |
1825 | "(ceiling/ 123 -10) @result{} -12 and 3\n" | |
1826 | "(ceiling/ -123 10) @result{} -12 and -3\n" | |
1827 | "(ceiling/ -123 -10) @result{} 13 and 7\n" | |
1828 | "(ceiling/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1829 | "(ceiling/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1830 | "@end lisp") | |
1831 | #define FUNC_NAME s_scm_i_ceiling_divide | |
1832 | { | |
1833 | SCM q, r; | |
1834 | ||
1835 | scm_ceiling_divide(x, y, &q, &r); | |
1836 | return scm_values (scm_list_2 (q, r)); | |
1837 | } | |
1838 | #undef FUNC_NAME | |
1839 | ||
1840 | #define s_scm_ceiling_divide s_scm_i_ceiling_divide | |
1841 | #define g_scm_ceiling_divide g_scm_i_ceiling_divide | |
1842 | ||
1843 | void | |
1844 | scm_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1845 | { | |
1846 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1847 | { | |
1848 | scm_t_inum xx = SCM_I_INUM (x); | |
1849 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1850 | { | |
1851 | scm_t_inum yy = SCM_I_INUM (y); | |
1852 | if (SCM_UNLIKELY (yy == 0)) | |
1853 | scm_num_overflow (s_scm_ceiling_divide); | |
1854 | else | |
1855 | { | |
1856 | scm_t_inum qq = xx / yy; | |
1857 | scm_t_inum rr = xx % yy; | |
1858 | int needs_adjustment; | |
1859 | ||
1860 | if (SCM_LIKELY (yy > 0)) | |
1861 | needs_adjustment = (rr > 0); | |
1862 | else | |
1863 | needs_adjustment = (rr < 0); | |
1864 | ||
1865 | if (needs_adjustment) | |
1866 | { | |
1867 | rr -= yy; | |
1868 | qq++; | |
1869 | } | |
1870 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1871 | *qp = SCM_I_MAKINUM (qq); | |
1872 | else | |
1873 | *qp = scm_i_inum2big (qq); | |
1874 | *rp = SCM_I_MAKINUM (rr); | |
1875 | } | |
1876 | return; | |
1877 | } | |
1878 | else if (SCM_BIGP (y)) | |
1879 | { | |
1880 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1881 | scm_remember_upto_here_1 (y); | |
1882 | if (SCM_LIKELY (sign > 0)) | |
1883 | { | |
1884 | if (SCM_LIKELY (xx > 0)) | |
1885 | { | |
1886 | SCM r = scm_i_mkbig (); | |
1887 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1888 | scm_remember_upto_here_1 (y); | |
1889 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1890 | *qp = SCM_INUM1; | |
1891 | *rp = scm_i_normbig (r); | |
1892 | } | |
1893 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1894 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1895 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1896 | { | |
1897 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1898 | scm_remember_upto_here_1 (y); | |
1899 | *qp = SCM_I_MAKINUM (-1); | |
1900 | *rp = SCM_INUM0; | |
1901 | } | |
1902 | else | |
1903 | { | |
1904 | *qp = SCM_INUM0; | |
1905 | *rp = x; | |
1906 | } | |
1907 | } | |
1908 | else if (xx >= 0) | |
1909 | { | |
1910 | *qp = SCM_INUM0; | |
1911 | *rp = x; | |
1912 | } | |
1913 | else | |
1914 | { | |
1915 | SCM r = scm_i_mkbig (); | |
1916 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1917 | scm_remember_upto_here_1 (y); | |
1918 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1919 | *qp = SCM_INUM1; | |
1920 | *rp = scm_i_normbig (r); | |
1921 | } | |
1922 | return; | |
1923 | } | |
1924 | else if (SCM_REALP (y)) | |
1925 | return scm_i_inexact_ceiling_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1926 | else if (SCM_FRACTIONP (y)) | |
1927 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
1928 | else | |
1929 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1930 | s_scm_ceiling_divide, qp, rp); | |
1931 | } | |
1932 | else if (SCM_BIGP (x)) | |
1933 | { | |
1934 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1935 | { | |
1936 | scm_t_inum yy = SCM_I_INUM (y); | |
1937 | if (SCM_UNLIKELY (yy == 0)) | |
1938 | scm_num_overflow (s_scm_ceiling_divide); | |
1939 | else | |
1940 | { | |
1941 | SCM q = scm_i_mkbig (); | |
1942 | SCM r = scm_i_mkbig (); | |
1943 | if (yy > 0) | |
1944 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1945 | SCM_I_BIG_MPZ (x), yy); | |
1946 | else | |
1947 | { | |
1948 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1949 | SCM_I_BIG_MPZ (x), -yy); | |
1950 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1951 | } | |
1952 | scm_remember_upto_here_1 (x); | |
1953 | *qp = scm_i_normbig (q); | |
1954 | *rp = scm_i_normbig (r); | |
1955 | } | |
1956 | return; | |
1957 | } | |
1958 | else if (SCM_BIGP (y)) | |
1959 | { | |
1960 | SCM q = scm_i_mkbig (); | |
1961 | SCM r = scm_i_mkbig (); | |
1962 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1963 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1964 | scm_remember_upto_here_2 (x, y); | |
1965 | *qp = scm_i_normbig (q); | |
1966 | *rp = scm_i_normbig (r); | |
1967 | return; | |
1968 | } | |
1969 | else if (SCM_REALP (y)) | |
1970 | return scm_i_inexact_ceiling_divide | |
1971 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1972 | else if (SCM_FRACTIONP (y)) | |
1973 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
1974 | else | |
1975 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1976 | s_scm_ceiling_divide, qp, rp); | |
1977 | } | |
1978 | else if (SCM_REALP (x)) | |
1979 | { | |
1980 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1981 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1982 | return scm_i_inexact_ceiling_divide | |
1983 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
1984 | else | |
1985 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1986 | s_scm_ceiling_divide, qp, rp); | |
1987 | } | |
1988 | else if (SCM_FRACTIONP (x)) | |
1989 | { | |
1990 | if (SCM_REALP (y)) | |
1991 | return scm_i_inexact_ceiling_divide | |
1992 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
1993 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1994 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
1995 | else | |
1996 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1997 | s_scm_ceiling_divide, qp, rp); | |
1998 | } | |
1999 | else | |
2000 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG1, | |
2001 | s_scm_ceiling_divide, qp, rp); | |
2002 | } | |
2003 | ||
2004 | static void | |
2005 | scm_i_inexact_ceiling_divide (double x, double y, SCM *qp, SCM *rp) | |
2006 | { | |
2007 | if (SCM_UNLIKELY (y == 0)) | |
2008 | scm_num_overflow (s_scm_ceiling_divide); /* or return a NaN? */ | |
2009 | else | |
2010 | { | |
2011 | double q = ceil (x / y); | |
2012 | double r = x - q * y; | |
2013 | *qp = scm_from_double (q); | |
2014 | *rp = scm_from_double (r); | |
2015 | } | |
2016 | } | |
2017 | ||
2018 | static void | |
2019 | scm_i_exact_rational_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2020 | { | |
2021 | SCM r1; | |
2022 | SCM xd = scm_denominator (x); | |
2023 | SCM yd = scm_denominator (y); | |
2024 | ||
2025 | scm_ceiling_divide (scm_product (scm_numerator (x), yd), | |
2026 | scm_product (scm_numerator (y), xd), | |
2027 | qp, &r1); | |
2028 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2029 | } | |
2030 | ||
2031 | static SCM scm_i_inexact_truncate_quotient (double x, double y); | |
2032 | static SCM scm_i_exact_rational_truncate_quotient (SCM x, SCM y); | |
2033 | ||
2034 | SCM_PRIMITIVE_GENERIC (scm_truncate_quotient, "truncate-quotient", 2, 0, 0, | |
2035 | (SCM x, SCM y), | |
2036 | "Return @math{@var{x} / @var{y}} rounded toward zero.\n" | |
2037 | "@lisp\n" | |
2038 | "(truncate-quotient 123 10) @result{} 12\n" | |
2039 | "(truncate-quotient 123 -10) @result{} -12\n" | |
2040 | "(truncate-quotient -123 10) @result{} -12\n" | |
2041 | "(truncate-quotient -123 -10) @result{} 12\n" | |
2042 | "(truncate-quotient -123.2 -63.5) @result{} 1.0\n" | |
2043 | "(truncate-quotient 16/3 -10/7) @result{} -3\n" | |
2044 | "@end lisp") | |
2045 | #define FUNC_NAME s_scm_truncate_quotient | |
2046 | { | |
2047 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2048 | { | |
2049 | scm_t_inum xx = SCM_I_INUM (x); | |
2050 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2051 | { | |
2052 | scm_t_inum yy = SCM_I_INUM (y); | |
2053 | if (SCM_UNLIKELY (yy == 0)) | |
2054 | scm_num_overflow (s_scm_truncate_quotient); | |
2055 | else | |
2056 | { | |
2057 | scm_t_inum qq = xx / yy; | |
2058 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2059 | return SCM_I_MAKINUM (qq); | |
2060 | else | |
2061 | return scm_i_inum2big (qq); | |
2062 | } | |
2063 | } | |
2064 | else if (SCM_BIGP (y)) | |
2065 | { | |
2066 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2067 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2068 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2069 | { | |
2070 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2071 | scm_remember_upto_here_1 (y); | |
2072 | return SCM_I_MAKINUM (-1); | |
2073 | } | |
2074 | else | |
2075 | return SCM_INUM0; | |
2076 | } | |
2077 | else if (SCM_REALP (y)) | |
2078 | return scm_i_inexact_truncate_quotient (xx, SCM_REAL_VALUE (y)); | |
2079 | else if (SCM_FRACTIONP (y)) | |
2080 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2081 | else | |
fa075d40 AW |
2082 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
2083 | s_scm_truncate_quotient); | |
8f9da340 MW |
2084 | } |
2085 | else if (SCM_BIGP (x)) | |
2086 | { | |
2087 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2088 | { | |
2089 | scm_t_inum yy = SCM_I_INUM (y); | |
2090 | if (SCM_UNLIKELY (yy == 0)) | |
2091 | scm_num_overflow (s_scm_truncate_quotient); | |
2092 | else if (SCM_UNLIKELY (yy == 1)) | |
2093 | return x; | |
2094 | else | |
2095 | { | |
2096 | SCM q = scm_i_mkbig (); | |
2097 | if (yy > 0) | |
2098 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
2099 | else | |
2100 | { | |
2101 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
2102 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2103 | } | |
2104 | scm_remember_upto_here_1 (x); | |
2105 | return scm_i_normbig (q); | |
2106 | } | |
2107 | } | |
2108 | else if (SCM_BIGP (y)) | |
2109 | { | |
2110 | SCM q = scm_i_mkbig (); | |
2111 | mpz_tdiv_q (SCM_I_BIG_MPZ (q), | |
2112 | SCM_I_BIG_MPZ (x), | |
2113 | SCM_I_BIG_MPZ (y)); | |
2114 | scm_remember_upto_here_2 (x, y); | |
2115 | return scm_i_normbig (q); | |
2116 | } | |
2117 | else if (SCM_REALP (y)) | |
2118 | return scm_i_inexact_truncate_quotient | |
2119 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2120 | else if (SCM_FRACTIONP (y)) | |
2121 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2122 | else | |
fa075d40 AW |
2123 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
2124 | s_scm_truncate_quotient); | |
8f9da340 MW |
2125 | } |
2126 | else if (SCM_REALP (x)) | |
2127 | { | |
2128 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2129 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2130 | return scm_i_inexact_truncate_quotient | |
2131 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2132 | else | |
fa075d40 AW |
2133 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
2134 | s_scm_truncate_quotient); | |
8f9da340 MW |
2135 | } |
2136 | else if (SCM_FRACTIONP (x)) | |
2137 | { | |
2138 | if (SCM_REALP (y)) | |
2139 | return scm_i_inexact_truncate_quotient | |
2140 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2141 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2142 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2143 | else | |
fa075d40 AW |
2144 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, |
2145 | s_scm_truncate_quotient); | |
8f9da340 MW |
2146 | } |
2147 | else | |
fa075d40 AW |
2148 | return scm_wta_dispatch_2 (g_scm_truncate_quotient, x, y, SCM_ARG1, |
2149 | s_scm_truncate_quotient); | |
8f9da340 MW |
2150 | } |
2151 | #undef FUNC_NAME | |
2152 | ||
2153 | static SCM | |
2154 | scm_i_inexact_truncate_quotient (double x, double y) | |
2155 | { | |
2156 | if (SCM_UNLIKELY (y == 0)) | |
2157 | scm_num_overflow (s_scm_truncate_quotient); /* or return a NaN? */ | |
2158 | else | |
c251ab63 | 2159 | return scm_from_double (trunc (x / y)); |
8f9da340 MW |
2160 | } |
2161 | ||
2162 | static SCM | |
2163 | scm_i_exact_rational_truncate_quotient (SCM x, SCM y) | |
2164 | { | |
2165 | return scm_truncate_quotient | |
2166 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2167 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2168 | } | |
2169 | ||
2170 | static SCM scm_i_inexact_truncate_remainder (double x, double y); | |
2171 | static SCM scm_i_exact_rational_truncate_remainder (SCM x, SCM y); | |
2172 | ||
2173 | SCM_PRIMITIVE_GENERIC (scm_truncate_remainder, "truncate-remainder", 2, 0, 0, | |
2174 | (SCM x, SCM y), | |
2175 | "Return the real number @var{r} such that\n" | |
2176 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2177 | "where @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2178 | "@lisp\n" | |
2179 | "(truncate-remainder 123 10) @result{} 3\n" | |
2180 | "(truncate-remainder 123 -10) @result{} 3\n" | |
2181 | "(truncate-remainder -123 10) @result{} -3\n" | |
2182 | "(truncate-remainder -123 -10) @result{} -3\n" | |
2183 | "(truncate-remainder -123.2 -63.5) @result{} -59.7\n" | |
2184 | "(truncate-remainder 16/3 -10/7) @result{} 22/21\n" | |
2185 | "@end lisp") | |
2186 | #define FUNC_NAME s_scm_truncate_remainder | |
2187 | { | |
2188 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2189 | { | |
2190 | scm_t_inum xx = SCM_I_INUM (x); | |
2191 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2192 | { | |
2193 | scm_t_inum yy = SCM_I_INUM (y); | |
2194 | if (SCM_UNLIKELY (yy == 0)) | |
2195 | scm_num_overflow (s_scm_truncate_remainder); | |
2196 | else | |
2197 | return SCM_I_MAKINUM (xx % yy); | |
2198 | } | |
2199 | else if (SCM_BIGP (y)) | |
2200 | { | |
2201 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2202 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2203 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2204 | { | |
2205 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2206 | scm_remember_upto_here_1 (y); | |
2207 | return SCM_INUM0; | |
2208 | } | |
2209 | else | |
2210 | return x; | |
2211 | } | |
2212 | else if (SCM_REALP (y)) | |
2213 | return scm_i_inexact_truncate_remainder (xx, SCM_REAL_VALUE (y)); | |
2214 | else if (SCM_FRACTIONP (y)) | |
2215 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2216 | else | |
fa075d40 AW |
2217 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
2218 | s_scm_truncate_remainder); | |
8f9da340 MW |
2219 | } |
2220 | else if (SCM_BIGP (x)) | |
2221 | { | |
2222 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2223 | { | |
2224 | scm_t_inum yy = SCM_I_INUM (y); | |
2225 | if (SCM_UNLIKELY (yy == 0)) | |
2226 | scm_num_overflow (s_scm_truncate_remainder); | |
2227 | else | |
2228 | { | |
2229 | scm_t_inum rr = (mpz_tdiv_ui (SCM_I_BIG_MPZ (x), | |
2230 | (yy > 0) ? yy : -yy) | |
2231 | * mpz_sgn (SCM_I_BIG_MPZ (x))); | |
2232 | scm_remember_upto_here_1 (x); | |
2233 | return SCM_I_MAKINUM (rr); | |
2234 | } | |
2235 | } | |
2236 | else if (SCM_BIGP (y)) | |
2237 | { | |
2238 | SCM r = scm_i_mkbig (); | |
2239 | mpz_tdiv_r (SCM_I_BIG_MPZ (r), | |
2240 | SCM_I_BIG_MPZ (x), | |
2241 | SCM_I_BIG_MPZ (y)); | |
2242 | scm_remember_upto_here_2 (x, y); | |
2243 | return scm_i_normbig (r); | |
2244 | } | |
2245 | else if (SCM_REALP (y)) | |
2246 | return scm_i_inexact_truncate_remainder | |
2247 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2248 | else if (SCM_FRACTIONP (y)) | |
2249 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2250 | else | |
fa075d40 AW |
2251 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
2252 | s_scm_truncate_remainder); | |
8f9da340 MW |
2253 | } |
2254 | else if (SCM_REALP (x)) | |
2255 | { | |
2256 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2257 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2258 | return scm_i_inexact_truncate_remainder | |
2259 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2260 | else | |
fa075d40 AW |
2261 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
2262 | s_scm_truncate_remainder); | |
8f9da340 MW |
2263 | } |
2264 | else if (SCM_FRACTIONP (x)) | |
2265 | { | |
2266 | if (SCM_REALP (y)) | |
2267 | return scm_i_inexact_truncate_remainder | |
2268 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2269 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2270 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2271 | else | |
fa075d40 AW |
2272 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, |
2273 | s_scm_truncate_remainder); | |
8f9da340 MW |
2274 | } |
2275 | else | |
fa075d40 AW |
2276 | return scm_wta_dispatch_2 (g_scm_truncate_remainder, x, y, SCM_ARG1, |
2277 | s_scm_truncate_remainder); | |
8f9da340 MW |
2278 | } |
2279 | #undef FUNC_NAME | |
2280 | ||
2281 | static SCM | |
2282 | scm_i_inexact_truncate_remainder (double x, double y) | |
2283 | { | |
2284 | /* Although it would be more efficient to use fmod here, we can't | |
2285 | because it would in some cases produce results inconsistent with | |
2286 | scm_i_inexact_truncate_quotient, such that x != q * y + r (not even | |
2287 | close). In particular, when x is very close to a multiple of y, | |
2288 | then r might be either 0.0 or sgn(x)*|y|, but those two cases must | |
2289 | correspond to different choices of q. If quotient chooses one and | |
2290 | remainder chooses the other, it would be bad. */ | |
2291 | if (SCM_UNLIKELY (y == 0)) | |
2292 | scm_num_overflow (s_scm_truncate_remainder); /* or return a NaN? */ | |
2293 | else | |
c251ab63 | 2294 | return scm_from_double (x - y * trunc (x / y)); |
8f9da340 MW |
2295 | } |
2296 | ||
2297 | static SCM | |
2298 | scm_i_exact_rational_truncate_remainder (SCM x, SCM y) | |
2299 | { | |
2300 | SCM xd = scm_denominator (x); | |
2301 | SCM yd = scm_denominator (y); | |
2302 | SCM r1 = scm_truncate_remainder (scm_product (scm_numerator (x), yd), | |
2303 | scm_product (scm_numerator (y), xd)); | |
2304 | return scm_divide (r1, scm_product (xd, yd)); | |
2305 | } | |
2306 | ||
2307 | ||
2308 | static void scm_i_inexact_truncate_divide (double x, double y, | |
2309 | SCM *qp, SCM *rp); | |
2310 | static void scm_i_exact_rational_truncate_divide (SCM x, SCM y, | |
2311 | SCM *qp, SCM *rp); | |
2312 | ||
2313 | SCM_PRIMITIVE_GENERIC (scm_i_truncate_divide, "truncate/", 2, 0, 0, | |
2314 | (SCM x, SCM y), | |
2315 | "Return the integer @var{q} and the real number @var{r}\n" | |
2316 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2317 | "and @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2318 | "@lisp\n" | |
2319 | "(truncate/ 123 10) @result{} 12 and 3\n" | |
2320 | "(truncate/ 123 -10) @result{} -12 and 3\n" | |
2321 | "(truncate/ -123 10) @result{} -12 and -3\n" | |
2322 | "(truncate/ -123 -10) @result{} 12 and -3\n" | |
2323 | "(truncate/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
2324 | "(truncate/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2325 | "@end lisp") | |
2326 | #define FUNC_NAME s_scm_i_truncate_divide | |
2327 | { | |
2328 | SCM q, r; | |
2329 | ||
2330 | scm_truncate_divide(x, y, &q, &r); | |
2331 | return scm_values (scm_list_2 (q, r)); | |
2332 | } | |
2333 | #undef FUNC_NAME | |
2334 | ||
2335 | #define s_scm_truncate_divide s_scm_i_truncate_divide | |
2336 | #define g_scm_truncate_divide g_scm_i_truncate_divide | |
2337 | ||
2338 | void | |
2339 | scm_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2340 | { | |
2341 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2342 | { | |
2343 | scm_t_inum xx = SCM_I_INUM (x); | |
2344 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2345 | { | |
2346 | scm_t_inum yy = SCM_I_INUM (y); | |
2347 | if (SCM_UNLIKELY (yy == 0)) | |
2348 | scm_num_overflow (s_scm_truncate_divide); | |
2349 | else | |
2350 | { | |
2351 | scm_t_inum qq = xx / yy; | |
2352 | scm_t_inum rr = xx % yy; | |
2353 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2354 | *qp = SCM_I_MAKINUM (qq); | |
2355 | else | |
2356 | *qp = scm_i_inum2big (qq); | |
2357 | *rp = SCM_I_MAKINUM (rr); | |
2358 | } | |
2359 | return; | |
2360 | } | |
2361 | else if (SCM_BIGP (y)) | |
2362 | { | |
2363 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2364 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2365 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2366 | { | |
2367 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2368 | scm_remember_upto_here_1 (y); | |
2369 | *qp = SCM_I_MAKINUM (-1); | |
2370 | *rp = SCM_INUM0; | |
2371 | } | |
2372 | else | |
2373 | { | |
2374 | *qp = SCM_INUM0; | |
2375 | *rp = x; | |
2376 | } | |
2377 | return; | |
2378 | } | |
2379 | else if (SCM_REALP (y)) | |
2380 | return scm_i_inexact_truncate_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2381 | else if (SCM_FRACTIONP (y)) | |
2382 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2383 | else | |
2384 | return two_valued_wta_dispatch_2 | |
2385 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2386 | s_scm_truncate_divide, qp, rp); | |
2387 | } | |
2388 | else if (SCM_BIGP (x)) | |
2389 | { | |
2390 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2391 | { | |
2392 | scm_t_inum yy = SCM_I_INUM (y); | |
2393 | if (SCM_UNLIKELY (yy == 0)) | |
2394 | scm_num_overflow (s_scm_truncate_divide); | |
2395 | else | |
2396 | { | |
2397 | SCM q = scm_i_mkbig (); | |
2398 | scm_t_inum rr; | |
2399 | if (yy > 0) | |
2400 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2401 | SCM_I_BIG_MPZ (x), yy); | |
2402 | else | |
2403 | { | |
2404 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2405 | SCM_I_BIG_MPZ (x), -yy); | |
2406 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2407 | } | |
2408 | rr *= mpz_sgn (SCM_I_BIG_MPZ (x)); | |
2409 | scm_remember_upto_here_1 (x); | |
2410 | *qp = scm_i_normbig (q); | |
2411 | *rp = SCM_I_MAKINUM (rr); | |
2412 | } | |
2413 | return; | |
2414 | } | |
2415 | else if (SCM_BIGP (y)) | |
2416 | { | |
2417 | SCM q = scm_i_mkbig (); | |
2418 | SCM r = scm_i_mkbig (); | |
2419 | mpz_tdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2420 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2421 | scm_remember_upto_here_2 (x, y); | |
2422 | *qp = scm_i_normbig (q); | |
2423 | *rp = scm_i_normbig (r); | |
2424 | } | |
2425 | else if (SCM_REALP (y)) | |
2426 | return scm_i_inexact_truncate_divide | |
2427 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2428 | else if (SCM_FRACTIONP (y)) | |
2429 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2430 | else | |
2431 | return two_valued_wta_dispatch_2 | |
2432 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2433 | s_scm_truncate_divide, qp, rp); | |
2434 | } | |
2435 | else if (SCM_REALP (x)) | |
2436 | { | |
2437 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2438 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2439 | return scm_i_inexact_truncate_divide | |
2440 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2441 | else | |
2442 | return two_valued_wta_dispatch_2 | |
2443 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2444 | s_scm_truncate_divide, qp, rp); | |
2445 | } | |
2446 | else if (SCM_FRACTIONP (x)) | |
2447 | { | |
2448 | if (SCM_REALP (y)) | |
2449 | return scm_i_inexact_truncate_divide | |
2450 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2451 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2452 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2453 | else | |
2454 | return two_valued_wta_dispatch_2 | |
2455 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2456 | s_scm_truncate_divide, qp, rp); | |
2457 | } | |
2458 | else | |
2459 | return two_valued_wta_dispatch_2 (g_scm_truncate_divide, x, y, SCM_ARG1, | |
2460 | s_scm_truncate_divide, qp, rp); | |
2461 | } | |
2462 | ||
2463 | static void | |
2464 | scm_i_inexact_truncate_divide (double x, double y, SCM *qp, SCM *rp) | |
2465 | { | |
2466 | if (SCM_UNLIKELY (y == 0)) | |
2467 | scm_num_overflow (s_scm_truncate_divide); /* or return a NaN? */ | |
2468 | else | |
2469 | { | |
c15fe499 MW |
2470 | double q = trunc (x / y); |
2471 | double r = x - q * y; | |
8f9da340 MW |
2472 | *qp = scm_from_double (q); |
2473 | *rp = scm_from_double (r); | |
2474 | } | |
2475 | } | |
2476 | ||
2477 | static void | |
2478 | scm_i_exact_rational_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2479 | { | |
2480 | SCM r1; | |
2481 | SCM xd = scm_denominator (x); | |
2482 | SCM yd = scm_denominator (y); | |
2483 | ||
2484 | scm_truncate_divide (scm_product (scm_numerator (x), yd), | |
2485 | scm_product (scm_numerator (y), xd), | |
2486 | qp, &r1); | |
2487 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2488 | } | |
2489 | ||
ff62c168 MW |
2490 | static SCM scm_i_inexact_centered_quotient (double x, double y); |
2491 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
03ddd15b | 2492 | static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y); |
ff62c168 | 2493 | |
8f9da340 MW |
2494 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, |
2495 | (SCM x, SCM y), | |
2496 | "Return the integer @var{q} such that\n" | |
2497 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
2498 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2499 | "@lisp\n" | |
2500 | "(centered-quotient 123 10) @result{} 12\n" | |
2501 | "(centered-quotient 123 -10) @result{} -12\n" | |
2502 | "(centered-quotient -123 10) @result{} -12\n" | |
2503 | "(centered-quotient -123 -10) @result{} 12\n" | |
2504 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
2505 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
2506 | "@end lisp") | |
2507 | #define FUNC_NAME s_scm_centered_quotient | |
2508 | { | |
2509 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2510 | { | |
2511 | scm_t_inum xx = SCM_I_INUM (x); | |
2512 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2513 | { | |
2514 | scm_t_inum yy = SCM_I_INUM (y); | |
2515 | if (SCM_UNLIKELY (yy == 0)) | |
2516 | scm_num_overflow (s_scm_centered_quotient); | |
2517 | else | |
2518 | { | |
2519 | scm_t_inum qq = xx / yy; | |
2520 | scm_t_inum rr = xx % yy; | |
2521 | if (SCM_LIKELY (xx > 0)) | |
2522 | { | |
2523 | if (SCM_LIKELY (yy > 0)) | |
2524 | { | |
2525 | if (rr >= (yy + 1) / 2) | |
2526 | qq++; | |
2527 | } | |
2528 | else | |
2529 | { | |
2530 | if (rr >= (1 - yy) / 2) | |
2531 | qq--; | |
2532 | } | |
2533 | } | |
2534 | else | |
2535 | { | |
2536 | if (SCM_LIKELY (yy > 0)) | |
2537 | { | |
2538 | if (rr < -yy / 2) | |
2539 | qq--; | |
2540 | } | |
2541 | else | |
2542 | { | |
2543 | if (rr < yy / 2) | |
2544 | qq++; | |
2545 | } | |
2546 | } | |
2547 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2548 | return SCM_I_MAKINUM (qq); | |
2549 | else | |
2550 | return scm_i_inum2big (qq); | |
2551 | } | |
2552 | } | |
2553 | else if (SCM_BIGP (y)) | |
2554 | { | |
2555 | /* Pass a denormalized bignum version of x (even though it | |
2556 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
2557 | return scm_i_bigint_centered_quotient (scm_i_long2big (xx), y); | |
2558 | } | |
2559 | else if (SCM_REALP (y)) | |
2560 | return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y)); | |
2561 | else if (SCM_FRACTIONP (y)) | |
2562 | return scm_i_exact_rational_centered_quotient (x, y); | |
2563 | else | |
fa075d40 AW |
2564 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
2565 | s_scm_centered_quotient); | |
8f9da340 MW |
2566 | } |
2567 | else if (SCM_BIGP (x)) | |
2568 | { | |
2569 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2570 | { | |
2571 | scm_t_inum yy = SCM_I_INUM (y); | |
2572 | if (SCM_UNLIKELY (yy == 0)) | |
2573 | scm_num_overflow (s_scm_centered_quotient); | |
2574 | else if (SCM_UNLIKELY (yy == 1)) | |
2575 | return x; | |
2576 | else | |
2577 | { | |
2578 | SCM q = scm_i_mkbig (); | |
2579 | scm_t_inum rr; | |
2580 | /* Arrange for rr to initially be non-positive, | |
2581 | because that simplifies the test to see | |
2582 | if it is within the needed bounds. */ | |
2583 | if (yy > 0) | |
2584 | { | |
2585 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2586 | SCM_I_BIG_MPZ (x), yy); | |
2587 | scm_remember_upto_here_1 (x); | |
2588 | if (rr < -yy / 2) | |
2589 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2590 | SCM_I_BIG_MPZ (q), 1); | |
2591 | } | |
2592 | else | |
2593 | { | |
2594 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2595 | SCM_I_BIG_MPZ (x), -yy); | |
2596 | scm_remember_upto_here_1 (x); | |
2597 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2598 | if (rr < yy / 2) | |
2599 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2600 | SCM_I_BIG_MPZ (q), 1); | |
2601 | } | |
2602 | return scm_i_normbig (q); | |
2603 | } | |
2604 | } | |
2605 | else if (SCM_BIGP (y)) | |
2606 | return scm_i_bigint_centered_quotient (x, y); | |
2607 | else if (SCM_REALP (y)) | |
2608 | return scm_i_inexact_centered_quotient | |
2609 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2610 | else if (SCM_FRACTIONP (y)) | |
2611 | return scm_i_exact_rational_centered_quotient (x, y); | |
2612 | else | |
fa075d40 AW |
2613 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
2614 | s_scm_centered_quotient); | |
8f9da340 MW |
2615 | } |
2616 | else if (SCM_REALP (x)) | |
2617 | { | |
2618 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2619 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2620 | return scm_i_inexact_centered_quotient | |
2621 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2622 | else | |
fa075d40 AW |
2623 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
2624 | s_scm_centered_quotient); | |
8f9da340 MW |
2625 | } |
2626 | else if (SCM_FRACTIONP (x)) | |
2627 | { | |
2628 | if (SCM_REALP (y)) | |
2629 | return scm_i_inexact_centered_quotient | |
2630 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2631 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2632 | return scm_i_exact_rational_centered_quotient (x, y); | |
2633 | else | |
fa075d40 AW |
2634 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
2635 | s_scm_centered_quotient); | |
8f9da340 MW |
2636 | } |
2637 | else | |
fa075d40 AW |
2638 | return scm_wta_dispatch_2 (g_scm_centered_quotient, x, y, SCM_ARG1, |
2639 | s_scm_centered_quotient); | |
8f9da340 MW |
2640 | } |
2641 | #undef FUNC_NAME | |
2642 | ||
2643 | static SCM | |
2644 | scm_i_inexact_centered_quotient (double x, double y) | |
2645 | { | |
2646 | if (SCM_LIKELY (y > 0)) | |
2647 | return scm_from_double (floor (x/y + 0.5)); | |
2648 | else if (SCM_LIKELY (y < 0)) | |
2649 | return scm_from_double (ceil (x/y - 0.5)); | |
2650 | else if (y == 0) | |
2651 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
2652 | else | |
2653 | return scm_nan (); | |
2654 | } | |
2655 | ||
2656 | /* Assumes that both x and y are bigints, though | |
2657 | x might be able to fit into a fixnum. */ | |
2658 | static SCM | |
2659 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
2660 | { | |
2661 | SCM q, r, min_r; | |
2662 | ||
2663 | /* Note that x might be small enough to fit into a | |
2664 | fixnum, so we must not let it escape into the wild */ | |
2665 | q = scm_i_mkbig (); | |
2666 | r = scm_i_mkbig (); | |
2667 | ||
2668 | /* min_r will eventually become -abs(y)/2 */ | |
2669 | min_r = scm_i_mkbig (); | |
2670 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2671 | SCM_I_BIG_MPZ (y), 1); | |
2672 | ||
2673 | /* Arrange for rr to initially be non-positive, | |
2674 | because that simplifies the test to see | |
2675 | if it is within the needed bounds. */ | |
2676 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2677 | { | |
2678 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2679 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2680 | scm_remember_upto_here_2 (x, y); | |
2681 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2682 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2683 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2684 | SCM_I_BIG_MPZ (q), 1); | |
2685 | } | |
2686 | else | |
2687 | { | |
2688 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2689 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2690 | scm_remember_upto_here_2 (x, y); | |
2691 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2692 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2693 | SCM_I_BIG_MPZ (q), 1); | |
2694 | } | |
2695 | scm_remember_upto_here_2 (r, min_r); | |
2696 | return scm_i_normbig (q); | |
2697 | } | |
2698 | ||
2699 | static SCM | |
2700 | scm_i_exact_rational_centered_quotient (SCM x, SCM y) | |
2701 | { | |
2702 | return scm_centered_quotient | |
2703 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2704 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2705 | } | |
2706 | ||
2707 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
2708 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
2709 | static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y); | |
2710 | ||
2711 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
2712 | (SCM x, SCM y), | |
2713 | "Return the real number @var{r} such that\n" | |
2714 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
2715 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2716 | "for some integer @var{q}.\n" | |
2717 | "@lisp\n" | |
2718 | "(centered-remainder 123 10) @result{} 3\n" | |
2719 | "(centered-remainder 123 -10) @result{} 3\n" | |
2720 | "(centered-remainder -123 10) @result{} -3\n" | |
2721 | "(centered-remainder -123 -10) @result{} -3\n" | |
2722 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
2723 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
2724 | "@end lisp") | |
2725 | #define FUNC_NAME s_scm_centered_remainder | |
2726 | { | |
2727 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2728 | { | |
2729 | scm_t_inum xx = SCM_I_INUM (x); | |
2730 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2731 | { | |
2732 | scm_t_inum yy = SCM_I_INUM (y); | |
2733 | if (SCM_UNLIKELY (yy == 0)) | |
2734 | scm_num_overflow (s_scm_centered_remainder); | |
2735 | else | |
2736 | { | |
2737 | scm_t_inum rr = xx % yy; | |
2738 | if (SCM_LIKELY (xx > 0)) | |
2739 | { | |
2740 | if (SCM_LIKELY (yy > 0)) | |
2741 | { | |
2742 | if (rr >= (yy + 1) / 2) | |
2743 | rr -= yy; | |
2744 | } | |
2745 | else | |
2746 | { | |
2747 | if (rr >= (1 - yy) / 2) | |
2748 | rr += yy; | |
2749 | } | |
2750 | } | |
2751 | else | |
2752 | { | |
2753 | if (SCM_LIKELY (yy > 0)) | |
2754 | { | |
2755 | if (rr < -yy / 2) | |
2756 | rr += yy; | |
2757 | } | |
2758 | else | |
2759 | { | |
2760 | if (rr < yy / 2) | |
2761 | rr -= yy; | |
2762 | } | |
2763 | } | |
2764 | return SCM_I_MAKINUM (rr); | |
2765 | } | |
2766 | } | |
2767 | else if (SCM_BIGP (y)) | |
2768 | { | |
2769 | /* Pass a denormalized bignum version of x (even though it | |
2770 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
2771 | return scm_i_bigint_centered_remainder (scm_i_long2big (xx), y); | |
2772 | } | |
2773 | else if (SCM_REALP (y)) | |
2774 | return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y)); | |
2775 | else if (SCM_FRACTIONP (y)) | |
2776 | return scm_i_exact_rational_centered_remainder (x, y); | |
2777 | else | |
fa075d40 AW |
2778 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
2779 | s_scm_centered_remainder); | |
8f9da340 MW |
2780 | } |
2781 | else if (SCM_BIGP (x)) | |
2782 | { | |
2783 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2784 | { | |
2785 | scm_t_inum yy = SCM_I_INUM (y); | |
2786 | if (SCM_UNLIKELY (yy == 0)) | |
2787 | scm_num_overflow (s_scm_centered_remainder); | |
2788 | else | |
2789 | { | |
2790 | scm_t_inum rr; | |
2791 | /* Arrange for rr to initially be non-positive, | |
2792 | because that simplifies the test to see | |
2793 | if it is within the needed bounds. */ | |
2794 | if (yy > 0) | |
2795 | { | |
2796 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
2797 | scm_remember_upto_here_1 (x); | |
2798 | if (rr < -yy / 2) | |
2799 | rr += yy; | |
2800 | } | |
2801 | else | |
2802 | { | |
2803 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
2804 | scm_remember_upto_here_1 (x); | |
2805 | if (rr < yy / 2) | |
2806 | rr -= yy; | |
2807 | } | |
2808 | return SCM_I_MAKINUM (rr); | |
2809 | } | |
2810 | } | |
2811 | else if (SCM_BIGP (y)) | |
2812 | return scm_i_bigint_centered_remainder (x, y); | |
2813 | else if (SCM_REALP (y)) | |
2814 | return scm_i_inexact_centered_remainder | |
2815 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2816 | else if (SCM_FRACTIONP (y)) | |
2817 | return scm_i_exact_rational_centered_remainder (x, y); | |
2818 | else | |
fa075d40 AW |
2819 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
2820 | s_scm_centered_remainder); | |
8f9da340 MW |
2821 | } |
2822 | else if (SCM_REALP (x)) | |
2823 | { | |
2824 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2825 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2826 | return scm_i_inexact_centered_remainder | |
2827 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2828 | else | |
fa075d40 AW |
2829 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
2830 | s_scm_centered_remainder); | |
8f9da340 MW |
2831 | } |
2832 | else if (SCM_FRACTIONP (x)) | |
2833 | { | |
2834 | if (SCM_REALP (y)) | |
2835 | return scm_i_inexact_centered_remainder | |
2836 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2837 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2838 | return scm_i_exact_rational_centered_remainder (x, y); | |
2839 | else | |
fa075d40 AW |
2840 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
2841 | s_scm_centered_remainder); | |
8f9da340 MW |
2842 | } |
2843 | else | |
fa075d40 AW |
2844 | return scm_wta_dispatch_2 (g_scm_centered_remainder, x, y, SCM_ARG1, |
2845 | s_scm_centered_remainder); | |
8f9da340 MW |
2846 | } |
2847 | #undef FUNC_NAME | |
2848 | ||
2849 | static SCM | |
2850 | scm_i_inexact_centered_remainder (double x, double y) | |
2851 | { | |
2852 | double q; | |
2853 | ||
2854 | /* Although it would be more efficient to use fmod here, we can't | |
2855 | because it would in some cases produce results inconsistent with | |
2856 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
2857 | close). In particular, when x-y/2 is very close to a multiple of | |
2858 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
2859 | two cases must correspond to different choices of q. If quotient | |
2860 | chooses one and remainder chooses the other, it would be bad. */ | |
2861 | if (SCM_LIKELY (y > 0)) | |
2862 | q = floor (x/y + 0.5); | |
2863 | else if (SCM_LIKELY (y < 0)) | |
2864 | q = ceil (x/y - 0.5); | |
2865 | else if (y == 0) | |
2866 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
2867 | else | |
2868 | return scm_nan (); | |
2869 | return scm_from_double (x - q * y); | |
2870 | } | |
2871 | ||
2872 | /* Assumes that both x and y are bigints, though | |
2873 | x might be able to fit into a fixnum. */ | |
2874 | static SCM | |
2875 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
2876 | { | |
2877 | SCM r, min_r; | |
2878 | ||
2879 | /* Note that x might be small enough to fit into a | |
2880 | fixnum, so we must not let it escape into the wild */ | |
2881 | r = scm_i_mkbig (); | |
2882 | ||
2883 | /* min_r will eventually become -abs(y)/2 */ | |
2884 | min_r = scm_i_mkbig (); | |
2885 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2886 | SCM_I_BIG_MPZ (y), 1); | |
2887 | ||
2888 | /* Arrange for rr to initially be non-positive, | |
2889 | because that simplifies the test to see | |
2890 | if it is within the needed bounds. */ | |
2891 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2892 | { | |
2893 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
2894 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2895 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2896 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2897 | mpz_add (SCM_I_BIG_MPZ (r), | |
2898 | SCM_I_BIG_MPZ (r), | |
2899 | SCM_I_BIG_MPZ (y)); | |
2900 | } | |
2901 | else | |
2902 | { | |
2903 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
2904 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2905 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2906 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2907 | SCM_I_BIG_MPZ (r), | |
2908 | SCM_I_BIG_MPZ (y)); | |
2909 | } | |
2910 | scm_remember_upto_here_2 (x, y); | |
2911 | return scm_i_normbig (r); | |
2912 | } | |
2913 | ||
2914 | static SCM | |
2915 | scm_i_exact_rational_centered_remainder (SCM x, SCM y) | |
2916 | { | |
2917 | SCM xd = scm_denominator (x); | |
2918 | SCM yd = scm_denominator (y); | |
2919 | SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd), | |
2920 | scm_product (scm_numerator (y), xd)); | |
2921 | return scm_divide (r1, scm_product (xd, yd)); | |
2922 | } | |
2923 | ||
2924 | ||
2925 | static void scm_i_inexact_centered_divide (double x, double y, | |
2926 | SCM *qp, SCM *rp); | |
2927 | static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
2928 | static void scm_i_exact_rational_centered_divide (SCM x, SCM y, | |
2929 | SCM *qp, SCM *rp); | |
2930 | ||
2931 | SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0, | |
2932 | (SCM x, SCM y), | |
2933 | "Return the integer @var{q} and the real number @var{r}\n" | |
2934 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2935 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2936 | "@lisp\n" | |
2937 | "(centered/ 123 10) @result{} 12 and 3\n" | |
2938 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
2939 | "(centered/ -123 10) @result{} -12 and -3\n" | |
2940 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
2941 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2942 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
2943 | "@end lisp") | |
2944 | #define FUNC_NAME s_scm_i_centered_divide | |
2945 | { | |
2946 | SCM q, r; | |
2947 | ||
2948 | scm_centered_divide(x, y, &q, &r); | |
2949 | return scm_values (scm_list_2 (q, r)); | |
2950 | } | |
2951 | #undef FUNC_NAME | |
2952 | ||
2953 | #define s_scm_centered_divide s_scm_i_centered_divide | |
2954 | #define g_scm_centered_divide g_scm_i_centered_divide | |
2955 | ||
2956 | void | |
2957 | scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2958 | { | |
2959 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2960 | { | |
2961 | scm_t_inum xx = SCM_I_INUM (x); | |
2962 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2963 | { | |
2964 | scm_t_inum yy = SCM_I_INUM (y); | |
2965 | if (SCM_UNLIKELY (yy == 0)) | |
2966 | scm_num_overflow (s_scm_centered_divide); | |
2967 | else | |
2968 | { | |
2969 | scm_t_inum qq = xx / yy; | |
2970 | scm_t_inum rr = xx % yy; | |
2971 | if (SCM_LIKELY (xx > 0)) | |
2972 | { | |
2973 | if (SCM_LIKELY (yy > 0)) | |
2974 | { | |
2975 | if (rr >= (yy + 1) / 2) | |
2976 | { qq++; rr -= yy; } | |
2977 | } | |
2978 | else | |
2979 | { | |
2980 | if (rr >= (1 - yy) / 2) | |
2981 | { qq--; rr += yy; } | |
2982 | } | |
2983 | } | |
2984 | else | |
2985 | { | |
2986 | if (SCM_LIKELY (yy > 0)) | |
2987 | { | |
2988 | if (rr < -yy / 2) | |
2989 | { qq--; rr += yy; } | |
2990 | } | |
2991 | else | |
2992 | { | |
2993 | if (rr < yy / 2) | |
2994 | { qq++; rr -= yy; } | |
2995 | } | |
2996 | } | |
2997 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2998 | *qp = SCM_I_MAKINUM (qq); | |
2999 | else | |
3000 | *qp = scm_i_inum2big (qq); | |
3001 | *rp = SCM_I_MAKINUM (rr); | |
3002 | } | |
3003 | return; | |
3004 | } | |
3005 | else if (SCM_BIGP (y)) | |
3006 | { | |
3007 | /* Pass a denormalized bignum version of x (even though it | |
3008 | can fit in a fixnum) to scm_i_bigint_centered_divide */ | |
3009 | return scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp); | |
3010 | } | |
3011 | else if (SCM_REALP (y)) | |
3012 | return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
3013 | else if (SCM_FRACTIONP (y)) | |
3014 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3015 | else | |
3016 | return two_valued_wta_dispatch_2 | |
3017 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3018 | s_scm_centered_divide, qp, rp); | |
3019 | } | |
3020 | else if (SCM_BIGP (x)) | |
3021 | { | |
3022 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3023 | { | |
3024 | scm_t_inum yy = SCM_I_INUM (y); | |
3025 | if (SCM_UNLIKELY (yy == 0)) | |
3026 | scm_num_overflow (s_scm_centered_divide); | |
3027 | else | |
3028 | { | |
3029 | SCM q = scm_i_mkbig (); | |
3030 | scm_t_inum rr; | |
3031 | /* Arrange for rr to initially be non-positive, | |
3032 | because that simplifies the test to see | |
3033 | if it is within the needed bounds. */ | |
3034 | if (yy > 0) | |
3035 | { | |
3036 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3037 | SCM_I_BIG_MPZ (x), yy); | |
3038 | scm_remember_upto_here_1 (x); | |
3039 | if (rr < -yy / 2) | |
3040 | { | |
3041 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3042 | SCM_I_BIG_MPZ (q), 1); | |
3043 | rr += yy; | |
3044 | } | |
3045 | } | |
3046 | else | |
3047 | { | |
3048 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3049 | SCM_I_BIG_MPZ (x), -yy); | |
3050 | scm_remember_upto_here_1 (x); | |
3051 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
3052 | if (rr < yy / 2) | |
3053 | { | |
3054 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3055 | SCM_I_BIG_MPZ (q), 1); | |
3056 | rr -= yy; | |
3057 | } | |
3058 | } | |
3059 | *qp = scm_i_normbig (q); | |
3060 | *rp = SCM_I_MAKINUM (rr); | |
3061 | } | |
3062 | return; | |
3063 | } | |
3064 | else if (SCM_BIGP (y)) | |
3065 | return scm_i_bigint_centered_divide (x, y, qp, rp); | |
3066 | else if (SCM_REALP (y)) | |
3067 | return scm_i_inexact_centered_divide | |
3068 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
3069 | else if (SCM_FRACTIONP (y)) | |
3070 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3071 | else | |
3072 | return two_valued_wta_dispatch_2 | |
3073 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3074 | s_scm_centered_divide, qp, rp); | |
3075 | } | |
3076 | else if (SCM_REALP (x)) | |
3077 | { | |
3078 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3079 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3080 | return scm_i_inexact_centered_divide | |
3081 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
3082 | else | |
3083 | return two_valued_wta_dispatch_2 | |
3084 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3085 | s_scm_centered_divide, qp, rp); | |
3086 | } | |
3087 | else if (SCM_FRACTIONP (x)) | |
3088 | { | |
3089 | if (SCM_REALP (y)) | |
3090 | return scm_i_inexact_centered_divide | |
3091 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
3092 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3093 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3094 | else | |
3095 | return two_valued_wta_dispatch_2 | |
3096 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3097 | s_scm_centered_divide, qp, rp); | |
3098 | } | |
3099 | else | |
3100 | return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1, | |
3101 | s_scm_centered_divide, qp, rp); | |
3102 | } | |
3103 | ||
3104 | static void | |
3105 | scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp) | |
3106 | { | |
3107 | double q, r; | |
3108 | ||
3109 | if (SCM_LIKELY (y > 0)) | |
3110 | q = floor (x/y + 0.5); | |
3111 | else if (SCM_LIKELY (y < 0)) | |
3112 | q = ceil (x/y - 0.5); | |
3113 | else if (y == 0) | |
3114 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ | |
3115 | else | |
3116 | q = guile_NaN; | |
3117 | r = x - q * y; | |
3118 | *qp = scm_from_double (q); | |
3119 | *rp = scm_from_double (r); | |
3120 | } | |
3121 | ||
3122 | /* Assumes that both x and y are bigints, though | |
3123 | x might be able to fit into a fixnum. */ | |
3124 | static void | |
3125 | scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3126 | { | |
3127 | SCM q, r, min_r; | |
3128 | ||
3129 | /* Note that x might be small enough to fit into a | |
3130 | fixnum, so we must not let it escape into the wild */ | |
3131 | q = scm_i_mkbig (); | |
3132 | r = scm_i_mkbig (); | |
3133 | ||
3134 | /* min_r will eventually become -abs(y/2) */ | |
3135 | min_r = scm_i_mkbig (); | |
3136 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3137 | SCM_I_BIG_MPZ (y), 1); | |
3138 | ||
3139 | /* Arrange for rr to initially be non-positive, | |
3140 | because that simplifies the test to see | |
3141 | if it is within the needed bounds. */ | |
3142 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3143 | { | |
3144 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3145 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3146 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3147 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3148 | { | |
3149 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3150 | SCM_I_BIG_MPZ (q), 1); | |
3151 | mpz_add (SCM_I_BIG_MPZ (r), | |
3152 | SCM_I_BIG_MPZ (r), | |
3153 | SCM_I_BIG_MPZ (y)); | |
3154 | } | |
3155 | } | |
3156 | else | |
3157 | { | |
3158 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3159 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3160 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3161 | { | |
3162 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3163 | SCM_I_BIG_MPZ (q), 1); | |
3164 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3165 | SCM_I_BIG_MPZ (r), | |
3166 | SCM_I_BIG_MPZ (y)); | |
3167 | } | |
3168 | } | |
3169 | scm_remember_upto_here_2 (x, y); | |
3170 | *qp = scm_i_normbig (q); | |
3171 | *rp = scm_i_normbig (r); | |
3172 | } | |
3173 | ||
3174 | static void | |
3175 | scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3176 | { | |
3177 | SCM r1; | |
3178 | SCM xd = scm_denominator (x); | |
3179 | SCM yd = scm_denominator (y); | |
3180 | ||
3181 | scm_centered_divide (scm_product (scm_numerator (x), yd), | |
3182 | scm_product (scm_numerator (y), xd), | |
3183 | qp, &r1); | |
3184 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
3185 | } | |
3186 | ||
3187 | static SCM scm_i_inexact_round_quotient (double x, double y); | |
3188 | static SCM scm_i_bigint_round_quotient (SCM x, SCM y); | |
3189 | static SCM scm_i_exact_rational_round_quotient (SCM x, SCM y); | |
3190 | ||
3191 | SCM_PRIMITIVE_GENERIC (scm_round_quotient, "round-quotient", 2, 0, 0, | |
ff62c168 | 3192 | (SCM x, SCM y), |
8f9da340 MW |
3193 | "Return @math{@var{x} / @var{y}} to the nearest integer,\n" |
3194 | "with ties going to the nearest even integer.\n" | |
ff62c168 | 3195 | "@lisp\n" |
8f9da340 MW |
3196 | "(round-quotient 123 10) @result{} 12\n" |
3197 | "(round-quotient 123 -10) @result{} -12\n" | |
3198 | "(round-quotient -123 10) @result{} -12\n" | |
3199 | "(round-quotient -123 -10) @result{} 12\n" | |
3200 | "(round-quotient 125 10) @result{} 12\n" | |
3201 | "(round-quotient 127 10) @result{} 13\n" | |
3202 | "(round-quotient 135 10) @result{} 14\n" | |
3203 | "(round-quotient -123.2 -63.5) @result{} 2.0\n" | |
3204 | "(round-quotient 16/3 -10/7) @result{} -4\n" | |
ff62c168 | 3205 | "@end lisp") |
8f9da340 | 3206 | #define FUNC_NAME s_scm_round_quotient |
ff62c168 MW |
3207 | { |
3208 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3209 | { | |
4a46bc2a | 3210 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3211 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3212 | { | |
3213 | scm_t_inum yy = SCM_I_INUM (y); | |
3214 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3215 | scm_num_overflow (s_scm_round_quotient); |
ff62c168 MW |
3216 | else |
3217 | { | |
ff62c168 | 3218 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3219 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3220 | scm_t_inum ay = yy; |
3221 | scm_t_inum r2 = 2 * rr; | |
3222 | ||
3223 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3224 | { |
8f9da340 MW |
3225 | ay = -ay; |
3226 | r2 = -r2; | |
3227 | } | |
3228 | ||
3229 | if (qq & 1L) | |
3230 | { | |
3231 | if (r2 >= ay) | |
3232 | qq++; | |
3233 | else if (r2 <= -ay) | |
3234 | qq--; | |
ff62c168 MW |
3235 | } |
3236 | else | |
3237 | { | |
8f9da340 MW |
3238 | if (r2 > ay) |
3239 | qq++; | |
3240 | else if (r2 < -ay) | |
3241 | qq--; | |
ff62c168 | 3242 | } |
4a46bc2a MW |
3243 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
3244 | return SCM_I_MAKINUM (qq); | |
3245 | else | |
3246 | return scm_i_inum2big (qq); | |
ff62c168 MW |
3247 | } |
3248 | } | |
3249 | else if (SCM_BIGP (y)) | |
3250 | { | |
3251 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3252 | can fit in a fixnum) to scm_i_bigint_round_quotient */ |
3253 | return scm_i_bigint_round_quotient (scm_i_long2big (xx), y); | |
ff62c168 MW |
3254 | } |
3255 | else if (SCM_REALP (y)) | |
8f9da340 | 3256 | return scm_i_inexact_round_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3257 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3258 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3259 | else |
fa075d40 AW |
3260 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3261 | s_scm_round_quotient); | |
ff62c168 MW |
3262 | } |
3263 | else if (SCM_BIGP (x)) | |
3264 | { | |
3265 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3266 | { | |
3267 | scm_t_inum yy = SCM_I_INUM (y); | |
3268 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3269 | scm_num_overflow (s_scm_round_quotient); |
4a46bc2a MW |
3270 | else if (SCM_UNLIKELY (yy == 1)) |
3271 | return x; | |
ff62c168 MW |
3272 | else |
3273 | { | |
3274 | SCM q = scm_i_mkbig (); | |
3275 | scm_t_inum rr; | |
8f9da340 MW |
3276 | int needs_adjustment; |
3277 | ||
ff62c168 MW |
3278 | if (yy > 0) |
3279 | { | |
8f9da340 MW |
3280 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3281 | SCM_I_BIG_MPZ (x), yy); | |
3282 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3283 | needs_adjustment = (2*rr >= yy); | |
3284 | else | |
3285 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3286 | } |
3287 | else | |
3288 | { | |
3289 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3290 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3291 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3292 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3293 | needs_adjustment = (2*rr <= yy); | |
3294 | else | |
3295 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3296 | } |
8f9da340 MW |
3297 | scm_remember_upto_here_1 (x); |
3298 | if (needs_adjustment) | |
3299 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
ff62c168 MW |
3300 | return scm_i_normbig (q); |
3301 | } | |
3302 | } | |
3303 | else if (SCM_BIGP (y)) | |
8f9da340 | 3304 | return scm_i_bigint_round_quotient (x, y); |
ff62c168 | 3305 | else if (SCM_REALP (y)) |
8f9da340 | 3306 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3307 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3308 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3309 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3310 | else |
fa075d40 AW |
3311 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3312 | s_scm_round_quotient); | |
ff62c168 MW |
3313 | } |
3314 | else if (SCM_REALP (x)) | |
3315 | { | |
3316 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3317 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3318 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3319 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3320 | else | |
fa075d40 AW |
3321 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3322 | s_scm_round_quotient); | |
ff62c168 MW |
3323 | } |
3324 | else if (SCM_FRACTIONP (x)) | |
3325 | { | |
3326 | if (SCM_REALP (y)) | |
8f9da340 | 3327 | return scm_i_inexact_round_quotient |
ff62c168 | 3328 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3329 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3330 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3331 | else |
fa075d40 AW |
3332 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3333 | s_scm_round_quotient); | |
ff62c168 MW |
3334 | } |
3335 | else | |
fa075d40 AW |
3336 | return scm_wta_dispatch_2 (g_scm_round_quotient, x, y, SCM_ARG1, |
3337 | s_scm_round_quotient); | |
ff62c168 MW |
3338 | } |
3339 | #undef FUNC_NAME | |
3340 | ||
3341 | static SCM | |
8f9da340 | 3342 | scm_i_inexact_round_quotient (double x, double y) |
ff62c168 | 3343 | { |
8f9da340 MW |
3344 | if (SCM_UNLIKELY (y == 0)) |
3345 | scm_num_overflow (s_scm_round_quotient); /* or return a NaN? */ | |
ff62c168 | 3346 | else |
8f9da340 | 3347 | return scm_from_double (scm_c_round (x / y)); |
ff62c168 MW |
3348 | } |
3349 | ||
3350 | /* Assumes that both x and y are bigints, though | |
3351 | x might be able to fit into a fixnum. */ | |
3352 | static SCM | |
8f9da340 | 3353 | scm_i_bigint_round_quotient (SCM x, SCM y) |
ff62c168 | 3354 | { |
8f9da340 MW |
3355 | SCM q, r, r2; |
3356 | int cmp, needs_adjustment; | |
ff62c168 MW |
3357 | |
3358 | /* Note that x might be small enough to fit into a | |
3359 | fixnum, so we must not let it escape into the wild */ | |
3360 | q = scm_i_mkbig (); | |
3361 | r = scm_i_mkbig (); | |
8f9da340 | 3362 | r2 = scm_i_mkbig (); |
ff62c168 | 3363 | |
8f9da340 MW |
3364 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3365 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3366 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
3367 | scm_remember_upto_here_2 (x, r); | |
ff62c168 | 3368 | |
8f9da340 MW |
3369 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3370 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3371 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3372 | else |
8f9da340 MW |
3373 | needs_adjustment = (cmp > 0); |
3374 | scm_remember_upto_here_2 (r2, y); | |
3375 | ||
3376 | if (needs_adjustment) | |
3377 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3378 | ||
ff62c168 MW |
3379 | return scm_i_normbig (q); |
3380 | } | |
3381 | ||
ff62c168 | 3382 | static SCM |
8f9da340 | 3383 | scm_i_exact_rational_round_quotient (SCM x, SCM y) |
ff62c168 | 3384 | { |
8f9da340 | 3385 | return scm_round_quotient |
03ddd15b MW |
3386 | (scm_product (scm_numerator (x), scm_denominator (y)), |
3387 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
3388 | } |
3389 | ||
8f9da340 MW |
3390 | static SCM scm_i_inexact_round_remainder (double x, double y); |
3391 | static SCM scm_i_bigint_round_remainder (SCM x, SCM y); | |
3392 | static SCM scm_i_exact_rational_round_remainder (SCM x, SCM y); | |
ff62c168 | 3393 | |
8f9da340 | 3394 | SCM_PRIMITIVE_GENERIC (scm_round_remainder, "round-remainder", 2, 0, 0, |
ff62c168 MW |
3395 | (SCM x, SCM y), |
3396 | "Return the real number @var{r} such that\n" | |
8f9da340 MW |
3397 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}, where\n" |
3398 | "@var{q} is @math{@var{x} / @var{y}} rounded to the\n" | |
3399 | "nearest integer, with ties going to the nearest\n" | |
3400 | "even integer.\n" | |
ff62c168 | 3401 | "@lisp\n" |
8f9da340 MW |
3402 | "(round-remainder 123 10) @result{} 3\n" |
3403 | "(round-remainder 123 -10) @result{} 3\n" | |
3404 | "(round-remainder -123 10) @result{} -3\n" | |
3405 | "(round-remainder -123 -10) @result{} -3\n" | |
3406 | "(round-remainder 125 10) @result{} 5\n" | |
3407 | "(round-remainder 127 10) @result{} -3\n" | |
3408 | "(round-remainder 135 10) @result{} -5\n" | |
3409 | "(round-remainder -123.2 -63.5) @result{} 3.8\n" | |
3410 | "(round-remainder 16/3 -10/7) @result{} -8/21\n" | |
ff62c168 | 3411 | "@end lisp") |
8f9da340 | 3412 | #define FUNC_NAME s_scm_round_remainder |
ff62c168 MW |
3413 | { |
3414 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3415 | { | |
4a46bc2a | 3416 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3417 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3418 | { | |
3419 | scm_t_inum yy = SCM_I_INUM (y); | |
3420 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3421 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3422 | else |
3423 | { | |
8f9da340 | 3424 | scm_t_inum qq = xx / yy; |
ff62c168 | 3425 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3426 | scm_t_inum ay = yy; |
3427 | scm_t_inum r2 = 2 * rr; | |
3428 | ||
3429 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3430 | { |
8f9da340 MW |
3431 | ay = -ay; |
3432 | r2 = -r2; | |
3433 | } | |
3434 | ||
3435 | if (qq & 1L) | |
3436 | { | |
3437 | if (r2 >= ay) | |
3438 | rr -= yy; | |
3439 | else if (r2 <= -ay) | |
3440 | rr += yy; | |
ff62c168 MW |
3441 | } |
3442 | else | |
3443 | { | |
8f9da340 MW |
3444 | if (r2 > ay) |
3445 | rr -= yy; | |
3446 | else if (r2 < -ay) | |
3447 | rr += yy; | |
ff62c168 MW |
3448 | } |
3449 | return SCM_I_MAKINUM (rr); | |
3450 | } | |
3451 | } | |
3452 | else if (SCM_BIGP (y)) | |
3453 | { | |
3454 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3455 | can fit in a fixnum) to scm_i_bigint_round_remainder */ |
3456 | return scm_i_bigint_round_remainder | |
3457 | (scm_i_long2big (xx), y); | |
ff62c168 MW |
3458 | } |
3459 | else if (SCM_REALP (y)) | |
8f9da340 | 3460 | return scm_i_inexact_round_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3461 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3462 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3463 | else |
fa075d40 AW |
3464 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3465 | s_scm_round_remainder); | |
ff62c168 MW |
3466 | } |
3467 | else if (SCM_BIGP (x)) | |
3468 | { | |
3469 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3470 | { | |
3471 | scm_t_inum yy = SCM_I_INUM (y); | |
3472 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3473 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3474 | else |
3475 | { | |
8f9da340 | 3476 | SCM q = scm_i_mkbig (); |
ff62c168 | 3477 | scm_t_inum rr; |
8f9da340 MW |
3478 | int needs_adjustment; |
3479 | ||
ff62c168 MW |
3480 | if (yy > 0) |
3481 | { | |
8f9da340 MW |
3482 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3483 | SCM_I_BIG_MPZ (x), yy); | |
3484 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3485 | needs_adjustment = (2*rr >= yy); | |
3486 | else | |
3487 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3488 | } |
3489 | else | |
3490 | { | |
8f9da340 MW |
3491 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
3492 | SCM_I_BIG_MPZ (x), -yy); | |
3493 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3494 | needs_adjustment = (2*rr <= yy); | |
3495 | else | |
3496 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3497 | } |
8f9da340 MW |
3498 | scm_remember_upto_here_2 (x, q); |
3499 | if (needs_adjustment) | |
3500 | rr -= yy; | |
ff62c168 MW |
3501 | return SCM_I_MAKINUM (rr); |
3502 | } | |
3503 | } | |
3504 | else if (SCM_BIGP (y)) | |
8f9da340 | 3505 | return scm_i_bigint_round_remainder (x, y); |
ff62c168 | 3506 | else if (SCM_REALP (y)) |
8f9da340 | 3507 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3508 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3509 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3510 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3511 | else |
fa075d40 AW |
3512 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3513 | s_scm_round_remainder); | |
ff62c168 MW |
3514 | } |
3515 | else if (SCM_REALP (x)) | |
3516 | { | |
3517 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3518 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3519 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3520 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3521 | else | |
fa075d40 AW |
3522 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3523 | s_scm_round_remainder); | |
ff62c168 MW |
3524 | } |
3525 | else if (SCM_FRACTIONP (x)) | |
3526 | { | |
3527 | if (SCM_REALP (y)) | |
8f9da340 | 3528 | return scm_i_inexact_round_remainder |
ff62c168 | 3529 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3530 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3531 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3532 | else |
fa075d40 AW |
3533 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3534 | s_scm_round_remainder); | |
ff62c168 MW |
3535 | } |
3536 | else | |
fa075d40 AW |
3537 | return scm_wta_dispatch_2 (g_scm_round_remainder, x, y, SCM_ARG1, |
3538 | s_scm_round_remainder); | |
ff62c168 MW |
3539 | } |
3540 | #undef FUNC_NAME | |
3541 | ||
3542 | static SCM | |
8f9da340 | 3543 | scm_i_inexact_round_remainder (double x, double y) |
ff62c168 | 3544 | { |
ff62c168 MW |
3545 | /* Although it would be more efficient to use fmod here, we can't |
3546 | because it would in some cases produce results inconsistent with | |
8f9da340 | 3547 | scm_i_inexact_round_quotient, such that x != r + q * y (not even |
ff62c168 | 3548 | close). In particular, when x-y/2 is very close to a multiple of |
8f9da340 MW |
3549 | y, then r might be either -abs(y/2) or abs(y/2), but those two |
3550 | cases must correspond to different choices of q. If quotient | |
ff62c168 | 3551 | chooses one and remainder chooses the other, it would be bad. */ |
8f9da340 MW |
3552 | |
3553 | if (SCM_UNLIKELY (y == 0)) | |
3554 | scm_num_overflow (s_scm_round_remainder); /* or return a NaN? */ | |
ff62c168 | 3555 | else |
8f9da340 MW |
3556 | { |
3557 | double q = scm_c_round (x / y); | |
3558 | return scm_from_double (x - q * y); | |
3559 | } | |
ff62c168 MW |
3560 | } |
3561 | ||
3562 | /* Assumes that both x and y are bigints, though | |
3563 | x might be able to fit into a fixnum. */ | |
3564 | static SCM | |
8f9da340 | 3565 | scm_i_bigint_round_remainder (SCM x, SCM y) |
ff62c168 | 3566 | { |
8f9da340 MW |
3567 | SCM q, r, r2; |
3568 | int cmp, needs_adjustment; | |
ff62c168 MW |
3569 | |
3570 | /* Note that x might be small enough to fit into a | |
3571 | fixnum, so we must not let it escape into the wild */ | |
8f9da340 | 3572 | q = scm_i_mkbig (); |
ff62c168 | 3573 | r = scm_i_mkbig (); |
8f9da340 | 3574 | r2 = scm_i_mkbig (); |
ff62c168 | 3575 | |
8f9da340 MW |
3576 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3577 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3578 | scm_remember_upto_here_1 (x); | |
3579 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3580 | |
8f9da340 MW |
3581 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3582 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3583 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3584 | else |
8f9da340 MW |
3585 | needs_adjustment = (cmp > 0); |
3586 | scm_remember_upto_here_2 (q, r2); | |
3587 | ||
3588 | if (needs_adjustment) | |
3589 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
3590 | ||
3591 | scm_remember_upto_here_1 (y); | |
ff62c168 MW |
3592 | return scm_i_normbig (r); |
3593 | } | |
3594 | ||
ff62c168 | 3595 | static SCM |
8f9da340 | 3596 | scm_i_exact_rational_round_remainder (SCM x, SCM y) |
ff62c168 | 3597 | { |
03ddd15b MW |
3598 | SCM xd = scm_denominator (x); |
3599 | SCM yd = scm_denominator (y); | |
8f9da340 MW |
3600 | SCM r1 = scm_round_remainder (scm_product (scm_numerator (x), yd), |
3601 | scm_product (scm_numerator (y), xd)); | |
03ddd15b | 3602 | return scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3603 | } |
3604 | ||
3605 | ||
8f9da340 MW |
3606 | static void scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp); |
3607 | static void scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3608 | static void scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
ff62c168 | 3609 | |
8f9da340 | 3610 | SCM_PRIMITIVE_GENERIC (scm_i_round_divide, "round/", 2, 0, 0, |
ff62c168 MW |
3611 | (SCM x, SCM y), |
3612 | "Return the integer @var{q} and the real number @var{r}\n" | |
3613 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
8f9da340 MW |
3614 | "and @var{q} is @math{@var{x} / @var{y}} rounded to the\n" |
3615 | "nearest integer, with ties going to the nearest even integer.\n" | |
ff62c168 | 3616 | "@lisp\n" |
8f9da340 MW |
3617 | "(round/ 123 10) @result{} 12 and 3\n" |
3618 | "(round/ 123 -10) @result{} -12 and 3\n" | |
3619 | "(round/ -123 10) @result{} -12 and -3\n" | |
3620 | "(round/ -123 -10) @result{} 12 and -3\n" | |
3621 | "(round/ 125 10) @result{} 12 and 5\n" | |
3622 | "(round/ 127 10) @result{} 13 and -3\n" | |
3623 | "(round/ 135 10) @result{} 14 and -5\n" | |
3624 | "(round/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3625 | "(round/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
ff62c168 | 3626 | "@end lisp") |
8f9da340 | 3627 | #define FUNC_NAME s_scm_i_round_divide |
5fbf680b MW |
3628 | { |
3629 | SCM q, r; | |
3630 | ||
8f9da340 | 3631 | scm_round_divide(x, y, &q, &r); |
5fbf680b MW |
3632 | return scm_values (scm_list_2 (q, r)); |
3633 | } | |
3634 | #undef FUNC_NAME | |
3635 | ||
8f9da340 MW |
3636 | #define s_scm_round_divide s_scm_i_round_divide |
3637 | #define g_scm_round_divide g_scm_i_round_divide | |
5fbf680b MW |
3638 | |
3639 | void | |
8f9da340 | 3640 | scm_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 MW |
3641 | { |
3642 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3643 | { | |
4a46bc2a | 3644 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3645 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3646 | { | |
3647 | scm_t_inum yy = SCM_I_INUM (y); | |
3648 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3649 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3650 | else |
3651 | { | |
ff62c168 | 3652 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3653 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3654 | scm_t_inum ay = yy; |
3655 | scm_t_inum r2 = 2 * rr; | |
3656 | ||
3657 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3658 | { |
8f9da340 MW |
3659 | ay = -ay; |
3660 | r2 = -r2; | |
3661 | } | |
3662 | ||
3663 | if (qq & 1L) | |
3664 | { | |
3665 | if (r2 >= ay) | |
3666 | { qq++; rr -= yy; } | |
3667 | else if (r2 <= -ay) | |
3668 | { qq--; rr += yy; } | |
ff62c168 MW |
3669 | } |
3670 | else | |
3671 | { | |
8f9da340 MW |
3672 | if (r2 > ay) |
3673 | { qq++; rr -= yy; } | |
3674 | else if (r2 < -ay) | |
3675 | { qq--; rr += yy; } | |
ff62c168 | 3676 | } |
4a46bc2a | 3677 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 3678 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 3679 | else |
5fbf680b MW |
3680 | *qp = scm_i_inum2big (qq); |
3681 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3682 | } |
5fbf680b | 3683 | return; |
ff62c168 MW |
3684 | } |
3685 | else if (SCM_BIGP (y)) | |
3686 | { | |
3687 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3688 | can fit in a fixnum) to scm_i_bigint_round_divide */ |
3689 | return scm_i_bigint_round_divide | |
3690 | (scm_i_long2big (SCM_I_INUM (x)), y, qp, rp); | |
ff62c168 MW |
3691 | } |
3692 | else if (SCM_REALP (y)) | |
8f9da340 | 3693 | return scm_i_inexact_round_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3694 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3695 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3696 | else |
8f9da340 MW |
3697 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3698 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3699 | } |
3700 | else if (SCM_BIGP (x)) | |
3701 | { | |
3702 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3703 | { | |
3704 | scm_t_inum yy = SCM_I_INUM (y); | |
3705 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3706 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3707 | else |
3708 | { | |
3709 | SCM q = scm_i_mkbig (); | |
3710 | scm_t_inum rr; | |
8f9da340 MW |
3711 | int needs_adjustment; |
3712 | ||
ff62c168 MW |
3713 | if (yy > 0) |
3714 | { | |
8f9da340 MW |
3715 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3716 | SCM_I_BIG_MPZ (x), yy); | |
3717 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3718 | needs_adjustment = (2*rr >= yy); | |
3719 | else | |
3720 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3721 | } |
3722 | else | |
3723 | { | |
3724 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3725 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3726 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3727 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3728 | needs_adjustment = (2*rr <= yy); | |
3729 | else | |
3730 | needs_adjustment = (2*rr < yy); | |
3731 | } | |
3732 | scm_remember_upto_here_1 (x); | |
3733 | if (needs_adjustment) | |
3734 | { | |
3735 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3736 | rr -= yy; | |
ff62c168 | 3737 | } |
5fbf680b MW |
3738 | *qp = scm_i_normbig (q); |
3739 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3740 | } |
5fbf680b | 3741 | return; |
ff62c168 MW |
3742 | } |
3743 | else if (SCM_BIGP (y)) | |
8f9da340 | 3744 | return scm_i_bigint_round_divide (x, y, qp, rp); |
ff62c168 | 3745 | else if (SCM_REALP (y)) |
8f9da340 | 3746 | return scm_i_inexact_round_divide |
5fbf680b | 3747 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3748 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3749 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3750 | else |
8f9da340 MW |
3751 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3752 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3753 | } |
3754 | else if (SCM_REALP (x)) | |
3755 | { | |
3756 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3757 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3758 | return scm_i_inexact_round_divide |
5fbf680b | 3759 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
03ddd15b | 3760 | else |
8f9da340 MW |
3761 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3762 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3763 | } |
3764 | else if (SCM_FRACTIONP (x)) | |
3765 | { | |
3766 | if (SCM_REALP (y)) | |
8f9da340 | 3767 | return scm_i_inexact_round_divide |
5fbf680b | 3768 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b | 3769 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3770 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3771 | else |
8f9da340 MW |
3772 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3773 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3774 | } |
3775 | else | |
8f9da340 MW |
3776 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG1, |
3777 | s_scm_round_divide, qp, rp); | |
ff62c168 | 3778 | } |
ff62c168 | 3779 | |
5fbf680b | 3780 | static void |
8f9da340 | 3781 | scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp) |
ff62c168 | 3782 | { |
8f9da340 MW |
3783 | if (SCM_UNLIKELY (y == 0)) |
3784 | scm_num_overflow (s_scm_round_divide); /* or return a NaN? */ | |
ff62c168 | 3785 | else |
8f9da340 MW |
3786 | { |
3787 | double q = scm_c_round (x / y); | |
3788 | double r = x - q * y; | |
3789 | *qp = scm_from_double (q); | |
3790 | *rp = scm_from_double (r); | |
3791 | } | |
ff62c168 MW |
3792 | } |
3793 | ||
3794 | /* Assumes that both x and y are bigints, though | |
3795 | x might be able to fit into a fixnum. */ | |
5fbf680b | 3796 | static void |
8f9da340 | 3797 | scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3798 | { |
8f9da340 MW |
3799 | SCM q, r, r2; |
3800 | int cmp, needs_adjustment; | |
ff62c168 MW |
3801 | |
3802 | /* Note that x might be small enough to fit into a | |
3803 | fixnum, so we must not let it escape into the wild */ | |
3804 | q = scm_i_mkbig (); | |
3805 | r = scm_i_mkbig (); | |
8f9da340 | 3806 | r2 = scm_i_mkbig (); |
ff62c168 | 3807 | |
8f9da340 MW |
3808 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3809 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3810 | scm_remember_upto_here_1 (x); | |
3811 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3812 | |
8f9da340 MW |
3813 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3814 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3815 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3816 | else |
8f9da340 MW |
3817 | needs_adjustment = (cmp > 0); |
3818 | ||
3819 | if (needs_adjustment) | |
ff62c168 | 3820 | { |
8f9da340 MW |
3821 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
3822 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
ff62c168 | 3823 | } |
8f9da340 MW |
3824 | |
3825 | scm_remember_upto_here_2 (r2, y); | |
5fbf680b MW |
3826 | *qp = scm_i_normbig (q); |
3827 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
3828 | } |
3829 | ||
5fbf680b | 3830 | static void |
8f9da340 | 3831 | scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3832 | { |
03ddd15b MW |
3833 | SCM r1; |
3834 | SCM xd = scm_denominator (x); | |
3835 | SCM yd = scm_denominator (y); | |
3836 | ||
8f9da340 MW |
3837 | scm_round_divide (scm_product (scm_numerator (x), yd), |
3838 | scm_product (scm_numerator (y), xd), | |
3839 | qp, &r1); | |
03ddd15b | 3840 | *rp = scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3841 | } |
3842 | ||
3843 | ||
78d3deb1 AW |
3844 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
3845 | (SCM x, SCM y, SCM rest), | |
3846 | "Return the greatest common divisor of all parameter values.\n" | |
3847 | "If called without arguments, 0 is returned.") | |
3848 | #define FUNC_NAME s_scm_i_gcd | |
3849 | { | |
3850 | while (!scm_is_null (rest)) | |
3851 | { x = scm_gcd (x, y); | |
3852 | y = scm_car (rest); | |
3853 | rest = scm_cdr (rest); | |
3854 | } | |
3855 | return scm_gcd (x, y); | |
3856 | } | |
3857 | #undef FUNC_NAME | |
3858 | ||
3859 | #define s_gcd s_scm_i_gcd | |
3860 | #define g_gcd g_scm_i_gcd | |
3861 | ||
0f2d19dd | 3862 | SCM |
6e8d25a6 | 3863 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 3864 | { |
ca46fb90 | 3865 | if (SCM_UNBNDP (y)) |
1dd79792 | 3866 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 3867 | |
e11e83f3 | 3868 | if (SCM_I_INUMP (x)) |
ca46fb90 | 3869 | { |
e11e83f3 | 3870 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3871 | { |
e25f3727 AW |
3872 | scm_t_inum xx = SCM_I_INUM (x); |
3873 | scm_t_inum yy = SCM_I_INUM (y); | |
3874 | scm_t_inum u = xx < 0 ? -xx : xx; | |
3875 | scm_t_inum v = yy < 0 ? -yy : yy; | |
3876 | scm_t_inum result; | |
0aacf84e MD |
3877 | if (xx == 0) |
3878 | result = v; | |
3879 | else if (yy == 0) | |
3880 | result = u; | |
3881 | else | |
3882 | { | |
e25f3727 AW |
3883 | scm_t_inum k = 1; |
3884 | scm_t_inum t; | |
0aacf84e MD |
3885 | /* Determine a common factor 2^k */ |
3886 | while (!(1 & (u | v))) | |
3887 | { | |
3888 | k <<= 1; | |
3889 | u >>= 1; | |
3890 | v >>= 1; | |
3891 | } | |
3892 | /* Now, any factor 2^n can be eliminated */ | |
3893 | if (u & 1) | |
3894 | t = -v; | |
3895 | else | |
3896 | { | |
3897 | t = u; | |
3898 | b3: | |
3899 | t = SCM_SRS (t, 1); | |
3900 | } | |
3901 | if (!(1 & t)) | |
3902 | goto b3; | |
3903 | if (t > 0) | |
3904 | u = t; | |
3905 | else | |
3906 | v = -t; | |
3907 | t = u - v; | |
3908 | if (t != 0) | |
3909 | goto b3; | |
3910 | result = u * k; | |
3911 | } | |
3912 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 3913 | ? SCM_I_MAKINUM (result) |
e25f3727 | 3914 | : scm_i_inum2big (result)); |
ca46fb90 RB |
3915 | } |
3916 | else if (SCM_BIGP (y)) | |
3917 | { | |
0bff4dce KR |
3918 | SCM_SWAP (x, y); |
3919 | goto big_inum; | |
ca46fb90 RB |
3920 | } |
3921 | else | |
fa075d40 | 3922 | return scm_wta_dispatch_2 (g_gcd, x, y, SCM_ARG2, s_gcd); |
f872b822 | 3923 | } |
ca46fb90 RB |
3924 | else if (SCM_BIGP (x)) |
3925 | { | |
e11e83f3 | 3926 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3927 | { |
e25f3727 AW |
3928 | scm_t_bits result; |
3929 | scm_t_inum yy; | |
0bff4dce | 3930 | big_inum: |
e11e83f3 | 3931 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
3932 | if (yy == 0) |
3933 | return scm_abs (x); | |
0aacf84e MD |
3934 | if (yy < 0) |
3935 | yy = -yy; | |
ca46fb90 RB |
3936 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
3937 | scm_remember_upto_here_1 (x); | |
0aacf84e | 3938 | return (SCM_POSFIXABLE (result) |
d956fa6f | 3939 | ? SCM_I_MAKINUM (result) |
e25f3727 | 3940 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
3941 | } |
3942 | else if (SCM_BIGP (y)) | |
3943 | { | |
3944 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
3945 | mpz_gcd (SCM_I_BIG_MPZ (result), |
3946 | SCM_I_BIG_MPZ (x), | |
3947 | SCM_I_BIG_MPZ (y)); | |
3948 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
3949 | return scm_i_normbig (result); |
3950 | } | |
3951 | else | |
fa075d40 | 3952 | return scm_wta_dispatch_2 (g_gcd, x, y, SCM_ARG2, s_gcd); |
09fb7599 | 3953 | } |
ca46fb90 | 3954 | else |
fa075d40 | 3955 | return scm_wta_dispatch_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
3956 | } |
3957 | ||
78d3deb1 AW |
3958 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
3959 | (SCM x, SCM y, SCM rest), | |
3960 | "Return the least common multiple of the arguments.\n" | |
3961 | "If called without arguments, 1 is returned.") | |
3962 | #define FUNC_NAME s_scm_i_lcm | |
3963 | { | |
3964 | while (!scm_is_null (rest)) | |
3965 | { x = scm_lcm (x, y); | |
3966 | y = scm_car (rest); | |
3967 | rest = scm_cdr (rest); | |
3968 | } | |
3969 | return scm_lcm (x, y); | |
3970 | } | |
3971 | #undef FUNC_NAME | |
3972 | ||
3973 | #define s_lcm s_scm_i_lcm | |
3974 | #define g_lcm g_scm_i_lcm | |
3975 | ||
0f2d19dd | 3976 | SCM |
6e8d25a6 | 3977 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 3978 | { |
ca46fb90 RB |
3979 | if (SCM_UNBNDP (n2)) |
3980 | { | |
3981 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
3982 | return SCM_I_MAKINUM (1L); |
3983 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 3984 | } |
09fb7599 | 3985 | |
fa075d40 AW |
3986 | if (SCM_UNLIKELY (!(SCM_I_INUMP (n1) || SCM_BIGP (n1)))) |
3987 | return scm_wta_dispatch_2 (g_lcm, n1, n2, SCM_ARG1, s_lcm); | |
3988 | ||
3989 | if (SCM_UNLIKELY (!(SCM_I_INUMP (n2) || SCM_BIGP (n2)))) | |
3990 | return scm_wta_dispatch_2 (g_lcm, n1, n2, SCM_ARG2, s_lcm); | |
09fb7599 | 3991 | |
e11e83f3 | 3992 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 3993 | { |
e11e83f3 | 3994 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
3995 | { |
3996 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 3997 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
3998 | return d; |
3999 | else | |
4000 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
4001 | } | |
4002 | else | |
4003 | { | |
4004 | /* inum n1, big n2 */ | |
4005 | inumbig: | |
4006 | { | |
4007 | SCM result = scm_i_mkbig (); | |
e25f3727 | 4008 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
4009 | if (nn1 == 0) return SCM_INUM0; |
4010 | if (nn1 < 0) nn1 = - nn1; | |
4011 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
4012 | scm_remember_upto_here_1 (n2); | |
4013 | return result; | |
4014 | } | |
4015 | } | |
4016 | } | |
4017 | else | |
4018 | { | |
4019 | /* big n1 */ | |
e11e83f3 | 4020 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4021 | { |
4022 | SCM_SWAP (n1, n2); | |
4023 | goto inumbig; | |
4024 | } | |
4025 | else | |
4026 | { | |
4027 | SCM result = scm_i_mkbig (); | |
4028 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
4029 | SCM_I_BIG_MPZ (n1), | |
4030 | SCM_I_BIG_MPZ (n2)); | |
4031 | scm_remember_upto_here_2(n1, n2); | |
4032 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
4033 | return result; | |
4034 | } | |
f872b822 | 4035 | } |
0f2d19dd JB |
4036 | } |
4037 | ||
8a525303 GB |
4038 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
4039 | ||
4040 | Logand: | |
4041 | X Y Result Method: | |
4042 | (len) | |
4043 | + + + x (map digit:logand X Y) | |
4044 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
4045 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
4046 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
4047 | ||
4048 | Logior: | |
4049 | X Y Result Method: | |
4050 | ||
4051 | + + + (map digit:logior X Y) | |
4052 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
4053 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
4054 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
4055 | ||
4056 | Logxor: | |
4057 | X Y Result Method: | |
4058 | ||
4059 | + + + (map digit:logxor X Y) | |
4060 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
4061 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
4062 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
4063 | ||
4064 | Logtest: | |
4065 | X Y Result | |
4066 | ||
4067 | + + (any digit:logand X Y) | |
4068 | + - (any digit:logand X (lognot (+ -1 Y))) | |
4069 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
4070 | - - #t | |
4071 | ||
4072 | */ | |
4073 | ||
78d3deb1 AW |
4074 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
4075 | (SCM x, SCM y, SCM rest), | |
4076 | "Return the bitwise AND of the integer arguments.\n\n" | |
4077 | "@lisp\n" | |
4078 | "(logand) @result{} -1\n" | |
4079 | "(logand 7) @result{} 7\n" | |
4080 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
4081 | "@end lisp") | |
4082 | #define FUNC_NAME s_scm_i_logand | |
4083 | { | |
4084 | while (!scm_is_null (rest)) | |
4085 | { x = scm_logand (x, y); | |
4086 | y = scm_car (rest); | |
4087 | rest = scm_cdr (rest); | |
4088 | } | |
4089 | return scm_logand (x, y); | |
4090 | } | |
4091 | #undef FUNC_NAME | |
4092 | ||
4093 | #define s_scm_logand s_scm_i_logand | |
4094 | ||
4095 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 4096 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 4097 | { |
e25f3727 | 4098 | scm_t_inum nn1; |
9a00c9fc | 4099 | |
0aacf84e MD |
4100 | if (SCM_UNBNDP (n2)) |
4101 | { | |
4102 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 4103 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
4104 | else if (!SCM_NUMBERP (n1)) |
4105 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
4106 | else if (SCM_NUMBERP (n1)) | |
4107 | return n1; | |
4108 | else | |
4109 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4110 | } |
09fb7599 | 4111 | |
e11e83f3 | 4112 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4113 | { |
e11e83f3 MV |
4114 | nn1 = SCM_I_INUM (n1); |
4115 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4116 | { |
e25f3727 | 4117 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4118 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
4119 | } |
4120 | else if SCM_BIGP (n2) | |
4121 | { | |
4122 | intbig: | |
2e16a342 | 4123 | if (nn1 == 0) |
0aacf84e MD |
4124 | return SCM_INUM0; |
4125 | { | |
4126 | SCM result_z = scm_i_mkbig (); | |
4127 | mpz_t nn1_z; | |
4128 | mpz_init_set_si (nn1_z, nn1); | |
4129 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4130 | scm_remember_upto_here_1 (n2); | |
4131 | mpz_clear (nn1_z); | |
4132 | return scm_i_normbig (result_z); | |
4133 | } | |
4134 | } | |
4135 | else | |
4136 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4137 | } | |
4138 | else if (SCM_BIGP (n1)) | |
4139 | { | |
e11e83f3 | 4140 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4141 | { |
4142 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4143 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4144 | goto intbig; |
4145 | } | |
4146 | else if (SCM_BIGP (n2)) | |
4147 | { | |
4148 | SCM result_z = scm_i_mkbig (); | |
4149 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
4150 | SCM_I_BIG_MPZ (n1), | |
4151 | SCM_I_BIG_MPZ (n2)); | |
4152 | scm_remember_upto_here_2 (n1, n2); | |
4153 | return scm_i_normbig (result_z); | |
4154 | } | |
4155 | else | |
4156 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4157 | } |
0aacf84e | 4158 | else |
09fb7599 | 4159 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4160 | } |
1bbd0b84 | 4161 | #undef FUNC_NAME |
0f2d19dd | 4162 | |
09fb7599 | 4163 | |
78d3deb1 AW |
4164 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
4165 | (SCM x, SCM y, SCM rest), | |
4166 | "Return the bitwise OR of the integer arguments.\n\n" | |
4167 | "@lisp\n" | |
4168 | "(logior) @result{} 0\n" | |
4169 | "(logior 7) @result{} 7\n" | |
4170 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
4171 | "@end lisp") | |
4172 | #define FUNC_NAME s_scm_i_logior | |
4173 | { | |
4174 | while (!scm_is_null (rest)) | |
4175 | { x = scm_logior (x, y); | |
4176 | y = scm_car (rest); | |
4177 | rest = scm_cdr (rest); | |
4178 | } | |
4179 | return scm_logior (x, y); | |
4180 | } | |
4181 | #undef FUNC_NAME | |
4182 | ||
4183 | #define s_scm_logior s_scm_i_logior | |
4184 | ||
4185 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 4186 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 4187 | { |
e25f3727 | 4188 | scm_t_inum nn1; |
9a00c9fc | 4189 | |
0aacf84e MD |
4190 | if (SCM_UNBNDP (n2)) |
4191 | { | |
4192 | if (SCM_UNBNDP (n1)) | |
4193 | return SCM_INUM0; | |
4194 | else if (SCM_NUMBERP (n1)) | |
4195 | return n1; | |
4196 | else | |
4197 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4198 | } |
09fb7599 | 4199 | |
e11e83f3 | 4200 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4201 | { |
e11e83f3 MV |
4202 | nn1 = SCM_I_INUM (n1); |
4203 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4204 | { |
e11e83f3 | 4205 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 4206 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
4207 | } |
4208 | else if (SCM_BIGP (n2)) | |
4209 | { | |
4210 | intbig: | |
4211 | if (nn1 == 0) | |
4212 | return n2; | |
4213 | { | |
4214 | SCM result_z = scm_i_mkbig (); | |
4215 | mpz_t nn1_z; | |
4216 | mpz_init_set_si (nn1_z, nn1); | |
4217 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4218 | scm_remember_upto_here_1 (n2); | |
4219 | mpz_clear (nn1_z); | |
9806de0d | 4220 | return scm_i_normbig (result_z); |
0aacf84e MD |
4221 | } |
4222 | } | |
4223 | else | |
4224 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4225 | } | |
4226 | else if (SCM_BIGP (n1)) | |
4227 | { | |
e11e83f3 | 4228 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4229 | { |
4230 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4231 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4232 | goto intbig; |
4233 | } | |
4234 | else if (SCM_BIGP (n2)) | |
4235 | { | |
4236 | SCM result_z = scm_i_mkbig (); | |
4237 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
4238 | SCM_I_BIG_MPZ (n1), | |
4239 | SCM_I_BIG_MPZ (n2)); | |
4240 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 4241 | return scm_i_normbig (result_z); |
0aacf84e MD |
4242 | } |
4243 | else | |
4244 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4245 | } |
0aacf84e | 4246 | else |
09fb7599 | 4247 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4248 | } |
1bbd0b84 | 4249 | #undef FUNC_NAME |
0f2d19dd | 4250 | |
09fb7599 | 4251 | |
78d3deb1 AW |
4252 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
4253 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
4254 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
4255 | "set in the result if it is set in an odd number of arguments.\n" | |
4256 | "@lisp\n" | |
4257 | "(logxor) @result{} 0\n" | |
4258 | "(logxor 7) @result{} 7\n" | |
4259 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
4260 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 4261 | "@end lisp") |
78d3deb1 AW |
4262 | #define FUNC_NAME s_scm_i_logxor |
4263 | { | |
4264 | while (!scm_is_null (rest)) | |
4265 | { x = scm_logxor (x, y); | |
4266 | y = scm_car (rest); | |
4267 | rest = scm_cdr (rest); | |
4268 | } | |
4269 | return scm_logxor (x, y); | |
4270 | } | |
4271 | #undef FUNC_NAME | |
4272 | ||
4273 | #define s_scm_logxor s_scm_i_logxor | |
4274 | ||
4275 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 4276 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 4277 | { |
e25f3727 | 4278 | scm_t_inum nn1; |
9a00c9fc | 4279 | |
0aacf84e MD |
4280 | if (SCM_UNBNDP (n2)) |
4281 | { | |
4282 | if (SCM_UNBNDP (n1)) | |
4283 | return SCM_INUM0; | |
4284 | else if (SCM_NUMBERP (n1)) | |
4285 | return n1; | |
4286 | else | |
4287 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4288 | } |
09fb7599 | 4289 | |
e11e83f3 | 4290 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4291 | { |
e11e83f3 MV |
4292 | nn1 = SCM_I_INUM (n1); |
4293 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4294 | { |
e25f3727 | 4295 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4296 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
4297 | } |
4298 | else if (SCM_BIGP (n2)) | |
4299 | { | |
4300 | intbig: | |
4301 | { | |
4302 | SCM result_z = scm_i_mkbig (); | |
4303 | mpz_t nn1_z; | |
4304 | mpz_init_set_si (nn1_z, nn1); | |
4305 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4306 | scm_remember_upto_here_1 (n2); | |
4307 | mpz_clear (nn1_z); | |
4308 | return scm_i_normbig (result_z); | |
4309 | } | |
4310 | } | |
4311 | else | |
4312 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4313 | } | |
4314 | else if (SCM_BIGP (n1)) | |
4315 | { | |
e11e83f3 | 4316 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4317 | { |
4318 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4319 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4320 | goto intbig; |
4321 | } | |
4322 | else if (SCM_BIGP (n2)) | |
4323 | { | |
4324 | SCM result_z = scm_i_mkbig (); | |
4325 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
4326 | SCM_I_BIG_MPZ (n1), | |
4327 | SCM_I_BIG_MPZ (n2)); | |
4328 | scm_remember_upto_here_2 (n1, n2); | |
4329 | return scm_i_normbig (result_z); | |
4330 | } | |
4331 | else | |
4332 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4333 | } |
0aacf84e | 4334 | else |
09fb7599 | 4335 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4336 | } |
1bbd0b84 | 4337 | #undef FUNC_NAME |
0f2d19dd | 4338 | |
09fb7599 | 4339 | |
a1ec6916 | 4340 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 4341 | (SCM j, SCM k), |
ba6e7231 KR |
4342 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
4343 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
4344 | "without actually calculating the @code{logand}, just testing\n" | |
4345 | "for non-zero.\n" | |
4346 | "\n" | |
1e6808ea | 4347 | "@lisp\n" |
b380b885 MD |
4348 | "(logtest #b0100 #b1011) @result{} #f\n" |
4349 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 4350 | "@end lisp") |
1bbd0b84 | 4351 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 4352 | { |
e25f3727 | 4353 | scm_t_inum nj; |
9a00c9fc | 4354 | |
e11e83f3 | 4355 | if (SCM_I_INUMP (j)) |
0aacf84e | 4356 | { |
e11e83f3 MV |
4357 | nj = SCM_I_INUM (j); |
4358 | if (SCM_I_INUMP (k)) | |
0aacf84e | 4359 | { |
e25f3727 | 4360 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 4361 | return scm_from_bool (nj & nk); |
0aacf84e MD |
4362 | } |
4363 | else if (SCM_BIGP (k)) | |
4364 | { | |
4365 | intbig: | |
4366 | if (nj == 0) | |
4367 | return SCM_BOOL_F; | |
4368 | { | |
4369 | SCM result; | |
4370 | mpz_t nj_z; | |
4371 | mpz_init_set_si (nj_z, nj); | |
4372 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
4373 | scm_remember_upto_here_1 (k); | |
73e4de09 | 4374 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
4375 | mpz_clear (nj_z); |
4376 | return result; | |
4377 | } | |
4378 | } | |
4379 | else | |
4380 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4381 | } | |
4382 | else if (SCM_BIGP (j)) | |
4383 | { | |
e11e83f3 | 4384 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
4385 | { |
4386 | SCM_SWAP (j, k); | |
e11e83f3 | 4387 | nj = SCM_I_INUM (j); |
0aacf84e MD |
4388 | goto intbig; |
4389 | } | |
4390 | else if (SCM_BIGP (k)) | |
4391 | { | |
4392 | SCM result; | |
4393 | mpz_t result_z; | |
4394 | mpz_init (result_z); | |
4395 | mpz_and (result_z, | |
4396 | SCM_I_BIG_MPZ (j), | |
4397 | SCM_I_BIG_MPZ (k)); | |
4398 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 4399 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
4400 | mpz_clear (result_z); |
4401 | return result; | |
4402 | } | |
4403 | else | |
4404 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4405 | } | |
4406 | else | |
4407 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 4408 | } |
1bbd0b84 | 4409 | #undef FUNC_NAME |
0f2d19dd | 4410 | |
c1bfcf60 | 4411 | |
a1ec6916 | 4412 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 4413 | (SCM index, SCM j), |
ba6e7231 KR |
4414 | "Test whether bit number @var{index} in @var{j} is set.\n" |
4415 | "@var{index} starts from 0 for the least significant bit.\n" | |
4416 | "\n" | |
1e6808ea | 4417 | "@lisp\n" |
b380b885 MD |
4418 | "(logbit? 0 #b1101) @result{} #t\n" |
4419 | "(logbit? 1 #b1101) @result{} #f\n" | |
4420 | "(logbit? 2 #b1101) @result{} #t\n" | |
4421 | "(logbit? 3 #b1101) @result{} #t\n" | |
4422 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 4423 | "@end lisp") |
1bbd0b84 | 4424 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 4425 | { |
78166ad5 | 4426 | unsigned long int iindex; |
5efd3c7d | 4427 | iindex = scm_to_ulong (index); |
78166ad5 | 4428 | |
e11e83f3 | 4429 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
4430 | { |
4431 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 4432 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 4433 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 4434 | } |
0aacf84e MD |
4435 | else if (SCM_BIGP (j)) |
4436 | { | |
4437 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
4438 | scm_remember_upto_here_1 (j); | |
73e4de09 | 4439 | return scm_from_bool (val); |
0aacf84e MD |
4440 | } |
4441 | else | |
78166ad5 | 4442 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 4443 | } |
1bbd0b84 | 4444 | #undef FUNC_NAME |
0f2d19dd | 4445 | |
78166ad5 | 4446 | |
a1ec6916 | 4447 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 4448 | (SCM n), |
4d814788 | 4449 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
4450 | "argument.\n" |
4451 | "\n" | |
b380b885 MD |
4452 | "@lisp\n" |
4453 | "(number->string (lognot #b10000000) 2)\n" | |
4454 | " @result{} \"-10000001\"\n" | |
4455 | "(number->string (lognot #b0) 2)\n" | |
4456 | " @result{} \"-1\"\n" | |
1e6808ea | 4457 | "@end lisp") |
1bbd0b84 | 4458 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 4459 | { |
e11e83f3 | 4460 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
4461 | /* No overflow here, just need to toggle all the bits making up the inum. |
4462 | Enhancement: No need to strip the tag and add it back, could just xor | |
4463 | a block of 1 bits, if that worked with the various debug versions of | |
4464 | the SCM typedef. */ | |
e11e83f3 | 4465 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
4466 | |
4467 | } else if (SCM_BIGP (n)) { | |
4468 | SCM result = scm_i_mkbig (); | |
4469 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
4470 | scm_remember_upto_here_1 (n); | |
4471 | return result; | |
4472 | ||
4473 | } else { | |
4474 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4475 | } | |
0f2d19dd | 4476 | } |
1bbd0b84 | 4477 | #undef FUNC_NAME |
0f2d19dd | 4478 | |
518b7508 KR |
4479 | /* returns 0 if IN is not an integer. OUT must already be |
4480 | initialized. */ | |
4481 | static int | |
4482 | coerce_to_big (SCM in, mpz_t out) | |
4483 | { | |
4484 | if (SCM_BIGP (in)) | |
4485 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
4486 | else if (SCM_I_INUMP (in)) |
4487 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
4488 | else |
4489 | return 0; | |
4490 | ||
4491 | return 1; | |
4492 | } | |
4493 | ||
d885e204 | 4494 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
4495 | (SCM n, SCM k, SCM m), |
4496 | "Return @var{n} raised to the integer exponent\n" | |
4497 | "@var{k}, modulo @var{m}.\n" | |
4498 | "\n" | |
4499 | "@lisp\n" | |
4500 | "(modulo-expt 2 3 5)\n" | |
4501 | " @result{} 3\n" | |
4502 | "@end lisp") | |
d885e204 | 4503 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
4504 | { |
4505 | mpz_t n_tmp; | |
4506 | mpz_t k_tmp; | |
4507 | mpz_t m_tmp; | |
4508 | ||
4509 | /* There are two classes of error we might encounter -- | |
4510 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
4511 | and | |
4512 | 2) wrong-type errors, which of course we'll report by calling | |
4513 | SCM_WRONG_TYPE_ARG. | |
4514 | We don't report those errors immediately, however; instead we do | |
4515 | some cleanup first. These variables tell us which error (if | |
4516 | any) we should report after cleaning up. | |
4517 | */ | |
4518 | int report_overflow = 0; | |
4519 | ||
4520 | int position_of_wrong_type = 0; | |
4521 | SCM value_of_wrong_type = SCM_INUM0; | |
4522 | ||
4523 | SCM result = SCM_UNDEFINED; | |
4524 | ||
4525 | mpz_init (n_tmp); | |
4526 | mpz_init (k_tmp); | |
4527 | mpz_init (m_tmp); | |
4528 | ||
bc36d050 | 4529 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
4530 | { |
4531 | report_overflow = 1; | |
4532 | goto cleanup; | |
4533 | } | |
4534 | ||
4535 | if (!coerce_to_big (n, n_tmp)) | |
4536 | { | |
4537 | value_of_wrong_type = n; | |
4538 | position_of_wrong_type = 1; | |
4539 | goto cleanup; | |
4540 | } | |
4541 | ||
4542 | if (!coerce_to_big (k, k_tmp)) | |
4543 | { | |
4544 | value_of_wrong_type = k; | |
4545 | position_of_wrong_type = 2; | |
4546 | goto cleanup; | |
4547 | } | |
4548 | ||
4549 | if (!coerce_to_big (m, m_tmp)) | |
4550 | { | |
4551 | value_of_wrong_type = m; | |
4552 | position_of_wrong_type = 3; | |
4553 | goto cleanup; | |
4554 | } | |
4555 | ||
4556 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
4557 | will get a divide-by-zero exception when an inverse 1/n mod m | |
4558 | doesn't exist (or is not unique). Since exceptions are hard to | |
4559 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
4560 | a simple failure code, which is easy to handle. */ | |
4561 | ||
4562 | if (-1 == mpz_sgn (k_tmp)) | |
4563 | { | |
4564 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
4565 | { | |
4566 | report_overflow = 1; | |
4567 | goto cleanup; | |
4568 | } | |
4569 | mpz_neg (k_tmp, k_tmp); | |
4570 | } | |
4571 | ||
4572 | result = scm_i_mkbig (); | |
4573 | mpz_powm (SCM_I_BIG_MPZ (result), | |
4574 | n_tmp, | |
4575 | k_tmp, | |
4576 | m_tmp); | |
b7b8c575 KR |
4577 | |
4578 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
4579 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
4580 | ||
518b7508 KR |
4581 | cleanup: |
4582 | mpz_clear (m_tmp); | |
4583 | mpz_clear (k_tmp); | |
4584 | mpz_clear (n_tmp); | |
4585 | ||
4586 | if (report_overflow) | |
4587 | scm_num_overflow (FUNC_NAME); | |
4588 | ||
4589 | if (position_of_wrong_type) | |
4590 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
4591 | value_of_wrong_type); | |
4592 | ||
4593 | return scm_i_normbig (result); | |
4594 | } | |
4595 | #undef FUNC_NAME | |
4596 | ||
a1ec6916 | 4597 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 4598 | (SCM n, SCM k), |
ba6e7231 KR |
4599 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
4600 | "exact integer, @var{n} can be any number.\n" | |
4601 | "\n" | |
2519490c MW |
4602 | "Negative @var{k} is supported, and results in\n" |
4603 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
4604 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 4605 | "includes @math{0^0} is 1.\n" |
1e6808ea | 4606 | "\n" |
b380b885 | 4607 | "@lisp\n" |
ba6e7231 KR |
4608 | "(integer-expt 2 5) @result{} 32\n" |
4609 | "(integer-expt -3 3) @result{} -27\n" | |
4610 | "(integer-expt 5 -3) @result{} 1/125\n" | |
4611 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 4612 | "@end lisp") |
1bbd0b84 | 4613 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 4614 | { |
e25f3727 | 4615 | scm_t_inum i2 = 0; |
1c35cb19 RB |
4616 | SCM z_i2 = SCM_BOOL_F; |
4617 | int i2_is_big = 0; | |
d956fa6f | 4618 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 4619 | |
bfe1f03a MW |
4620 | /* Specifically refrain from checking the type of the first argument. |
4621 | This allows us to exponentiate any object that can be multiplied. | |
4622 | If we must raise to a negative power, we must also be able to | |
4623 | take its reciprocal. */ | |
4624 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 4625 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 4626 | |
bfe1f03a MW |
4627 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
4628 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
4629 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
4630 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
4631 | /* The next check is necessary only because R6RS specifies different | |
4632 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
4633 | we simply skip this case and move on. */ | |
4634 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
4635 | { | |
4636 | /* k cannot be 0 at this point, because we | |
4637 | have already checked for that case above */ | |
4638 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
4639 | return n; |
4640 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
4641 | return scm_nan (); | |
4642 | } | |
ca46fb90 | 4643 | |
e11e83f3 MV |
4644 | if (SCM_I_INUMP (k)) |
4645 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
4646 | else if (SCM_BIGP (k)) |
4647 | { | |
4648 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
4649 | scm_remember_upto_here_1 (k); |
4650 | i2_is_big = 1; | |
4651 | } | |
2830fd91 | 4652 | else |
ca46fb90 RB |
4653 | SCM_WRONG_TYPE_ARG (2, k); |
4654 | ||
4655 | if (i2_is_big) | |
f872b822 | 4656 | { |
ca46fb90 RB |
4657 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
4658 | { | |
4659 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
4660 | n = scm_divide (n, SCM_UNDEFINED); | |
4661 | } | |
4662 | while (1) | |
4663 | { | |
4664 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
4665 | { | |
ca46fb90 RB |
4666 | return acc; |
4667 | } | |
4668 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
4669 | { | |
ca46fb90 RB |
4670 | return scm_product (acc, n); |
4671 | } | |
4672 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
4673 | acc = scm_product (acc, n); | |
4674 | n = scm_product (n, n); | |
4675 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
4676 | } | |
f872b822 | 4677 | } |
ca46fb90 | 4678 | else |
f872b822 | 4679 | { |
ca46fb90 RB |
4680 | if (i2 < 0) |
4681 | { | |
4682 | i2 = -i2; | |
4683 | n = scm_divide (n, SCM_UNDEFINED); | |
4684 | } | |
4685 | while (1) | |
4686 | { | |
4687 | if (0 == i2) | |
4688 | return acc; | |
4689 | if (1 == i2) | |
4690 | return scm_product (acc, n); | |
4691 | if (i2 & 1) | |
4692 | acc = scm_product (acc, n); | |
4693 | n = scm_product (n, n); | |
4694 | i2 >>= 1; | |
4695 | } | |
f872b822 | 4696 | } |
0f2d19dd | 4697 | } |
1bbd0b84 | 4698 | #undef FUNC_NAME |
0f2d19dd | 4699 | |
a1ec6916 | 4700 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 4701 | (SCM n, SCM cnt), |
32f19569 KR |
4702 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
4703 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 4704 | "\n" |
e7644cb2 | 4705 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
4706 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
4707 | "infinity. (Note that this is not the same rounding as\n" | |
4708 | "@code{quotient} does.)\n" | |
4709 | "\n" | |
4710 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
4711 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
4712 | "shift dropping bits.\n" | |
1e6808ea | 4713 | "\n" |
b380b885 | 4714 | "@lisp\n" |
1e6808ea MG |
4715 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
4716 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
4717 | "\n" |
4718 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
4719 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 4720 | "@end lisp") |
1bbd0b84 | 4721 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 4722 | { |
3ab9f56e | 4723 | long bits_to_shift; |
5efd3c7d | 4724 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 4725 | |
788aca27 KR |
4726 | if (SCM_I_INUMP (n)) |
4727 | { | |
e25f3727 | 4728 | scm_t_inum nn = SCM_I_INUM (n); |
788aca27 KR |
4729 | |
4730 | if (bits_to_shift > 0) | |
4731 | { | |
4732 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
4733 | overflow a non-zero fixnum. For smaller shifts we check the | |
4734 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
4735 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
4736 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
4737 | bits_to_shift)". */ | |
4738 | ||
4739 | if (nn == 0) | |
4740 | return n; | |
4741 | ||
4742 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4743 | && ((scm_t_bits) |
788aca27 KR |
4744 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) |
4745 | <= 1)) | |
4746 | { | |
4747 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
4748 | } | |
4749 | else | |
4750 | { | |
e25f3727 | 4751 | SCM result = scm_i_inum2big (nn); |
788aca27 KR |
4752 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
4753 | bits_to_shift); | |
4754 | return result; | |
4755 | } | |
4756 | } | |
4757 | else | |
4758 | { | |
4759 | bits_to_shift = -bits_to_shift; | |
4760 | if (bits_to_shift >= SCM_LONG_BIT) | |
cff5fa33 | 4761 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1)); |
788aca27 KR |
4762 | else |
4763 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
4764 | } | |
4765 | ||
4766 | } | |
4767 | else if (SCM_BIGP (n)) | |
ca46fb90 | 4768 | { |
788aca27 KR |
4769 | SCM result; |
4770 | ||
4771 | if (bits_to_shift == 0) | |
4772 | return n; | |
4773 | ||
4774 | result = scm_i_mkbig (); | |
4775 | if (bits_to_shift >= 0) | |
4776 | { | |
4777 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
4778 | bits_to_shift); | |
4779 | return result; | |
4780 | } | |
ca46fb90 | 4781 | else |
788aca27 KR |
4782 | { |
4783 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
4784 | we have to allocate a bignum even if the result is going to be a | |
4785 | fixnum. */ | |
4786 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
4787 | -bits_to_shift); | |
4788 | return scm_i_normbig (result); | |
4789 | } | |
4790 | ||
ca46fb90 RB |
4791 | } |
4792 | else | |
788aca27 KR |
4793 | { |
4794 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4795 | } | |
0f2d19dd | 4796 | } |
1bbd0b84 | 4797 | #undef FUNC_NAME |
0f2d19dd | 4798 | |
3c9f20f8 | 4799 | |
a1ec6916 | 4800 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 4801 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
4802 | "Return the integer composed of the @var{start} (inclusive)\n" |
4803 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
4804 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
4805 | "\n" | |
b380b885 MD |
4806 | "@lisp\n" |
4807 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
4808 | " @result{} \"1010\"\n" | |
4809 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
4810 | " @result{} \"10110\"\n" | |
4811 | "@end lisp") | |
1bbd0b84 | 4812 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 4813 | { |
7f848242 | 4814 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
4815 | istart = scm_to_ulong (start); |
4816 | iend = scm_to_ulong (end); | |
c1bfcf60 | 4817 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 4818 | |
7f848242 KR |
4819 | /* how many bits to keep */ |
4820 | bits = iend - istart; | |
4821 | ||
e11e83f3 | 4822 | if (SCM_I_INUMP (n)) |
0aacf84e | 4823 | { |
e25f3727 | 4824 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
4825 | |
4826 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 4827 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 4828 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 4829 | |
0aacf84e MD |
4830 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
4831 | { | |
4832 | /* Since we emulate two's complement encoded numbers, this | |
4833 | * special case requires us to produce a result that has | |
7f848242 | 4834 | * more bits than can be stored in a fixnum. |
0aacf84e | 4835 | */ |
e25f3727 | 4836 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
4837 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
4838 | bits); | |
4839 | return result; | |
0aacf84e | 4840 | } |
ac0c002c | 4841 | |
7f848242 | 4842 | /* mask down to requisite bits */ |
857ae6af | 4843 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 4844 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
4845 | } |
4846 | else if (SCM_BIGP (n)) | |
ac0c002c | 4847 | { |
7f848242 KR |
4848 | SCM result; |
4849 | if (bits == 1) | |
4850 | { | |
d956fa6f | 4851 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
4852 | } |
4853 | else | |
4854 | { | |
4855 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
4856 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
4857 | such bits into a ulong. */ | |
4858 | result = scm_i_mkbig (); | |
4859 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
4860 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
4861 | result = scm_i_normbig (result); | |
4862 | } | |
4863 | scm_remember_upto_here_1 (n); | |
4864 | return result; | |
ac0c002c | 4865 | } |
0aacf84e | 4866 | else |
78166ad5 | 4867 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 4868 | } |
1bbd0b84 | 4869 | #undef FUNC_NAME |
0f2d19dd | 4870 | |
7f848242 | 4871 | |
e4755e5c JB |
4872 | static const char scm_logtab[] = { |
4873 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
4874 | }; | |
1cc91f1b | 4875 | |
a1ec6916 | 4876 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 4877 | (SCM n), |
1e6808ea MG |
4878 | "Return the number of bits in integer @var{n}. If integer is\n" |
4879 | "positive, the 1-bits in its binary representation are counted.\n" | |
4880 | "If negative, the 0-bits in its two's-complement binary\n" | |
4881 | "representation are counted. If 0, 0 is returned.\n" | |
4882 | "\n" | |
b380b885 MD |
4883 | "@lisp\n" |
4884 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
4885 | " @result{} 4\n" |
4886 | "(logcount 0)\n" | |
4887 | " @result{} 0\n" | |
4888 | "(logcount -2)\n" | |
4889 | " @result{} 1\n" | |
4890 | "@end lisp") | |
4891 | #define FUNC_NAME s_scm_logcount | |
4892 | { | |
e11e83f3 | 4893 | if (SCM_I_INUMP (n)) |
f872b822 | 4894 | { |
e25f3727 AW |
4895 | unsigned long c = 0; |
4896 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
4897 | if (nn < 0) |
4898 | nn = -1 - nn; | |
4899 | while (nn) | |
4900 | { | |
4901 | c += scm_logtab[15 & nn]; | |
4902 | nn >>= 4; | |
4903 | } | |
d956fa6f | 4904 | return SCM_I_MAKINUM (c); |
f872b822 | 4905 | } |
ca46fb90 | 4906 | else if (SCM_BIGP (n)) |
f872b822 | 4907 | { |
ca46fb90 | 4908 | unsigned long count; |
713a4259 KR |
4909 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
4910 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 4911 | else |
713a4259 KR |
4912 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
4913 | scm_remember_upto_here_1 (n); | |
d956fa6f | 4914 | return SCM_I_MAKINUM (count); |
f872b822 | 4915 | } |
ca46fb90 RB |
4916 | else |
4917 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 4918 | } |
ca46fb90 | 4919 | #undef FUNC_NAME |
0f2d19dd JB |
4920 | |
4921 | ||
ca46fb90 RB |
4922 | static const char scm_ilentab[] = { |
4923 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
4924 | }; | |
4925 | ||
0f2d19dd | 4926 | |
ca46fb90 RB |
4927 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
4928 | (SCM n), | |
4929 | "Return the number of bits necessary to represent @var{n}.\n" | |
4930 | "\n" | |
4931 | "@lisp\n" | |
4932 | "(integer-length #b10101010)\n" | |
4933 | " @result{} 8\n" | |
4934 | "(integer-length 0)\n" | |
4935 | " @result{} 0\n" | |
4936 | "(integer-length #b1111)\n" | |
4937 | " @result{} 4\n" | |
4938 | "@end lisp") | |
4939 | #define FUNC_NAME s_scm_integer_length | |
4940 | { | |
e11e83f3 | 4941 | if (SCM_I_INUMP (n)) |
0aacf84e | 4942 | { |
e25f3727 | 4943 | unsigned long c = 0; |
0aacf84e | 4944 | unsigned int l = 4; |
e25f3727 | 4945 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
4946 | if (nn < 0) |
4947 | nn = -1 - nn; | |
4948 | while (nn) | |
4949 | { | |
4950 | c += 4; | |
4951 | l = scm_ilentab [15 & nn]; | |
4952 | nn >>= 4; | |
4953 | } | |
d956fa6f | 4954 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
4955 | } |
4956 | else if (SCM_BIGP (n)) | |
4957 | { | |
4958 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
4959 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
4960 | 1 too big, so check for that and adjust. */ | |
4961 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
4962 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
4963 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
4964 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
4965 | size--; | |
4966 | scm_remember_upto_here_1 (n); | |
d956fa6f | 4967 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
4968 | } |
4969 | else | |
ca46fb90 | 4970 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
4971 | } |
4972 | #undef FUNC_NAME | |
0f2d19dd JB |
4973 | |
4974 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
4975 | #define SCM_MAX_DBL_PREC 60 |
4976 | #define SCM_MAX_DBL_RADIX 36 | |
4977 | ||
4978 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
4979 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
4980 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
4981 | ||
4982 | static | |
4983 | void init_dblprec(int *prec, int radix) { | |
4984 | /* determine floating point precision by adding successively | |
4985 | smaller increments to 1.0 until it is considered == 1.0 */ | |
4986 | double f = ((double)1.0)/radix; | |
4987 | double fsum = 1.0 + f; | |
4988 | ||
4989 | *prec = 0; | |
4990 | while (fsum != 1.0) | |
4991 | { | |
4992 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
4993 | fsum = 1.0; | |
4994 | else | |
4995 | { | |
4996 | f /= radix; | |
4997 | fsum = f + 1.0; | |
4998 | } | |
4999 | } | |
5000 | (*prec) -= 1; | |
5001 | } | |
5002 | ||
5003 | static | |
5004 | void init_fx_radix(double *fx_list, int radix) | |
5005 | { | |
5006 | /* initialize a per-radix list of tolerances. When added | |
5007 | to a number < 1.0, we can determine if we should raund | |
5008 | up and quit converting a number to a string. */ | |
5009 | int i; | |
5010 | fx_list[0] = 0.0; | |
5011 | fx_list[1] = 0.5; | |
5012 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
5013 | fx_list[i] = (fx_list[i-1] / radix); | |
5014 | } | |
5015 | ||
5016 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 5017 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 5018 | |
1be6b49c | 5019 | static size_t |
0b799eea | 5020 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 5021 | { |
0b799eea MV |
5022 | int efmt, dpt, d, i, wp; |
5023 | double *fx; | |
5024 | #ifdef DBL_MIN_10_EXP | |
5025 | double f_cpy; | |
5026 | int exp_cpy; | |
5027 | #endif /* DBL_MIN_10_EXP */ | |
5028 | size_t ch = 0; | |
5029 | int exp = 0; | |
5030 | ||
5031 | if(radix < 2 || | |
5032 | radix > SCM_MAX_DBL_RADIX) | |
5033 | { | |
5034 | /* revert to existing behavior */ | |
5035 | radix = 10; | |
5036 | } | |
5037 | ||
5038 | wp = scm_dblprec[radix-2]; | |
5039 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 5040 | |
f872b822 | 5041 | if (f == 0.0) |
abb7e44d MV |
5042 | { |
5043 | #ifdef HAVE_COPYSIGN | |
5044 | double sgn = copysign (1.0, f); | |
5045 | ||
5046 | if (sgn < 0.0) | |
5047 | a[ch++] = '-'; | |
5048 | #endif | |
abb7e44d MV |
5049 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
5050 | } | |
7351e207 | 5051 | |
2e65b52f | 5052 | if (isinf (f)) |
7351e207 MV |
5053 | { |
5054 | if (f < 0) | |
5055 | strcpy (a, "-inf.0"); | |
5056 | else | |
5057 | strcpy (a, "+inf.0"); | |
5058 | return ch+6; | |
5059 | } | |
2e65b52f | 5060 | else if (isnan (f)) |
7351e207 MV |
5061 | { |
5062 | strcpy (a, "+nan.0"); | |
5063 | return ch+6; | |
5064 | } | |
5065 | ||
f872b822 MD |
5066 | if (f < 0.0) |
5067 | { | |
5068 | f = -f; | |
5069 | a[ch++] = '-'; | |
5070 | } | |
7351e207 | 5071 | |
f872b822 MD |
5072 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
5073 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
5074 | /* just do the checking...if it passes, we do the conversion for our |
5075 | radix again below */ | |
5076 | f_cpy = f; | |
5077 | exp_cpy = exp; | |
5078 | ||
5079 | while (f_cpy < 1.0) | |
f872b822 | 5080 | { |
0b799eea MV |
5081 | f_cpy *= 10.0; |
5082 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
5083 | { |
5084 | a[ch++] = '#'; | |
5085 | a[ch++] = '.'; | |
5086 | a[ch++] = '#'; | |
5087 | return ch; | |
5088 | } | |
f872b822 | 5089 | } |
0b799eea | 5090 | while (f_cpy > 10.0) |
f872b822 | 5091 | { |
0b799eea MV |
5092 | f_cpy *= 0.10; |
5093 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
5094 | { |
5095 | a[ch++] = '#'; | |
5096 | a[ch++] = '.'; | |
5097 | a[ch++] = '#'; | |
5098 | return ch; | |
5099 | } | |
f872b822 | 5100 | } |
0b799eea MV |
5101 | #endif |
5102 | ||
f872b822 MD |
5103 | while (f < 1.0) |
5104 | { | |
0b799eea | 5105 | f *= radix; |
f872b822 MD |
5106 | exp--; |
5107 | } | |
0b799eea | 5108 | while (f > radix) |
f872b822 | 5109 | { |
0b799eea | 5110 | f /= radix; |
f872b822 MD |
5111 | exp++; |
5112 | } | |
0b799eea MV |
5113 | |
5114 | if (f + fx[wp] >= radix) | |
f872b822 MD |
5115 | { |
5116 | f = 1.0; | |
5117 | exp++; | |
5118 | } | |
0f2d19dd | 5119 | zero: |
f872b822 | 5120 | efmt = (exp < -3) || (exp > wp + 2); |
0f2d19dd | 5121 | if (!efmt) |
cda139a7 MD |
5122 | { |
5123 | if (exp < 0) | |
5124 | { | |
5125 | a[ch++] = '0'; | |
5126 | a[ch++] = '.'; | |
5127 | dpt = exp; | |
f872b822 MD |
5128 | while (++dpt) |
5129 | a[ch++] = '0'; | |
cda139a7 MD |
5130 | } |
5131 | else | |
f872b822 | 5132 | dpt = exp + 1; |
cda139a7 | 5133 | } |
0f2d19dd JB |
5134 | else |
5135 | dpt = 1; | |
f872b822 MD |
5136 | |
5137 | do | |
5138 | { | |
5139 | d = f; | |
5140 | f -= d; | |
0b799eea | 5141 | a[ch++] = number_chars[d]; |
f872b822 MD |
5142 | if (f < fx[wp]) |
5143 | break; | |
5144 | if (f + fx[wp] >= 1.0) | |
5145 | { | |
0b799eea | 5146 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
5147 | break; |
5148 | } | |
0b799eea | 5149 | f *= radix; |
f872b822 MD |
5150 | if (!(--dpt)) |
5151 | a[ch++] = '.'; | |
0f2d19dd | 5152 | } |
f872b822 | 5153 | while (wp--); |
0f2d19dd JB |
5154 | |
5155 | if (dpt > 0) | |
cda139a7 | 5156 | { |
cda139a7 MD |
5157 | if ((dpt > 4) && (exp > 6)) |
5158 | { | |
f872b822 | 5159 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 5160 | for (i = ch++; i > d; i--) |
f872b822 | 5161 | a[i] = a[i - 1]; |
cda139a7 MD |
5162 | a[d] = '.'; |
5163 | efmt = 1; | |
5164 | } | |
5165 | else | |
cda139a7 | 5166 | { |
f872b822 MD |
5167 | while (--dpt) |
5168 | a[ch++] = '0'; | |
cda139a7 MD |
5169 | a[ch++] = '.'; |
5170 | } | |
5171 | } | |
f872b822 MD |
5172 | if (a[ch - 1] == '.') |
5173 | a[ch++] = '0'; /* trailing zero */ | |
5174 | if (efmt && exp) | |
5175 | { | |
5176 | a[ch++] = 'e'; | |
5177 | if (exp < 0) | |
5178 | { | |
5179 | exp = -exp; | |
5180 | a[ch++] = '-'; | |
5181 | } | |
0b799eea MV |
5182 | for (i = radix; i <= exp; i *= radix); |
5183 | for (i /= radix; i; i /= radix) | |
f872b822 | 5184 | { |
0b799eea | 5185 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
5186 | exp %= i; |
5187 | } | |
0f2d19dd | 5188 | } |
0f2d19dd JB |
5189 | return ch; |
5190 | } | |
5191 | ||
7a1aba42 MV |
5192 | |
5193 | static size_t | |
5194 | icmplx2str (double real, double imag, char *str, int radix) | |
5195 | { | |
5196 | size_t i; | |
c7218482 | 5197 | double sgn; |
7a1aba42 MV |
5198 | |
5199 | i = idbl2str (real, str, radix); | |
c7218482 MW |
5200 | #ifdef HAVE_COPYSIGN |
5201 | sgn = copysign (1.0, imag); | |
5202 | #else | |
5203 | sgn = imag; | |
5204 | #endif | |
5205 | /* Don't output a '+' for negative numbers or for Inf and | |
5206 | NaN. They will provide their own sign. */ | |
5207 | if (sgn >= 0 && DOUBLE_IS_FINITE (imag)) | |
5208 | str[i++] = '+'; | |
5209 | i += idbl2str (imag, &str[i], radix); | |
5210 | str[i++] = 'i'; | |
7a1aba42 MV |
5211 | return i; |
5212 | } | |
5213 | ||
1be6b49c | 5214 | static size_t |
0b799eea | 5215 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 5216 | { |
1be6b49c | 5217 | size_t i; |
3c9a524f | 5218 | if (SCM_REALP (flt)) |
0b799eea | 5219 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 5220 | else |
7a1aba42 MV |
5221 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
5222 | str, radix); | |
0f2d19dd JB |
5223 | return i; |
5224 | } | |
0f2d19dd | 5225 | |
2881e77b | 5226 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
5227 | characters in the result. |
5228 | rad is output base | |
5229 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 5230 | size_t |
2881e77b MV |
5231 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
5232 | { | |
5233 | if (num < 0) | |
5234 | { | |
5235 | *p++ = '-'; | |
5236 | return scm_iuint2str (-num, rad, p) + 1; | |
5237 | } | |
5238 | else | |
5239 | return scm_iuint2str (num, rad, p); | |
5240 | } | |
5241 | ||
5242 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
5243 | characters in the result. | |
5244 | rad is output base | |
5245 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
5246 | size_t | |
5247 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 5248 | { |
1be6b49c ML |
5249 | size_t j = 1; |
5250 | size_t i; | |
2881e77b | 5251 | scm_t_uintmax n = num; |
5c11cc9d | 5252 | |
a6f3af16 AW |
5253 | if (rad < 2 || rad > 36) |
5254 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
5255 | ||
f872b822 | 5256 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
5257 | j++; |
5258 | ||
5259 | i = j; | |
2881e77b | 5260 | n = num; |
f872b822 MD |
5261 | while (i--) |
5262 | { | |
5c11cc9d GH |
5263 | int d = n % rad; |
5264 | ||
f872b822 | 5265 | n /= rad; |
a6f3af16 | 5266 | p[i] = number_chars[d]; |
f872b822 | 5267 | } |
0f2d19dd JB |
5268 | return j; |
5269 | } | |
5270 | ||
a1ec6916 | 5271 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
5272 | (SCM n, SCM radix), |
5273 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
5274 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
5275 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 5276 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 5277 | { |
1bbd0b84 | 5278 | int base; |
98cb6e75 | 5279 | |
0aacf84e | 5280 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 5281 | base = 10; |
0aacf84e | 5282 | else |
5efd3c7d | 5283 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 5284 | |
e11e83f3 | 5285 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
5286 | { |
5287 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 5288 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 5289 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
5290 | } |
5291 | else if (SCM_BIGP (n)) | |
5292 | { | |
5293 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
5294 | scm_remember_upto_here_1 (n); | |
cc95e00a | 5295 | return scm_take_locale_string (str); |
0aacf84e | 5296 | } |
f92e85f7 MV |
5297 | else if (SCM_FRACTIONP (n)) |
5298 | { | |
f92e85f7 | 5299 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 5300 | scm_from_locale_string ("/"), |
f92e85f7 MV |
5301 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
5302 | } | |
0aacf84e MD |
5303 | else if (SCM_INEXACTP (n)) |
5304 | { | |
5305 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 5306 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
5307 | } |
5308 | else | |
bb628794 | 5309 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 5310 | } |
1bbd0b84 | 5311 | #undef FUNC_NAME |
0f2d19dd JB |
5312 | |
5313 | ||
ca46fb90 RB |
5314 | /* These print routines used to be stubbed here so that scm_repl.c |
5315 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 5316 | |
0f2d19dd | 5317 | int |
e81d98ec | 5318 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5319 | { |
56e55ac7 | 5320 | char num_buf[FLOBUFLEN]; |
0b799eea | 5321 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
5322 | return !0; |
5323 | } | |
5324 | ||
b479fe9a MV |
5325 | void |
5326 | scm_i_print_double (double val, SCM port) | |
5327 | { | |
5328 | char num_buf[FLOBUFLEN]; | |
5329 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
5330 | } | |
5331 | ||
f3ae5d60 | 5332 | int |
e81d98ec | 5333 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 5334 | |
f3ae5d60 | 5335 | { |
56e55ac7 | 5336 | char num_buf[FLOBUFLEN]; |
0b799eea | 5337 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
5338 | return !0; |
5339 | } | |
1cc91f1b | 5340 | |
7a1aba42 MV |
5341 | void |
5342 | scm_i_print_complex (double real, double imag, SCM port) | |
5343 | { | |
5344 | char num_buf[FLOBUFLEN]; | |
5345 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
5346 | } | |
5347 | ||
f92e85f7 MV |
5348 | int |
5349 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
5350 | { | |
5351 | SCM str; | |
f92e85f7 | 5352 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 5353 | scm_display (str, port); |
f92e85f7 MV |
5354 | scm_remember_upto_here_1 (str); |
5355 | return !0; | |
5356 | } | |
5357 | ||
0f2d19dd | 5358 | int |
e81d98ec | 5359 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5360 | { |
ca46fb90 RB |
5361 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
5362 | scm_remember_upto_here_1 (exp); | |
5363 | scm_lfwrite (str, (size_t) strlen (str), port); | |
5364 | free (str); | |
0f2d19dd JB |
5365 | return !0; |
5366 | } | |
5367 | /*** END nums->strs ***/ | |
5368 | ||
3c9a524f | 5369 | |
0f2d19dd | 5370 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 5371 | |
3c9a524f DH |
5372 | /* The following functions implement the conversion from strings to numbers. |
5373 | * The implementation somehow follows the grammar for numbers as it is given | |
5374 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
5375 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
5376 | * points should be noted about the implementation: | |
bc3d34f5 | 5377 | * |
3c9a524f DH |
5378 | * * Each function keeps a local index variable 'idx' that points at the |
5379 | * current position within the parsed string. The global index is only | |
5380 | * updated if the function could parse the corresponding syntactic unit | |
5381 | * successfully. | |
bc3d34f5 | 5382 | * |
3c9a524f | 5383 | * * Similarly, the functions keep track of indicators of inexactness ('#', |
bc3d34f5 MW |
5384 | * '.' or exponents) using local variables ('hash_seen', 'x'). |
5385 | * | |
3c9a524f DH |
5386 | * * Sequences of digits are parsed into temporary variables holding fixnums. |
5387 | * Only if these fixnums would overflow, the result variables are updated | |
5388 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
5389 | * the temporary variables holding the fixnums are cleared, and the process | |
5390 | * starts over again. If for example fixnums were able to store five decimal | |
5391 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
5392 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
5393 | * only every five digits two bignum operations were performed. | |
bc3d34f5 MW |
5394 | * |
5395 | * Notes on the handling of exactness specifiers: | |
5396 | * | |
5397 | * When parsing non-real complex numbers, we apply exactness specifiers on | |
5398 | * per-component basis, as is done in PLT Scheme. For complex numbers | |
5399 | * written in rectangular form, exactness specifiers are applied to the | |
5400 | * real and imaginary parts before calling scm_make_rectangular. For | |
5401 | * complex numbers written in polar form, exactness specifiers are applied | |
5402 | * to the magnitude and angle before calling scm_make_polar. | |
5403 | * | |
5404 | * There are two kinds of exactness specifiers: forced and implicit. A | |
5405 | * forced exactness specifier is a "#e" or "#i" prefix at the beginning of | |
5406 | * the entire number, and applies to both components of a complex number. | |
5407 | * "#e" causes each component to be made exact, and "#i" causes each | |
5408 | * component to be made inexact. If no forced exactness specifier is | |
5409 | * present, then the exactness of each component is determined | |
5410 | * independently by the presence or absence of a decimal point or hash mark | |
5411 | * within that component. If a decimal point or hash mark is present, the | |
5412 | * component is made inexact, otherwise it is made exact. | |
5413 | * | |
5414 | * After the exactness specifiers have been applied to each component, they | |
5415 | * are passed to either scm_make_rectangular or scm_make_polar to produce | |
5416 | * the final result. Note that this will result in a real number if the | |
5417 | * imaginary part, magnitude, or angle is an exact 0. | |
5418 | * | |
5419 | * For example, (string->number "#i5.0+0i") does the equivalent of: | |
5420 | * | |
5421 | * (make-rectangular (exact->inexact 5) (exact->inexact 0)) | |
3c9a524f DH |
5422 | */ |
5423 | ||
5424 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
5425 | ||
5426 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
5427 | ||
a6f3af16 AW |
5428 | /* Caller is responsible for checking that the return value is in range |
5429 | for the given radix, which should be <= 36. */ | |
5430 | static unsigned int | |
5431 | char_decimal_value (scm_t_uint32 c) | |
5432 | { | |
5433 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
5434 | that's certainly above any valid decimal, so we take advantage of | |
5435 | that to elide some tests. */ | |
5436 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
5437 | ||
5438 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
5439 | hexadecimals. */ | |
5440 | if (d >= 10U) | |
5441 | { | |
5442 | c = uc_tolower (c); | |
5443 | if (c >= (scm_t_uint32) 'a') | |
5444 | d = c - (scm_t_uint32)'a' + 10U; | |
5445 | } | |
5446 | return d; | |
5447 | } | |
3c9a524f | 5448 | |
91db4a37 LC |
5449 | /* Parse the substring of MEM starting at *P_IDX for an unsigned integer |
5450 | in base RADIX. Upon success, return the unsigned integer and update | |
5451 | *P_IDX and *P_EXACTNESS accordingly. Return #f on failure. */ | |
2a8fecee | 5452 | static SCM |
3f47e526 | 5453 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 5454 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 5455 | { |
3c9a524f DH |
5456 | unsigned int idx = *p_idx; |
5457 | unsigned int hash_seen = 0; | |
5458 | scm_t_bits shift = 1; | |
5459 | scm_t_bits add = 0; | |
5460 | unsigned int digit_value; | |
5461 | SCM result; | |
5462 | char c; | |
3f47e526 | 5463 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5464 | |
5465 | if (idx == len) | |
5466 | return SCM_BOOL_F; | |
2a8fecee | 5467 | |
3f47e526 | 5468 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5469 | digit_value = char_decimal_value (c); |
3c9a524f DH |
5470 | if (digit_value >= radix) |
5471 | return SCM_BOOL_F; | |
5472 | ||
5473 | idx++; | |
d956fa6f | 5474 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 5475 | while (idx != len) |
f872b822 | 5476 | { |
3f47e526 | 5477 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5478 | if (c == '#') |
3c9a524f DH |
5479 | { |
5480 | hash_seen = 1; | |
5481 | digit_value = 0; | |
5482 | } | |
a6f3af16 AW |
5483 | else if (hash_seen) |
5484 | break; | |
3c9a524f | 5485 | else |
a6f3af16 AW |
5486 | { |
5487 | digit_value = char_decimal_value (c); | |
5488 | /* This check catches non-decimals in addition to out-of-range | |
5489 | decimals. */ | |
5490 | if (digit_value >= radix) | |
5491 | break; | |
5492 | } | |
3c9a524f DH |
5493 | |
5494 | idx++; | |
5495 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
5496 | { | |
d956fa6f | 5497 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5498 | if (add > 0) |
d956fa6f | 5499 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5500 | |
5501 | shift = radix; | |
5502 | add = digit_value; | |
5503 | } | |
5504 | else | |
5505 | { | |
5506 | shift = shift * radix; | |
5507 | add = add * radix + digit_value; | |
5508 | } | |
5509 | }; | |
5510 | ||
5511 | if (shift > 1) | |
d956fa6f | 5512 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5513 | if (add > 0) |
d956fa6f | 5514 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5515 | |
5516 | *p_idx = idx; | |
5517 | if (hash_seen) | |
5518 | *p_exactness = INEXACT; | |
5519 | ||
5520 | return result; | |
2a8fecee JB |
5521 | } |
5522 | ||
5523 | ||
3c9a524f DH |
5524 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
5525 | * covers the parts of the rules that start at a potential point. The value | |
5526 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
5527 | * in variable result. The content of *p_exactness indicates, whether a hash |
5528 | * has already been seen in the digits before the point. | |
3c9a524f | 5529 | */ |
1cc91f1b | 5530 | |
3f47e526 | 5531 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
5532 | |
5533 | static SCM | |
3f47e526 | 5534 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 5535 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 5536 | { |
3c9a524f DH |
5537 | unsigned int idx = *p_idx; |
5538 | enum t_exactness x = *p_exactness; | |
3f47e526 | 5539 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5540 | |
5541 | if (idx == len) | |
79d34f68 | 5542 | return result; |
3c9a524f | 5543 | |
3f47e526 | 5544 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5545 | { |
5546 | scm_t_bits shift = 1; | |
5547 | scm_t_bits add = 0; | |
5548 | unsigned int digit_value; | |
cff5fa33 | 5549 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
5550 | |
5551 | idx++; | |
5552 | while (idx != len) | |
5553 | { | |
3f47e526 MG |
5554 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5555 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5556 | { |
5557 | if (x == INEXACT) | |
5558 | return SCM_BOOL_F; | |
5559 | else | |
5560 | digit_value = DIGIT2UINT (c); | |
5561 | } | |
5562 | else if (c == '#') | |
5563 | { | |
5564 | x = INEXACT; | |
5565 | digit_value = 0; | |
5566 | } | |
5567 | else | |
5568 | break; | |
5569 | ||
5570 | idx++; | |
5571 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
5572 | { | |
d956fa6f MV |
5573 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5574 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 5575 | if (add > 0) |
d956fa6f | 5576 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5577 | |
5578 | shift = 10; | |
5579 | add = digit_value; | |
5580 | } | |
5581 | else | |
5582 | { | |
5583 | shift = shift * 10; | |
5584 | add = add * 10 + digit_value; | |
5585 | } | |
5586 | }; | |
5587 | ||
5588 | if (add > 0) | |
5589 | { | |
d956fa6f MV |
5590 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5591 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
5592 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
5593 | } |
5594 | ||
d8592269 | 5595 | result = scm_divide (result, big_shift); |
79d34f68 | 5596 | |
3c9a524f DH |
5597 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
5598 | x = INEXACT; | |
f872b822 | 5599 | } |
3c9a524f | 5600 | |
3c9a524f | 5601 | if (idx != len) |
f872b822 | 5602 | { |
3c9a524f DH |
5603 | int sign = 1; |
5604 | unsigned int start; | |
3f47e526 | 5605 | scm_t_wchar c; |
3c9a524f DH |
5606 | int exponent; |
5607 | SCM e; | |
5608 | ||
5609 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
5610 | ||
3f47e526 | 5611 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 5612 | { |
3c9a524f DH |
5613 | case 'd': case 'D': |
5614 | case 'e': case 'E': | |
5615 | case 'f': case 'F': | |
5616 | case 'l': case 'L': | |
5617 | case 's': case 'S': | |
5618 | idx++; | |
ee0ddd21 AW |
5619 | if (idx == len) |
5620 | return SCM_BOOL_F; | |
5621 | ||
3c9a524f | 5622 | start = idx; |
3f47e526 | 5623 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5624 | if (c == '-') |
5625 | { | |
5626 | idx++; | |
ee0ddd21 AW |
5627 | if (idx == len) |
5628 | return SCM_BOOL_F; | |
5629 | ||
3c9a524f | 5630 | sign = -1; |
3f47e526 | 5631 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5632 | } |
5633 | else if (c == '+') | |
5634 | { | |
5635 | idx++; | |
ee0ddd21 AW |
5636 | if (idx == len) |
5637 | return SCM_BOOL_F; | |
5638 | ||
3c9a524f | 5639 | sign = 1; |
3f47e526 | 5640 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5641 | } |
5642 | else | |
5643 | sign = 1; | |
5644 | ||
3f47e526 | 5645 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
5646 | return SCM_BOOL_F; |
5647 | ||
5648 | idx++; | |
5649 | exponent = DIGIT2UINT (c); | |
5650 | while (idx != len) | |
f872b822 | 5651 | { |
3f47e526 MG |
5652 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5653 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5654 | { |
5655 | idx++; | |
5656 | if (exponent <= SCM_MAXEXP) | |
5657 | exponent = exponent * 10 + DIGIT2UINT (c); | |
5658 | } | |
5659 | else | |
5660 | break; | |
f872b822 | 5661 | } |
3c9a524f DH |
5662 | |
5663 | if (exponent > SCM_MAXEXP) | |
f872b822 | 5664 | { |
3c9a524f | 5665 | size_t exp_len = idx - start; |
3f47e526 | 5666 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
5667 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
5668 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 5669 | } |
3c9a524f | 5670 | |
d956fa6f | 5671 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
5672 | if (sign == 1) |
5673 | result = scm_product (result, e); | |
5674 | else | |
6ebecdeb | 5675 | result = scm_divide (result, e); |
3c9a524f DH |
5676 | |
5677 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
5678 | x = INEXACT; | |
5679 | ||
f872b822 | 5680 | break; |
3c9a524f | 5681 | |
f872b822 | 5682 | default: |
3c9a524f | 5683 | break; |
f872b822 | 5684 | } |
0f2d19dd | 5685 | } |
3c9a524f DH |
5686 | |
5687 | *p_idx = idx; | |
5688 | if (x == INEXACT) | |
5689 | *p_exactness = x; | |
5690 | ||
5691 | return result; | |
0f2d19dd | 5692 | } |
0f2d19dd | 5693 | |
3c9a524f DH |
5694 | |
5695 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
5696 | ||
5697 | static SCM | |
3f47e526 | 5698 | mem2ureal (SCM mem, unsigned int *p_idx, |
9d427b2c | 5699 | unsigned int radix, enum t_exactness forced_x) |
0f2d19dd | 5700 | { |
3c9a524f | 5701 | unsigned int idx = *p_idx; |
164d2481 | 5702 | SCM result; |
3f47e526 | 5703 | size_t len = scm_i_string_length (mem); |
3c9a524f | 5704 | |
40f89215 NJ |
5705 | /* Start off believing that the number will be exact. This changes |
5706 | to INEXACT if we see a decimal point or a hash. */ | |
9d427b2c | 5707 | enum t_exactness implicit_x = EXACT; |
40f89215 | 5708 | |
3c9a524f DH |
5709 | if (idx == len) |
5710 | return SCM_BOOL_F; | |
5711 | ||
3f47e526 | 5712 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
5713 | { |
5714 | *p_idx = idx+5; | |
5715 | return scm_inf (); | |
5716 | } | |
5717 | ||
3f47e526 | 5718 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 5719 | { |
d8592269 MV |
5720 | /* Cobble up the fractional part. We might want to set the |
5721 | NaN's mantissa from it. */ | |
7351e207 | 5722 | idx += 4; |
91db4a37 | 5723 | if (!scm_is_eq (mem2uinteger (mem, &idx, 10, &implicit_x), SCM_INUM0)) |
5f237d6e AW |
5724 | { |
5725 | #if SCM_ENABLE_DEPRECATED == 1 | |
5726 | scm_c_issue_deprecation_warning | |
5727 | ("Non-zero suffixes to `+nan.' are deprecated. Use `+nan.0'."); | |
5728 | #else | |
5729 | return SCM_BOOL_F; | |
5730 | #endif | |
5731 | } | |
5732 | ||
7351e207 MV |
5733 | *p_idx = idx; |
5734 | return scm_nan (); | |
5735 | } | |
5736 | ||
3f47e526 | 5737 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5738 | { |
5739 | if (radix != 10) | |
5740 | return SCM_BOOL_F; | |
5741 | else if (idx + 1 == len) | |
5742 | return SCM_BOOL_F; | |
3f47e526 | 5743 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
5744 | return SCM_BOOL_F; |
5745 | else | |
cff5fa33 | 5746 | result = mem2decimal_from_point (SCM_INUM0, mem, |
9d427b2c | 5747 | p_idx, &implicit_x); |
f872b822 | 5748 | } |
3c9a524f DH |
5749 | else |
5750 | { | |
3c9a524f | 5751 | SCM uinteger; |
3c9a524f | 5752 | |
9d427b2c | 5753 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 5754 | if (scm_is_false (uinteger)) |
3c9a524f DH |
5755 | return SCM_BOOL_F; |
5756 | ||
5757 | if (idx == len) | |
5758 | result = uinteger; | |
3f47e526 | 5759 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 5760 | { |
3c9a524f DH |
5761 | SCM divisor; |
5762 | ||
5763 | idx++; | |
ee0ddd21 AW |
5764 | if (idx == len) |
5765 | return SCM_BOOL_F; | |
3c9a524f | 5766 | |
9d427b2c | 5767 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 5768 | if (scm_is_false (divisor)) |
3c9a524f DH |
5769 | return SCM_BOOL_F; |
5770 | ||
f92e85f7 | 5771 | /* both are int/big here, I assume */ |
cba42c93 | 5772 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 5773 | } |
3c9a524f DH |
5774 | else if (radix == 10) |
5775 | { | |
9d427b2c | 5776 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
73e4de09 | 5777 | if (scm_is_false (result)) |
3c9a524f DH |
5778 | return SCM_BOOL_F; |
5779 | } | |
5780 | else | |
5781 | result = uinteger; | |
5782 | ||
5783 | *p_idx = idx; | |
f872b822 | 5784 | } |
164d2481 | 5785 | |
9d427b2c MW |
5786 | switch (forced_x) |
5787 | { | |
5788 | case EXACT: | |
5789 | if (SCM_INEXACTP (result)) | |
5790 | return scm_inexact_to_exact (result); | |
5791 | else | |
5792 | return result; | |
5793 | case INEXACT: | |
5794 | if (SCM_INEXACTP (result)) | |
5795 | return result; | |
5796 | else | |
5797 | return scm_exact_to_inexact (result); | |
5798 | case NO_EXACTNESS: | |
5799 | if (implicit_x == INEXACT) | |
5800 | { | |
5801 | if (SCM_INEXACTP (result)) | |
5802 | return result; | |
5803 | else | |
5804 | return scm_exact_to_inexact (result); | |
5805 | } | |
5806 | else | |
5807 | return result; | |
5808 | } | |
164d2481 | 5809 | |
9d427b2c MW |
5810 | /* We should never get here */ |
5811 | scm_syserror ("mem2ureal"); | |
3c9a524f | 5812 | } |
0f2d19dd | 5813 | |
0f2d19dd | 5814 | |
3c9a524f | 5815 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 5816 | |
3c9a524f | 5817 | static SCM |
3f47e526 | 5818 | mem2complex (SCM mem, unsigned int idx, |
9d427b2c | 5819 | unsigned int radix, enum t_exactness forced_x) |
3c9a524f | 5820 | { |
3f47e526 | 5821 | scm_t_wchar c; |
3c9a524f DH |
5822 | int sign = 0; |
5823 | SCM ureal; | |
3f47e526 | 5824 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5825 | |
5826 | if (idx == len) | |
5827 | return SCM_BOOL_F; | |
5828 | ||
3f47e526 | 5829 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5830 | if (c == '+') |
5831 | { | |
5832 | idx++; | |
5833 | sign = 1; | |
5834 | } | |
5835 | else if (c == '-') | |
5836 | { | |
5837 | idx++; | |
5838 | sign = -1; | |
0f2d19dd | 5839 | } |
0f2d19dd | 5840 | |
3c9a524f DH |
5841 | if (idx == len) |
5842 | return SCM_BOOL_F; | |
5843 | ||
9d427b2c | 5844 | ureal = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 5845 | if (scm_is_false (ureal)) |
f872b822 | 5846 | { |
3c9a524f DH |
5847 | /* input must be either +i or -i */ |
5848 | ||
5849 | if (sign == 0) | |
5850 | return SCM_BOOL_F; | |
5851 | ||
3f47e526 MG |
5852 | if (scm_i_string_ref (mem, idx) == 'i' |
5853 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 5854 | { |
3c9a524f DH |
5855 | idx++; |
5856 | if (idx != len) | |
5857 | return SCM_BOOL_F; | |
5858 | ||
cff5fa33 | 5859 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 5860 | } |
3c9a524f DH |
5861 | else |
5862 | return SCM_BOOL_F; | |
0f2d19dd | 5863 | } |
3c9a524f DH |
5864 | else |
5865 | { | |
73e4de09 | 5866 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 5867 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 5868 | |
3c9a524f DH |
5869 | if (idx == len) |
5870 | return ureal; | |
5871 | ||
3f47e526 | 5872 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 5873 | switch (c) |
f872b822 | 5874 | { |
3c9a524f DH |
5875 | case 'i': case 'I': |
5876 | /* either +<ureal>i or -<ureal>i */ | |
5877 | ||
5878 | idx++; | |
5879 | if (sign == 0) | |
5880 | return SCM_BOOL_F; | |
5881 | if (idx != len) | |
5882 | return SCM_BOOL_F; | |
cff5fa33 | 5883 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
5884 | |
5885 | case '@': | |
5886 | /* polar input: <real>@<real>. */ | |
5887 | ||
5888 | idx++; | |
5889 | if (idx == len) | |
5890 | return SCM_BOOL_F; | |
5891 | else | |
f872b822 | 5892 | { |
3c9a524f DH |
5893 | int sign; |
5894 | SCM angle; | |
5895 | SCM result; | |
5896 | ||
3f47e526 | 5897 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5898 | if (c == '+') |
5899 | { | |
5900 | idx++; | |
ee0ddd21 AW |
5901 | if (idx == len) |
5902 | return SCM_BOOL_F; | |
3c9a524f DH |
5903 | sign = 1; |
5904 | } | |
5905 | else if (c == '-') | |
5906 | { | |
5907 | idx++; | |
ee0ddd21 AW |
5908 | if (idx == len) |
5909 | return SCM_BOOL_F; | |
3c9a524f DH |
5910 | sign = -1; |
5911 | } | |
5912 | else | |
5913 | sign = 1; | |
5914 | ||
9d427b2c | 5915 | angle = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 5916 | if (scm_is_false (angle)) |
3c9a524f DH |
5917 | return SCM_BOOL_F; |
5918 | if (idx != len) | |
5919 | return SCM_BOOL_F; | |
5920 | ||
73e4de09 | 5921 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
5922 | angle = scm_difference (angle, SCM_UNDEFINED); |
5923 | ||
5924 | result = scm_make_polar (ureal, angle); | |
5925 | return result; | |
f872b822 | 5926 | } |
3c9a524f DH |
5927 | case '+': |
5928 | case '-': | |
5929 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 5930 | |
3c9a524f DH |
5931 | idx++; |
5932 | if (idx == len) | |
5933 | return SCM_BOOL_F; | |
5934 | else | |
5935 | { | |
5936 | int sign = (c == '+') ? 1 : -1; | |
9d427b2c | 5937 | SCM imag = mem2ureal (mem, &idx, radix, forced_x); |
0f2d19dd | 5938 | |
73e4de09 | 5939 | if (scm_is_false (imag)) |
d956fa6f | 5940 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 5941 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 5942 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 5943 | |
3c9a524f DH |
5944 | if (idx == len) |
5945 | return SCM_BOOL_F; | |
3f47e526 MG |
5946 | if (scm_i_string_ref (mem, idx) != 'i' |
5947 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 5948 | return SCM_BOOL_F; |
0f2d19dd | 5949 | |
3c9a524f DH |
5950 | idx++; |
5951 | if (idx != len) | |
5952 | return SCM_BOOL_F; | |
0f2d19dd | 5953 | |
1fe5e088 | 5954 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
5955 | } |
5956 | default: | |
5957 | return SCM_BOOL_F; | |
5958 | } | |
5959 | } | |
0f2d19dd | 5960 | } |
0f2d19dd JB |
5961 | |
5962 | ||
3c9a524f DH |
5963 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
5964 | ||
5965 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 5966 | |
0f2d19dd | 5967 | SCM |
3f47e526 | 5968 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 5969 | { |
3c9a524f DH |
5970 | unsigned int idx = 0; |
5971 | unsigned int radix = NO_RADIX; | |
5972 | enum t_exactness forced_x = NO_EXACTNESS; | |
3f47e526 | 5973 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5974 | |
5975 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 5976 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 5977 | { |
3f47e526 | 5978 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
5979 | { |
5980 | case 'b': case 'B': | |
5981 | if (radix != NO_RADIX) | |
5982 | return SCM_BOOL_F; | |
5983 | radix = DUAL; | |
5984 | break; | |
5985 | case 'd': case 'D': | |
5986 | if (radix != NO_RADIX) | |
5987 | return SCM_BOOL_F; | |
5988 | radix = DEC; | |
5989 | break; | |
5990 | case 'i': case 'I': | |
5991 | if (forced_x != NO_EXACTNESS) | |
5992 | return SCM_BOOL_F; | |
5993 | forced_x = INEXACT; | |
5994 | break; | |
5995 | case 'e': case 'E': | |
5996 | if (forced_x != NO_EXACTNESS) | |
5997 | return SCM_BOOL_F; | |
5998 | forced_x = EXACT; | |
5999 | break; | |
6000 | case 'o': case 'O': | |
6001 | if (radix != NO_RADIX) | |
6002 | return SCM_BOOL_F; | |
6003 | radix = OCT; | |
6004 | break; | |
6005 | case 'x': case 'X': | |
6006 | if (radix != NO_RADIX) | |
6007 | return SCM_BOOL_F; | |
6008 | radix = HEX; | |
6009 | break; | |
6010 | default: | |
f872b822 | 6011 | return SCM_BOOL_F; |
3c9a524f DH |
6012 | } |
6013 | idx += 2; | |
6014 | } | |
6015 | ||
6016 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
6017 | if (radix == NO_RADIX) | |
9d427b2c | 6018 | radix = default_radix; |
f872b822 | 6019 | |
9d427b2c | 6020 | return mem2complex (mem, idx, radix, forced_x); |
0f2d19dd JB |
6021 | } |
6022 | ||
3f47e526 MG |
6023 | SCM |
6024 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
6025 | unsigned int default_radix) | |
6026 | { | |
6027 | SCM str = scm_from_locale_stringn (mem, len); | |
6028 | ||
6029 | return scm_i_string_to_number (str, default_radix); | |
6030 | } | |
6031 | ||
0f2d19dd | 6032 | |
a1ec6916 | 6033 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 6034 | (SCM string, SCM radix), |
1e6808ea | 6035 | "Return a number of the maximally precise representation\n" |
942e5b91 | 6036 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
6037 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
6038 | "is a default radix that may be overridden by an explicit radix\n" | |
6039 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
6040 | "supplied, then the default radix is 10. If string is not a\n" | |
6041 | "syntactically valid notation for a number, then\n" | |
6042 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 6043 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
6044 | { |
6045 | SCM answer; | |
5efd3c7d | 6046 | unsigned int base; |
a6d9e5ab | 6047 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
6048 | |
6049 | if (SCM_UNBNDP (radix)) | |
6050 | base = 10; | |
6051 | else | |
6052 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
6053 | ||
3f47e526 | 6054 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
6055 | scm_remember_upto_here_1 (string); |
6056 | return answer; | |
0f2d19dd | 6057 | } |
1bbd0b84 | 6058 | #undef FUNC_NAME |
3c9a524f DH |
6059 | |
6060 | ||
0f2d19dd JB |
6061 | /*** END strs->nums ***/ |
6062 | ||
5986c47d | 6063 | |
8507ec80 MV |
6064 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
6065 | (SCM x), | |
6066 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
6067 | "otherwise.") | |
6068 | #define FUNC_NAME s_scm_number_p | |
6069 | { | |
6070 | return scm_from_bool (SCM_NUMBERP (x)); | |
6071 | } | |
6072 | #undef FUNC_NAME | |
6073 | ||
6074 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 6075 | (SCM x), |
942e5b91 | 6076 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 6077 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
6078 | "values form subsets of the set of complex numbers, i. e. the\n" |
6079 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
6080 | "rational or integer number.") | |
8507ec80 | 6081 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 6082 | { |
8507ec80 MV |
6083 | /* all numbers are complex. */ |
6084 | return scm_number_p (x); | |
0f2d19dd | 6085 | } |
1bbd0b84 | 6086 | #undef FUNC_NAME |
0f2d19dd | 6087 | |
f92e85f7 MV |
6088 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
6089 | (SCM x), | |
6090 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
6091 | "otherwise. Note that the set of integer values forms a subset of\n" | |
6092 | "the set of real numbers, i. e. the predicate will also be\n" | |
6093 | "fulfilled if @var{x} is an integer number.") | |
6094 | #define FUNC_NAME s_scm_real_p | |
6095 | { | |
c960e556 MW |
6096 | return scm_from_bool |
6097 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
6098 | } |
6099 | #undef FUNC_NAME | |
6100 | ||
6101 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 6102 | (SCM x), |
942e5b91 | 6103 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 6104 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 6105 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
6106 | "fulfilled if @var{x} is an integer number.") |
6107 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 6108 | { |
c960e556 | 6109 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
6110 | return SCM_BOOL_T; |
6111 | else if (SCM_REALP (x)) | |
c960e556 MW |
6112 | /* due to their limited precision, finite floating point numbers are |
6113 | rational as well. (finite means neither infinity nor a NaN) */ | |
6114 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 6115 | else |
bb628794 | 6116 | return SCM_BOOL_F; |
0f2d19dd | 6117 | } |
1bbd0b84 | 6118 | #undef FUNC_NAME |
0f2d19dd | 6119 | |
a1ec6916 | 6120 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 6121 | (SCM x), |
942e5b91 MG |
6122 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
6123 | "else.") | |
1bbd0b84 | 6124 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 6125 | { |
c960e556 | 6126 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 6127 | return SCM_BOOL_T; |
c960e556 MW |
6128 | else if (SCM_REALP (x)) |
6129 | { | |
6130 | double val = SCM_REAL_VALUE (x); | |
6131 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
6132 | } | |
6133 | else | |
8e43ed5d | 6134 | return SCM_BOOL_F; |
0f2d19dd | 6135 | } |
1bbd0b84 | 6136 | #undef FUNC_NAME |
0f2d19dd JB |
6137 | |
6138 | ||
8a1f4f98 AW |
6139 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
6140 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
6141 | (SCM x, SCM y, SCM rest), | |
6142 | "Return @code{#t} if all parameters are numerically equal.") | |
6143 | #define FUNC_NAME s_scm_i_num_eq_p | |
6144 | { | |
6145 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6146 | return SCM_BOOL_T; | |
6147 | while (!scm_is_null (rest)) | |
6148 | { | |
6149 | if (scm_is_false (scm_num_eq_p (x, y))) | |
6150 | return SCM_BOOL_F; | |
6151 | x = y; | |
6152 | y = scm_car (rest); | |
6153 | rest = scm_cdr (rest); | |
6154 | } | |
6155 | return scm_num_eq_p (x, y); | |
6156 | } | |
6157 | #undef FUNC_NAME | |
0f2d19dd | 6158 | SCM |
6e8d25a6 | 6159 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 6160 | { |
d8b95e27 | 6161 | again: |
e11e83f3 | 6162 | if (SCM_I_INUMP (x)) |
0aacf84e | 6163 | { |
e25f3727 | 6164 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 6165 | if (SCM_I_INUMP (y)) |
0aacf84e | 6166 | { |
e25f3727 | 6167 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 6168 | return scm_from_bool (xx == yy); |
0aacf84e MD |
6169 | } |
6170 | else if (SCM_BIGP (y)) | |
6171 | return SCM_BOOL_F; | |
6172 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
6173 | { |
6174 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
6175 | to a double and compare. | |
6176 | ||
6177 | But on a 64-bit system an inum is bigger than a double and | |
6178 | casting it to a double (call that dxx) will round. dxx is at | |
6179 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
6180 | an integer and fits a long. So we cast yy to a long and | |
6181 | compare with plain xx. | |
6182 | ||
6183 | An alternative (for any size system actually) would be to check | |
6184 | yy is an integer (with floor) and is in range of an inum | |
6185 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
6186 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
6187 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
6188 | |
6189 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
6190 | return scm_from_bool ((double) xx == yy |
6191 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6192 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 6193 | } |
0aacf84e | 6194 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6195 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6196 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
6197 | else if (SCM_FRACTIONP (y)) |
6198 | return SCM_BOOL_F; | |
0aacf84e | 6199 | else |
fa075d40 AW |
6200 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6201 | s_scm_i_num_eq_p); | |
f872b822 | 6202 | } |
0aacf84e MD |
6203 | else if (SCM_BIGP (x)) |
6204 | { | |
e11e83f3 | 6205 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6206 | return SCM_BOOL_F; |
6207 | else if (SCM_BIGP (y)) | |
6208 | { | |
6209 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6210 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6211 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6212 | } |
6213 | else if (SCM_REALP (y)) | |
6214 | { | |
6215 | int cmp; | |
2e65b52f | 6216 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6217 | return SCM_BOOL_F; |
6218 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6219 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6220 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6221 | } |
6222 | else if (SCM_COMPLEXP (y)) | |
6223 | { | |
6224 | int cmp; | |
6225 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
6226 | return SCM_BOOL_F; | |
2e65b52f | 6227 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
6228 | return SCM_BOOL_F; |
6229 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
6230 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6231 | return scm_from_bool (0 == cmp); |
0aacf84e | 6232 | } |
f92e85f7 MV |
6233 | else if (SCM_FRACTIONP (y)) |
6234 | return SCM_BOOL_F; | |
0aacf84e | 6235 | else |
fa075d40 AW |
6236 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6237 | s_scm_i_num_eq_p); | |
f4c627b3 | 6238 | } |
0aacf84e MD |
6239 | else if (SCM_REALP (x)) |
6240 | { | |
e8c5b1f2 | 6241 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 6242 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
6243 | { |
6244 | /* see comments with inum/real above */ | |
e25f3727 | 6245 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
6246 | return scm_from_bool (xx == (double) yy |
6247 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6248 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 6249 | } |
0aacf84e MD |
6250 | else if (SCM_BIGP (y)) |
6251 | { | |
6252 | int cmp; | |
2e65b52f | 6253 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6254 | return SCM_BOOL_F; |
6255 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6256 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6257 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6258 | } |
6259 | else if (SCM_REALP (y)) | |
73e4de09 | 6260 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 6261 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6262 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6263 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6264 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6265 | { |
6266 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6267 | if (isnan (xx)) |
d8b95e27 | 6268 | return SCM_BOOL_F; |
2e65b52f | 6269 | if (isinf (xx)) |
73e4de09 | 6270 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6271 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6272 | goto again; | |
6273 | } | |
0aacf84e | 6274 | else |
fa075d40 AW |
6275 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6276 | s_scm_i_num_eq_p); | |
f872b822 | 6277 | } |
0aacf84e MD |
6278 | else if (SCM_COMPLEXP (x)) |
6279 | { | |
e11e83f3 MV |
6280 | if (SCM_I_INUMP (y)) |
6281 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
6282 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6283 | else if (SCM_BIGP (y)) | |
6284 | { | |
6285 | int cmp; | |
6286 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
6287 | return SCM_BOOL_F; | |
2e65b52f | 6288 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
6289 | return SCM_BOOL_F; |
6290 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
6291 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6292 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6293 | } |
6294 | else if (SCM_REALP (y)) | |
73e4de09 | 6295 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
6296 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6297 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 6298 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6299 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6300 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6301 | { |
6302 | double xx; | |
6303 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
6304 | return SCM_BOOL_F; | |
6305 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 6306 | if (isnan (xx)) |
d8b95e27 | 6307 | return SCM_BOOL_F; |
2e65b52f | 6308 | if (isinf (xx)) |
73e4de09 | 6309 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6310 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6311 | goto again; | |
6312 | } | |
f92e85f7 | 6313 | else |
fa075d40 AW |
6314 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6315 | s_scm_i_num_eq_p); | |
f92e85f7 MV |
6316 | } |
6317 | else if (SCM_FRACTIONP (x)) | |
6318 | { | |
e11e83f3 | 6319 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
6320 | return SCM_BOOL_F; |
6321 | else if (SCM_BIGP (y)) | |
6322 | return SCM_BOOL_F; | |
6323 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
6324 | { |
6325 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6326 | if (isnan (yy)) |
d8b95e27 | 6327 | return SCM_BOOL_F; |
2e65b52f | 6328 | if (isinf (yy)) |
73e4de09 | 6329 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6330 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6331 | goto again; | |
6332 | } | |
f92e85f7 | 6333 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
6334 | { |
6335 | double yy; | |
6336 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
6337 | return SCM_BOOL_F; | |
6338 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 6339 | if (isnan (yy)) |
d8b95e27 | 6340 | return SCM_BOOL_F; |
2e65b52f | 6341 | if (isinf (yy)) |
73e4de09 | 6342 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6343 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6344 | goto again; | |
6345 | } | |
f92e85f7 MV |
6346 | else if (SCM_FRACTIONP (y)) |
6347 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 6348 | else |
fa075d40 AW |
6349 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, |
6350 | s_scm_i_num_eq_p); | |
f4c627b3 | 6351 | } |
0aacf84e | 6352 | else |
fa075d40 AW |
6353 | return scm_wta_dispatch_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, |
6354 | s_scm_i_num_eq_p); | |
0f2d19dd JB |
6355 | } |
6356 | ||
6357 | ||
a5f0b599 KR |
6358 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
6359 | done are good for inums, but for bignums an answer can almost always be | |
6360 | had by just examining a few high bits of the operands, as done by GMP in | |
6361 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
6362 | of the float exponent to take into account. */ | |
6363 | ||
8c93b597 | 6364 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
6365 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
6366 | (SCM x, SCM y, SCM rest), | |
6367 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6368 | "increasing.") | |
6369 | #define FUNC_NAME s_scm_i_num_less_p | |
6370 | { | |
6371 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6372 | return SCM_BOOL_T; | |
6373 | while (!scm_is_null (rest)) | |
6374 | { | |
6375 | if (scm_is_false (scm_less_p (x, y))) | |
6376 | return SCM_BOOL_F; | |
6377 | x = y; | |
6378 | y = scm_car (rest); | |
6379 | rest = scm_cdr (rest); | |
6380 | } | |
6381 | return scm_less_p (x, y); | |
6382 | } | |
6383 | #undef FUNC_NAME | |
0f2d19dd | 6384 | SCM |
6e8d25a6 | 6385 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 6386 | { |
a5f0b599 | 6387 | again: |
e11e83f3 | 6388 | if (SCM_I_INUMP (x)) |
0aacf84e | 6389 | { |
e25f3727 | 6390 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6391 | if (SCM_I_INUMP (y)) |
0aacf84e | 6392 | { |
e25f3727 | 6393 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 6394 | return scm_from_bool (xx < yy); |
0aacf84e MD |
6395 | } |
6396 | else if (SCM_BIGP (y)) | |
6397 | { | |
6398 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6399 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6400 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6401 | } |
6402 | else if (SCM_REALP (y)) | |
73e4de09 | 6403 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 6404 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6405 | { |
6406 | /* "x < a/b" becomes "x*b < a" */ | |
6407 | int_frac: | |
6408 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
6409 | y = SCM_FRACTION_NUMERATOR (y); | |
6410 | goto again; | |
6411 | } | |
0aacf84e | 6412 | else |
fa075d40 AW |
6413 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, |
6414 | s_scm_i_num_less_p); | |
f872b822 | 6415 | } |
0aacf84e MD |
6416 | else if (SCM_BIGP (x)) |
6417 | { | |
e11e83f3 | 6418 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6419 | { |
6420 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6421 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6422 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6423 | } |
6424 | else if (SCM_BIGP (y)) | |
6425 | { | |
6426 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6427 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6428 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
6429 | } |
6430 | else if (SCM_REALP (y)) | |
6431 | { | |
6432 | int cmp; | |
2e65b52f | 6433 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6434 | return SCM_BOOL_F; |
6435 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6436 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6437 | return scm_from_bool (cmp < 0); |
0aacf84e | 6438 | } |
f92e85f7 | 6439 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 6440 | goto int_frac; |
0aacf84e | 6441 | else |
fa075d40 AW |
6442 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, |
6443 | s_scm_i_num_less_p); | |
f4c627b3 | 6444 | } |
0aacf84e MD |
6445 | else if (SCM_REALP (x)) |
6446 | { | |
e11e83f3 MV |
6447 | if (SCM_I_INUMP (y)) |
6448 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
6449 | else if (SCM_BIGP (y)) |
6450 | { | |
6451 | int cmp; | |
2e65b52f | 6452 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6453 | return SCM_BOOL_F; |
6454 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6455 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6456 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
6457 | } |
6458 | else if (SCM_REALP (y)) | |
73e4de09 | 6459 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 6460 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6461 | { |
6462 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6463 | if (isnan (xx)) |
a5f0b599 | 6464 | return SCM_BOOL_F; |
2e65b52f | 6465 | if (isinf (xx)) |
73e4de09 | 6466 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
6467 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6468 | goto again; | |
6469 | } | |
f92e85f7 | 6470 | else |
fa075d40 AW |
6471 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, |
6472 | s_scm_i_num_less_p); | |
f92e85f7 MV |
6473 | } |
6474 | else if (SCM_FRACTIONP (x)) | |
6475 | { | |
e11e83f3 | 6476 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
6477 | { |
6478 | /* "a/b < y" becomes "a < y*b" */ | |
6479 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
6480 | x = SCM_FRACTION_NUMERATOR (x); | |
6481 | goto again; | |
6482 | } | |
f92e85f7 | 6483 | else if (SCM_REALP (y)) |
a5f0b599 KR |
6484 | { |
6485 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6486 | if (isnan (yy)) |
a5f0b599 | 6487 | return SCM_BOOL_F; |
2e65b52f | 6488 | if (isinf (yy)) |
73e4de09 | 6489 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
6490 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6491 | goto again; | |
6492 | } | |
f92e85f7 | 6493 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6494 | { |
6495 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
6496 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
6497 | SCM_FRACTION_DENOMINATOR (y)); | |
6498 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
6499 | SCM_FRACTION_DENOMINATOR (x)); | |
6500 | x = new_x; | |
6501 | y = new_y; | |
6502 | goto again; | |
6503 | } | |
0aacf84e | 6504 | else |
fa075d40 AW |
6505 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, |
6506 | s_scm_i_num_less_p); | |
f872b822 | 6507 | } |
0aacf84e | 6508 | else |
fa075d40 AW |
6509 | return scm_wta_dispatch_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, |
6510 | s_scm_i_num_less_p); | |
0f2d19dd JB |
6511 | } |
6512 | ||
6513 | ||
8a1f4f98 AW |
6514 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
6515 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
6516 | (SCM x, SCM y, SCM rest), | |
6517 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6518 | "decreasing.") | |
6519 | #define FUNC_NAME s_scm_i_num_gr_p | |
6520 | { | |
6521 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6522 | return SCM_BOOL_T; | |
6523 | while (!scm_is_null (rest)) | |
6524 | { | |
6525 | if (scm_is_false (scm_gr_p (x, y))) | |
6526 | return SCM_BOOL_F; | |
6527 | x = y; | |
6528 | y = scm_car (rest); | |
6529 | rest = scm_cdr (rest); | |
6530 | } | |
6531 | return scm_gr_p (x, y); | |
6532 | } | |
6533 | #undef FUNC_NAME | |
6534 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
6535 | SCM |
6536 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 6537 | { |
c76b1eaf | 6538 | if (!SCM_NUMBERP (x)) |
fa075d40 | 6539 | return scm_wta_dispatch_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6540 | else if (!SCM_NUMBERP (y)) |
fa075d40 | 6541 | return scm_wta_dispatch_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
6542 | else |
6543 | return scm_less_p (y, x); | |
0f2d19dd | 6544 | } |
1bbd0b84 | 6545 | #undef FUNC_NAME |
0f2d19dd JB |
6546 | |
6547 | ||
8a1f4f98 AW |
6548 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
6549 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
6550 | (SCM x, SCM y, SCM rest), | |
6551 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6552 | "non-decreasing.") | |
6553 | #define FUNC_NAME s_scm_i_num_leq_p | |
6554 | { | |
6555 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6556 | return SCM_BOOL_T; | |
6557 | while (!scm_is_null (rest)) | |
6558 | { | |
6559 | if (scm_is_false (scm_leq_p (x, y))) | |
6560 | return SCM_BOOL_F; | |
6561 | x = y; | |
6562 | y = scm_car (rest); | |
6563 | rest = scm_cdr (rest); | |
6564 | } | |
6565 | return scm_leq_p (x, y); | |
6566 | } | |
6567 | #undef FUNC_NAME | |
6568 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
6569 | SCM |
6570 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 6571 | { |
c76b1eaf | 6572 | if (!SCM_NUMBERP (x)) |
fa075d40 | 6573 | return scm_wta_dispatch_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6574 | else if (!SCM_NUMBERP (y)) |
fa075d40 | 6575 | return scm_wta_dispatch_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6576 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6577 | return SCM_BOOL_F; |
c76b1eaf | 6578 | else |
73e4de09 | 6579 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 6580 | } |
1bbd0b84 | 6581 | #undef FUNC_NAME |
0f2d19dd JB |
6582 | |
6583 | ||
8a1f4f98 AW |
6584 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
6585 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
6586 | (SCM x, SCM y, SCM rest), | |
6587 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6588 | "non-increasing.") | |
6589 | #define FUNC_NAME s_scm_i_num_geq_p | |
6590 | { | |
6591 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6592 | return SCM_BOOL_T; | |
6593 | while (!scm_is_null (rest)) | |
6594 | { | |
6595 | if (scm_is_false (scm_geq_p (x, y))) | |
6596 | return SCM_BOOL_F; | |
6597 | x = y; | |
6598 | y = scm_car (rest); | |
6599 | rest = scm_cdr (rest); | |
6600 | } | |
6601 | return scm_geq_p (x, y); | |
6602 | } | |
6603 | #undef FUNC_NAME | |
6604 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
6605 | SCM |
6606 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 6607 | { |
c76b1eaf | 6608 | if (!SCM_NUMBERP (x)) |
fa075d40 | 6609 | return scm_wta_dispatch_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6610 | else if (!SCM_NUMBERP (y)) |
fa075d40 | 6611 | return scm_wta_dispatch_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6612 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6613 | return SCM_BOOL_F; |
c76b1eaf | 6614 | else |
73e4de09 | 6615 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 6616 | } |
1bbd0b84 | 6617 | #undef FUNC_NAME |
0f2d19dd JB |
6618 | |
6619 | ||
2519490c MW |
6620 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
6621 | (SCM z), | |
6622 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
6623 | "zero.") | |
6624 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 6625 | { |
e11e83f3 | 6626 | if (SCM_I_INUMP (z)) |
bc36d050 | 6627 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 6628 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 6629 | return SCM_BOOL_F; |
0aacf84e | 6630 | else if (SCM_REALP (z)) |
73e4de09 | 6631 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 6632 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 6633 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 6634 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
6635 | else if (SCM_FRACTIONP (z)) |
6636 | return SCM_BOOL_F; | |
0aacf84e | 6637 | else |
fa075d40 | 6638 | return scm_wta_dispatch_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 6639 | } |
2519490c | 6640 | #undef FUNC_NAME |
0f2d19dd JB |
6641 | |
6642 | ||
2519490c MW |
6643 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
6644 | (SCM x), | |
6645 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
6646 | "zero.") | |
6647 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 6648 | { |
e11e83f3 MV |
6649 | if (SCM_I_INUMP (x)) |
6650 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
6651 | else if (SCM_BIGP (x)) |
6652 | { | |
6653 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6654 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6655 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6656 | } |
6657 | else if (SCM_REALP (x)) | |
73e4de09 | 6658 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
6659 | else if (SCM_FRACTIONP (x)) |
6660 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6661 | else |
fa075d40 | 6662 | return scm_wta_dispatch_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 6663 | } |
2519490c | 6664 | #undef FUNC_NAME |
0f2d19dd JB |
6665 | |
6666 | ||
2519490c MW |
6667 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
6668 | (SCM x), | |
6669 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
6670 | "zero.") | |
6671 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 6672 | { |
e11e83f3 MV |
6673 | if (SCM_I_INUMP (x)) |
6674 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
6675 | else if (SCM_BIGP (x)) |
6676 | { | |
6677 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6678 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6679 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6680 | } |
6681 | else if (SCM_REALP (x)) | |
73e4de09 | 6682 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
6683 | else if (SCM_FRACTIONP (x)) |
6684 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6685 | else |
fa075d40 | 6686 | return scm_wta_dispatch_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 6687 | } |
2519490c | 6688 | #undef FUNC_NAME |
0f2d19dd JB |
6689 | |
6690 | ||
2a06f791 KR |
6691 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
6692 | required by r5rs. On that basis, for exact/inexact combinations the | |
6693 | exact is converted to inexact to compare and possibly return. This is | |
6694 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
6695 | its test, such trouble is not required for min and max. */ | |
6696 | ||
78d3deb1 AW |
6697 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
6698 | (SCM x, SCM y, SCM rest), | |
6699 | "Return the maximum of all parameter values.") | |
6700 | #define FUNC_NAME s_scm_i_max | |
6701 | { | |
6702 | while (!scm_is_null (rest)) | |
6703 | { x = scm_max (x, y); | |
6704 | y = scm_car (rest); | |
6705 | rest = scm_cdr (rest); | |
6706 | } | |
6707 | return scm_max (x, y); | |
6708 | } | |
6709 | #undef FUNC_NAME | |
6710 | ||
6711 | #define s_max s_scm_i_max | |
6712 | #define g_max g_scm_i_max | |
6713 | ||
0f2d19dd | 6714 | SCM |
6e8d25a6 | 6715 | scm_max (SCM x, SCM y) |
0f2d19dd | 6716 | { |
0aacf84e MD |
6717 | if (SCM_UNBNDP (y)) |
6718 | { | |
6719 | if (SCM_UNBNDP (x)) | |
fa075d40 | 6720 | return scm_wta_dispatch_0 (g_max, s_max); |
e11e83f3 | 6721 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
6722 | return x; |
6723 | else | |
fa075d40 | 6724 | return scm_wta_dispatch_1 (g_max, x, SCM_ARG1, s_max); |
f872b822 | 6725 | } |
f4c627b3 | 6726 | |
e11e83f3 | 6727 | if (SCM_I_INUMP (x)) |
0aacf84e | 6728 | { |
e25f3727 | 6729 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6730 | if (SCM_I_INUMP (y)) |
0aacf84e | 6731 | { |
e25f3727 | 6732 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6733 | return (xx < yy) ? y : x; |
6734 | } | |
6735 | else if (SCM_BIGP (y)) | |
6736 | { | |
6737 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6738 | scm_remember_upto_here_1 (y); | |
6739 | return (sgn < 0) ? x : y; | |
6740 | } | |
6741 | else if (SCM_REALP (y)) | |
6742 | { | |
2e274311 MW |
6743 | double xxd = xx; |
6744 | double yyd = SCM_REAL_VALUE (y); | |
6745 | ||
6746 | if (xxd > yyd) | |
6747 | return scm_from_double (xxd); | |
6748 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
6749 | else if (SCM_LIKELY (!(xxd == yyd))) | |
6750 | return y; | |
6751 | /* Handle signed zeroes properly */ | |
6752 | else if (xx == 0) | |
6753 | return flo0; | |
6754 | else | |
6755 | return y; | |
0aacf84e | 6756 | } |
f92e85f7 MV |
6757 | else if (SCM_FRACTIONP (y)) |
6758 | { | |
e4bc5d6c | 6759 | use_less: |
73e4de09 | 6760 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 6761 | } |
0aacf84e | 6762 | else |
fa075d40 | 6763 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARGn, s_max); |
f872b822 | 6764 | } |
0aacf84e MD |
6765 | else if (SCM_BIGP (x)) |
6766 | { | |
e11e83f3 | 6767 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6768 | { |
6769 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6770 | scm_remember_upto_here_1 (x); | |
6771 | return (sgn < 0) ? y : x; | |
6772 | } | |
6773 | else if (SCM_BIGP (y)) | |
6774 | { | |
6775 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6776 | scm_remember_upto_here_2 (x, y); | |
6777 | return (cmp > 0) ? x : y; | |
6778 | } | |
6779 | else if (SCM_REALP (y)) | |
6780 | { | |
2a06f791 KR |
6781 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
6782 | double xx, yy; | |
6783 | big_real: | |
6784 | xx = scm_i_big2dbl (x); | |
6785 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 6786 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 6787 | } |
f92e85f7 MV |
6788 | else if (SCM_FRACTIONP (y)) |
6789 | { | |
e4bc5d6c | 6790 | goto use_less; |
f92e85f7 | 6791 | } |
0aacf84e | 6792 | else |
fa075d40 | 6793 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARGn, s_max); |
f4c627b3 | 6794 | } |
0aacf84e MD |
6795 | else if (SCM_REALP (x)) |
6796 | { | |
e11e83f3 | 6797 | if (SCM_I_INUMP (y)) |
0aacf84e | 6798 | { |
2e274311 MW |
6799 | scm_t_inum yy = SCM_I_INUM (y); |
6800 | double xxd = SCM_REAL_VALUE (x); | |
6801 | double yyd = yy; | |
6802 | ||
6803 | if (yyd > xxd) | |
6804 | return scm_from_double (yyd); | |
6805 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
6806 | else if (SCM_LIKELY (!(xxd == yyd))) | |
6807 | return x; | |
6808 | /* Handle signed zeroes properly */ | |
6809 | else if (yy == 0) | |
6810 | return flo0; | |
6811 | else | |
6812 | return x; | |
0aacf84e MD |
6813 | } |
6814 | else if (SCM_BIGP (y)) | |
6815 | { | |
b6f8f763 | 6816 | SCM_SWAP (x, y); |
2a06f791 | 6817 | goto big_real; |
0aacf84e MD |
6818 | } |
6819 | else if (SCM_REALP (y)) | |
6820 | { | |
0aacf84e | 6821 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
6822 | double yy = SCM_REAL_VALUE (y); |
6823 | ||
6824 | /* For purposes of max: +inf.0 > nan > everything else, per R6RS */ | |
6825 | if (xx > yy) | |
6826 | return x; | |
6827 | else if (SCM_LIKELY (xx < yy)) | |
6828 | return y; | |
6829 | /* If neither (xx > yy) nor (xx < yy), then | |
6830 | either they're equal or one is a NaN */ | |
6831 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 6832 | return DOUBLE_IS_POSITIVE_INFINITY (yy) ? y : x; |
2e274311 | 6833 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 6834 | return DOUBLE_IS_POSITIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
6835 | /* xx == yy, but handle signed zeroes properly */ |
6836 | else if (double_is_non_negative_zero (yy)) | |
6837 | return y; | |
6838 | else | |
6839 | return x; | |
0aacf84e | 6840 | } |
f92e85f7 MV |
6841 | else if (SCM_FRACTIONP (y)) |
6842 | { | |
6843 | double yy = scm_i_fraction2double (y); | |
6844 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 6845 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
6846 | } |
6847 | else | |
fa075d40 | 6848 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARGn, s_max); |
f92e85f7 MV |
6849 | } |
6850 | else if (SCM_FRACTIONP (x)) | |
6851 | { | |
e11e83f3 | 6852 | if (SCM_I_INUMP (y)) |
f92e85f7 | 6853 | { |
e4bc5d6c | 6854 | goto use_less; |
f92e85f7 MV |
6855 | } |
6856 | else if (SCM_BIGP (y)) | |
6857 | { | |
e4bc5d6c | 6858 | goto use_less; |
f92e85f7 MV |
6859 | } |
6860 | else if (SCM_REALP (y)) | |
6861 | { | |
6862 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
6863 | /* if y==NaN then ">" is false, so we return the NaN y */ |
6864 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
6865 | } |
6866 | else if (SCM_FRACTIONP (y)) | |
6867 | { | |
e4bc5d6c | 6868 | goto use_less; |
f92e85f7 | 6869 | } |
0aacf84e | 6870 | else |
fa075d40 | 6871 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARGn, s_max); |
f872b822 | 6872 | } |
0aacf84e | 6873 | else |
fa075d40 | 6874 | return scm_wta_dispatch_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
6875 | } |
6876 | ||
6877 | ||
78d3deb1 AW |
6878 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
6879 | (SCM x, SCM y, SCM rest), | |
6880 | "Return the minimum of all parameter values.") | |
6881 | #define FUNC_NAME s_scm_i_min | |
6882 | { | |
6883 | while (!scm_is_null (rest)) | |
6884 | { x = scm_min (x, y); | |
6885 | y = scm_car (rest); | |
6886 | rest = scm_cdr (rest); | |
6887 | } | |
6888 | return scm_min (x, y); | |
6889 | } | |
6890 | #undef FUNC_NAME | |
6891 | ||
6892 | #define s_min s_scm_i_min | |
6893 | #define g_min g_scm_i_min | |
6894 | ||
0f2d19dd | 6895 | SCM |
6e8d25a6 | 6896 | scm_min (SCM x, SCM y) |
0f2d19dd | 6897 | { |
0aacf84e MD |
6898 | if (SCM_UNBNDP (y)) |
6899 | { | |
6900 | if (SCM_UNBNDP (x)) | |
fa075d40 | 6901 | return scm_wta_dispatch_0 (g_min, s_min); |
e11e83f3 | 6902 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
6903 | return x; |
6904 | else | |
fa075d40 | 6905 | return scm_wta_dispatch_1 (g_min, x, SCM_ARG1, s_min); |
f872b822 | 6906 | } |
f4c627b3 | 6907 | |
e11e83f3 | 6908 | if (SCM_I_INUMP (x)) |
0aacf84e | 6909 | { |
e25f3727 | 6910 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6911 | if (SCM_I_INUMP (y)) |
0aacf84e | 6912 | { |
e25f3727 | 6913 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6914 | return (xx < yy) ? x : y; |
6915 | } | |
6916 | else if (SCM_BIGP (y)) | |
6917 | { | |
6918 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6919 | scm_remember_upto_here_1 (y); | |
6920 | return (sgn < 0) ? y : x; | |
6921 | } | |
6922 | else if (SCM_REALP (y)) | |
6923 | { | |
6924 | double z = xx; | |
6925 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 6926 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 6927 | } |
f92e85f7 MV |
6928 | else if (SCM_FRACTIONP (y)) |
6929 | { | |
e4bc5d6c | 6930 | use_less: |
73e4de09 | 6931 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 6932 | } |
0aacf84e | 6933 | else |
fa075d40 | 6934 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARGn, s_min); |
f872b822 | 6935 | } |
0aacf84e MD |
6936 | else if (SCM_BIGP (x)) |
6937 | { | |
e11e83f3 | 6938 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6939 | { |
6940 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6941 | scm_remember_upto_here_1 (x); | |
6942 | return (sgn < 0) ? x : y; | |
6943 | } | |
6944 | else if (SCM_BIGP (y)) | |
6945 | { | |
6946 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6947 | scm_remember_upto_here_2 (x, y); | |
6948 | return (cmp > 0) ? y : x; | |
6949 | } | |
6950 | else if (SCM_REALP (y)) | |
6951 | { | |
2a06f791 KR |
6952 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
6953 | double xx, yy; | |
6954 | big_real: | |
6955 | xx = scm_i_big2dbl (x); | |
6956 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 6957 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 6958 | } |
f92e85f7 MV |
6959 | else if (SCM_FRACTIONP (y)) |
6960 | { | |
e4bc5d6c | 6961 | goto use_less; |
f92e85f7 | 6962 | } |
0aacf84e | 6963 | else |
fa075d40 | 6964 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARGn, s_min); |
f4c627b3 | 6965 | } |
0aacf84e MD |
6966 | else if (SCM_REALP (x)) |
6967 | { | |
e11e83f3 | 6968 | if (SCM_I_INUMP (y)) |
0aacf84e | 6969 | { |
e11e83f3 | 6970 | double z = SCM_I_INUM (y); |
0aacf84e | 6971 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 6972 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
6973 | } |
6974 | else if (SCM_BIGP (y)) | |
6975 | { | |
b6f8f763 | 6976 | SCM_SWAP (x, y); |
2a06f791 | 6977 | goto big_real; |
0aacf84e MD |
6978 | } |
6979 | else if (SCM_REALP (y)) | |
6980 | { | |
0aacf84e | 6981 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
6982 | double yy = SCM_REAL_VALUE (y); |
6983 | ||
6984 | /* For purposes of min: -inf.0 < nan < everything else, per R6RS */ | |
6985 | if (xx < yy) | |
6986 | return x; | |
6987 | else if (SCM_LIKELY (xx > yy)) | |
6988 | return y; | |
6989 | /* If neither (xx < yy) nor (xx > yy), then | |
6990 | either they're equal or one is a NaN */ | |
6991 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 6992 | return DOUBLE_IS_NEGATIVE_INFINITY (yy) ? y : x; |
2e274311 | 6993 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 6994 | return DOUBLE_IS_NEGATIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
6995 | /* xx == yy, but handle signed zeroes properly */ |
6996 | else if (double_is_non_negative_zero (xx)) | |
6997 | return y; | |
6998 | else | |
6999 | return x; | |
0aacf84e | 7000 | } |
f92e85f7 MV |
7001 | else if (SCM_FRACTIONP (y)) |
7002 | { | |
7003 | double yy = scm_i_fraction2double (y); | |
7004 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 7005 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 7006 | } |
0aacf84e | 7007 | else |
fa075d40 | 7008 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARGn, s_min); |
f872b822 | 7009 | } |
f92e85f7 MV |
7010 | else if (SCM_FRACTIONP (x)) |
7011 | { | |
e11e83f3 | 7012 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7013 | { |
e4bc5d6c | 7014 | goto use_less; |
f92e85f7 MV |
7015 | } |
7016 | else if (SCM_BIGP (y)) | |
7017 | { | |
e4bc5d6c | 7018 | goto use_less; |
f92e85f7 MV |
7019 | } |
7020 | else if (SCM_REALP (y)) | |
7021 | { | |
7022 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7023 | /* if y==NaN then "<" is false, so we return the NaN y */ |
7024 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7025 | } |
7026 | else if (SCM_FRACTIONP (y)) | |
7027 | { | |
e4bc5d6c | 7028 | goto use_less; |
f92e85f7 MV |
7029 | } |
7030 | else | |
fa075d40 | 7031 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 7032 | } |
0aacf84e | 7033 | else |
fa075d40 | 7034 | return scm_wta_dispatch_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
7035 | } |
7036 | ||
7037 | ||
8ccd24f7 AW |
7038 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
7039 | (SCM x, SCM y, SCM rest), | |
7040 | "Return the sum of all parameter values. Return 0 if called without\n" | |
7041 | "any parameters." ) | |
7042 | #define FUNC_NAME s_scm_i_sum | |
7043 | { | |
7044 | while (!scm_is_null (rest)) | |
7045 | { x = scm_sum (x, y); | |
7046 | y = scm_car (rest); | |
7047 | rest = scm_cdr (rest); | |
7048 | } | |
7049 | return scm_sum (x, y); | |
7050 | } | |
7051 | #undef FUNC_NAME | |
7052 | ||
7053 | #define s_sum s_scm_i_sum | |
7054 | #define g_sum g_scm_i_sum | |
7055 | ||
0f2d19dd | 7056 | SCM |
6e8d25a6 | 7057 | scm_sum (SCM x, SCM y) |
0f2d19dd | 7058 | { |
9cc37597 | 7059 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7060 | { |
7061 | if (SCM_NUMBERP (x)) return x; | |
7062 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
fa075d40 | 7063 | return scm_wta_dispatch_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 7064 | } |
c209c88e | 7065 | |
9cc37597 | 7066 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 7067 | { |
9cc37597 | 7068 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 7069 | { |
e25f3727 AW |
7070 | scm_t_inum xx = SCM_I_INUM (x); |
7071 | scm_t_inum yy = SCM_I_INUM (y); | |
7072 | scm_t_inum z = xx + yy; | |
7073 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
7074 | } |
7075 | else if (SCM_BIGP (y)) | |
7076 | { | |
7077 | SCM_SWAP (x, y); | |
7078 | goto add_big_inum; | |
7079 | } | |
7080 | else if (SCM_REALP (y)) | |
7081 | { | |
e25f3727 | 7082 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 7083 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
7084 | } |
7085 | else if (SCM_COMPLEXP (y)) | |
7086 | { | |
e25f3727 | 7087 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 7088 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
7089 | SCM_COMPLEX_IMAG (y)); |
7090 | } | |
f92e85f7 | 7091 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7092 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7093 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7094 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 | 7095 | else |
fa075d40 | 7096 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
0aacf84e MD |
7097 | } else if (SCM_BIGP (x)) |
7098 | { | |
e11e83f3 | 7099 | if (SCM_I_INUMP (y)) |
0aacf84e | 7100 | { |
e25f3727 | 7101 | scm_t_inum inum; |
0aacf84e MD |
7102 | int bigsgn; |
7103 | add_big_inum: | |
e11e83f3 | 7104 | inum = SCM_I_INUM (y); |
0aacf84e MD |
7105 | if (inum == 0) |
7106 | return x; | |
7107 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7108 | if (inum < 0) | |
7109 | { | |
7110 | SCM result = scm_i_mkbig (); | |
7111 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
7112 | scm_remember_upto_here_1 (x); | |
7113 | /* we know the result will have to be a bignum */ | |
7114 | if (bigsgn == -1) | |
7115 | return result; | |
7116 | return scm_i_normbig (result); | |
7117 | } | |
7118 | else | |
7119 | { | |
7120 | SCM result = scm_i_mkbig (); | |
7121 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
7122 | scm_remember_upto_here_1 (x); | |
7123 | /* we know the result will have to be a bignum */ | |
7124 | if (bigsgn == 1) | |
7125 | return result; | |
7126 | return scm_i_normbig (result); | |
7127 | } | |
7128 | } | |
7129 | else if (SCM_BIGP (y)) | |
7130 | { | |
7131 | SCM result = scm_i_mkbig (); | |
7132 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7133 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7134 | mpz_add (SCM_I_BIG_MPZ (result), | |
7135 | SCM_I_BIG_MPZ (x), | |
7136 | SCM_I_BIG_MPZ (y)); | |
7137 | scm_remember_upto_here_2 (x, y); | |
7138 | /* we know the result will have to be a bignum */ | |
7139 | if (sgn_x == sgn_y) | |
7140 | return result; | |
7141 | return scm_i_normbig (result); | |
7142 | } | |
7143 | else if (SCM_REALP (y)) | |
7144 | { | |
7145 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
7146 | scm_remember_upto_here_1 (x); | |
55f26379 | 7147 | return scm_from_double (result); |
0aacf84e MD |
7148 | } |
7149 | else if (SCM_COMPLEXP (y)) | |
7150 | { | |
7151 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7152 | + SCM_COMPLEX_REAL (y)); | |
7153 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7154 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7155 | } |
f92e85f7 | 7156 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7157 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7158 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7159 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 7160 | else |
fa075d40 | 7161 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
0f2d19dd | 7162 | } |
0aacf84e MD |
7163 | else if (SCM_REALP (x)) |
7164 | { | |
e11e83f3 | 7165 | if (SCM_I_INUMP (y)) |
55f26379 | 7166 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
7167 | else if (SCM_BIGP (y)) |
7168 | { | |
7169 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
7170 | scm_remember_upto_here_1 (y); | |
55f26379 | 7171 | return scm_from_double (result); |
0aacf84e MD |
7172 | } |
7173 | else if (SCM_REALP (y)) | |
55f26379 | 7174 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 7175 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7176 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7177 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7178 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7179 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e | 7180 | else |
fa075d40 | 7181 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
f872b822 | 7182 | } |
0aacf84e MD |
7183 | else if (SCM_COMPLEXP (x)) |
7184 | { | |
e11e83f3 | 7185 | if (SCM_I_INUMP (y)) |
8507ec80 | 7186 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
7187 | SCM_COMPLEX_IMAG (x)); |
7188 | else if (SCM_BIGP (y)) | |
7189 | { | |
7190 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
7191 | + SCM_COMPLEX_REAL (x)); | |
7192 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7193 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7194 | } |
7195 | else if (SCM_REALP (y)) | |
8507ec80 | 7196 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
7197 | SCM_COMPLEX_IMAG (x)); |
7198 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7199 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7200 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7201 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7202 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
7203 | SCM_COMPLEX_IMAG (x)); |
7204 | else | |
fa075d40 | 7205 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
f92e85f7 MV |
7206 | } |
7207 | else if (SCM_FRACTIONP (x)) | |
7208 | { | |
e11e83f3 | 7209 | if (SCM_I_INUMP (y)) |
cba42c93 | 7210 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7211 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7212 | SCM_FRACTION_DENOMINATOR (x)); | |
7213 | else if (SCM_BIGP (y)) | |
cba42c93 | 7214 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7215 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7216 | SCM_FRACTION_DENOMINATOR (x)); | |
7217 | else if (SCM_REALP (y)) | |
55f26379 | 7218 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 7219 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7220 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
7221 | SCM_COMPLEX_IMAG (y)); |
7222 | else if (SCM_FRACTIONP (y)) | |
7223 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 7224 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7225 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7226 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e | 7227 | else |
fa075d40 | 7228 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARGn, s_sum); |
98cb6e75 | 7229 | } |
0aacf84e | 7230 | else |
fa075d40 | 7231 | return scm_wta_dispatch_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
7232 | } |
7233 | ||
7234 | ||
40882e3d KR |
7235 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
7236 | (SCM x), | |
7237 | "Return @math{@var{x}+1}.") | |
7238 | #define FUNC_NAME s_scm_oneplus | |
7239 | { | |
cff5fa33 | 7240 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
7241 | } |
7242 | #undef FUNC_NAME | |
7243 | ||
7244 | ||
78d3deb1 AW |
7245 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
7246 | (SCM x, SCM y, SCM rest), | |
7247 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
7248 | "the sum of all but the first argument are subtracted from the first\n" | |
7249 | "argument.") | |
7250 | #define FUNC_NAME s_scm_i_difference | |
7251 | { | |
7252 | while (!scm_is_null (rest)) | |
7253 | { x = scm_difference (x, y); | |
7254 | y = scm_car (rest); | |
7255 | rest = scm_cdr (rest); | |
7256 | } | |
7257 | return scm_difference (x, y); | |
7258 | } | |
7259 | #undef FUNC_NAME | |
7260 | ||
7261 | #define s_difference s_scm_i_difference | |
7262 | #define g_difference g_scm_i_difference | |
7263 | ||
0f2d19dd | 7264 | SCM |
6e8d25a6 | 7265 | scm_difference (SCM x, SCM y) |
78d3deb1 | 7266 | #define FUNC_NAME s_difference |
0f2d19dd | 7267 | { |
9cc37597 | 7268 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7269 | { |
7270 | if (SCM_UNBNDP (x)) | |
fa075d40 | 7271 | return scm_wta_dispatch_0 (g_difference, s_difference); |
ca46fb90 | 7272 | else |
e11e83f3 | 7273 | if (SCM_I_INUMP (x)) |
ca46fb90 | 7274 | { |
e25f3727 | 7275 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 7276 | if (SCM_FIXABLE (xx)) |
d956fa6f | 7277 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 7278 | else |
e25f3727 | 7279 | return scm_i_inum2big (xx); |
ca46fb90 RB |
7280 | } |
7281 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
7282 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
7283 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
7284 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
7285 | else if (SCM_REALP (x)) | |
55f26379 | 7286 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 7287 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 7288 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 7289 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 7290 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 7291 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 7292 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 | 7293 | else |
fa075d40 | 7294 | return scm_wta_dispatch_1 (g_difference, x, SCM_ARG1, s_difference); |
f872b822 | 7295 | } |
ca46fb90 | 7296 | |
9cc37597 | 7297 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7298 | { |
9cc37597 | 7299 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7300 | { |
e25f3727 AW |
7301 | scm_t_inum xx = SCM_I_INUM (x); |
7302 | scm_t_inum yy = SCM_I_INUM (y); | |
7303 | scm_t_inum z = xx - yy; | |
0aacf84e | 7304 | if (SCM_FIXABLE (z)) |
d956fa6f | 7305 | return SCM_I_MAKINUM (z); |
0aacf84e | 7306 | else |
e25f3727 | 7307 | return scm_i_inum2big (z); |
0aacf84e MD |
7308 | } |
7309 | else if (SCM_BIGP (y)) | |
7310 | { | |
7311 | /* inum-x - big-y */ | |
e25f3727 | 7312 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 7313 | |
0aacf84e | 7314 | if (xx == 0) |
b5c40589 MW |
7315 | { |
7316 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
7317 | bignum, but negating that gives a fixnum. */ | |
7318 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
7319 | } | |
0aacf84e MD |
7320 | else |
7321 | { | |
7322 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7323 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7324 | |
0aacf84e MD |
7325 | if (xx >= 0) |
7326 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
7327 | else | |
7328 | { | |
7329 | /* x - y == -(y + -x) */ | |
7330 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
7331 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7332 | } | |
7333 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 7334 | |
0aacf84e MD |
7335 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
7336 | /* we know the result will have to be a bignum */ | |
7337 | return result; | |
7338 | else | |
7339 | return scm_i_normbig (result); | |
7340 | } | |
7341 | } | |
7342 | else if (SCM_REALP (y)) | |
7343 | { | |
e25f3727 | 7344 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7345 | |
7346 | /* | |
7347 | * We need to handle x == exact 0 | |
7348 | * specially because R6RS states that: | |
7349 | * (- 0.0) ==> -0.0 and | |
7350 | * (- 0.0 0.0) ==> 0.0 | |
7351 | * and the scheme compiler changes | |
7352 | * (- 0.0) into (- 0 0.0) | |
7353 | * So we need to treat (- 0 0.0) like (- 0.0). | |
7354 | * At the C level, (-x) is different than (0.0 - x). | |
7355 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
7356 | */ | |
7357 | if (xx == 0) | |
7358 | return scm_from_double (- SCM_REAL_VALUE (y)); | |
7359 | else | |
7360 | return scm_from_double (xx - SCM_REAL_VALUE (y)); | |
0aacf84e MD |
7361 | } |
7362 | else if (SCM_COMPLEXP (y)) | |
7363 | { | |
e25f3727 | 7364 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7365 | |
7366 | /* We need to handle x == exact 0 specially. | |
7367 | See the comment above (for SCM_REALP (y)) */ | |
7368 | if (xx == 0) | |
7369 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
7370 | - SCM_COMPLEX_IMAG (y)); | |
7371 | else | |
7372 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
7373 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 7374 | } |
f92e85f7 MV |
7375 | else if (SCM_FRACTIONP (y)) |
7376 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 7377 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7378 | SCM_FRACTION_NUMERATOR (y)), |
7379 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 7380 | else |
fa075d40 | 7381 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); |
f872b822 | 7382 | } |
0aacf84e MD |
7383 | else if (SCM_BIGP (x)) |
7384 | { | |
e11e83f3 | 7385 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7386 | { |
7387 | /* big-x - inum-y */ | |
e25f3727 | 7388 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 7389 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 7390 | |
0aacf84e MD |
7391 | scm_remember_upto_here_1 (x); |
7392 | if (sgn_x == 0) | |
c71b0706 | 7393 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 7394 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
7395 | else |
7396 | { | |
7397 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7398 | |
708f22c6 KR |
7399 | if (yy >= 0) |
7400 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
7401 | else | |
7402 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 7403 | scm_remember_upto_here_1 (x); |
ca46fb90 | 7404 | |
0aacf84e MD |
7405 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
7406 | /* we know the result will have to be a bignum */ | |
7407 | return result; | |
7408 | else | |
7409 | return scm_i_normbig (result); | |
7410 | } | |
7411 | } | |
7412 | else if (SCM_BIGP (y)) | |
7413 | { | |
7414 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7415 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7416 | SCM result = scm_i_mkbig (); | |
7417 | mpz_sub (SCM_I_BIG_MPZ (result), | |
7418 | SCM_I_BIG_MPZ (x), | |
7419 | SCM_I_BIG_MPZ (y)); | |
7420 | scm_remember_upto_here_2 (x, y); | |
7421 | /* we know the result will have to be a bignum */ | |
7422 | if ((sgn_x == 1) && (sgn_y == -1)) | |
7423 | return result; | |
7424 | if ((sgn_x == -1) && (sgn_y == 1)) | |
7425 | return result; | |
7426 | return scm_i_normbig (result); | |
7427 | } | |
7428 | else if (SCM_REALP (y)) | |
7429 | { | |
7430 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
7431 | scm_remember_upto_here_1 (x); | |
55f26379 | 7432 | return scm_from_double (result); |
0aacf84e MD |
7433 | } |
7434 | else if (SCM_COMPLEXP (y)) | |
7435 | { | |
7436 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7437 | - SCM_COMPLEX_REAL (y)); | |
7438 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7439 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7440 | } |
f92e85f7 | 7441 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7442 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7443 | SCM_FRACTION_NUMERATOR (y)), |
7444 | SCM_FRACTION_DENOMINATOR (y)); | |
fa075d40 AW |
7445 | else |
7446 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
ca46fb90 | 7447 | } |
0aacf84e MD |
7448 | else if (SCM_REALP (x)) |
7449 | { | |
e11e83f3 | 7450 | if (SCM_I_INUMP (y)) |
55f26379 | 7451 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
7452 | else if (SCM_BIGP (y)) |
7453 | { | |
7454 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7455 | scm_remember_upto_here_1 (x); | |
55f26379 | 7456 | return scm_from_double (result); |
0aacf84e MD |
7457 | } |
7458 | else if (SCM_REALP (y)) | |
55f26379 | 7459 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 7460 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7461 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7462 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7463 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7464 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e | 7465 | else |
fa075d40 | 7466 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); |
98cb6e75 | 7467 | } |
0aacf84e MD |
7468 | else if (SCM_COMPLEXP (x)) |
7469 | { | |
e11e83f3 | 7470 | if (SCM_I_INUMP (y)) |
8507ec80 | 7471 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
7472 | SCM_COMPLEX_IMAG (x)); |
7473 | else if (SCM_BIGP (y)) | |
7474 | { | |
7475 | double real_part = (SCM_COMPLEX_REAL (x) | |
7476 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
7477 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7478 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
7479 | } |
7480 | else if (SCM_REALP (y)) | |
8507ec80 | 7481 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
7482 | SCM_COMPLEX_IMAG (x)); |
7483 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7484 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7485 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7486 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7487 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
7488 | SCM_COMPLEX_IMAG (x)); |
7489 | else | |
fa075d40 | 7490 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); |
f92e85f7 MV |
7491 | } |
7492 | else if (SCM_FRACTIONP (x)) | |
7493 | { | |
e11e83f3 | 7494 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7495 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 7496 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7497 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7498 | SCM_FRACTION_DENOMINATOR (x)); | |
7499 | else if (SCM_BIGP (y)) | |
cba42c93 | 7500 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7501 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7502 | SCM_FRACTION_DENOMINATOR (x)); | |
7503 | else if (SCM_REALP (y)) | |
55f26379 | 7504 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 7505 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7506 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7507 | -SCM_COMPLEX_IMAG (y)); |
7508 | else if (SCM_FRACTIONP (y)) | |
7509 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 7510 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7511 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7512 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e | 7513 | else |
fa075d40 | 7514 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARGn, s_difference); |
98cb6e75 | 7515 | } |
0aacf84e | 7516 | else |
fa075d40 | 7517 | return scm_wta_dispatch_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 7518 | } |
c05e97b7 | 7519 | #undef FUNC_NAME |
0f2d19dd | 7520 | |
ca46fb90 | 7521 | |
40882e3d KR |
7522 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
7523 | (SCM x), | |
7524 | "Return @math{@var{x}-1}.") | |
7525 | #define FUNC_NAME s_scm_oneminus | |
7526 | { | |
cff5fa33 | 7527 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
7528 | } |
7529 | #undef FUNC_NAME | |
7530 | ||
7531 | ||
78d3deb1 AW |
7532 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
7533 | (SCM x, SCM y, SCM rest), | |
7534 | "Return the product of all arguments. If called without arguments,\n" | |
7535 | "1 is returned.") | |
7536 | #define FUNC_NAME s_scm_i_product | |
7537 | { | |
7538 | while (!scm_is_null (rest)) | |
7539 | { x = scm_product (x, y); | |
7540 | y = scm_car (rest); | |
7541 | rest = scm_cdr (rest); | |
7542 | } | |
7543 | return scm_product (x, y); | |
7544 | } | |
7545 | #undef FUNC_NAME | |
7546 | ||
7547 | #define s_product s_scm_i_product | |
7548 | #define g_product g_scm_i_product | |
7549 | ||
0f2d19dd | 7550 | SCM |
6e8d25a6 | 7551 | scm_product (SCM x, SCM y) |
0f2d19dd | 7552 | { |
9cc37597 | 7553 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7554 | { |
7555 | if (SCM_UNBNDP (x)) | |
d956fa6f | 7556 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
7557 | else if (SCM_NUMBERP (x)) |
7558 | return x; | |
7559 | else | |
fa075d40 | 7560 | return scm_wta_dispatch_1 (g_product, x, SCM_ARG1, s_product); |
f872b822 | 7561 | } |
ca46fb90 | 7562 | |
9cc37597 | 7563 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7564 | { |
e25f3727 | 7565 | scm_t_inum xx; |
f4c627b3 | 7566 | |
5e791807 | 7567 | xinum: |
e11e83f3 | 7568 | xx = SCM_I_INUM (x); |
f4c627b3 | 7569 | |
0aacf84e MD |
7570 | switch (xx) |
7571 | { | |
5e791807 MW |
7572 | case 1: |
7573 | /* exact1 is the universal multiplicative identity */ | |
7574 | return y; | |
7575 | break; | |
7576 | case 0: | |
7577 | /* exact0 times a fixnum is exact0: optimize this case */ | |
7578 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
7579 | return SCM_INUM0; | |
7580 | /* if the other argument is inexact, the result is inexact, | |
7581 | and we must do the multiplication in order to handle | |
7582 | infinities and NaNs properly. */ | |
7583 | else if (SCM_REALP (y)) | |
7584 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
7585 | else if (SCM_COMPLEXP (y)) | |
7586 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
7587 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
7588 | /* we've already handled inexact numbers, | |
7589 | so y must be exact, and we return exact0 */ | |
7590 | else if (SCM_NUMP (y)) | |
7591 | return SCM_INUM0; | |
7592 | else | |
fa075d40 | 7593 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
5e791807 MW |
7594 | break; |
7595 | case -1: | |
b5c40589 | 7596 | /* |
5e791807 MW |
7597 | * This case is important for more than just optimization. |
7598 | * It handles the case of negating | |
b5c40589 MW |
7599 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
7600 | * which is a bignum that must be changed back into a fixnum. | |
7601 | * Failure to do so will cause the following to return #f: | |
7602 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
7603 | */ | |
b5c40589 MW |
7604 | return scm_difference(y, SCM_UNDEFINED); |
7605 | break; | |
0aacf84e | 7606 | } |
f4c627b3 | 7607 | |
9cc37597 | 7608 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7609 | { |
e25f3727 AW |
7610 | scm_t_inum yy = SCM_I_INUM (y); |
7611 | scm_t_inum kk = xx * yy; | |
d956fa6f | 7612 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 7613 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
7614 | return k; |
7615 | else | |
7616 | { | |
e25f3727 | 7617 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
7618 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
7619 | return scm_i_normbig (result); | |
7620 | } | |
7621 | } | |
7622 | else if (SCM_BIGP (y)) | |
7623 | { | |
7624 | SCM result = scm_i_mkbig (); | |
7625 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
7626 | scm_remember_upto_here_1 (y); | |
7627 | return result; | |
7628 | } | |
7629 | else if (SCM_REALP (y)) | |
55f26379 | 7630 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 7631 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7632 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 7633 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7634 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7635 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7636 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e | 7637 | else |
fa075d40 | 7638 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f4c627b3 | 7639 | } |
0aacf84e MD |
7640 | else if (SCM_BIGP (x)) |
7641 | { | |
e11e83f3 | 7642 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7643 | { |
7644 | SCM_SWAP (x, y); | |
5e791807 | 7645 | goto xinum; |
0aacf84e MD |
7646 | } |
7647 | else if (SCM_BIGP (y)) | |
7648 | { | |
7649 | SCM result = scm_i_mkbig (); | |
7650 | mpz_mul (SCM_I_BIG_MPZ (result), | |
7651 | SCM_I_BIG_MPZ (x), | |
7652 | SCM_I_BIG_MPZ (y)); | |
7653 | scm_remember_upto_here_2 (x, y); | |
7654 | return result; | |
7655 | } | |
7656 | else if (SCM_REALP (y)) | |
7657 | { | |
7658 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
7659 | scm_remember_upto_here_1 (x); | |
55f26379 | 7660 | return scm_from_double (result); |
0aacf84e MD |
7661 | } |
7662 | else if (SCM_COMPLEXP (y)) | |
7663 | { | |
7664 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
7665 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7666 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
7667 | z * SCM_COMPLEX_IMAG (y)); |
7668 | } | |
f92e85f7 | 7669 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7670 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7671 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e | 7672 | else |
fa075d40 | 7673 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f4c627b3 | 7674 | } |
0aacf84e MD |
7675 | else if (SCM_REALP (x)) |
7676 | { | |
e11e83f3 | 7677 | if (SCM_I_INUMP (y)) |
5e791807 MW |
7678 | { |
7679 | SCM_SWAP (x, y); | |
7680 | goto xinum; | |
7681 | } | |
0aacf84e MD |
7682 | else if (SCM_BIGP (y)) |
7683 | { | |
7684 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
7685 | scm_remember_upto_here_1 (y); | |
55f26379 | 7686 | return scm_from_double (result); |
0aacf84e MD |
7687 | } |
7688 | else if (SCM_REALP (y)) | |
55f26379 | 7689 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 7690 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7691 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 7692 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7693 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7694 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e | 7695 | else |
fa075d40 | 7696 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f4c627b3 | 7697 | } |
0aacf84e MD |
7698 | else if (SCM_COMPLEXP (x)) |
7699 | { | |
e11e83f3 | 7700 | if (SCM_I_INUMP (y)) |
5e791807 MW |
7701 | { |
7702 | SCM_SWAP (x, y); | |
7703 | goto xinum; | |
7704 | } | |
0aacf84e MD |
7705 | else if (SCM_BIGP (y)) |
7706 | { | |
7707 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7708 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7709 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 7710 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7711 | } |
7712 | else if (SCM_REALP (y)) | |
8507ec80 | 7713 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
7714 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
7715 | else if (SCM_COMPLEXP (y)) | |
7716 | { | |
8507ec80 | 7717 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
7718 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
7719 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
7720 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
7721 | } | |
f92e85f7 MV |
7722 | else if (SCM_FRACTIONP (y)) |
7723 | { | |
7724 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 7725 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
7726 | yy * SCM_COMPLEX_IMAG (x)); |
7727 | } | |
7728 | else | |
fa075d40 | 7729 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f92e85f7 MV |
7730 | } |
7731 | else if (SCM_FRACTIONP (x)) | |
7732 | { | |
e11e83f3 | 7733 | if (SCM_I_INUMP (y)) |
cba42c93 | 7734 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
7735 | SCM_FRACTION_DENOMINATOR (x)); |
7736 | else if (SCM_BIGP (y)) | |
cba42c93 | 7737 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
7738 | SCM_FRACTION_DENOMINATOR (x)); |
7739 | else if (SCM_REALP (y)) | |
55f26379 | 7740 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
7741 | else if (SCM_COMPLEXP (y)) |
7742 | { | |
7743 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 7744 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7745 | xx * SCM_COMPLEX_IMAG (y)); |
7746 | } | |
7747 | else if (SCM_FRACTIONP (y)) | |
7748 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 7749 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7750 | SCM_FRACTION_NUMERATOR (y)), |
7751 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
7752 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e | 7753 | else |
fa075d40 | 7754 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARGn, s_product); |
f4c627b3 | 7755 | } |
0aacf84e | 7756 | else |
fa075d40 | 7757 | return scm_wta_dispatch_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
7758 | } |
7759 | ||
7351e207 MV |
7760 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
7761 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
7762 | #define ALLOW_DIVIDE_BY_ZERO | |
7763 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
7764 | #endif | |
0f2d19dd | 7765 | |
ba74ef4e MV |
7766 | /* The code below for complex division is adapted from the GNU |
7767 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
7768 | this copyright: */ | |
7769 | ||
7770 | /**************************************************************** | |
7771 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
7772 | ||
7773 | Permission to use, copy, modify, and distribute this software | |
7774 | and its documentation for any purpose and without fee is hereby | |
7775 | granted, provided that the above copyright notice appear in all | |
7776 | copies and that both that the copyright notice and this | |
7777 | permission notice and warranty disclaimer appear in supporting | |
7778 | documentation, and that the names of AT&T Bell Laboratories or | |
7779 | Bellcore or any of their entities not be used in advertising or | |
7780 | publicity pertaining to distribution of the software without | |
7781 | specific, written prior permission. | |
7782 | ||
7783 | AT&T and Bellcore disclaim all warranties with regard to this | |
7784 | software, including all implied warranties of merchantability | |
7785 | and fitness. In no event shall AT&T or Bellcore be liable for | |
7786 | any special, indirect or consequential damages or any damages | |
7787 | whatsoever resulting from loss of use, data or profits, whether | |
7788 | in an action of contract, negligence or other tortious action, | |
7789 | arising out of or in connection with the use or performance of | |
7790 | this software. | |
7791 | ****************************************************************/ | |
7792 | ||
78d3deb1 AW |
7793 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
7794 | (SCM x, SCM y, SCM rest), | |
7795 | "Divide the first argument by the product of the remaining\n" | |
7796 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
7797 | "returned.") | |
7798 | #define FUNC_NAME s_scm_i_divide | |
7799 | { | |
7800 | while (!scm_is_null (rest)) | |
7801 | { x = scm_divide (x, y); | |
7802 | y = scm_car (rest); | |
7803 | rest = scm_cdr (rest); | |
7804 | } | |
7805 | return scm_divide (x, y); | |
7806 | } | |
7807 | #undef FUNC_NAME | |
7808 | ||
7809 | #define s_divide s_scm_i_divide | |
7810 | #define g_divide g_scm_i_divide | |
7811 | ||
f92e85f7 | 7812 | static SCM |
78d3deb1 AW |
7813 | do_divide (SCM x, SCM y, int inexact) |
7814 | #define FUNC_NAME s_divide | |
0f2d19dd | 7815 | { |
f8de44c1 DH |
7816 | double a; |
7817 | ||
9cc37597 | 7818 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7819 | { |
7820 | if (SCM_UNBNDP (x)) | |
fa075d40 | 7821 | return scm_wta_dispatch_0 (g_divide, s_divide); |
e11e83f3 | 7822 | else if (SCM_I_INUMP (x)) |
0aacf84e | 7823 | { |
e25f3727 | 7824 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
7825 | if (xx == 1 || xx == -1) |
7826 | return x; | |
7351e207 | 7827 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
7828 | else if (xx == 0) |
7829 | scm_num_overflow (s_divide); | |
7351e207 | 7830 | #endif |
0aacf84e | 7831 | else |
f92e85f7 MV |
7832 | { |
7833 | if (inexact) | |
55f26379 | 7834 | return scm_from_double (1.0 / (double) xx); |
cff5fa33 | 7835 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 7836 | } |
0aacf84e MD |
7837 | } |
7838 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
7839 | { |
7840 | if (inexact) | |
55f26379 | 7841 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cff5fa33 | 7842 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 7843 | } |
0aacf84e MD |
7844 | else if (SCM_REALP (x)) |
7845 | { | |
7846 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 7847 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
7848 | if (xx == 0.0) |
7849 | scm_num_overflow (s_divide); | |
7850 | else | |
7351e207 | 7851 | #endif |
55f26379 | 7852 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
7853 | } |
7854 | else if (SCM_COMPLEXP (x)) | |
7855 | { | |
7856 | double r = SCM_COMPLEX_REAL (x); | |
7857 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 7858 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
7859 | { |
7860 | double t = r / i; | |
7861 | double d = i * (1.0 + t * t); | |
8507ec80 | 7862 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
7863 | } |
7864 | else | |
7865 | { | |
7866 | double t = i / r; | |
7867 | double d = r * (1.0 + t * t); | |
8507ec80 | 7868 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
7869 | } |
7870 | } | |
f92e85f7 | 7871 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 7872 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 7873 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e | 7874 | else |
fa075d40 | 7875 | return scm_wta_dispatch_1 (g_divide, x, SCM_ARG1, s_divide); |
f8de44c1 | 7876 | } |
f8de44c1 | 7877 | |
9cc37597 | 7878 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7879 | { |
e25f3727 | 7880 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 7881 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7882 | { |
e25f3727 | 7883 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7884 | if (yy == 0) |
7885 | { | |
7351e207 | 7886 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 7887 | scm_num_overflow (s_divide); |
7351e207 | 7888 | #else |
55f26379 | 7889 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 7890 | #endif |
0aacf84e MD |
7891 | } |
7892 | else if (xx % yy != 0) | |
f92e85f7 MV |
7893 | { |
7894 | if (inexact) | |
55f26379 | 7895 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 7896 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 7897 | } |
0aacf84e MD |
7898 | else |
7899 | { | |
e25f3727 | 7900 | scm_t_inum z = xx / yy; |
0aacf84e | 7901 | if (SCM_FIXABLE (z)) |
d956fa6f | 7902 | return SCM_I_MAKINUM (z); |
0aacf84e | 7903 | else |
e25f3727 | 7904 | return scm_i_inum2big (z); |
0aacf84e | 7905 | } |
f872b822 | 7906 | } |
0aacf84e | 7907 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
7908 | { |
7909 | if (inexact) | |
55f26379 | 7910 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 7911 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 7912 | } |
0aacf84e MD |
7913 | else if (SCM_REALP (y)) |
7914 | { | |
7915 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 7916 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
7917 | if (yy == 0.0) |
7918 | scm_num_overflow (s_divide); | |
7919 | else | |
7351e207 | 7920 | #endif |
55f26379 | 7921 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 7922 | } |
0aacf84e MD |
7923 | else if (SCM_COMPLEXP (y)) |
7924 | { | |
7925 | a = xx; | |
7926 | complex_div: /* y _must_ be a complex number */ | |
7927 | { | |
7928 | double r = SCM_COMPLEX_REAL (y); | |
7929 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 7930 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
7931 | { |
7932 | double t = r / i; | |
7933 | double d = i * (1.0 + t * t); | |
8507ec80 | 7934 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
7935 | } |
7936 | else | |
7937 | { | |
7938 | double t = i / r; | |
7939 | double d = r * (1.0 + t * t); | |
8507ec80 | 7940 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
7941 | } |
7942 | } | |
7943 | } | |
f92e85f7 MV |
7944 | else if (SCM_FRACTIONP (y)) |
7945 | /* a / b/c = ac / b */ | |
cba42c93 | 7946 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 7947 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e | 7948 | else |
fa075d40 | 7949 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f8de44c1 | 7950 | } |
0aacf84e MD |
7951 | else if (SCM_BIGP (x)) |
7952 | { | |
e11e83f3 | 7953 | if (SCM_I_INUMP (y)) |
0aacf84e | 7954 | { |
e25f3727 | 7955 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7956 | if (yy == 0) |
7957 | { | |
7351e207 | 7958 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 7959 | scm_num_overflow (s_divide); |
7351e207 | 7960 | #else |
0aacf84e MD |
7961 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
7962 | scm_remember_upto_here_1 (x); | |
7963 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 7964 | #endif |
0aacf84e MD |
7965 | } |
7966 | else if (yy == 1) | |
7967 | return x; | |
7968 | else | |
7969 | { | |
7970 | /* FIXME: HMM, what are the relative performance issues here? | |
7971 | We need to test. Is it faster on average to test | |
7972 | divisible_p, then perform whichever operation, or is it | |
7973 | faster to perform the integer div opportunistically and | |
7974 | switch to real if there's a remainder? For now we take the | |
7975 | middle ground: test, then if divisible, use the faster div | |
7976 | func. */ | |
7977 | ||
e25f3727 | 7978 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
7979 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
7980 | ||
7981 | if (divisible_p) | |
7982 | { | |
7983 | SCM result = scm_i_mkbig (); | |
7984 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
7985 | scm_remember_upto_here_1 (x); | |
7986 | if (yy < 0) | |
7987 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7988 | return scm_i_normbig (result); | |
7989 | } | |
7990 | else | |
f92e85f7 MV |
7991 | { |
7992 | if (inexact) | |
55f26379 | 7993 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 7994 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 7995 | } |
0aacf84e MD |
7996 | } |
7997 | } | |
7998 | else if (SCM_BIGP (y)) | |
7999 | { | |
a4955a04 MW |
8000 | /* big_x / big_y */ |
8001 | if (inexact) | |
0aacf84e | 8002 | { |
a4955a04 MW |
8003 | /* It's easily possible for the ratio x/y to fit a double |
8004 | but one or both x and y be too big to fit a double, | |
8005 | hence the use of mpq_get_d rather than converting and | |
8006 | dividing. */ | |
8007 | mpq_t q; | |
8008 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
8009 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
8010 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
8011 | } |
8012 | else | |
8013 | { | |
a4955a04 MW |
8014 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
8015 | SCM_I_BIG_MPZ (y)); | |
8016 | if (divisible_p) | |
8017 | { | |
8018 | SCM result = scm_i_mkbig (); | |
8019 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
8020 | SCM_I_BIG_MPZ (x), | |
8021 | SCM_I_BIG_MPZ (y)); | |
8022 | scm_remember_upto_here_2 (x, y); | |
8023 | return scm_i_normbig (result); | |
8024 | } | |
8025 | else | |
8026 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
8027 | } |
8028 | } | |
8029 | else if (SCM_REALP (y)) | |
8030 | { | |
8031 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8032 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8033 | if (yy == 0.0) |
8034 | scm_num_overflow (s_divide); | |
8035 | else | |
7351e207 | 8036 | #endif |
55f26379 | 8037 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
8038 | } |
8039 | else if (SCM_COMPLEXP (y)) | |
8040 | { | |
8041 | a = scm_i_big2dbl (x); | |
8042 | goto complex_div; | |
8043 | } | |
f92e85f7 | 8044 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8045 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 8046 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e | 8047 | else |
fa075d40 | 8048 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f872b822 | 8049 | } |
0aacf84e MD |
8050 | else if (SCM_REALP (x)) |
8051 | { | |
8052 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 8053 | if (SCM_I_INUMP (y)) |
0aacf84e | 8054 | { |
e25f3727 | 8055 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8056 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8057 | if (yy == 0) |
8058 | scm_num_overflow (s_divide); | |
8059 | else | |
7351e207 | 8060 | #endif |
55f26379 | 8061 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
8062 | } |
8063 | else if (SCM_BIGP (y)) | |
8064 | { | |
8065 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8066 | scm_remember_upto_here_1 (y); | |
55f26379 | 8067 | return scm_from_double (rx / dby); |
0aacf84e MD |
8068 | } |
8069 | else if (SCM_REALP (y)) | |
8070 | { | |
8071 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8072 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8073 | if (yy == 0.0) |
8074 | scm_num_overflow (s_divide); | |
8075 | else | |
7351e207 | 8076 | #endif |
55f26379 | 8077 | return scm_from_double (rx / yy); |
0aacf84e MD |
8078 | } |
8079 | else if (SCM_COMPLEXP (y)) | |
8080 | { | |
8081 | a = rx; | |
8082 | goto complex_div; | |
8083 | } | |
f92e85f7 | 8084 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8085 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e | 8086 | else |
fa075d40 | 8087 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f872b822 | 8088 | } |
0aacf84e MD |
8089 | else if (SCM_COMPLEXP (x)) |
8090 | { | |
8091 | double rx = SCM_COMPLEX_REAL (x); | |
8092 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 8093 | if (SCM_I_INUMP (y)) |
0aacf84e | 8094 | { |
e25f3727 | 8095 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8096 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8097 | if (yy == 0) |
8098 | scm_num_overflow (s_divide); | |
8099 | else | |
7351e207 | 8100 | #endif |
0aacf84e MD |
8101 | { |
8102 | double d = yy; | |
8507ec80 | 8103 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
8104 | } |
8105 | } | |
8106 | else if (SCM_BIGP (y)) | |
8107 | { | |
8108 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8109 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8110 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
8111 | } |
8112 | else if (SCM_REALP (y)) | |
8113 | { | |
8114 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8115 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8116 | if (yy == 0.0) |
8117 | scm_num_overflow (s_divide); | |
8118 | else | |
7351e207 | 8119 | #endif |
8507ec80 | 8120 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
8121 | } |
8122 | else if (SCM_COMPLEXP (y)) | |
8123 | { | |
8124 | double ry = SCM_COMPLEX_REAL (y); | |
8125 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8126 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
8127 | { |
8128 | double t = ry / iy; | |
8129 | double d = iy * (1.0 + t * t); | |
8507ec80 | 8130 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
8131 | } |
8132 | else | |
8133 | { | |
8134 | double t = iy / ry; | |
8135 | double d = ry * (1.0 + t * t); | |
8507ec80 | 8136 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
8137 | } |
8138 | } | |
f92e85f7 MV |
8139 | else if (SCM_FRACTIONP (y)) |
8140 | { | |
8141 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 8142 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 8143 | } |
0aacf84e | 8144 | else |
fa075d40 | 8145 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f8de44c1 | 8146 | } |
f92e85f7 MV |
8147 | else if (SCM_FRACTIONP (x)) |
8148 | { | |
e11e83f3 | 8149 | if (SCM_I_INUMP (y)) |
f92e85f7 | 8150 | { |
e25f3727 | 8151 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
8152 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
8153 | if (yy == 0) | |
8154 | scm_num_overflow (s_divide); | |
8155 | else | |
8156 | #endif | |
cba42c93 | 8157 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8158 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8159 | } | |
8160 | else if (SCM_BIGP (y)) | |
8161 | { | |
cba42c93 | 8162 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8163 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8164 | } | |
8165 | else if (SCM_REALP (y)) | |
8166 | { | |
8167 | double yy = SCM_REAL_VALUE (y); | |
8168 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8169 | if (yy == 0.0) | |
8170 | scm_num_overflow (s_divide); | |
8171 | else | |
8172 | #endif | |
55f26379 | 8173 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
8174 | } |
8175 | else if (SCM_COMPLEXP (y)) | |
8176 | { | |
8177 | a = scm_i_fraction2double (x); | |
8178 | goto complex_div; | |
8179 | } | |
8180 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 8181 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
8182 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
8183 | else | |
fa075d40 | 8184 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARGn, s_divide); |
f92e85f7 | 8185 | } |
0aacf84e | 8186 | else |
fa075d40 | 8187 | return scm_wta_dispatch_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 8188 | } |
f92e85f7 MV |
8189 | |
8190 | SCM | |
8191 | scm_divide (SCM x, SCM y) | |
8192 | { | |
78d3deb1 | 8193 | return do_divide (x, y, 0); |
f92e85f7 MV |
8194 | } |
8195 | ||
8196 | static SCM scm_divide2real (SCM x, SCM y) | |
8197 | { | |
78d3deb1 | 8198 | return do_divide (x, y, 1); |
f92e85f7 | 8199 | } |
c05e97b7 | 8200 | #undef FUNC_NAME |
0f2d19dd | 8201 | |
fa605590 | 8202 | |
0f2d19dd | 8203 | double |
3101f40f | 8204 | scm_c_truncate (double x) |
0f2d19dd | 8205 | { |
fa605590 | 8206 | return trunc (x); |
0f2d19dd | 8207 | } |
0f2d19dd | 8208 | |
3101f40f MV |
8209 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
8210 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
8211 | Then half-way cases are identified and adjusted down if the | |
8212 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
8213 | |
8214 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
8215 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
8216 | ||
8217 | An odd "result" value is identified with result/2 != floor(result/2). | |
8218 | This is done with plus_half, since that value is ready for use sooner in | |
8219 | a pipelined cpu, and we're already requiring plus_half == result. | |
8220 | ||
8221 | Note however that we need to be careful when x is big and already an | |
8222 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
8223 | us to return such a value, incorrectly. For instance if the hardware is | |
8224 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
8225 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
8226 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
8227 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
8228 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
8229 | ||
8230 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
8231 | x is already an integer. If it is then clearly that's the desired result | |
8232 | already. And if it's not then the exponent must be small enough to allow | |
8233 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
8234 | ||
0f2d19dd | 8235 | double |
3101f40f | 8236 | scm_c_round (double x) |
0f2d19dd | 8237 | { |
6187f48b KR |
8238 | double plus_half, result; |
8239 | ||
8240 | if (x == floor (x)) | |
8241 | return x; | |
8242 | ||
8243 | plus_half = x + 0.5; | |
8244 | result = floor (plus_half); | |
3101f40f | 8245 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
8246 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
8247 | ? result - 1 | |
8248 | : result); | |
0f2d19dd JB |
8249 | } |
8250 | ||
8b56bcec MW |
8251 | SCM_PRIMITIVE_GENERIC (scm_truncate_number, "truncate", 1, 0, 0, |
8252 | (SCM x), | |
8253 | "Round the number @var{x} towards zero.") | |
f92e85f7 MV |
8254 | #define FUNC_NAME s_scm_truncate_number |
8255 | { | |
8b56bcec MW |
8256 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
8257 | return x; | |
8258 | else if (SCM_REALP (x)) | |
c251ab63 | 8259 | return scm_from_double (trunc (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8260 | else if (SCM_FRACTIONP (x)) |
8261 | return scm_truncate_quotient (SCM_FRACTION_NUMERATOR (x), | |
8262 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8263 | else |
fa075d40 | 8264 | return scm_wta_dispatch_1 (g_scm_truncate_number, x, SCM_ARG1, |
8b56bcec | 8265 | s_scm_truncate_number); |
f92e85f7 MV |
8266 | } |
8267 | #undef FUNC_NAME | |
8268 | ||
8b56bcec MW |
8269 | SCM_PRIMITIVE_GENERIC (scm_round_number, "round", 1, 0, 0, |
8270 | (SCM x), | |
8271 | "Round the number @var{x} towards the nearest integer. " | |
8272 | "When it is exactly halfway between two integers, " | |
8273 | "round towards the even one.") | |
f92e85f7 MV |
8274 | #define FUNC_NAME s_scm_round_number |
8275 | { | |
e11e83f3 | 8276 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
8277 | return x; |
8278 | else if (SCM_REALP (x)) | |
3101f40f | 8279 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8280 | else if (SCM_FRACTIONP (x)) |
8281 | return scm_round_quotient (SCM_FRACTION_NUMERATOR (x), | |
8282 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8283 | else |
fa075d40 AW |
8284 | return scm_wta_dispatch_1 (g_scm_round_number, x, SCM_ARG1, |
8285 | s_scm_round_number); | |
f92e85f7 MV |
8286 | } |
8287 | #undef FUNC_NAME | |
8288 | ||
8289 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
8290 | (SCM x), | |
8291 | "Round the number @var{x} towards minus infinity.") | |
8292 | #define FUNC_NAME s_scm_floor | |
8293 | { | |
e11e83f3 | 8294 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8295 | return x; |
8296 | else if (SCM_REALP (x)) | |
55f26379 | 8297 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 | 8298 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8299 | return scm_floor_quotient (SCM_FRACTION_NUMERATOR (x), |
8300 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8301 | else |
fa075d40 | 8302 | return scm_wta_dispatch_1 (g_scm_floor, x, 1, s_scm_floor); |
f92e85f7 MV |
8303 | } |
8304 | #undef FUNC_NAME | |
8305 | ||
8306 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
8307 | (SCM x), | |
8308 | "Round the number @var{x} towards infinity.") | |
8309 | #define FUNC_NAME s_scm_ceiling | |
8310 | { | |
e11e83f3 | 8311 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8312 | return x; |
8313 | else if (SCM_REALP (x)) | |
55f26379 | 8314 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 | 8315 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8316 | return scm_ceiling_quotient (SCM_FRACTION_NUMERATOR (x), |
8317 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8318 | else |
fa075d40 | 8319 | return scm_wta_dispatch_1 (g_scm_ceiling, x, 1, s_scm_ceiling); |
f92e85f7 MV |
8320 | } |
8321 | #undef FUNC_NAME | |
0f2d19dd | 8322 | |
2519490c MW |
8323 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
8324 | (SCM x, SCM y), | |
8325 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 8326 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 8327 | { |
01c7284a MW |
8328 | if (scm_is_integer (y)) |
8329 | { | |
8330 | if (scm_is_true (scm_exact_p (y))) | |
8331 | return scm_integer_expt (x, y); | |
8332 | else | |
8333 | { | |
8334 | /* Here we handle the case where the exponent is an inexact | |
8335 | integer. We make the exponent exact in order to use | |
8336 | scm_integer_expt, and thus avoid the spurious imaginary | |
8337 | parts that may result from round-off errors in the general | |
8338 | e^(y log x) method below (for example when squaring a large | |
8339 | negative number). In this case, we must return an inexact | |
8340 | result for correctness. We also make the base inexact so | |
8341 | that scm_integer_expt will use fast inexact arithmetic | |
8342 | internally. Note that making the base inexact is not | |
8343 | sufficient to guarantee an inexact result, because | |
8344 | scm_integer_expt will return an exact 1 when the exponent | |
8345 | is 0, even if the base is inexact. */ | |
8346 | return scm_exact_to_inexact | |
8347 | (scm_integer_expt (scm_exact_to_inexact (x), | |
8348 | scm_inexact_to_exact (y))); | |
8349 | } | |
8350 | } | |
6fc4d012 AW |
8351 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
8352 | { | |
8353 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
8354 | } | |
2519490c | 8355 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 8356 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c | 8357 | else if (scm_is_complex (x)) |
fa075d40 | 8358 | return scm_wta_dispatch_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); |
2519490c | 8359 | else |
fa075d40 | 8360 | return scm_wta_dispatch_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); |
0f2d19dd | 8361 | } |
1bbd0b84 | 8362 | #undef FUNC_NAME |
0f2d19dd | 8363 | |
7f41099e MW |
8364 | /* sin/cos/tan/asin/acos/atan |
8365 | sinh/cosh/tanh/asinh/acosh/atanh | |
8366 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
8367 | Written by Jerry D. Hedden, (C) FSF. | |
8368 | See the file `COPYING' for terms applying to this program. */ | |
8369 | ||
ad79736c AW |
8370 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
8371 | (SCM z), | |
8372 | "Compute the sine of @var{z}.") | |
8373 | #define FUNC_NAME s_scm_sin | |
8374 | { | |
8deddc94 MW |
8375 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8376 | return z; /* sin(exact0) = exact0 */ | |
8377 | else if (scm_is_real (z)) | |
ad79736c AW |
8378 | return scm_from_double (sin (scm_to_double (z))); |
8379 | else if (SCM_COMPLEXP (z)) | |
8380 | { double x, y; | |
8381 | x = SCM_COMPLEX_REAL (z); | |
8382 | y = SCM_COMPLEX_IMAG (z); | |
8383 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
8384 | cos (x) * sinh (y)); | |
8385 | } | |
8386 | else | |
fa075d40 | 8387 | return scm_wta_dispatch_1 (g_scm_sin, z, 1, s_scm_sin); |
ad79736c AW |
8388 | } |
8389 | #undef FUNC_NAME | |
0f2d19dd | 8390 | |
ad79736c AW |
8391 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
8392 | (SCM z), | |
8393 | "Compute the cosine of @var{z}.") | |
8394 | #define FUNC_NAME s_scm_cos | |
8395 | { | |
8deddc94 MW |
8396 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8397 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
8398 | else if (scm_is_real (z)) | |
ad79736c AW |
8399 | return scm_from_double (cos (scm_to_double (z))); |
8400 | else if (SCM_COMPLEXP (z)) | |
8401 | { double x, y; | |
8402 | x = SCM_COMPLEX_REAL (z); | |
8403 | y = SCM_COMPLEX_IMAG (z); | |
8404 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
8405 | -sin (x) * sinh (y)); | |
8406 | } | |
8407 | else | |
fa075d40 | 8408 | return scm_wta_dispatch_1 (g_scm_cos, z, 1, s_scm_cos); |
ad79736c AW |
8409 | } |
8410 | #undef FUNC_NAME | |
8411 | ||
8412 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
8413 | (SCM z), | |
8414 | "Compute the tangent of @var{z}.") | |
8415 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 8416 | { |
8deddc94 MW |
8417 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8418 | return z; /* tan(exact0) = exact0 */ | |
8419 | else if (scm_is_real (z)) | |
ad79736c AW |
8420 | return scm_from_double (tan (scm_to_double (z))); |
8421 | else if (SCM_COMPLEXP (z)) | |
8422 | { double x, y, w; | |
8423 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8424 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8425 | w = cos (x) + cosh (y); | |
8426 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8427 | if (w == 0.0) | |
8428 | scm_num_overflow (s_scm_tan); | |
8429 | #endif | |
8430 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
8431 | } | |
8432 | else | |
fa075d40 | 8433 | return scm_wta_dispatch_1 (g_scm_tan, z, 1, s_scm_tan); |
ad79736c AW |
8434 | } |
8435 | #undef FUNC_NAME | |
8436 | ||
8437 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
8438 | (SCM z), | |
8439 | "Compute the hyperbolic sine of @var{z}.") | |
8440 | #define FUNC_NAME s_scm_sinh | |
8441 | { | |
8deddc94 MW |
8442 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8443 | return z; /* sinh(exact0) = exact0 */ | |
8444 | else if (scm_is_real (z)) | |
ad79736c AW |
8445 | return scm_from_double (sinh (scm_to_double (z))); |
8446 | else if (SCM_COMPLEXP (z)) | |
8447 | { double x, y; | |
8448 | x = SCM_COMPLEX_REAL (z); | |
8449 | y = SCM_COMPLEX_IMAG (z); | |
8450 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
8451 | cosh (x) * sin (y)); | |
8452 | } | |
8453 | else | |
fa075d40 | 8454 | return scm_wta_dispatch_1 (g_scm_sinh, z, 1, s_scm_sinh); |
ad79736c AW |
8455 | } |
8456 | #undef FUNC_NAME | |
8457 | ||
8458 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
8459 | (SCM z), | |
8460 | "Compute the hyperbolic cosine of @var{z}.") | |
8461 | #define FUNC_NAME s_scm_cosh | |
8462 | { | |
8deddc94 MW |
8463 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8464 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
8465 | else if (scm_is_real (z)) | |
ad79736c AW |
8466 | return scm_from_double (cosh (scm_to_double (z))); |
8467 | else if (SCM_COMPLEXP (z)) | |
8468 | { double x, y; | |
8469 | x = SCM_COMPLEX_REAL (z); | |
8470 | y = SCM_COMPLEX_IMAG (z); | |
8471 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
8472 | sinh (x) * sin (y)); | |
8473 | } | |
8474 | else | |
fa075d40 | 8475 | return scm_wta_dispatch_1 (g_scm_cosh, z, 1, s_scm_cosh); |
ad79736c AW |
8476 | } |
8477 | #undef FUNC_NAME | |
8478 | ||
8479 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
8480 | (SCM z), | |
8481 | "Compute the hyperbolic tangent of @var{z}.") | |
8482 | #define FUNC_NAME s_scm_tanh | |
8483 | { | |
8deddc94 MW |
8484 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8485 | return z; /* tanh(exact0) = exact0 */ | |
8486 | else if (scm_is_real (z)) | |
ad79736c AW |
8487 | return scm_from_double (tanh (scm_to_double (z))); |
8488 | else if (SCM_COMPLEXP (z)) | |
8489 | { double x, y, w; | |
8490 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8491 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8492 | w = cosh (x) + cos (y); | |
8493 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8494 | if (w == 0.0) | |
8495 | scm_num_overflow (s_scm_tanh); | |
8496 | #endif | |
8497 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
8498 | } | |
8499 | else | |
fa075d40 | 8500 | return scm_wta_dispatch_1 (g_scm_tanh, z, 1, s_scm_tanh); |
ad79736c AW |
8501 | } |
8502 | #undef FUNC_NAME | |
8503 | ||
8504 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
8505 | (SCM z), | |
8506 | "Compute the arc sine of @var{z}.") | |
8507 | #define FUNC_NAME s_scm_asin | |
8508 | { | |
8deddc94 MW |
8509 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8510 | return z; /* asin(exact0) = exact0 */ | |
8511 | else if (scm_is_real (z)) | |
ad79736c AW |
8512 | { |
8513 | double w = scm_to_double (z); | |
8514 | if (w >= -1.0 && w <= 1.0) | |
8515 | return scm_from_double (asin (w)); | |
8516 | else | |
8517 | return scm_product (scm_c_make_rectangular (0, -1), | |
8518 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
8519 | } | |
8520 | else if (SCM_COMPLEXP (z)) | |
8521 | { double x, y; | |
8522 | x = SCM_COMPLEX_REAL (z); | |
8523 | y = SCM_COMPLEX_IMAG (z); | |
8524 | return scm_product (scm_c_make_rectangular (0, -1), | |
8525 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
8526 | } | |
8527 | else | |
fa075d40 | 8528 | return scm_wta_dispatch_1 (g_scm_asin, z, 1, s_scm_asin); |
ad79736c AW |
8529 | } |
8530 | #undef FUNC_NAME | |
8531 | ||
8532 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
8533 | (SCM z), | |
8534 | "Compute the arc cosine of @var{z}.") | |
8535 | #define FUNC_NAME s_scm_acos | |
8536 | { | |
8deddc94 MW |
8537 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8538 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
8539 | else if (scm_is_real (z)) | |
ad79736c AW |
8540 | { |
8541 | double w = scm_to_double (z); | |
8542 | if (w >= -1.0 && w <= 1.0) | |
8543 | return scm_from_double (acos (w)); | |
8544 | else | |
8545 | return scm_sum (scm_from_double (acos (0.0)), | |
8546 | scm_product (scm_c_make_rectangular (0, 1), | |
8547 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
8548 | } | |
8549 | else if (SCM_COMPLEXP (z)) | |
8550 | { double x, y; | |
8551 | x = SCM_COMPLEX_REAL (z); | |
8552 | y = SCM_COMPLEX_IMAG (z); | |
8553 | return scm_sum (scm_from_double (acos (0.0)), | |
8554 | scm_product (scm_c_make_rectangular (0, 1), | |
8555 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
8556 | } | |
8557 | else | |
fa075d40 | 8558 | return scm_wta_dispatch_1 (g_scm_acos, z, 1, s_scm_acos); |
ad79736c AW |
8559 | } |
8560 | #undef FUNC_NAME | |
8561 | ||
8562 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
8563 | (SCM z, SCM y), | |
8564 | "With one argument, compute the arc tangent of @var{z}.\n" | |
8565 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
8566 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
8567 | #define FUNC_NAME s_scm_atan | |
8568 | { | |
8569 | if (SCM_UNBNDP (y)) | |
8570 | { | |
8deddc94 MW |
8571 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8572 | return z; /* atan(exact0) = exact0 */ | |
8573 | else if (scm_is_real (z)) | |
ad79736c AW |
8574 | return scm_from_double (atan (scm_to_double (z))); |
8575 | else if (SCM_COMPLEXP (z)) | |
8576 | { | |
8577 | double v, w; | |
8578 | v = SCM_COMPLEX_REAL (z); | |
8579 | w = SCM_COMPLEX_IMAG (z); | |
8580 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
8581 | scm_c_make_rectangular (v, w + 1.0))), | |
8582 | scm_c_make_rectangular (0, 2)); | |
8583 | } | |
8584 | else | |
fa075d40 | 8585 | return scm_wta_dispatch_1 (g_scm_atan, z, SCM_ARG1, s_scm_atan); |
ad79736c AW |
8586 | } |
8587 | else if (scm_is_real (z)) | |
8588 | { | |
8589 | if (scm_is_real (y)) | |
8590 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
8591 | else | |
fa075d40 | 8592 | return scm_wta_dispatch_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); |
ad79736c AW |
8593 | } |
8594 | else | |
fa075d40 | 8595 | return scm_wta_dispatch_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); |
ad79736c AW |
8596 | } |
8597 | #undef FUNC_NAME | |
8598 | ||
8599 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
8600 | (SCM z), | |
8601 | "Compute the inverse hyperbolic sine of @var{z}.") | |
8602 | #define FUNC_NAME s_scm_sys_asinh | |
8603 | { | |
8deddc94 MW |
8604 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8605 | return z; /* asinh(exact0) = exact0 */ | |
8606 | else if (scm_is_real (z)) | |
ad79736c AW |
8607 | return scm_from_double (asinh (scm_to_double (z))); |
8608 | else if (scm_is_number (z)) | |
8609 | return scm_log (scm_sum (z, | |
8610 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 8611 | SCM_INUM1)))); |
ad79736c | 8612 | else |
fa075d40 | 8613 | return scm_wta_dispatch_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); |
ad79736c AW |
8614 | } |
8615 | #undef FUNC_NAME | |
8616 | ||
8617 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
8618 | (SCM z), | |
8619 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
8620 | #define FUNC_NAME s_scm_sys_acosh | |
8621 | { | |
8deddc94 MW |
8622 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8623 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
8624 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
8625 | return scm_from_double (acosh (scm_to_double (z))); |
8626 | else if (scm_is_number (z)) | |
8627 | return scm_log (scm_sum (z, | |
8628 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 8629 | SCM_INUM1)))); |
ad79736c | 8630 | else |
fa075d40 | 8631 | return scm_wta_dispatch_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); |
ad79736c AW |
8632 | } |
8633 | #undef FUNC_NAME | |
8634 | ||
8635 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
8636 | (SCM z), | |
8637 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
8638 | #define FUNC_NAME s_scm_sys_atanh | |
8639 | { | |
8deddc94 MW |
8640 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8641 | return z; /* atanh(exact0) = exact0 */ | |
8642 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
8643 | return scm_from_double (atanh (scm_to_double (z))); |
8644 | else if (scm_is_number (z)) | |
cff5fa33 MW |
8645 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
8646 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
8647 | SCM_I_MAKINUM (2)); |
8648 | else | |
fa075d40 | 8649 | return scm_wta_dispatch_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); |
0f2d19dd | 8650 | } |
1bbd0b84 | 8651 | #undef FUNC_NAME |
0f2d19dd | 8652 | |
8507ec80 MV |
8653 | SCM |
8654 | scm_c_make_rectangular (double re, double im) | |
8655 | { | |
c7218482 | 8656 | SCM z; |
03604fcf | 8657 | |
21041372 | 8658 | z = SCM_PACK_POINTER (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
c7218482 MW |
8659 | "complex")); |
8660 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); | |
8661 | SCM_COMPLEX_REAL (z) = re; | |
8662 | SCM_COMPLEX_IMAG (z) = im; | |
8663 | return z; | |
8507ec80 | 8664 | } |
0f2d19dd | 8665 | |
a1ec6916 | 8666 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
8667 | (SCM real_part, SCM imaginary_part), |
8668 | "Return a complex number constructed of the given @var{real-part} " | |
8669 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 8670 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 8671 | { |
ad79736c AW |
8672 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
8673 | SCM_ARG1, FUNC_NAME, "real"); | |
8674 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
8675 | SCM_ARG2, FUNC_NAME, "real"); | |
c7218482 MW |
8676 | |
8677 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ | |
8678 | if (scm_is_eq (imaginary_part, SCM_INUM0)) | |
8679 | return real_part; | |
8680 | else | |
8681 | return scm_c_make_rectangular (scm_to_double (real_part), | |
8682 | scm_to_double (imaginary_part)); | |
0f2d19dd | 8683 | } |
1bbd0b84 | 8684 | #undef FUNC_NAME |
0f2d19dd | 8685 | |
8507ec80 MV |
8686 | SCM |
8687 | scm_c_make_polar (double mag, double ang) | |
8688 | { | |
8689 | double s, c; | |
5e647d08 LC |
8690 | |
8691 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
8692 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
8693 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
8694 | details. */ | |
8695 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
8696 | sincos (ang, &s, &c); |
8697 | #else | |
8698 | s = sin (ang); | |
8699 | c = cos (ang); | |
8700 | #endif | |
9d427b2c MW |
8701 | |
8702 | /* If s and c are NaNs, this indicates that the angle is a NaN, | |
8703 | infinite, or perhaps simply too large to determine its value | |
8704 | mod 2*pi. However, we know something that the floating-point | |
8705 | implementation doesn't know: We know that s and c are finite. | |
8706 | Therefore, if the magnitude is zero, return a complex zero. | |
8707 | ||
8708 | The reason we check for the NaNs instead of using this case | |
8709 | whenever mag == 0.0 is because when the angle is known, we'd | |
8710 | like to return the correct kind of non-real complex zero: | |
8711 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending | |
8712 | on which quadrant the angle is in. | |
8713 | */ | |
8714 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) | |
8715 | return scm_c_make_rectangular (0.0, 0.0); | |
8716 | else | |
8717 | return scm_c_make_rectangular (mag * c, mag * s); | |
8507ec80 | 8718 | } |
0f2d19dd | 8719 | |
a1ec6916 | 8720 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
c7218482 MW |
8721 | (SCM mag, SCM ang), |
8722 | "Return the complex number @var{mag} * e^(i * @var{ang}).") | |
1bbd0b84 | 8723 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 8724 | { |
c7218482 MW |
8725 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
8726 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); | |
8727 | ||
8728 | /* If mag is exact0, return exact0 */ | |
8729 | if (scm_is_eq (mag, SCM_INUM0)) | |
8730 | return SCM_INUM0; | |
8731 | /* Return a real if ang is exact0 */ | |
8732 | else if (scm_is_eq (ang, SCM_INUM0)) | |
8733 | return mag; | |
8734 | else | |
8735 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); | |
0f2d19dd | 8736 | } |
1bbd0b84 | 8737 | #undef FUNC_NAME |
0f2d19dd JB |
8738 | |
8739 | ||
2519490c MW |
8740 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
8741 | (SCM z), | |
8742 | "Return the real part of the number @var{z}.") | |
8743 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 8744 | { |
2519490c | 8745 | if (SCM_COMPLEXP (z)) |
55f26379 | 8746 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 8747 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 8748 | return z; |
0aacf84e | 8749 | else |
fa075d40 | 8750 | return scm_wta_dispatch_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 8751 | } |
2519490c | 8752 | #undef FUNC_NAME |
0f2d19dd JB |
8753 | |
8754 | ||
2519490c MW |
8755 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
8756 | (SCM z), | |
8757 | "Return the imaginary part of the number @var{z}.") | |
8758 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 8759 | { |
2519490c MW |
8760 | if (SCM_COMPLEXP (z)) |
8761 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
c7218482 | 8762 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 8763 | return SCM_INUM0; |
0aacf84e | 8764 | else |
fa075d40 | 8765 | return scm_wta_dispatch_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 8766 | } |
2519490c | 8767 | #undef FUNC_NAME |
0f2d19dd | 8768 | |
2519490c MW |
8769 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
8770 | (SCM z), | |
8771 | "Return the numerator of the number @var{z}.") | |
8772 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 8773 | { |
2519490c | 8774 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
8775 | return z; |
8776 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 8777 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
8778 | else if (SCM_REALP (z)) |
8779 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
8780 | else | |
fa075d40 | 8781 | return scm_wta_dispatch_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 8782 | } |
2519490c | 8783 | #undef FUNC_NAME |
f92e85f7 MV |
8784 | |
8785 | ||
2519490c MW |
8786 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
8787 | (SCM z), | |
8788 | "Return the denominator of the number @var{z}.") | |
8789 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 8790 | { |
2519490c | 8791 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 8792 | return SCM_INUM1; |
f92e85f7 | 8793 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 8794 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
8795 | else if (SCM_REALP (z)) |
8796 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
8797 | else | |
fa075d40 AW |
8798 | return scm_wta_dispatch_1 (g_scm_denominator, z, SCM_ARG1, |
8799 | s_scm_denominator); | |
f92e85f7 | 8800 | } |
2519490c | 8801 | #undef FUNC_NAME |
0f2d19dd | 8802 | |
2519490c MW |
8803 | |
8804 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
8805 | (SCM z), | |
8806 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
8807 | "@code{abs} for real arguments, but also allows complex numbers.") | |
8808 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 8809 | { |
e11e83f3 | 8810 | if (SCM_I_INUMP (z)) |
0aacf84e | 8811 | { |
e25f3727 | 8812 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
8813 | if (zz >= 0) |
8814 | return z; | |
8815 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 8816 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 8817 | else |
e25f3727 | 8818 | return scm_i_inum2big (-zz); |
5986c47d | 8819 | } |
0aacf84e MD |
8820 | else if (SCM_BIGP (z)) |
8821 | { | |
8822 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
8823 | scm_remember_upto_here_1 (z); | |
8824 | if (sgn < 0) | |
8825 | return scm_i_clonebig (z, 0); | |
8826 | else | |
8827 | return z; | |
5986c47d | 8828 | } |
0aacf84e | 8829 | else if (SCM_REALP (z)) |
55f26379 | 8830 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 8831 | else if (SCM_COMPLEXP (z)) |
55f26379 | 8832 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
8833 | else if (SCM_FRACTIONP (z)) |
8834 | { | |
73e4de09 | 8835 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 8836 | return z; |
cba42c93 | 8837 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
8838 | SCM_FRACTION_DENOMINATOR (z)); |
8839 | } | |
0aacf84e | 8840 | else |
fa075d40 AW |
8841 | return scm_wta_dispatch_1 (g_scm_magnitude, z, SCM_ARG1, |
8842 | s_scm_magnitude); | |
0f2d19dd | 8843 | } |
2519490c | 8844 | #undef FUNC_NAME |
0f2d19dd JB |
8845 | |
8846 | ||
2519490c MW |
8847 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
8848 | (SCM z), | |
8849 | "Return the angle of the complex number @var{z}.") | |
8850 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 8851 | { |
c8ae173e | 8852 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 8853 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
8854 | But if atan2 follows the floating point rounding mode, then the value |
8855 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 8856 | if (SCM_I_INUMP (z)) |
0aacf84e | 8857 | { |
e11e83f3 | 8858 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 8859 | return flo0; |
0aacf84e | 8860 | else |
55f26379 | 8861 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 8862 | } |
0aacf84e MD |
8863 | else if (SCM_BIGP (z)) |
8864 | { | |
8865 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
8866 | scm_remember_upto_here_1 (z); | |
8867 | if (sgn < 0) | |
55f26379 | 8868 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 8869 | else |
e7efe8e7 | 8870 | return flo0; |
0f2d19dd | 8871 | } |
0aacf84e | 8872 | else if (SCM_REALP (z)) |
c8ae173e KR |
8873 | { |
8874 | if (SCM_REAL_VALUE (z) >= 0) | |
e7efe8e7 | 8875 | return flo0; |
c8ae173e | 8876 | else |
55f26379 | 8877 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 8878 | } |
0aacf84e | 8879 | else if (SCM_COMPLEXP (z)) |
55f26379 | 8880 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
8881 | else if (SCM_FRACTIONP (z)) |
8882 | { | |
73e4de09 | 8883 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 8884 | return flo0; |
55f26379 | 8885 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 8886 | } |
0aacf84e | 8887 | else |
fa075d40 | 8888 | return scm_wta_dispatch_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 8889 | } |
2519490c | 8890 | #undef FUNC_NAME |
0f2d19dd JB |
8891 | |
8892 | ||
2519490c MW |
8893 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
8894 | (SCM z), | |
8895 | "Convert the number @var{z} to its inexact representation.\n") | |
8896 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 8897 | { |
e11e83f3 | 8898 | if (SCM_I_INUMP (z)) |
55f26379 | 8899 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 8900 | else if (SCM_BIGP (z)) |
55f26379 | 8901 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 8902 | else if (SCM_FRACTIONP (z)) |
55f26379 | 8903 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
8904 | else if (SCM_INEXACTP (z)) |
8905 | return z; | |
8906 | else | |
fa075d40 AW |
8907 | return scm_wta_dispatch_1 (g_scm_exact_to_inexact, z, 1, |
8908 | s_scm_exact_to_inexact); | |
3c9a524f | 8909 | } |
2519490c | 8910 | #undef FUNC_NAME |
3c9a524f DH |
8911 | |
8912 | ||
2519490c MW |
8913 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
8914 | (SCM z), | |
8915 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 8916 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 8917 | { |
c7218482 | 8918 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f872b822 | 8919 | return z; |
c7218482 | 8920 | else |
0aacf84e | 8921 | { |
c7218482 MW |
8922 | double val; |
8923 | ||
8924 | if (SCM_REALP (z)) | |
8925 | val = SCM_REAL_VALUE (z); | |
8926 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) | |
8927 | val = SCM_COMPLEX_REAL (z); | |
8928 | else | |
fa075d40 AW |
8929 | return scm_wta_dispatch_1 (g_scm_inexact_to_exact, z, 1, |
8930 | s_scm_inexact_to_exact); | |
c7218482 MW |
8931 | |
8932 | if (!SCM_LIKELY (DOUBLE_IS_FINITE (val))) | |
f92e85f7 | 8933 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 8934 | else |
f92e85f7 MV |
8935 | { |
8936 | mpq_t frac; | |
8937 | SCM q; | |
8938 | ||
8939 | mpq_init (frac); | |
c7218482 | 8940 | mpq_set_d (frac, val); |
cba42c93 | 8941 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
c7218482 | 8942 | scm_i_mpz2num (mpq_denref (frac))); |
f92e85f7 | 8943 | |
cba42c93 | 8944 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
8945 | for frac... |
8946 | */ | |
8947 | mpq_clear (frac); | |
8948 | return q; | |
8949 | } | |
c2ff8ab0 | 8950 | } |
0f2d19dd | 8951 | } |
1bbd0b84 | 8952 | #undef FUNC_NAME |
0f2d19dd | 8953 | |
f92e85f7 | 8954 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
8955 | (SCM x, SCM eps), |
8956 | "Returns the @emph{simplest} rational number differing\n" | |
8957 | "from @var{x} by no more than @var{eps}.\n" | |
8958 | "\n" | |
8959 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
8960 | "exact result when both its arguments are exact. Thus, you might need\n" | |
8961 | "to use @code{inexact->exact} on the arguments.\n" | |
8962 | "\n" | |
8963 | "@lisp\n" | |
8964 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
8965 | "@result{} 6/5\n" | |
8966 | "@end lisp") | |
f92e85f7 MV |
8967 | #define FUNC_NAME s_scm_rationalize |
8968 | { | |
605f6980 MW |
8969 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
8970 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
8971 | eps = scm_abs (eps); | |
8972 | if (scm_is_false (scm_positive_p (eps))) | |
8973 | { | |
8974 | /* eps is either zero or a NaN */ | |
8975 | if (scm_is_true (scm_nan_p (eps))) | |
8976 | return scm_nan (); | |
8977 | else if (SCM_INEXACTP (eps)) | |
8978 | return scm_exact_to_inexact (x); | |
8979 | else | |
8980 | return x; | |
8981 | } | |
8982 | else if (scm_is_false (scm_finite_p (eps))) | |
8983 | { | |
8984 | if (scm_is_true (scm_finite_p (x))) | |
8985 | return flo0; | |
8986 | else | |
8987 | return scm_nan (); | |
8988 | } | |
8989 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 8990 | return x; |
605f6980 MW |
8991 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
8992 | scm_ceiling (scm_difference (x, eps))))) | |
8993 | { | |
8994 | /* There's an integer within range; we want the one closest to zero */ | |
8995 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
8996 | { | |
8997 | /* zero is within range */ | |
8998 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
8999 | return flo0; | |
9000 | else | |
9001 | return SCM_INUM0; | |
9002 | } | |
9003 | else if (scm_is_true (scm_positive_p (x))) | |
9004 | return scm_ceiling (scm_difference (x, eps)); | |
9005 | else | |
9006 | return scm_floor (scm_sum (x, eps)); | |
9007 | } | |
9008 | else | |
f92e85f7 MV |
9009 | { |
9010 | /* Use continued fractions to find closest ratio. All | |
9011 | arithmetic is done with exact numbers. | |
9012 | */ | |
9013 | ||
9014 | SCM ex = scm_inexact_to_exact (x); | |
9015 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
9016 | SCM tt = SCM_INUM1; |
9017 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
9018 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
9019 | SCM rx; |
9020 | int i = 0; | |
9021 | ||
f92e85f7 MV |
9022 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
9023 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
9024 | ||
9025 | /* We stop after a million iterations just to be absolutely sure | |
9026 | that we don't go into an infinite loop. The process normally | |
9027 | converges after less than a dozen iterations. | |
9028 | */ | |
9029 | ||
f92e85f7 MV |
9030 | while (++i < 1000000) |
9031 | { | |
9032 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
9033 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
9034 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
9035 | scm_is_false | |
f92e85f7 | 9036 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 9037 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
9038 | { |
9039 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 9040 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
9041 | return scm_exact_to_inexact (res); |
9042 | else | |
9043 | return res; | |
9044 | } | |
f92e85f7 MV |
9045 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
9046 | SCM_UNDEFINED); | |
9047 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
9048 | a2 = a1; | |
9049 | b2 = b1; | |
9050 | a1 = a; | |
9051 | b1 = b; | |
9052 | } | |
9053 | scm_num_overflow (s_scm_rationalize); | |
9054 | } | |
f92e85f7 MV |
9055 | } |
9056 | #undef FUNC_NAME | |
9057 | ||
73e4de09 MV |
9058 | /* conversion functions */ |
9059 | ||
9060 | int | |
9061 | scm_is_integer (SCM val) | |
9062 | { | |
9063 | return scm_is_true (scm_integer_p (val)); | |
9064 | } | |
9065 | ||
9066 | int | |
9067 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
9068 | { | |
e11e83f3 | 9069 | if (SCM_I_INUMP (val)) |
73e4de09 | 9070 | { |
e11e83f3 | 9071 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9072 | return n >= min && n <= max; |
9073 | } | |
9074 | else if (SCM_BIGP (val)) | |
9075 | { | |
9076 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
9077 | return 0; | |
9078 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
9079 | { |
9080 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
9081 | { | |
9082 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
9083 | return n >= min && n <= max; | |
9084 | } | |
9085 | else | |
9086 | return 0; | |
9087 | } | |
73e4de09 MV |
9088 | else |
9089 | { | |
d956fa6f MV |
9090 | scm_t_intmax n; |
9091 | size_t count; | |
73e4de09 | 9092 | |
d956fa6f MV |
9093 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9094 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
9095 | return 0; | |
9096 | ||
9097 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9098 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9099 | |
d956fa6f | 9100 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 9101 | { |
d956fa6f MV |
9102 | if (n < 0) |
9103 | return 0; | |
73e4de09 | 9104 | } |
73e4de09 MV |
9105 | else |
9106 | { | |
d956fa6f MV |
9107 | n = -n; |
9108 | if (n >= 0) | |
9109 | return 0; | |
73e4de09 | 9110 | } |
d956fa6f MV |
9111 | |
9112 | return n >= min && n <= max; | |
73e4de09 MV |
9113 | } |
9114 | } | |
73e4de09 MV |
9115 | else |
9116 | return 0; | |
9117 | } | |
9118 | ||
9119 | int | |
9120 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
9121 | { | |
e11e83f3 | 9122 | if (SCM_I_INUMP (val)) |
73e4de09 | 9123 | { |
e11e83f3 | 9124 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9125 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
9126 | } | |
9127 | else if (SCM_BIGP (val)) | |
9128 | { | |
9129 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
9130 | return 0; | |
9131 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
9132 | { |
9133 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
9134 | { | |
9135 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
9136 | return n >= min && n <= max; | |
9137 | } | |
9138 | else | |
9139 | return 0; | |
9140 | } | |
73e4de09 MV |
9141 | else |
9142 | { | |
d956fa6f MV |
9143 | scm_t_uintmax n; |
9144 | size_t count; | |
73e4de09 | 9145 | |
d956fa6f MV |
9146 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
9147 | return 0; | |
73e4de09 | 9148 | |
d956fa6f MV |
9149 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9150 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 9151 | return 0; |
d956fa6f MV |
9152 | |
9153 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9154 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9155 | |
d956fa6f | 9156 | return n >= min && n <= max; |
73e4de09 MV |
9157 | } |
9158 | } | |
73e4de09 MV |
9159 | else |
9160 | return 0; | |
9161 | } | |
9162 | ||
1713d319 MV |
9163 | static void |
9164 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
9165 | { | |
9166 | scm_error (scm_out_of_range_key, | |
9167 | NULL, | |
9168 | "Value out of range ~S to ~S: ~S", | |
9169 | scm_list_3 (min, max, bad_val), | |
9170 | scm_list_1 (bad_val)); | |
9171 | } | |
9172 | ||
bfd7932e MV |
9173 | #define TYPE scm_t_intmax |
9174 | #define TYPE_MIN min | |
9175 | #define TYPE_MAX max | |
9176 | #define SIZEOF_TYPE 0 | |
9177 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
9178 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
9179 | #include "libguile/conv-integer.i.c" | |
9180 | ||
9181 | #define TYPE scm_t_uintmax | |
9182 | #define TYPE_MIN min | |
9183 | #define TYPE_MAX max | |
9184 | #define SIZEOF_TYPE 0 | |
9185 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
9186 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
9187 | #include "libguile/conv-uinteger.i.c" | |
9188 | ||
9189 | #define TYPE scm_t_int8 | |
9190 | #define TYPE_MIN SCM_T_INT8_MIN | |
9191 | #define TYPE_MAX SCM_T_INT8_MAX | |
9192 | #define SIZEOF_TYPE 1 | |
9193 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
9194 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
9195 | #include "libguile/conv-integer.i.c" | |
9196 | ||
9197 | #define TYPE scm_t_uint8 | |
9198 | #define TYPE_MIN 0 | |
9199 | #define TYPE_MAX SCM_T_UINT8_MAX | |
9200 | #define SIZEOF_TYPE 1 | |
9201 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
9202 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
9203 | #include "libguile/conv-uinteger.i.c" | |
9204 | ||
9205 | #define TYPE scm_t_int16 | |
9206 | #define TYPE_MIN SCM_T_INT16_MIN | |
9207 | #define TYPE_MAX SCM_T_INT16_MAX | |
9208 | #define SIZEOF_TYPE 2 | |
9209 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
9210 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
9211 | #include "libguile/conv-integer.i.c" | |
9212 | ||
9213 | #define TYPE scm_t_uint16 | |
9214 | #define TYPE_MIN 0 | |
9215 | #define TYPE_MAX SCM_T_UINT16_MAX | |
9216 | #define SIZEOF_TYPE 2 | |
9217 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
9218 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
9219 | #include "libguile/conv-uinteger.i.c" | |
9220 | ||
9221 | #define TYPE scm_t_int32 | |
9222 | #define TYPE_MIN SCM_T_INT32_MIN | |
9223 | #define TYPE_MAX SCM_T_INT32_MAX | |
9224 | #define SIZEOF_TYPE 4 | |
9225 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
9226 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
9227 | #include "libguile/conv-integer.i.c" | |
9228 | ||
9229 | #define TYPE scm_t_uint32 | |
9230 | #define TYPE_MIN 0 | |
9231 | #define TYPE_MAX SCM_T_UINT32_MAX | |
9232 | #define SIZEOF_TYPE 4 | |
9233 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
9234 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
9235 | #include "libguile/conv-uinteger.i.c" | |
9236 | ||
904a78f1 MG |
9237 | #define TYPE scm_t_wchar |
9238 | #define TYPE_MIN (scm_t_int32)-1 | |
9239 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
9240 | #define SIZEOF_TYPE 4 | |
9241 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
9242 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
9243 | #include "libguile/conv-integer.i.c" | |
9244 | ||
bfd7932e MV |
9245 | #define TYPE scm_t_int64 |
9246 | #define TYPE_MIN SCM_T_INT64_MIN | |
9247 | #define TYPE_MAX SCM_T_INT64_MAX | |
9248 | #define SIZEOF_TYPE 8 | |
9249 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
9250 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
9251 | #include "libguile/conv-integer.i.c" | |
9252 | ||
9253 | #define TYPE scm_t_uint64 | |
9254 | #define TYPE_MIN 0 | |
9255 | #define TYPE_MAX SCM_T_UINT64_MAX | |
9256 | #define SIZEOF_TYPE 8 | |
9257 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
9258 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
9259 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 9260 | |
cd036260 MV |
9261 | void |
9262 | scm_to_mpz (SCM val, mpz_t rop) | |
9263 | { | |
9264 | if (SCM_I_INUMP (val)) | |
9265 | mpz_set_si (rop, SCM_I_INUM (val)); | |
9266 | else if (SCM_BIGP (val)) | |
9267 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
9268 | else | |
9269 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
9270 | } | |
9271 | ||
9272 | SCM | |
9273 | scm_from_mpz (mpz_t val) | |
9274 | { | |
9275 | return scm_i_mpz2num (val); | |
9276 | } | |
9277 | ||
73e4de09 MV |
9278 | int |
9279 | scm_is_real (SCM val) | |
9280 | { | |
9281 | return scm_is_true (scm_real_p (val)); | |
9282 | } | |
9283 | ||
55f26379 MV |
9284 | int |
9285 | scm_is_rational (SCM val) | |
9286 | { | |
9287 | return scm_is_true (scm_rational_p (val)); | |
9288 | } | |
9289 | ||
73e4de09 MV |
9290 | double |
9291 | scm_to_double (SCM val) | |
9292 | { | |
55f26379 MV |
9293 | if (SCM_I_INUMP (val)) |
9294 | return SCM_I_INUM (val); | |
9295 | else if (SCM_BIGP (val)) | |
9296 | return scm_i_big2dbl (val); | |
9297 | else if (SCM_FRACTIONP (val)) | |
9298 | return scm_i_fraction2double (val); | |
9299 | else if (SCM_REALP (val)) | |
9300 | return SCM_REAL_VALUE (val); | |
9301 | else | |
7a1aba42 | 9302 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
9303 | } |
9304 | ||
9305 | SCM | |
9306 | scm_from_double (double val) | |
9307 | { | |
978c52d1 LC |
9308 | SCM z; |
9309 | ||
21041372 | 9310 | z = SCM_PACK_POINTER (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); |
978c52d1 LC |
9311 | |
9312 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 9313 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 9314 | |
55f26379 | 9315 | return z; |
73e4de09 MV |
9316 | } |
9317 | ||
8507ec80 MV |
9318 | int |
9319 | scm_is_complex (SCM val) | |
9320 | { | |
9321 | return scm_is_true (scm_complex_p (val)); | |
9322 | } | |
9323 | ||
9324 | double | |
9325 | scm_c_real_part (SCM z) | |
9326 | { | |
9327 | if (SCM_COMPLEXP (z)) | |
9328 | return SCM_COMPLEX_REAL (z); | |
9329 | else | |
9330 | { | |
9331 | /* Use the scm_real_part to get proper error checking and | |
9332 | dispatching. | |
9333 | */ | |
9334 | return scm_to_double (scm_real_part (z)); | |
9335 | } | |
9336 | } | |
9337 | ||
9338 | double | |
9339 | scm_c_imag_part (SCM z) | |
9340 | { | |
9341 | if (SCM_COMPLEXP (z)) | |
9342 | return SCM_COMPLEX_IMAG (z); | |
9343 | else | |
9344 | { | |
9345 | /* Use the scm_imag_part to get proper error checking and | |
9346 | dispatching. The result will almost always be 0.0, but not | |
9347 | always. | |
9348 | */ | |
9349 | return scm_to_double (scm_imag_part (z)); | |
9350 | } | |
9351 | } | |
9352 | ||
9353 | double | |
9354 | scm_c_magnitude (SCM z) | |
9355 | { | |
9356 | return scm_to_double (scm_magnitude (z)); | |
9357 | } | |
9358 | ||
9359 | double | |
9360 | scm_c_angle (SCM z) | |
9361 | { | |
9362 | return scm_to_double (scm_angle (z)); | |
9363 | } | |
9364 | ||
9365 | int | |
9366 | scm_is_number (SCM z) | |
9367 | { | |
9368 | return scm_is_true (scm_number_p (z)); | |
9369 | } | |
9370 | ||
8ab3d8a0 | 9371 | |
a5f6b751 MW |
9372 | /* Returns log(x * 2^shift) */ |
9373 | static SCM | |
9374 | log_of_shifted_double (double x, long shift) | |
9375 | { | |
9376 | double ans = log (fabs (x)) + shift * M_LN2; | |
9377 | ||
9378 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
9379 | return scm_from_double (ans); | |
9380 | else | |
9381 | return scm_c_make_rectangular (ans, M_PI); | |
9382 | } | |
9383 | ||
9384 | /* Returns log(n), for exact integer n of integer-length size */ | |
9385 | static SCM | |
9386 | log_of_exact_integer_with_size (SCM n, long size) | |
9387 | { | |
9388 | long shift = size - 2 * scm_dblprec[0]; | |
9389 | ||
9390 | if (shift > 0) | |
9391 | return log_of_shifted_double | |
9392 | (scm_to_double (scm_ash (n, scm_from_long(-shift))), | |
9393 | shift); | |
9394 | else | |
9395 | return log_of_shifted_double (scm_to_double (n), 0); | |
9396 | } | |
9397 | ||
85bdb6ac | 9398 | /* Returns log(n), for exact integer n */ |
a5f6b751 MW |
9399 | static SCM |
9400 | log_of_exact_integer (SCM n) | |
9401 | { | |
9402 | return log_of_exact_integer_with_size | |
9403 | (n, scm_to_long (scm_integer_length (n))); | |
9404 | } | |
9405 | ||
9406 | /* Returns log(n/d), for exact non-zero integers n and d */ | |
9407 | static SCM | |
9408 | log_of_fraction (SCM n, SCM d) | |
9409 | { | |
9410 | long n_size = scm_to_long (scm_integer_length (n)); | |
9411 | long d_size = scm_to_long (scm_integer_length (d)); | |
9412 | ||
9413 | if (abs (n_size - d_size) > 1) | |
9414 | return (scm_difference (log_of_exact_integer_with_size (n, n_size), | |
9415 | log_of_exact_integer_with_size (d, d_size))); | |
9416 | else if (scm_is_false (scm_negative_p (n))) | |
9417 | return scm_from_double | |
9418 | (log1p (scm_to_double (scm_divide2real (scm_difference (n, d), d)))); | |
9419 | else | |
9420 | return scm_c_make_rectangular | |
9421 | (log1p (scm_to_double (scm_divide2real | |
9422 | (scm_difference (scm_abs (n), d), | |
9423 | d))), | |
9424 | M_PI); | |
9425 | } | |
9426 | ||
9427 | ||
8ab3d8a0 KR |
9428 | /* In the following functions we dispatch to the real-arg funcs like log() |
9429 | when we know the arg is real, instead of just handing everything to | |
9430 | clog() for instance. This is in case clog() doesn't optimize for a | |
9431 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
9432 | well use it to go straight to the applicable C func. */ | |
9433 | ||
2519490c MW |
9434 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
9435 | (SCM z), | |
9436 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
9437 | #define FUNC_NAME s_scm_log |
9438 | { | |
9439 | if (SCM_COMPLEXP (z)) | |
9440 | { | |
03976fee AW |
9441 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG \ |
9442 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
9443 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
9444 | #else | |
9445 | double re = SCM_COMPLEX_REAL (z); | |
9446 | double im = SCM_COMPLEX_IMAG (z); | |
9447 | return scm_c_make_rectangular (log (hypot (re, im)), | |
9448 | atan2 (im, re)); | |
9449 | #endif | |
9450 | } | |
a5f6b751 MW |
9451 | else if (SCM_REALP (z)) |
9452 | return log_of_shifted_double (SCM_REAL_VALUE (z), 0); | |
9453 | else if (SCM_I_INUMP (z)) | |
8ab3d8a0 | 9454 | { |
a5f6b751 MW |
9455 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9456 | if (scm_is_eq (z, SCM_INUM0)) | |
9457 | scm_num_overflow (s_scm_log); | |
9458 | #endif | |
9459 | return log_of_shifted_double (SCM_I_INUM (z), 0); | |
8ab3d8a0 | 9460 | } |
a5f6b751 MW |
9461 | else if (SCM_BIGP (z)) |
9462 | return log_of_exact_integer (z); | |
9463 | else if (SCM_FRACTIONP (z)) | |
9464 | return log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9465 | SCM_FRACTION_DENOMINATOR (z)); | |
2519490c | 9466 | else |
fa075d40 | 9467 | return scm_wta_dispatch_1 (g_scm_log, z, 1, s_scm_log); |
8ab3d8a0 KR |
9468 | } |
9469 | #undef FUNC_NAME | |
9470 | ||
9471 | ||
2519490c MW |
9472 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
9473 | (SCM z), | |
9474 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
9475 | #define FUNC_NAME s_scm_log10 |
9476 | { | |
9477 | if (SCM_COMPLEXP (z)) | |
9478 | { | |
9479 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
9480 | clog() and a multiply by M_LOG10E, rather than the fallback | |
9481 | log10+hypot+atan2.) */ | |
f328f862 LC |
9482 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
9483 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
9484 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
9485 | #else | |
9486 | double re = SCM_COMPLEX_REAL (z); | |
9487 | double im = SCM_COMPLEX_IMAG (z); | |
9488 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
9489 | M_LOG10E * atan2 (im, re)); | |
9490 | #endif | |
9491 | } | |
a5f6b751 | 9492 | else if (SCM_REALP (z) || SCM_I_INUMP (z)) |
8ab3d8a0 | 9493 | { |
a5f6b751 MW |
9494 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9495 | if (scm_is_eq (z, SCM_INUM0)) | |
9496 | scm_num_overflow (s_scm_log10); | |
9497 | #endif | |
9498 | { | |
9499 | double re = scm_to_double (z); | |
9500 | double l = log10 (fabs (re)); | |
9501 | if (re > 0.0 || double_is_non_negative_zero (re)) | |
9502 | return scm_from_double (l); | |
9503 | else | |
9504 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
9505 | } | |
8ab3d8a0 | 9506 | } |
a5f6b751 MW |
9507 | else if (SCM_BIGP (z)) |
9508 | return scm_product (flo_log10e, log_of_exact_integer (z)); | |
9509 | else if (SCM_FRACTIONP (z)) | |
9510 | return scm_product (flo_log10e, | |
9511 | log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9512 | SCM_FRACTION_DENOMINATOR (z))); | |
2519490c | 9513 | else |
fa075d40 | 9514 | return scm_wta_dispatch_1 (g_scm_log10, z, 1, s_scm_log10); |
8ab3d8a0 KR |
9515 | } |
9516 | #undef FUNC_NAME | |
9517 | ||
9518 | ||
2519490c MW |
9519 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
9520 | (SCM z), | |
9521 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
9522 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
9523 | #define FUNC_NAME s_scm_exp |
9524 | { | |
9525 | if (SCM_COMPLEXP (z)) | |
9526 | { | |
03976fee AW |
9527 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CEXP \ |
9528 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
9529 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
9530 | #else | |
9531 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
9532 | SCM_COMPLEX_IMAG (z)); | |
9533 | #endif | |
9534 | } | |
2519490c | 9535 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
9536 | { |
9537 | /* When z is a negative bignum the conversion to double overflows, | |
9538 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
9539 | return scm_from_double (exp (scm_to_double (z))); | |
9540 | } | |
2519490c | 9541 | else |
fa075d40 | 9542 | return scm_wta_dispatch_1 (g_scm_exp, z, 1, s_scm_exp); |
8ab3d8a0 KR |
9543 | } |
9544 | #undef FUNC_NAME | |
9545 | ||
9546 | ||
882c8963 MW |
9547 | SCM_DEFINE (scm_i_exact_integer_sqrt, "exact-integer-sqrt", 1, 0, 0, |
9548 | (SCM k), | |
9549 | "Return two exact non-negative integers @var{s} and @var{r}\n" | |
9550 | "such that @math{@var{k} = @var{s}^2 + @var{r}} and\n" | |
9551 | "@math{@var{s}^2 <= @var{k} < (@var{s} + 1)^2}.\n" | |
9552 | "An error is raised if @var{k} is not an exact non-negative integer.\n" | |
9553 | "\n" | |
9554 | "@lisp\n" | |
9555 | "(exact-integer-sqrt 10) @result{} 3 and 1\n" | |
9556 | "@end lisp") | |
9557 | #define FUNC_NAME s_scm_i_exact_integer_sqrt | |
9558 | { | |
9559 | SCM s, r; | |
9560 | ||
9561 | scm_exact_integer_sqrt (k, &s, &r); | |
9562 | return scm_values (scm_list_2 (s, r)); | |
9563 | } | |
9564 | #undef FUNC_NAME | |
9565 | ||
9566 | void | |
9567 | scm_exact_integer_sqrt (SCM k, SCM *sp, SCM *rp) | |
9568 | { | |
9569 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
9570 | { | |
9571 | scm_t_inum kk = SCM_I_INUM (k); | |
9572 | scm_t_inum uu = kk; | |
9573 | scm_t_inum ss; | |
9574 | ||
9575 | if (SCM_LIKELY (kk > 0)) | |
9576 | { | |
9577 | do | |
9578 | { | |
9579 | ss = uu; | |
9580 | uu = (ss + kk/ss) / 2; | |
9581 | } while (uu < ss); | |
9582 | *sp = SCM_I_MAKINUM (ss); | |
9583 | *rp = SCM_I_MAKINUM (kk - ss*ss); | |
9584 | } | |
9585 | else if (SCM_LIKELY (kk == 0)) | |
9586 | *sp = *rp = SCM_INUM0; | |
9587 | else | |
9588 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9589 | "exact non-negative integer"); | |
9590 | } | |
9591 | else if (SCM_LIKELY (SCM_BIGP (k))) | |
9592 | { | |
9593 | SCM s, r; | |
9594 | ||
9595 | if (mpz_sgn (SCM_I_BIG_MPZ (k)) < 0) | |
9596 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9597 | "exact non-negative integer"); | |
9598 | s = scm_i_mkbig (); | |
9599 | r = scm_i_mkbig (); | |
9600 | mpz_sqrtrem (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (k)); | |
9601 | scm_remember_upto_here_1 (k); | |
9602 | *sp = scm_i_normbig (s); | |
9603 | *rp = scm_i_normbig (r); | |
9604 | } | |
9605 | else | |
9606 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9607 | "exact non-negative integer"); | |
9608 | } | |
9609 | ||
9610 | ||
2519490c MW |
9611 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
9612 | (SCM z), | |
9613 | "Return the square root of @var{z}. Of the two possible roots\n" | |
ffb62a43 | 9614 | "(positive and negative), the one with positive real part\n" |
2519490c MW |
9615 | "is returned, or if that's zero then a positive imaginary part.\n" |
9616 | "Thus,\n" | |
9617 | "\n" | |
9618 | "@example\n" | |
9619 | "(sqrt 9.0) @result{} 3.0\n" | |
9620 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
9621 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
9622 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
9623 | "@end example") | |
8ab3d8a0 KR |
9624 | #define FUNC_NAME s_scm_sqrt |
9625 | { | |
2519490c | 9626 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 9627 | { |
f328f862 LC |
9628 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
9629 | && defined SCM_COMPLEX_VALUE | |
2519490c | 9630 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 9631 | #else |
2519490c MW |
9632 | double re = SCM_COMPLEX_REAL (z); |
9633 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
9634 | return scm_c_make_polar (sqrt (hypot (re, im)), |
9635 | 0.5 * atan2 (im, re)); | |
9636 | #endif | |
9637 | } | |
2519490c | 9638 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 9639 | { |
2519490c | 9640 | double xx = scm_to_double (z); |
8ab3d8a0 KR |
9641 | if (xx < 0) |
9642 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
9643 | else | |
9644 | return scm_from_double (sqrt (xx)); | |
9645 | } | |
2519490c | 9646 | else |
fa075d40 | 9647 | return scm_wta_dispatch_1 (g_scm_sqrt, z, 1, s_scm_sqrt); |
8ab3d8a0 KR |
9648 | } |
9649 | #undef FUNC_NAME | |
9650 | ||
9651 | ||
9652 | ||
0f2d19dd JB |
9653 | void |
9654 | scm_init_numbers () | |
0f2d19dd | 9655 | { |
0b799eea MV |
9656 | int i; |
9657 | ||
713a4259 KR |
9658 | mpz_init_set_si (z_negative_one, -1); |
9659 | ||
a261c0e9 DH |
9660 | /* It may be possible to tune the performance of some algorithms by using |
9661 | * the following constants to avoid the creation of bignums. Please, before | |
9662 | * using these values, remember the two rules of program optimization: | |
9663 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 9664 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 9665 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 9666 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 9667 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 9668 | |
f3ae5d60 MD |
9669 | scm_add_feature ("complex"); |
9670 | scm_add_feature ("inexact"); | |
e7efe8e7 | 9671 | flo0 = scm_from_double (0.0); |
a5f6b751 | 9672 | flo_log10e = scm_from_double (M_LOG10E); |
0b799eea MV |
9673 | |
9674 | /* determine floating point precision */ | |
55f26379 | 9675 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
9676 | { |
9677 | init_dblprec(&scm_dblprec[i-2],i); | |
9678 | init_fx_radix(fx_per_radix[i-2],i); | |
9679 | } | |
f872b822 | 9680 | #ifdef DBL_DIG |
0b799eea | 9681 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 9682 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 9683 | #endif |
1be6b49c | 9684 | |
cff5fa33 | 9685 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 9686 | #include "libguile/numbers.x" |
0f2d19dd | 9687 | } |
89e00824 ML |
9688 | |
9689 | /* | |
9690 | Local Variables: | |
9691 | c-file-style: "gnu" | |
9692 | End: | |
9693 | */ |