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 | ||
181 | bignum = PTR2SCM (ptr); | |
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 |
2519490c | 535 | SCM_WTA_DISPATCH_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
536 | } |
537 | #undef FUNC_NAME | |
538 | ||
539 | ||
2519490c | 540 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
541 | (SCM x), |
542 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
543 | "else.") | |
544 | #define FUNC_NAME s_scm_inexact_p | |
545 | { | |
546 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 547 | return SCM_BOOL_T; |
41df63cf | 548 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 549 | return SCM_BOOL_F; |
41df63cf | 550 | else |
2519490c | 551 | SCM_WTA_DISPATCH_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 552 | } |
1bbd0b84 | 553 | #undef FUNC_NAME |
0f2d19dd | 554 | |
4219f20d | 555 | |
2519490c | 556 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 557 | (SCM n), |
942e5b91 MG |
558 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
559 | "otherwise.") | |
1bbd0b84 | 560 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 561 | { |
e11e83f3 | 562 | if (SCM_I_INUMP (n)) |
0aacf84e | 563 | { |
e25f3727 | 564 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 565 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
566 | } |
567 | else if (SCM_BIGP (n)) | |
568 | { | |
569 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
570 | scm_remember_upto_here_1 (n); | |
73e4de09 | 571 | return scm_from_bool (odd_p); |
0aacf84e | 572 | } |
f92e85f7 MV |
573 | else if (SCM_REALP (n)) |
574 | { | |
2519490c MW |
575 | double val = SCM_REAL_VALUE (n); |
576 | if (DOUBLE_IS_FINITE (val)) | |
577 | { | |
578 | double rem = fabs (fmod (val, 2.0)); | |
579 | if (rem == 1.0) | |
580 | return SCM_BOOL_T; | |
581 | else if (rem == 0.0) | |
582 | return SCM_BOOL_F; | |
583 | } | |
f92e85f7 | 584 | } |
2519490c | 585 | SCM_WTA_DISPATCH_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 586 | } |
1bbd0b84 | 587 | #undef FUNC_NAME |
0f2d19dd | 588 | |
4219f20d | 589 | |
2519490c | 590 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 591 | (SCM n), |
942e5b91 MG |
592 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
593 | "otherwise.") | |
1bbd0b84 | 594 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 595 | { |
e11e83f3 | 596 | if (SCM_I_INUMP (n)) |
0aacf84e | 597 | { |
e25f3727 | 598 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 599 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
600 | } |
601 | else if (SCM_BIGP (n)) | |
602 | { | |
603 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
604 | scm_remember_upto_here_1 (n); | |
73e4de09 | 605 | return scm_from_bool (even_p); |
0aacf84e | 606 | } |
f92e85f7 MV |
607 | else if (SCM_REALP (n)) |
608 | { | |
2519490c MW |
609 | double val = SCM_REAL_VALUE (n); |
610 | if (DOUBLE_IS_FINITE (val)) | |
611 | { | |
612 | double rem = fabs (fmod (val, 2.0)); | |
613 | if (rem == 1.0) | |
614 | return SCM_BOOL_F; | |
615 | else if (rem == 0.0) | |
616 | return SCM_BOOL_T; | |
617 | } | |
f92e85f7 | 618 | } |
2519490c | 619 | SCM_WTA_DISPATCH_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 620 | } |
1bbd0b84 | 621 | #undef FUNC_NAME |
0f2d19dd | 622 | |
2519490c MW |
623 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
624 | (SCM x), | |
10391e06 AW |
625 | "Return @code{#t} if the real number @var{x} is neither\n" |
626 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
627 | #define FUNC_NAME s_scm_finite_p |
628 | { | |
629 | if (SCM_REALP (x)) | |
630 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 631 | else if (scm_is_real (x)) |
7112615f MW |
632 | return SCM_BOOL_T; |
633 | else | |
2519490c | 634 | SCM_WTA_DISPATCH_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
635 | } |
636 | #undef FUNC_NAME | |
637 | ||
2519490c MW |
638 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
639 | (SCM x), | |
640 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
641 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
642 | #define FUNC_NAME s_scm_inf_p |
643 | { | |
b1092b3a | 644 | if (SCM_REALP (x)) |
2e65b52f | 645 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 646 | else if (scm_is_real (x)) |
7351e207 | 647 | return SCM_BOOL_F; |
10391e06 | 648 | else |
2519490c | 649 | SCM_WTA_DISPATCH_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
650 | } |
651 | #undef FUNC_NAME | |
652 | ||
2519490c MW |
653 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
654 | (SCM x), | |
10391e06 AW |
655 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
656 | "or @code{#f} otherwise.") | |
7351e207 MV |
657 | #define FUNC_NAME s_scm_nan_p |
658 | { | |
10391e06 AW |
659 | if (SCM_REALP (x)) |
660 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
661 | else if (scm_is_real (x)) | |
7351e207 | 662 | return SCM_BOOL_F; |
10391e06 | 663 | else |
2519490c | 664 | SCM_WTA_DISPATCH_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
665 | } |
666 | #undef FUNC_NAME | |
667 | ||
668 | /* Guile's idea of infinity. */ | |
669 | static double guile_Inf; | |
670 | ||
671 | /* Guile's idea of not a number. */ | |
672 | static double guile_NaN; | |
673 | ||
674 | static void | |
675 | guile_ieee_init (void) | |
676 | { | |
7351e207 MV |
677 | /* Some version of gcc on some old version of Linux used to crash when |
678 | trying to make Inf and NaN. */ | |
679 | ||
240a27d2 KR |
680 | #ifdef INFINITY |
681 | /* C99 INFINITY, when available. | |
682 | FIXME: The standard allows for INFINITY to be something that overflows | |
683 | at compile time. We ought to have a configure test to check for that | |
684 | before trying to use it. (But in practice we believe this is not a | |
685 | problem on any system guile is likely to target.) */ | |
686 | guile_Inf = INFINITY; | |
56a3dcd4 | 687 | #elif defined HAVE_DINFINITY |
240a27d2 | 688 | /* OSF */ |
7351e207 | 689 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 690 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
691 | #else |
692 | double tmp = 1e+10; | |
693 | guile_Inf = tmp; | |
694 | for (;;) | |
695 | { | |
696 | guile_Inf *= 1e+10; | |
697 | if (guile_Inf == tmp) | |
698 | break; | |
699 | tmp = guile_Inf; | |
700 | } | |
701 | #endif | |
702 | ||
240a27d2 KR |
703 | #ifdef NAN |
704 | /* C99 NAN, when available */ | |
705 | guile_NaN = NAN; | |
56a3dcd4 | 706 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
707 | { |
708 | /* OSF */ | |
709 | extern unsigned int DQNAN[2]; | |
710 | guile_NaN = (*((double *)(DQNAN))); | |
711 | } | |
7351e207 MV |
712 | #else |
713 | guile_NaN = guile_Inf / guile_Inf; | |
714 | #endif | |
7351e207 MV |
715 | } |
716 | ||
717 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
718 | (void), | |
719 | "Return Inf.") | |
720 | #define FUNC_NAME s_scm_inf | |
721 | { | |
722 | static int initialized = 0; | |
723 | if (! initialized) | |
724 | { | |
725 | guile_ieee_init (); | |
726 | initialized = 1; | |
727 | } | |
55f26379 | 728 | return scm_from_double (guile_Inf); |
7351e207 MV |
729 | } |
730 | #undef FUNC_NAME | |
731 | ||
732 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
733 | (void), | |
734 | "Return NaN.") | |
735 | #define FUNC_NAME s_scm_nan | |
736 | { | |
737 | static int initialized = 0; | |
0aacf84e | 738 | if (!initialized) |
7351e207 MV |
739 | { |
740 | guile_ieee_init (); | |
741 | initialized = 1; | |
742 | } | |
55f26379 | 743 | return scm_from_double (guile_NaN); |
7351e207 MV |
744 | } |
745 | #undef FUNC_NAME | |
746 | ||
4219f20d | 747 | |
a48d60b1 MD |
748 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
749 | (SCM x), | |
750 | "Return the absolute value of @var{x}.") | |
2519490c | 751 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 752 | { |
e11e83f3 | 753 | if (SCM_I_INUMP (x)) |
0aacf84e | 754 | { |
e25f3727 | 755 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
756 | if (xx >= 0) |
757 | return x; | |
758 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 759 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 760 | else |
e25f3727 | 761 | return scm_i_inum2big (-xx); |
4219f20d | 762 | } |
9b9ef10c MW |
763 | else if (SCM_LIKELY (SCM_REALP (x))) |
764 | { | |
765 | double xx = SCM_REAL_VALUE (x); | |
766 | /* If x is a NaN then xx<0 is false so we return x unchanged */ | |
767 | if (xx < 0.0) | |
768 | return scm_from_double (-xx); | |
769 | /* Handle signed zeroes properly */ | |
770 | else if (SCM_UNLIKELY (xx == 0.0)) | |
771 | return flo0; | |
772 | else | |
773 | return x; | |
774 | } | |
0aacf84e MD |
775 | else if (SCM_BIGP (x)) |
776 | { | |
777 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
778 | if (sgn < 0) | |
779 | return scm_i_clonebig (x, 0); | |
780 | else | |
781 | return x; | |
4219f20d | 782 | } |
f92e85f7 MV |
783 | else if (SCM_FRACTIONP (x)) |
784 | { | |
73e4de09 | 785 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 786 | return x; |
cba42c93 | 787 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
788 | SCM_FRACTION_DENOMINATOR (x)); |
789 | } | |
0aacf84e | 790 | else |
a48d60b1 | 791 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 792 | } |
a48d60b1 | 793 | #undef FUNC_NAME |
0f2d19dd | 794 | |
4219f20d | 795 | |
2519490c MW |
796 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
797 | (SCM x, SCM y), | |
798 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
799 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 800 | { |
495a39c4 | 801 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 802 | { |
495a39c4 | 803 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 804 | return scm_truncate_quotient (x, y); |
0aacf84e | 805 | else |
2519490c | 806 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 807 | } |
0aacf84e | 808 | else |
2519490c | 809 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 810 | } |
2519490c | 811 | #undef FUNC_NAME |
0f2d19dd | 812 | |
2519490c MW |
813 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
814 | (SCM x, SCM y), | |
815 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
816 | "@lisp\n" | |
817 | "(remainder 13 4) @result{} 1\n" | |
818 | "(remainder -13 4) @result{} -1\n" | |
819 | "@end lisp") | |
820 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 821 | { |
495a39c4 | 822 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 823 | { |
495a39c4 | 824 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 825 | return scm_truncate_remainder (x, y); |
0aacf84e | 826 | else |
2519490c | 827 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 828 | } |
0aacf84e | 829 | else |
2519490c | 830 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 831 | } |
2519490c | 832 | #undef FUNC_NAME |
0f2d19dd | 833 | |
89a7e495 | 834 | |
2519490c MW |
835 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
836 | (SCM x, SCM y), | |
837 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
838 | "@lisp\n" | |
839 | "(modulo 13 4) @result{} 1\n" | |
840 | "(modulo -13 4) @result{} 3\n" | |
841 | "@end lisp") | |
842 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 843 | { |
495a39c4 | 844 | if (SCM_LIKELY (scm_is_integer (x))) |
0aacf84e | 845 | { |
495a39c4 | 846 | if (SCM_LIKELY (scm_is_integer (y))) |
a8da6d93 | 847 | return scm_floor_remainder (x, y); |
0aacf84e | 848 | else |
2519490c | 849 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 850 | } |
0aacf84e | 851 | else |
2519490c | 852 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 853 | } |
2519490c | 854 | #undef FUNC_NAME |
0f2d19dd | 855 | |
5fbf680b MW |
856 | /* two_valued_wta_dispatch_2 is a version of SCM_WTA_DISPATCH_2 for |
857 | two-valued functions. It is called from primitive generics that take | |
858 | two arguments and return two values, when the core procedure is | |
859 | unable to handle the given argument types. If there are GOOPS | |
860 | methods for this primitive generic, it dispatches to GOOPS and, if | |
861 | successful, expects two values to be returned, which are placed in | |
862 | *rp1 and *rp2. If there are no GOOPS methods, it throws a | |
863 | wrong-type-arg exception. | |
864 | ||
865 | FIXME: This obviously belongs somewhere else, but until we decide on | |
866 | the right API, it is here as a static function, because it is needed | |
867 | by the *_divide functions below. | |
868 | */ | |
869 | static void | |
870 | two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos, | |
871 | const char *subr, SCM *rp1, SCM *rp2) | |
872 | { | |
873 | if (SCM_UNPACK (gf)) | |
874 | scm_i_extract_values_2 (scm_call_generic_2 (gf, a1, a2), rp1, rp2); | |
875 | else | |
876 | scm_wrong_type_arg (subr, pos, (pos == SCM_ARG1) ? a1 : a2); | |
877 | } | |
878 | ||
a8da6d93 MW |
879 | SCM_DEFINE (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, |
880 | (SCM x, SCM y), | |
881 | "Return the integer @var{q} such that\n" | |
882 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
883 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
884 | "@lisp\n" | |
885 | "(euclidean-quotient 123 10) @result{} 12\n" | |
886 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
887 | "(euclidean-quotient -123 10) @result{} -13\n" | |
888 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
889 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
890 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
891 | "@end lisp") | |
ff62c168 MW |
892 | #define FUNC_NAME s_scm_euclidean_quotient |
893 | { | |
a8da6d93 MW |
894 | if (scm_is_false (scm_negative_p (y))) |
895 | return scm_floor_quotient (x, y); | |
ff62c168 | 896 | else |
a8da6d93 | 897 | return scm_ceiling_quotient (x, y); |
ff62c168 MW |
898 | } |
899 | #undef FUNC_NAME | |
900 | ||
a8da6d93 MW |
901 | SCM_DEFINE (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, |
902 | (SCM x, SCM y), | |
903 | "Return the real number @var{r} such that\n" | |
904 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
905 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
906 | "for some integer @var{q}.\n" | |
907 | "@lisp\n" | |
908 | "(euclidean-remainder 123 10) @result{} 3\n" | |
909 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
910 | "(euclidean-remainder -123 10) @result{} 7\n" | |
911 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
912 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
913 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
914 | "@end lisp") | |
ff62c168 MW |
915 | #define FUNC_NAME s_scm_euclidean_remainder |
916 | { | |
a8da6d93 MW |
917 | if (scm_is_false (scm_negative_p (y))) |
918 | return scm_floor_remainder (x, y); | |
ff62c168 | 919 | else |
a8da6d93 | 920 | return scm_ceiling_remainder (x, y); |
ff62c168 MW |
921 | } |
922 | #undef FUNC_NAME | |
923 | ||
a8da6d93 MW |
924 | SCM_DEFINE (scm_i_euclidean_divide, "euclidean/", 2, 0, 0, |
925 | (SCM x, SCM y), | |
926 | "Return the integer @var{q} and the real number @var{r}\n" | |
927 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
928 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
929 | "@lisp\n" | |
930 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
931 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
932 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
933 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
934 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
935 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
936 | "@end lisp") | |
5fbf680b MW |
937 | #define FUNC_NAME s_scm_i_euclidean_divide |
938 | { | |
a8da6d93 MW |
939 | if (scm_is_false (scm_negative_p (y))) |
940 | return scm_i_floor_divide (x, y); | |
941 | else | |
942 | return scm_i_ceiling_divide (x, y); | |
5fbf680b MW |
943 | } |
944 | #undef FUNC_NAME | |
945 | ||
5fbf680b MW |
946 | void |
947 | scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 | 948 | { |
a8da6d93 MW |
949 | if (scm_is_false (scm_negative_p (y))) |
950 | return scm_floor_divide (x, y, qp, rp); | |
ff62c168 | 951 | else |
a8da6d93 | 952 | return scm_ceiling_divide (x, y, qp, rp); |
ff62c168 MW |
953 | } |
954 | ||
8f9da340 MW |
955 | static SCM scm_i_inexact_floor_quotient (double x, double y); |
956 | static SCM scm_i_exact_rational_floor_quotient (SCM x, SCM y); | |
957 | ||
958 | SCM_PRIMITIVE_GENERIC (scm_floor_quotient, "floor-quotient", 2, 0, 0, | |
959 | (SCM x, SCM y), | |
960 | "Return the floor of @math{@var{x} / @var{y}}.\n" | |
961 | "@lisp\n" | |
962 | "(floor-quotient 123 10) @result{} 12\n" | |
963 | "(floor-quotient 123 -10) @result{} -13\n" | |
964 | "(floor-quotient -123 10) @result{} -13\n" | |
965 | "(floor-quotient -123 -10) @result{} 12\n" | |
966 | "(floor-quotient -123.2 -63.5) @result{} 1.0\n" | |
967 | "(floor-quotient 16/3 -10/7) @result{} -4\n" | |
968 | "@end lisp") | |
969 | #define FUNC_NAME s_scm_floor_quotient | |
970 | { | |
971 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
972 | { | |
973 | scm_t_inum xx = SCM_I_INUM (x); | |
974 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
975 | { | |
976 | scm_t_inum yy = SCM_I_INUM (y); | |
977 | scm_t_inum xx1 = xx; | |
978 | scm_t_inum qq; | |
979 | if (SCM_LIKELY (yy > 0)) | |
980 | { | |
981 | if (SCM_UNLIKELY (xx < 0)) | |
982 | xx1 = xx - yy + 1; | |
983 | } | |
984 | else if (SCM_UNLIKELY (yy == 0)) | |
985 | scm_num_overflow (s_scm_floor_quotient); | |
986 | else if (xx > 0) | |
987 | xx1 = xx - yy - 1; | |
988 | qq = xx1 / yy; | |
989 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
990 | return SCM_I_MAKINUM (qq); | |
991 | else | |
992 | return scm_i_inum2big (qq); | |
993 | } | |
994 | else if (SCM_BIGP (y)) | |
995 | { | |
996 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
997 | scm_remember_upto_here_1 (y); | |
998 | if (sign > 0) | |
999 | return SCM_I_MAKINUM ((xx < 0) ? -1 : 0); | |
1000 | else | |
1001 | return SCM_I_MAKINUM ((xx > 0) ? -1 : 0); | |
1002 | } | |
1003 | else if (SCM_REALP (y)) | |
1004 | return scm_i_inexact_floor_quotient (xx, SCM_REAL_VALUE (y)); | |
1005 | else if (SCM_FRACTIONP (y)) | |
1006 | return scm_i_exact_rational_floor_quotient (x, y); | |
1007 | else | |
1008 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1009 | s_scm_floor_quotient); | |
1010 | } | |
1011 | else if (SCM_BIGP (x)) | |
1012 | { | |
1013 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1014 | { | |
1015 | scm_t_inum yy = SCM_I_INUM (y); | |
1016 | if (SCM_UNLIKELY (yy == 0)) | |
1017 | scm_num_overflow (s_scm_floor_quotient); | |
1018 | else if (SCM_UNLIKELY (yy == 1)) | |
1019 | return x; | |
1020 | else | |
1021 | { | |
1022 | SCM q = scm_i_mkbig (); | |
1023 | if (yy > 0) | |
1024 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1025 | else | |
1026 | { | |
1027 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1028 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1029 | } | |
1030 | scm_remember_upto_here_1 (x); | |
1031 | return scm_i_normbig (q); | |
1032 | } | |
1033 | } | |
1034 | else if (SCM_BIGP (y)) | |
1035 | { | |
1036 | SCM q = scm_i_mkbig (); | |
1037 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1038 | SCM_I_BIG_MPZ (x), | |
1039 | SCM_I_BIG_MPZ (y)); | |
1040 | scm_remember_upto_here_2 (x, y); | |
1041 | return scm_i_normbig (q); | |
1042 | } | |
1043 | else if (SCM_REALP (y)) | |
1044 | return scm_i_inexact_floor_quotient | |
1045 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1046 | else if (SCM_FRACTIONP (y)) | |
1047 | return scm_i_exact_rational_floor_quotient (x, y); | |
1048 | else | |
1049 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1050 | s_scm_floor_quotient); | |
1051 | } | |
1052 | else if (SCM_REALP (x)) | |
1053 | { | |
1054 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1055 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1056 | return scm_i_inexact_floor_quotient | |
1057 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1058 | else | |
1059 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1060 | s_scm_floor_quotient); | |
1061 | } | |
1062 | else if (SCM_FRACTIONP (x)) | |
1063 | { | |
1064 | if (SCM_REALP (y)) | |
1065 | return scm_i_inexact_floor_quotient | |
1066 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1067 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1068 | return scm_i_exact_rational_floor_quotient (x, y); | |
1069 | else | |
1070 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1071 | s_scm_floor_quotient); | |
1072 | } | |
1073 | else | |
1074 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG1, | |
1075 | s_scm_floor_quotient); | |
1076 | } | |
1077 | #undef FUNC_NAME | |
1078 | ||
1079 | static SCM | |
1080 | scm_i_inexact_floor_quotient (double x, double y) | |
1081 | { | |
1082 | if (SCM_UNLIKELY (y == 0)) | |
1083 | scm_num_overflow (s_scm_floor_quotient); /* or return a NaN? */ | |
1084 | else | |
1085 | return scm_from_double (floor (x / y)); | |
1086 | } | |
1087 | ||
1088 | static SCM | |
1089 | scm_i_exact_rational_floor_quotient (SCM x, SCM y) | |
1090 | { | |
1091 | return scm_floor_quotient | |
1092 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1093 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1094 | } | |
1095 | ||
1096 | static SCM scm_i_inexact_floor_remainder (double x, double y); | |
1097 | static SCM scm_i_exact_rational_floor_remainder (SCM x, SCM y); | |
1098 | ||
1099 | SCM_PRIMITIVE_GENERIC (scm_floor_remainder, "floor-remainder", 2, 0, 0, | |
1100 | (SCM x, SCM y), | |
1101 | "Return the real number @var{r} such that\n" | |
1102 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1103 | "where @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1104 | "@lisp\n" | |
1105 | "(floor-remainder 123 10) @result{} 3\n" | |
1106 | "(floor-remainder 123 -10) @result{} -7\n" | |
1107 | "(floor-remainder -123 10) @result{} 7\n" | |
1108 | "(floor-remainder -123 -10) @result{} -3\n" | |
1109 | "(floor-remainder -123.2 -63.5) @result{} -59.7\n" | |
1110 | "(floor-remainder 16/3 -10/7) @result{} -8/21\n" | |
1111 | "@end lisp") | |
1112 | #define FUNC_NAME s_scm_floor_remainder | |
1113 | { | |
1114 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1115 | { | |
1116 | scm_t_inum xx = SCM_I_INUM (x); | |
1117 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1118 | { | |
1119 | scm_t_inum yy = SCM_I_INUM (y); | |
1120 | if (SCM_UNLIKELY (yy == 0)) | |
1121 | scm_num_overflow (s_scm_floor_remainder); | |
1122 | else | |
1123 | { | |
1124 | scm_t_inum rr = xx % yy; | |
1125 | int needs_adjustment; | |
1126 | ||
1127 | if (SCM_LIKELY (yy > 0)) | |
1128 | needs_adjustment = (rr < 0); | |
1129 | else | |
1130 | needs_adjustment = (rr > 0); | |
1131 | ||
1132 | if (needs_adjustment) | |
1133 | rr += yy; | |
1134 | return SCM_I_MAKINUM (rr); | |
1135 | } | |
1136 | } | |
1137 | else if (SCM_BIGP (y)) | |
1138 | { | |
1139 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1140 | scm_remember_upto_here_1 (y); | |
1141 | if (sign > 0) | |
1142 | { | |
1143 | if (xx < 0) | |
1144 | { | |
1145 | SCM r = scm_i_mkbig (); | |
1146 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1147 | scm_remember_upto_here_1 (y); | |
1148 | return scm_i_normbig (r); | |
1149 | } | |
1150 | else | |
1151 | return x; | |
1152 | } | |
1153 | else if (xx <= 0) | |
1154 | return x; | |
1155 | else | |
1156 | { | |
1157 | SCM r = scm_i_mkbig (); | |
1158 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1159 | scm_remember_upto_here_1 (y); | |
1160 | return scm_i_normbig (r); | |
1161 | } | |
1162 | } | |
1163 | else if (SCM_REALP (y)) | |
1164 | return scm_i_inexact_floor_remainder (xx, SCM_REAL_VALUE (y)); | |
1165 | else if (SCM_FRACTIONP (y)) | |
1166 | return scm_i_exact_rational_floor_remainder (x, y); | |
1167 | else | |
1168 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1169 | s_scm_floor_remainder); | |
1170 | } | |
1171 | else if (SCM_BIGP (x)) | |
1172 | { | |
1173 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1174 | { | |
1175 | scm_t_inum yy = SCM_I_INUM (y); | |
1176 | if (SCM_UNLIKELY (yy == 0)) | |
1177 | scm_num_overflow (s_scm_floor_remainder); | |
1178 | else | |
1179 | { | |
1180 | scm_t_inum rr; | |
1181 | if (yy > 0) | |
1182 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1183 | else | |
1184 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1185 | scm_remember_upto_here_1 (x); | |
1186 | return SCM_I_MAKINUM (rr); | |
1187 | } | |
1188 | } | |
1189 | else if (SCM_BIGP (y)) | |
1190 | { | |
1191 | SCM r = scm_i_mkbig (); | |
1192 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
1193 | SCM_I_BIG_MPZ (x), | |
1194 | SCM_I_BIG_MPZ (y)); | |
1195 | scm_remember_upto_here_2 (x, y); | |
1196 | return scm_i_normbig (r); | |
1197 | } | |
1198 | else if (SCM_REALP (y)) | |
1199 | return scm_i_inexact_floor_remainder | |
1200 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1201 | else if (SCM_FRACTIONP (y)) | |
1202 | return scm_i_exact_rational_floor_remainder (x, y); | |
1203 | else | |
1204 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1205 | s_scm_floor_remainder); | |
1206 | } | |
1207 | else if (SCM_REALP (x)) | |
1208 | { | |
1209 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1210 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1211 | return scm_i_inexact_floor_remainder | |
1212 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1213 | else | |
1214 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1215 | s_scm_floor_remainder); | |
1216 | } | |
1217 | else if (SCM_FRACTIONP (x)) | |
1218 | { | |
1219 | if (SCM_REALP (y)) | |
1220 | return scm_i_inexact_floor_remainder | |
1221 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1222 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1223 | return scm_i_exact_rational_floor_remainder (x, y); | |
1224 | else | |
1225 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1226 | s_scm_floor_remainder); | |
1227 | } | |
1228 | else | |
1229 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG1, | |
1230 | s_scm_floor_remainder); | |
1231 | } | |
1232 | #undef FUNC_NAME | |
1233 | ||
1234 | static SCM | |
1235 | scm_i_inexact_floor_remainder (double x, double y) | |
1236 | { | |
1237 | /* Although it would be more efficient to use fmod here, we can't | |
1238 | because it would in some cases produce results inconsistent with | |
1239 | scm_i_inexact_floor_quotient, such that x != q * y + r (not even | |
1240 | close). In particular, when x is very close to a multiple of y, | |
1241 | then r might be either 0.0 or y, but those two cases must | |
1242 | correspond to different choices of q. If r = 0.0 then q must be | |
1243 | x/y, and if r = y then q must be x/y-1. If quotient chooses one | |
1244 | and remainder chooses the other, it would be bad. */ | |
1245 | if (SCM_UNLIKELY (y == 0)) | |
1246 | scm_num_overflow (s_scm_floor_remainder); /* or return a NaN? */ | |
1247 | else | |
1248 | return scm_from_double (x - y * floor (x / y)); | |
1249 | } | |
1250 | ||
1251 | static SCM | |
1252 | scm_i_exact_rational_floor_remainder (SCM x, SCM y) | |
1253 | { | |
1254 | SCM xd = scm_denominator (x); | |
1255 | SCM yd = scm_denominator (y); | |
1256 | SCM r1 = scm_floor_remainder (scm_product (scm_numerator (x), yd), | |
1257 | scm_product (scm_numerator (y), xd)); | |
1258 | return scm_divide (r1, scm_product (xd, yd)); | |
1259 | } | |
1260 | ||
1261 | ||
1262 | static void scm_i_inexact_floor_divide (double x, double y, | |
1263 | SCM *qp, SCM *rp); | |
1264 | static void scm_i_exact_rational_floor_divide (SCM x, SCM y, | |
1265 | SCM *qp, SCM *rp); | |
1266 | ||
1267 | SCM_PRIMITIVE_GENERIC (scm_i_floor_divide, "floor/", 2, 0, 0, | |
1268 | (SCM x, SCM y), | |
1269 | "Return the integer @var{q} and the real number @var{r}\n" | |
1270 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1271 | "and @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1272 | "@lisp\n" | |
1273 | "(floor/ 123 10) @result{} 12 and 3\n" | |
1274 | "(floor/ 123 -10) @result{} -13 and -7\n" | |
1275 | "(floor/ -123 10) @result{} -13 and 7\n" | |
1276 | "(floor/ -123 -10) @result{} 12 and -3\n" | |
1277 | "(floor/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
1278 | "(floor/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
1279 | "@end lisp") | |
1280 | #define FUNC_NAME s_scm_i_floor_divide | |
1281 | { | |
1282 | SCM q, r; | |
1283 | ||
1284 | scm_floor_divide(x, y, &q, &r); | |
1285 | return scm_values (scm_list_2 (q, r)); | |
1286 | } | |
1287 | #undef FUNC_NAME | |
1288 | ||
1289 | #define s_scm_floor_divide s_scm_i_floor_divide | |
1290 | #define g_scm_floor_divide g_scm_i_floor_divide | |
1291 | ||
1292 | void | |
1293 | scm_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1294 | { | |
1295 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1296 | { | |
1297 | scm_t_inum xx = SCM_I_INUM (x); | |
1298 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1299 | { | |
1300 | scm_t_inum yy = SCM_I_INUM (y); | |
1301 | if (SCM_UNLIKELY (yy == 0)) | |
1302 | scm_num_overflow (s_scm_floor_divide); | |
1303 | else | |
1304 | { | |
1305 | scm_t_inum qq = xx / yy; | |
1306 | scm_t_inum rr = xx % yy; | |
1307 | int needs_adjustment; | |
1308 | ||
1309 | if (SCM_LIKELY (yy > 0)) | |
1310 | needs_adjustment = (rr < 0); | |
1311 | else | |
1312 | needs_adjustment = (rr > 0); | |
1313 | ||
1314 | if (needs_adjustment) | |
1315 | { | |
1316 | rr += yy; | |
1317 | qq--; | |
1318 | } | |
1319 | ||
1320 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1321 | *qp = SCM_I_MAKINUM (qq); | |
1322 | else | |
1323 | *qp = scm_i_inum2big (qq); | |
1324 | *rp = SCM_I_MAKINUM (rr); | |
1325 | } | |
1326 | return; | |
1327 | } | |
1328 | else if (SCM_BIGP (y)) | |
1329 | { | |
1330 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1331 | scm_remember_upto_here_1 (y); | |
1332 | if (sign > 0) | |
1333 | { | |
1334 | if (xx < 0) | |
1335 | { | |
1336 | SCM r = scm_i_mkbig (); | |
1337 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1338 | scm_remember_upto_here_1 (y); | |
1339 | *qp = SCM_I_MAKINUM (-1); | |
1340 | *rp = scm_i_normbig (r); | |
1341 | } | |
1342 | else | |
1343 | { | |
1344 | *qp = SCM_INUM0; | |
1345 | *rp = x; | |
1346 | } | |
1347 | } | |
1348 | else if (xx <= 0) | |
1349 | { | |
1350 | *qp = SCM_INUM0; | |
1351 | *rp = x; | |
1352 | } | |
1353 | else | |
1354 | { | |
1355 | SCM r = scm_i_mkbig (); | |
1356 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1357 | scm_remember_upto_here_1 (y); | |
1358 | *qp = SCM_I_MAKINUM (-1); | |
1359 | *rp = scm_i_normbig (r); | |
1360 | } | |
1361 | return; | |
1362 | } | |
1363 | else if (SCM_REALP (y)) | |
1364 | return scm_i_inexact_floor_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1365 | else if (SCM_FRACTIONP (y)) | |
1366 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1367 | else | |
1368 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1369 | s_scm_floor_divide, qp, rp); | |
1370 | } | |
1371 | else if (SCM_BIGP (x)) | |
1372 | { | |
1373 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1374 | { | |
1375 | scm_t_inum yy = SCM_I_INUM (y); | |
1376 | if (SCM_UNLIKELY (yy == 0)) | |
1377 | scm_num_overflow (s_scm_floor_divide); | |
1378 | else | |
1379 | { | |
1380 | SCM q = scm_i_mkbig (); | |
1381 | SCM r = scm_i_mkbig (); | |
1382 | if (yy > 0) | |
1383 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1384 | SCM_I_BIG_MPZ (x), yy); | |
1385 | else | |
1386 | { | |
1387 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1388 | SCM_I_BIG_MPZ (x), -yy); | |
1389 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1390 | } | |
1391 | scm_remember_upto_here_1 (x); | |
1392 | *qp = scm_i_normbig (q); | |
1393 | *rp = scm_i_normbig (r); | |
1394 | } | |
1395 | return; | |
1396 | } | |
1397 | else if (SCM_BIGP (y)) | |
1398 | { | |
1399 | SCM q = scm_i_mkbig (); | |
1400 | SCM r = scm_i_mkbig (); | |
1401 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1402 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1403 | scm_remember_upto_here_2 (x, y); | |
1404 | *qp = scm_i_normbig (q); | |
1405 | *rp = scm_i_normbig (r); | |
1406 | return; | |
1407 | } | |
1408 | else if (SCM_REALP (y)) | |
1409 | return scm_i_inexact_floor_divide | |
1410 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1411 | else if (SCM_FRACTIONP (y)) | |
1412 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1413 | else | |
1414 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1415 | s_scm_floor_divide, qp, rp); | |
1416 | } | |
1417 | else if (SCM_REALP (x)) | |
1418 | { | |
1419 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1420 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1421 | return scm_i_inexact_floor_divide | |
1422 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
1423 | else | |
1424 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1425 | s_scm_floor_divide, qp, rp); | |
1426 | } | |
1427 | else if (SCM_FRACTIONP (x)) | |
1428 | { | |
1429 | if (SCM_REALP (y)) | |
1430 | return scm_i_inexact_floor_divide | |
1431 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
1432 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1433 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1434 | else | |
1435 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1436 | s_scm_floor_divide, qp, rp); | |
1437 | } | |
1438 | else | |
1439 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG1, | |
1440 | s_scm_floor_divide, qp, rp); | |
1441 | } | |
1442 | ||
1443 | static void | |
1444 | scm_i_inexact_floor_divide (double x, double y, SCM *qp, SCM *rp) | |
1445 | { | |
1446 | if (SCM_UNLIKELY (y == 0)) | |
1447 | scm_num_overflow (s_scm_floor_divide); /* or return a NaN? */ | |
1448 | else | |
1449 | { | |
1450 | double q = floor (x / y); | |
1451 | double r = x - q * y; | |
1452 | *qp = scm_from_double (q); | |
1453 | *rp = scm_from_double (r); | |
1454 | } | |
1455 | } | |
1456 | ||
1457 | static void | |
1458 | scm_i_exact_rational_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1459 | { | |
1460 | SCM r1; | |
1461 | SCM xd = scm_denominator (x); | |
1462 | SCM yd = scm_denominator (y); | |
1463 | ||
1464 | scm_floor_divide (scm_product (scm_numerator (x), yd), | |
1465 | scm_product (scm_numerator (y), xd), | |
1466 | qp, &r1); | |
1467 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
1468 | } | |
1469 | ||
1470 | static SCM scm_i_inexact_ceiling_quotient (double x, double y); | |
1471 | static SCM scm_i_exact_rational_ceiling_quotient (SCM x, SCM y); | |
1472 | ||
1473 | SCM_PRIMITIVE_GENERIC (scm_ceiling_quotient, "ceiling-quotient", 2, 0, 0, | |
1474 | (SCM x, SCM y), | |
1475 | "Return the ceiling of @math{@var{x} / @var{y}}.\n" | |
1476 | "@lisp\n" | |
1477 | "(ceiling-quotient 123 10) @result{} 13\n" | |
1478 | "(ceiling-quotient 123 -10) @result{} -12\n" | |
1479 | "(ceiling-quotient -123 10) @result{} -12\n" | |
1480 | "(ceiling-quotient -123 -10) @result{} 13\n" | |
1481 | "(ceiling-quotient -123.2 -63.5) @result{} 2.0\n" | |
1482 | "(ceiling-quotient 16/3 -10/7) @result{} -3\n" | |
1483 | "@end lisp") | |
1484 | #define FUNC_NAME s_scm_ceiling_quotient | |
1485 | { | |
1486 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1487 | { | |
1488 | scm_t_inum xx = SCM_I_INUM (x); | |
1489 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1490 | { | |
1491 | scm_t_inum yy = SCM_I_INUM (y); | |
1492 | if (SCM_UNLIKELY (yy == 0)) | |
1493 | scm_num_overflow (s_scm_ceiling_quotient); | |
1494 | else | |
1495 | { | |
1496 | scm_t_inum xx1 = xx; | |
1497 | scm_t_inum qq; | |
1498 | if (SCM_LIKELY (yy > 0)) | |
1499 | { | |
1500 | if (SCM_LIKELY (xx >= 0)) | |
1501 | xx1 = xx + yy - 1; | |
1502 | } | |
1503 | else if (SCM_UNLIKELY (yy == 0)) | |
1504 | scm_num_overflow (s_scm_ceiling_quotient); | |
1505 | else if (xx < 0) | |
1506 | xx1 = xx + yy + 1; | |
1507 | qq = xx1 / yy; | |
1508 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1509 | return SCM_I_MAKINUM (qq); | |
1510 | else | |
1511 | return scm_i_inum2big (qq); | |
1512 | } | |
1513 | } | |
1514 | else if (SCM_BIGP (y)) | |
1515 | { | |
1516 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1517 | scm_remember_upto_here_1 (y); | |
1518 | if (SCM_LIKELY (sign > 0)) | |
1519 | { | |
1520 | if (SCM_LIKELY (xx > 0)) | |
1521 | return SCM_INUM1; | |
1522 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1523 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1524 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1525 | { | |
1526 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1527 | scm_remember_upto_here_1 (y); | |
1528 | return SCM_I_MAKINUM (-1); | |
1529 | } | |
1530 | else | |
1531 | return SCM_INUM0; | |
1532 | } | |
1533 | else if (xx >= 0) | |
1534 | return SCM_INUM0; | |
1535 | else | |
1536 | return SCM_INUM1; | |
1537 | } | |
1538 | else if (SCM_REALP (y)) | |
1539 | return scm_i_inexact_ceiling_quotient (xx, SCM_REAL_VALUE (y)); | |
1540 | else if (SCM_FRACTIONP (y)) | |
1541 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1542 | else | |
1543 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1544 | s_scm_ceiling_quotient); | |
1545 | } | |
1546 | else if (SCM_BIGP (x)) | |
1547 | { | |
1548 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1549 | { | |
1550 | scm_t_inum yy = SCM_I_INUM (y); | |
1551 | if (SCM_UNLIKELY (yy == 0)) | |
1552 | scm_num_overflow (s_scm_ceiling_quotient); | |
1553 | else if (SCM_UNLIKELY (yy == 1)) | |
1554 | return x; | |
1555 | else | |
1556 | { | |
1557 | SCM q = scm_i_mkbig (); | |
1558 | if (yy > 0) | |
1559 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1560 | else | |
1561 | { | |
1562 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1563 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1564 | } | |
1565 | scm_remember_upto_here_1 (x); | |
1566 | return scm_i_normbig (q); | |
1567 | } | |
1568 | } | |
1569 | else if (SCM_BIGP (y)) | |
1570 | { | |
1571 | SCM q = scm_i_mkbig (); | |
1572 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1573 | SCM_I_BIG_MPZ (x), | |
1574 | SCM_I_BIG_MPZ (y)); | |
1575 | scm_remember_upto_here_2 (x, y); | |
1576 | return scm_i_normbig (q); | |
1577 | } | |
1578 | else if (SCM_REALP (y)) | |
1579 | return scm_i_inexact_ceiling_quotient | |
1580 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1581 | else if (SCM_FRACTIONP (y)) | |
1582 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1583 | else | |
1584 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1585 | s_scm_ceiling_quotient); | |
1586 | } | |
1587 | else if (SCM_REALP (x)) | |
1588 | { | |
1589 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1590 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1591 | return scm_i_inexact_ceiling_quotient | |
1592 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1593 | else | |
1594 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1595 | s_scm_ceiling_quotient); | |
1596 | } | |
1597 | else if (SCM_FRACTIONP (x)) | |
1598 | { | |
1599 | if (SCM_REALP (y)) | |
1600 | return scm_i_inexact_ceiling_quotient | |
1601 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1602 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1603 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1604 | else | |
1605 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1606 | s_scm_ceiling_quotient); | |
1607 | } | |
1608 | else | |
1609 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG1, | |
1610 | s_scm_ceiling_quotient); | |
1611 | } | |
1612 | #undef FUNC_NAME | |
1613 | ||
1614 | static SCM | |
1615 | scm_i_inexact_ceiling_quotient (double x, double y) | |
1616 | { | |
1617 | if (SCM_UNLIKELY (y == 0)) | |
1618 | scm_num_overflow (s_scm_ceiling_quotient); /* or return a NaN? */ | |
1619 | else | |
1620 | return scm_from_double (ceil (x / y)); | |
1621 | } | |
1622 | ||
1623 | static SCM | |
1624 | scm_i_exact_rational_ceiling_quotient (SCM x, SCM y) | |
1625 | { | |
1626 | return scm_ceiling_quotient | |
1627 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1628 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1629 | } | |
1630 | ||
1631 | static SCM scm_i_inexact_ceiling_remainder (double x, double y); | |
1632 | static SCM scm_i_exact_rational_ceiling_remainder (SCM x, SCM y); | |
1633 | ||
1634 | SCM_PRIMITIVE_GENERIC (scm_ceiling_remainder, "ceiling-remainder", 2, 0, 0, | |
1635 | (SCM x, SCM y), | |
1636 | "Return the real number @var{r} such that\n" | |
1637 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1638 | "where @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1639 | "@lisp\n" | |
1640 | "(ceiling-remainder 123 10) @result{} -7\n" | |
1641 | "(ceiling-remainder 123 -10) @result{} 3\n" | |
1642 | "(ceiling-remainder -123 10) @result{} -3\n" | |
1643 | "(ceiling-remainder -123 -10) @result{} 7\n" | |
1644 | "(ceiling-remainder -123.2 -63.5) @result{} 3.8\n" | |
1645 | "(ceiling-remainder 16/3 -10/7) @result{} 22/21\n" | |
1646 | "@end lisp") | |
1647 | #define FUNC_NAME s_scm_ceiling_remainder | |
1648 | { | |
1649 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1650 | { | |
1651 | scm_t_inum xx = SCM_I_INUM (x); | |
1652 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1653 | { | |
1654 | scm_t_inum yy = SCM_I_INUM (y); | |
1655 | if (SCM_UNLIKELY (yy == 0)) | |
1656 | scm_num_overflow (s_scm_ceiling_remainder); | |
1657 | else | |
1658 | { | |
1659 | scm_t_inum rr = xx % yy; | |
1660 | int needs_adjustment; | |
1661 | ||
1662 | if (SCM_LIKELY (yy > 0)) | |
1663 | needs_adjustment = (rr > 0); | |
1664 | else | |
1665 | needs_adjustment = (rr < 0); | |
1666 | ||
1667 | if (needs_adjustment) | |
1668 | rr -= yy; | |
1669 | return SCM_I_MAKINUM (rr); | |
1670 | } | |
1671 | } | |
1672 | else if (SCM_BIGP (y)) | |
1673 | { | |
1674 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1675 | scm_remember_upto_here_1 (y); | |
1676 | if (SCM_LIKELY (sign > 0)) | |
1677 | { | |
1678 | if (SCM_LIKELY (xx > 0)) | |
1679 | { | |
1680 | SCM r = scm_i_mkbig (); | |
1681 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1682 | scm_remember_upto_here_1 (y); | |
1683 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1684 | return scm_i_normbig (r); | |
1685 | } | |
1686 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1687 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1688 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1689 | { | |
1690 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1691 | scm_remember_upto_here_1 (y); | |
1692 | return SCM_INUM0; | |
1693 | } | |
1694 | else | |
1695 | return x; | |
1696 | } | |
1697 | else if (xx >= 0) | |
1698 | return x; | |
1699 | else | |
1700 | { | |
1701 | SCM r = scm_i_mkbig (); | |
1702 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1703 | scm_remember_upto_here_1 (y); | |
1704 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1705 | return scm_i_normbig (r); | |
1706 | } | |
1707 | } | |
1708 | else if (SCM_REALP (y)) | |
1709 | return scm_i_inexact_ceiling_remainder (xx, SCM_REAL_VALUE (y)); | |
1710 | else if (SCM_FRACTIONP (y)) | |
1711 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1712 | else | |
1713 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1714 | s_scm_ceiling_remainder); | |
1715 | } | |
1716 | else if (SCM_BIGP (x)) | |
1717 | { | |
1718 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1719 | { | |
1720 | scm_t_inum yy = SCM_I_INUM (y); | |
1721 | if (SCM_UNLIKELY (yy == 0)) | |
1722 | scm_num_overflow (s_scm_ceiling_remainder); | |
1723 | else | |
1724 | { | |
1725 | scm_t_inum rr; | |
1726 | if (yy > 0) | |
1727 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1728 | else | |
1729 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1730 | scm_remember_upto_here_1 (x); | |
1731 | return SCM_I_MAKINUM (rr); | |
1732 | } | |
1733 | } | |
1734 | else if (SCM_BIGP (y)) | |
1735 | { | |
1736 | SCM r = scm_i_mkbig (); | |
1737 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
1738 | SCM_I_BIG_MPZ (x), | |
1739 | SCM_I_BIG_MPZ (y)); | |
1740 | scm_remember_upto_here_2 (x, y); | |
1741 | return scm_i_normbig (r); | |
1742 | } | |
1743 | else if (SCM_REALP (y)) | |
1744 | return scm_i_inexact_ceiling_remainder | |
1745 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1746 | else if (SCM_FRACTIONP (y)) | |
1747 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1748 | else | |
1749 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1750 | s_scm_ceiling_remainder); | |
1751 | } | |
1752 | else if (SCM_REALP (x)) | |
1753 | { | |
1754 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1755 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1756 | return scm_i_inexact_ceiling_remainder | |
1757 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1758 | else | |
1759 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1760 | s_scm_ceiling_remainder); | |
1761 | } | |
1762 | else if (SCM_FRACTIONP (x)) | |
1763 | { | |
1764 | if (SCM_REALP (y)) | |
1765 | return scm_i_inexact_ceiling_remainder | |
1766 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1767 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1768 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1769 | else | |
1770 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1771 | s_scm_ceiling_remainder); | |
1772 | } | |
1773 | else | |
1774 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG1, | |
1775 | s_scm_ceiling_remainder); | |
1776 | } | |
1777 | #undef FUNC_NAME | |
1778 | ||
1779 | static SCM | |
1780 | scm_i_inexact_ceiling_remainder (double x, double y) | |
1781 | { | |
1782 | /* Although it would be more efficient to use fmod here, we can't | |
1783 | because it would in some cases produce results inconsistent with | |
1784 | scm_i_inexact_ceiling_quotient, such that x != q * y + r (not even | |
1785 | close). In particular, when x is very close to a multiple of y, | |
1786 | then r might be either 0.0 or -y, but those two cases must | |
1787 | correspond to different choices of q. If r = 0.0 then q must be | |
1788 | x/y, and if r = -y then q must be x/y+1. If quotient chooses one | |
1789 | and remainder chooses the other, it would be bad. */ | |
1790 | if (SCM_UNLIKELY (y == 0)) | |
1791 | scm_num_overflow (s_scm_ceiling_remainder); /* or return a NaN? */ | |
1792 | else | |
1793 | return scm_from_double (x - y * ceil (x / y)); | |
1794 | } | |
1795 | ||
1796 | static SCM | |
1797 | scm_i_exact_rational_ceiling_remainder (SCM x, SCM y) | |
1798 | { | |
1799 | SCM xd = scm_denominator (x); | |
1800 | SCM yd = scm_denominator (y); | |
1801 | SCM r1 = scm_ceiling_remainder (scm_product (scm_numerator (x), yd), | |
1802 | scm_product (scm_numerator (y), xd)); | |
1803 | return scm_divide (r1, scm_product (xd, yd)); | |
1804 | } | |
1805 | ||
1806 | static void scm_i_inexact_ceiling_divide (double x, double y, | |
1807 | SCM *qp, SCM *rp); | |
1808 | static void scm_i_exact_rational_ceiling_divide (SCM x, SCM y, | |
1809 | SCM *qp, SCM *rp); | |
1810 | ||
1811 | SCM_PRIMITIVE_GENERIC (scm_i_ceiling_divide, "ceiling/", 2, 0, 0, | |
1812 | (SCM x, SCM y), | |
1813 | "Return the integer @var{q} and the real number @var{r}\n" | |
1814 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1815 | "and @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1816 | "@lisp\n" | |
1817 | "(ceiling/ 123 10) @result{} 13 and -7\n" | |
1818 | "(ceiling/ 123 -10) @result{} -12 and 3\n" | |
1819 | "(ceiling/ -123 10) @result{} -12 and -3\n" | |
1820 | "(ceiling/ -123 -10) @result{} 13 and 7\n" | |
1821 | "(ceiling/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1822 | "(ceiling/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1823 | "@end lisp") | |
1824 | #define FUNC_NAME s_scm_i_ceiling_divide | |
1825 | { | |
1826 | SCM q, r; | |
1827 | ||
1828 | scm_ceiling_divide(x, y, &q, &r); | |
1829 | return scm_values (scm_list_2 (q, r)); | |
1830 | } | |
1831 | #undef FUNC_NAME | |
1832 | ||
1833 | #define s_scm_ceiling_divide s_scm_i_ceiling_divide | |
1834 | #define g_scm_ceiling_divide g_scm_i_ceiling_divide | |
1835 | ||
1836 | void | |
1837 | scm_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1838 | { | |
1839 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1840 | { | |
1841 | scm_t_inum xx = SCM_I_INUM (x); | |
1842 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1843 | { | |
1844 | scm_t_inum yy = SCM_I_INUM (y); | |
1845 | if (SCM_UNLIKELY (yy == 0)) | |
1846 | scm_num_overflow (s_scm_ceiling_divide); | |
1847 | else | |
1848 | { | |
1849 | scm_t_inum qq = xx / yy; | |
1850 | scm_t_inum rr = xx % yy; | |
1851 | int needs_adjustment; | |
1852 | ||
1853 | if (SCM_LIKELY (yy > 0)) | |
1854 | needs_adjustment = (rr > 0); | |
1855 | else | |
1856 | needs_adjustment = (rr < 0); | |
1857 | ||
1858 | if (needs_adjustment) | |
1859 | { | |
1860 | rr -= yy; | |
1861 | qq++; | |
1862 | } | |
1863 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1864 | *qp = SCM_I_MAKINUM (qq); | |
1865 | else | |
1866 | *qp = scm_i_inum2big (qq); | |
1867 | *rp = SCM_I_MAKINUM (rr); | |
1868 | } | |
1869 | return; | |
1870 | } | |
1871 | else if (SCM_BIGP (y)) | |
1872 | { | |
1873 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1874 | scm_remember_upto_here_1 (y); | |
1875 | if (SCM_LIKELY (sign > 0)) | |
1876 | { | |
1877 | if (SCM_LIKELY (xx > 0)) | |
1878 | { | |
1879 | SCM r = scm_i_mkbig (); | |
1880 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1881 | scm_remember_upto_here_1 (y); | |
1882 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1883 | *qp = SCM_INUM1; | |
1884 | *rp = scm_i_normbig (r); | |
1885 | } | |
1886 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1887 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1888 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1889 | { | |
1890 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1891 | scm_remember_upto_here_1 (y); | |
1892 | *qp = SCM_I_MAKINUM (-1); | |
1893 | *rp = SCM_INUM0; | |
1894 | } | |
1895 | else | |
1896 | { | |
1897 | *qp = SCM_INUM0; | |
1898 | *rp = x; | |
1899 | } | |
1900 | } | |
1901 | else if (xx >= 0) | |
1902 | { | |
1903 | *qp = SCM_INUM0; | |
1904 | *rp = x; | |
1905 | } | |
1906 | else | |
1907 | { | |
1908 | SCM r = scm_i_mkbig (); | |
1909 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1910 | scm_remember_upto_here_1 (y); | |
1911 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1912 | *qp = SCM_INUM1; | |
1913 | *rp = scm_i_normbig (r); | |
1914 | } | |
1915 | return; | |
1916 | } | |
1917 | else if (SCM_REALP (y)) | |
1918 | return scm_i_inexact_ceiling_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1919 | else if (SCM_FRACTIONP (y)) | |
1920 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
1921 | else | |
1922 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1923 | s_scm_ceiling_divide, qp, rp); | |
1924 | } | |
1925 | else if (SCM_BIGP (x)) | |
1926 | { | |
1927 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1928 | { | |
1929 | scm_t_inum yy = SCM_I_INUM (y); | |
1930 | if (SCM_UNLIKELY (yy == 0)) | |
1931 | scm_num_overflow (s_scm_ceiling_divide); | |
1932 | else | |
1933 | { | |
1934 | SCM q = scm_i_mkbig (); | |
1935 | SCM r = scm_i_mkbig (); | |
1936 | if (yy > 0) | |
1937 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1938 | SCM_I_BIG_MPZ (x), yy); | |
1939 | else | |
1940 | { | |
1941 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1942 | SCM_I_BIG_MPZ (x), -yy); | |
1943 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1944 | } | |
1945 | scm_remember_upto_here_1 (x); | |
1946 | *qp = scm_i_normbig (q); | |
1947 | *rp = scm_i_normbig (r); | |
1948 | } | |
1949 | return; | |
1950 | } | |
1951 | else if (SCM_BIGP (y)) | |
1952 | { | |
1953 | SCM q = scm_i_mkbig (); | |
1954 | SCM r = scm_i_mkbig (); | |
1955 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1956 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1957 | scm_remember_upto_here_2 (x, y); | |
1958 | *qp = scm_i_normbig (q); | |
1959 | *rp = scm_i_normbig (r); | |
1960 | return; | |
1961 | } | |
1962 | else if (SCM_REALP (y)) | |
1963 | return scm_i_inexact_ceiling_divide | |
1964 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1965 | else if (SCM_FRACTIONP (y)) | |
1966 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
1967 | else | |
1968 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1969 | s_scm_ceiling_divide, qp, rp); | |
1970 | } | |
1971 | else if (SCM_REALP (x)) | |
1972 | { | |
1973 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1974 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1975 | return scm_i_inexact_ceiling_divide | |
1976 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
1977 | else | |
1978 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1979 | s_scm_ceiling_divide, qp, rp); | |
1980 | } | |
1981 | else if (SCM_FRACTIONP (x)) | |
1982 | { | |
1983 | if (SCM_REALP (y)) | |
1984 | return scm_i_inexact_ceiling_divide | |
1985 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
1986 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1987 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
1988 | else | |
1989 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1990 | s_scm_ceiling_divide, qp, rp); | |
1991 | } | |
1992 | else | |
1993 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG1, | |
1994 | s_scm_ceiling_divide, qp, rp); | |
1995 | } | |
1996 | ||
1997 | static void | |
1998 | scm_i_inexact_ceiling_divide (double x, double y, SCM *qp, SCM *rp) | |
1999 | { | |
2000 | if (SCM_UNLIKELY (y == 0)) | |
2001 | scm_num_overflow (s_scm_ceiling_divide); /* or return a NaN? */ | |
2002 | else | |
2003 | { | |
2004 | double q = ceil (x / y); | |
2005 | double r = x - q * y; | |
2006 | *qp = scm_from_double (q); | |
2007 | *rp = scm_from_double (r); | |
2008 | } | |
2009 | } | |
2010 | ||
2011 | static void | |
2012 | scm_i_exact_rational_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2013 | { | |
2014 | SCM r1; | |
2015 | SCM xd = scm_denominator (x); | |
2016 | SCM yd = scm_denominator (y); | |
2017 | ||
2018 | scm_ceiling_divide (scm_product (scm_numerator (x), yd), | |
2019 | scm_product (scm_numerator (y), xd), | |
2020 | qp, &r1); | |
2021 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2022 | } | |
2023 | ||
2024 | static SCM scm_i_inexact_truncate_quotient (double x, double y); | |
2025 | static SCM scm_i_exact_rational_truncate_quotient (SCM x, SCM y); | |
2026 | ||
2027 | SCM_PRIMITIVE_GENERIC (scm_truncate_quotient, "truncate-quotient", 2, 0, 0, | |
2028 | (SCM x, SCM y), | |
2029 | "Return @math{@var{x} / @var{y}} rounded toward zero.\n" | |
2030 | "@lisp\n" | |
2031 | "(truncate-quotient 123 10) @result{} 12\n" | |
2032 | "(truncate-quotient 123 -10) @result{} -12\n" | |
2033 | "(truncate-quotient -123 10) @result{} -12\n" | |
2034 | "(truncate-quotient -123 -10) @result{} 12\n" | |
2035 | "(truncate-quotient -123.2 -63.5) @result{} 1.0\n" | |
2036 | "(truncate-quotient 16/3 -10/7) @result{} -3\n" | |
2037 | "@end lisp") | |
2038 | #define FUNC_NAME s_scm_truncate_quotient | |
2039 | { | |
2040 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2041 | { | |
2042 | scm_t_inum xx = SCM_I_INUM (x); | |
2043 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2044 | { | |
2045 | scm_t_inum yy = SCM_I_INUM (y); | |
2046 | if (SCM_UNLIKELY (yy == 0)) | |
2047 | scm_num_overflow (s_scm_truncate_quotient); | |
2048 | else | |
2049 | { | |
2050 | scm_t_inum qq = xx / yy; | |
2051 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2052 | return SCM_I_MAKINUM (qq); | |
2053 | else | |
2054 | return scm_i_inum2big (qq); | |
2055 | } | |
2056 | } | |
2057 | else if (SCM_BIGP (y)) | |
2058 | { | |
2059 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2060 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2061 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2062 | { | |
2063 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2064 | scm_remember_upto_here_1 (y); | |
2065 | return SCM_I_MAKINUM (-1); | |
2066 | } | |
2067 | else | |
2068 | return SCM_INUM0; | |
2069 | } | |
2070 | else if (SCM_REALP (y)) | |
2071 | return scm_i_inexact_truncate_quotient (xx, SCM_REAL_VALUE (y)); | |
2072 | else if (SCM_FRACTIONP (y)) | |
2073 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2074 | else | |
2075 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2076 | s_scm_truncate_quotient); | |
2077 | } | |
2078 | else if (SCM_BIGP (x)) | |
2079 | { | |
2080 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2081 | { | |
2082 | scm_t_inum yy = SCM_I_INUM (y); | |
2083 | if (SCM_UNLIKELY (yy == 0)) | |
2084 | scm_num_overflow (s_scm_truncate_quotient); | |
2085 | else if (SCM_UNLIKELY (yy == 1)) | |
2086 | return x; | |
2087 | else | |
2088 | { | |
2089 | SCM q = scm_i_mkbig (); | |
2090 | if (yy > 0) | |
2091 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
2092 | else | |
2093 | { | |
2094 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
2095 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2096 | } | |
2097 | scm_remember_upto_here_1 (x); | |
2098 | return scm_i_normbig (q); | |
2099 | } | |
2100 | } | |
2101 | else if (SCM_BIGP (y)) | |
2102 | { | |
2103 | SCM q = scm_i_mkbig (); | |
2104 | mpz_tdiv_q (SCM_I_BIG_MPZ (q), | |
2105 | SCM_I_BIG_MPZ (x), | |
2106 | SCM_I_BIG_MPZ (y)); | |
2107 | scm_remember_upto_here_2 (x, y); | |
2108 | return scm_i_normbig (q); | |
2109 | } | |
2110 | else if (SCM_REALP (y)) | |
2111 | return scm_i_inexact_truncate_quotient | |
2112 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2113 | else if (SCM_FRACTIONP (y)) | |
2114 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2115 | else | |
2116 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2117 | s_scm_truncate_quotient); | |
2118 | } | |
2119 | else if (SCM_REALP (x)) | |
2120 | { | |
2121 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2122 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2123 | return scm_i_inexact_truncate_quotient | |
2124 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2125 | else | |
2126 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2127 | s_scm_truncate_quotient); | |
2128 | } | |
2129 | else if (SCM_FRACTIONP (x)) | |
2130 | { | |
2131 | if (SCM_REALP (y)) | |
2132 | return scm_i_inexact_truncate_quotient | |
2133 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2134 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2135 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2136 | else | |
2137 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2138 | s_scm_truncate_quotient); | |
2139 | } | |
2140 | else | |
2141 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG1, | |
2142 | s_scm_truncate_quotient); | |
2143 | } | |
2144 | #undef FUNC_NAME | |
2145 | ||
2146 | static SCM | |
2147 | scm_i_inexact_truncate_quotient (double x, double y) | |
2148 | { | |
2149 | if (SCM_UNLIKELY (y == 0)) | |
2150 | scm_num_overflow (s_scm_truncate_quotient); /* or return a NaN? */ | |
2151 | else | |
c251ab63 | 2152 | return scm_from_double (trunc (x / y)); |
8f9da340 MW |
2153 | } |
2154 | ||
2155 | static SCM | |
2156 | scm_i_exact_rational_truncate_quotient (SCM x, SCM y) | |
2157 | { | |
2158 | return scm_truncate_quotient | |
2159 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2160 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2161 | } | |
2162 | ||
2163 | static SCM scm_i_inexact_truncate_remainder (double x, double y); | |
2164 | static SCM scm_i_exact_rational_truncate_remainder (SCM x, SCM y); | |
2165 | ||
2166 | SCM_PRIMITIVE_GENERIC (scm_truncate_remainder, "truncate-remainder", 2, 0, 0, | |
2167 | (SCM x, SCM y), | |
2168 | "Return the real number @var{r} such that\n" | |
2169 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2170 | "where @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2171 | "@lisp\n" | |
2172 | "(truncate-remainder 123 10) @result{} 3\n" | |
2173 | "(truncate-remainder 123 -10) @result{} 3\n" | |
2174 | "(truncate-remainder -123 10) @result{} -3\n" | |
2175 | "(truncate-remainder -123 -10) @result{} -3\n" | |
2176 | "(truncate-remainder -123.2 -63.5) @result{} -59.7\n" | |
2177 | "(truncate-remainder 16/3 -10/7) @result{} 22/21\n" | |
2178 | "@end lisp") | |
2179 | #define FUNC_NAME s_scm_truncate_remainder | |
2180 | { | |
2181 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2182 | { | |
2183 | scm_t_inum xx = SCM_I_INUM (x); | |
2184 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2185 | { | |
2186 | scm_t_inum yy = SCM_I_INUM (y); | |
2187 | if (SCM_UNLIKELY (yy == 0)) | |
2188 | scm_num_overflow (s_scm_truncate_remainder); | |
2189 | else | |
2190 | return SCM_I_MAKINUM (xx % yy); | |
2191 | } | |
2192 | else if (SCM_BIGP (y)) | |
2193 | { | |
2194 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2195 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2196 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2197 | { | |
2198 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2199 | scm_remember_upto_here_1 (y); | |
2200 | return SCM_INUM0; | |
2201 | } | |
2202 | else | |
2203 | return x; | |
2204 | } | |
2205 | else if (SCM_REALP (y)) | |
2206 | return scm_i_inexact_truncate_remainder (xx, SCM_REAL_VALUE (y)); | |
2207 | else if (SCM_FRACTIONP (y)) | |
2208 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2209 | else | |
2210 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2211 | s_scm_truncate_remainder); | |
2212 | } | |
2213 | else if (SCM_BIGP (x)) | |
2214 | { | |
2215 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2216 | { | |
2217 | scm_t_inum yy = SCM_I_INUM (y); | |
2218 | if (SCM_UNLIKELY (yy == 0)) | |
2219 | scm_num_overflow (s_scm_truncate_remainder); | |
2220 | else | |
2221 | { | |
2222 | scm_t_inum rr = (mpz_tdiv_ui (SCM_I_BIG_MPZ (x), | |
2223 | (yy > 0) ? yy : -yy) | |
2224 | * mpz_sgn (SCM_I_BIG_MPZ (x))); | |
2225 | scm_remember_upto_here_1 (x); | |
2226 | return SCM_I_MAKINUM (rr); | |
2227 | } | |
2228 | } | |
2229 | else if (SCM_BIGP (y)) | |
2230 | { | |
2231 | SCM r = scm_i_mkbig (); | |
2232 | mpz_tdiv_r (SCM_I_BIG_MPZ (r), | |
2233 | SCM_I_BIG_MPZ (x), | |
2234 | SCM_I_BIG_MPZ (y)); | |
2235 | scm_remember_upto_here_2 (x, y); | |
2236 | return scm_i_normbig (r); | |
2237 | } | |
2238 | else if (SCM_REALP (y)) | |
2239 | return scm_i_inexact_truncate_remainder | |
2240 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2241 | else if (SCM_FRACTIONP (y)) | |
2242 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2243 | else | |
2244 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2245 | s_scm_truncate_remainder); | |
2246 | } | |
2247 | else if (SCM_REALP (x)) | |
2248 | { | |
2249 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2250 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2251 | return scm_i_inexact_truncate_remainder | |
2252 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2253 | else | |
2254 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2255 | s_scm_truncate_remainder); | |
2256 | } | |
2257 | else if (SCM_FRACTIONP (x)) | |
2258 | { | |
2259 | if (SCM_REALP (y)) | |
2260 | return scm_i_inexact_truncate_remainder | |
2261 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2262 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2263 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2264 | else | |
2265 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2266 | s_scm_truncate_remainder); | |
2267 | } | |
2268 | else | |
2269 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG1, | |
2270 | s_scm_truncate_remainder); | |
2271 | } | |
2272 | #undef FUNC_NAME | |
2273 | ||
2274 | static SCM | |
2275 | scm_i_inexact_truncate_remainder (double x, double y) | |
2276 | { | |
2277 | /* Although it would be more efficient to use fmod here, we can't | |
2278 | because it would in some cases produce results inconsistent with | |
2279 | scm_i_inexact_truncate_quotient, such that x != q * y + r (not even | |
2280 | close). In particular, when x is very close to a multiple of y, | |
2281 | then r might be either 0.0 or sgn(x)*|y|, but those two cases must | |
2282 | correspond to different choices of q. If quotient chooses one and | |
2283 | remainder chooses the other, it would be bad. */ | |
2284 | if (SCM_UNLIKELY (y == 0)) | |
2285 | scm_num_overflow (s_scm_truncate_remainder); /* or return a NaN? */ | |
2286 | else | |
c251ab63 | 2287 | return scm_from_double (x - y * trunc (x / y)); |
8f9da340 MW |
2288 | } |
2289 | ||
2290 | static SCM | |
2291 | scm_i_exact_rational_truncate_remainder (SCM x, SCM y) | |
2292 | { | |
2293 | SCM xd = scm_denominator (x); | |
2294 | SCM yd = scm_denominator (y); | |
2295 | SCM r1 = scm_truncate_remainder (scm_product (scm_numerator (x), yd), | |
2296 | scm_product (scm_numerator (y), xd)); | |
2297 | return scm_divide (r1, scm_product (xd, yd)); | |
2298 | } | |
2299 | ||
2300 | ||
2301 | static void scm_i_inexact_truncate_divide (double x, double y, | |
2302 | SCM *qp, SCM *rp); | |
2303 | static void scm_i_exact_rational_truncate_divide (SCM x, SCM y, | |
2304 | SCM *qp, SCM *rp); | |
2305 | ||
2306 | SCM_PRIMITIVE_GENERIC (scm_i_truncate_divide, "truncate/", 2, 0, 0, | |
2307 | (SCM x, SCM y), | |
2308 | "Return the integer @var{q} and the real number @var{r}\n" | |
2309 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2310 | "and @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2311 | "@lisp\n" | |
2312 | "(truncate/ 123 10) @result{} 12 and 3\n" | |
2313 | "(truncate/ 123 -10) @result{} -12 and 3\n" | |
2314 | "(truncate/ -123 10) @result{} -12 and -3\n" | |
2315 | "(truncate/ -123 -10) @result{} 12 and -3\n" | |
2316 | "(truncate/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
2317 | "(truncate/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2318 | "@end lisp") | |
2319 | #define FUNC_NAME s_scm_i_truncate_divide | |
2320 | { | |
2321 | SCM q, r; | |
2322 | ||
2323 | scm_truncate_divide(x, y, &q, &r); | |
2324 | return scm_values (scm_list_2 (q, r)); | |
2325 | } | |
2326 | #undef FUNC_NAME | |
2327 | ||
2328 | #define s_scm_truncate_divide s_scm_i_truncate_divide | |
2329 | #define g_scm_truncate_divide g_scm_i_truncate_divide | |
2330 | ||
2331 | void | |
2332 | scm_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2333 | { | |
2334 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2335 | { | |
2336 | scm_t_inum xx = SCM_I_INUM (x); | |
2337 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2338 | { | |
2339 | scm_t_inum yy = SCM_I_INUM (y); | |
2340 | if (SCM_UNLIKELY (yy == 0)) | |
2341 | scm_num_overflow (s_scm_truncate_divide); | |
2342 | else | |
2343 | { | |
2344 | scm_t_inum qq = xx / yy; | |
2345 | scm_t_inum rr = xx % yy; | |
2346 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2347 | *qp = SCM_I_MAKINUM (qq); | |
2348 | else | |
2349 | *qp = scm_i_inum2big (qq); | |
2350 | *rp = SCM_I_MAKINUM (rr); | |
2351 | } | |
2352 | return; | |
2353 | } | |
2354 | else if (SCM_BIGP (y)) | |
2355 | { | |
2356 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2357 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2358 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2359 | { | |
2360 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2361 | scm_remember_upto_here_1 (y); | |
2362 | *qp = SCM_I_MAKINUM (-1); | |
2363 | *rp = SCM_INUM0; | |
2364 | } | |
2365 | else | |
2366 | { | |
2367 | *qp = SCM_INUM0; | |
2368 | *rp = x; | |
2369 | } | |
2370 | return; | |
2371 | } | |
2372 | else if (SCM_REALP (y)) | |
2373 | return scm_i_inexact_truncate_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2374 | else if (SCM_FRACTIONP (y)) | |
2375 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2376 | else | |
2377 | return two_valued_wta_dispatch_2 | |
2378 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2379 | s_scm_truncate_divide, qp, rp); | |
2380 | } | |
2381 | else if (SCM_BIGP (x)) | |
2382 | { | |
2383 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2384 | { | |
2385 | scm_t_inum yy = SCM_I_INUM (y); | |
2386 | if (SCM_UNLIKELY (yy == 0)) | |
2387 | scm_num_overflow (s_scm_truncate_divide); | |
2388 | else | |
2389 | { | |
2390 | SCM q = scm_i_mkbig (); | |
2391 | scm_t_inum rr; | |
2392 | if (yy > 0) | |
2393 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2394 | SCM_I_BIG_MPZ (x), yy); | |
2395 | else | |
2396 | { | |
2397 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2398 | SCM_I_BIG_MPZ (x), -yy); | |
2399 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2400 | } | |
2401 | rr *= mpz_sgn (SCM_I_BIG_MPZ (x)); | |
2402 | scm_remember_upto_here_1 (x); | |
2403 | *qp = scm_i_normbig (q); | |
2404 | *rp = SCM_I_MAKINUM (rr); | |
2405 | } | |
2406 | return; | |
2407 | } | |
2408 | else if (SCM_BIGP (y)) | |
2409 | { | |
2410 | SCM q = scm_i_mkbig (); | |
2411 | SCM r = scm_i_mkbig (); | |
2412 | mpz_tdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2413 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2414 | scm_remember_upto_here_2 (x, y); | |
2415 | *qp = scm_i_normbig (q); | |
2416 | *rp = scm_i_normbig (r); | |
2417 | } | |
2418 | else if (SCM_REALP (y)) | |
2419 | return scm_i_inexact_truncate_divide | |
2420 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2421 | else if (SCM_FRACTIONP (y)) | |
2422 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2423 | else | |
2424 | return two_valued_wta_dispatch_2 | |
2425 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2426 | s_scm_truncate_divide, qp, rp); | |
2427 | } | |
2428 | else if (SCM_REALP (x)) | |
2429 | { | |
2430 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2431 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2432 | return scm_i_inexact_truncate_divide | |
2433 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2434 | else | |
2435 | return two_valued_wta_dispatch_2 | |
2436 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2437 | s_scm_truncate_divide, qp, rp); | |
2438 | } | |
2439 | else if (SCM_FRACTIONP (x)) | |
2440 | { | |
2441 | if (SCM_REALP (y)) | |
2442 | return scm_i_inexact_truncate_divide | |
2443 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2444 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2445 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2446 | else | |
2447 | return two_valued_wta_dispatch_2 | |
2448 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2449 | s_scm_truncate_divide, qp, rp); | |
2450 | } | |
2451 | else | |
2452 | return two_valued_wta_dispatch_2 (g_scm_truncate_divide, x, y, SCM_ARG1, | |
2453 | s_scm_truncate_divide, qp, rp); | |
2454 | } | |
2455 | ||
2456 | static void | |
2457 | scm_i_inexact_truncate_divide (double x, double y, SCM *qp, SCM *rp) | |
2458 | { | |
2459 | if (SCM_UNLIKELY (y == 0)) | |
2460 | scm_num_overflow (s_scm_truncate_divide); /* or return a NaN? */ | |
2461 | else | |
2462 | { | |
c15fe499 MW |
2463 | double q = trunc (x / y); |
2464 | double r = x - q * y; | |
8f9da340 MW |
2465 | *qp = scm_from_double (q); |
2466 | *rp = scm_from_double (r); | |
2467 | } | |
2468 | } | |
2469 | ||
2470 | static void | |
2471 | scm_i_exact_rational_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2472 | { | |
2473 | SCM r1; | |
2474 | SCM xd = scm_denominator (x); | |
2475 | SCM yd = scm_denominator (y); | |
2476 | ||
2477 | scm_truncate_divide (scm_product (scm_numerator (x), yd), | |
2478 | scm_product (scm_numerator (y), xd), | |
2479 | qp, &r1); | |
2480 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2481 | } | |
2482 | ||
ff62c168 MW |
2483 | static SCM scm_i_inexact_centered_quotient (double x, double y); |
2484 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
03ddd15b | 2485 | static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y); |
ff62c168 | 2486 | |
8f9da340 MW |
2487 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, |
2488 | (SCM x, SCM y), | |
2489 | "Return the integer @var{q} such that\n" | |
2490 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
2491 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2492 | "@lisp\n" | |
2493 | "(centered-quotient 123 10) @result{} 12\n" | |
2494 | "(centered-quotient 123 -10) @result{} -12\n" | |
2495 | "(centered-quotient -123 10) @result{} -12\n" | |
2496 | "(centered-quotient -123 -10) @result{} 12\n" | |
2497 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
2498 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
2499 | "@end lisp") | |
2500 | #define FUNC_NAME s_scm_centered_quotient | |
2501 | { | |
2502 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2503 | { | |
2504 | scm_t_inum xx = SCM_I_INUM (x); | |
2505 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2506 | { | |
2507 | scm_t_inum yy = SCM_I_INUM (y); | |
2508 | if (SCM_UNLIKELY (yy == 0)) | |
2509 | scm_num_overflow (s_scm_centered_quotient); | |
2510 | else | |
2511 | { | |
2512 | scm_t_inum qq = xx / yy; | |
2513 | scm_t_inum rr = xx % yy; | |
2514 | if (SCM_LIKELY (xx > 0)) | |
2515 | { | |
2516 | if (SCM_LIKELY (yy > 0)) | |
2517 | { | |
2518 | if (rr >= (yy + 1) / 2) | |
2519 | qq++; | |
2520 | } | |
2521 | else | |
2522 | { | |
2523 | if (rr >= (1 - yy) / 2) | |
2524 | qq--; | |
2525 | } | |
2526 | } | |
2527 | else | |
2528 | { | |
2529 | if (SCM_LIKELY (yy > 0)) | |
2530 | { | |
2531 | if (rr < -yy / 2) | |
2532 | qq--; | |
2533 | } | |
2534 | else | |
2535 | { | |
2536 | if (rr < yy / 2) | |
2537 | qq++; | |
2538 | } | |
2539 | } | |
2540 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2541 | return SCM_I_MAKINUM (qq); | |
2542 | else | |
2543 | return scm_i_inum2big (qq); | |
2544 | } | |
2545 | } | |
2546 | else if (SCM_BIGP (y)) | |
2547 | { | |
2548 | /* Pass a denormalized bignum version of x (even though it | |
2549 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
2550 | return scm_i_bigint_centered_quotient (scm_i_long2big (xx), y); | |
2551 | } | |
2552 | else if (SCM_REALP (y)) | |
2553 | return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y)); | |
2554 | else if (SCM_FRACTIONP (y)) | |
2555 | return scm_i_exact_rational_centered_quotient (x, y); | |
2556 | else | |
2557 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2558 | s_scm_centered_quotient); | |
2559 | } | |
2560 | else if (SCM_BIGP (x)) | |
2561 | { | |
2562 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2563 | { | |
2564 | scm_t_inum yy = SCM_I_INUM (y); | |
2565 | if (SCM_UNLIKELY (yy == 0)) | |
2566 | scm_num_overflow (s_scm_centered_quotient); | |
2567 | else if (SCM_UNLIKELY (yy == 1)) | |
2568 | return x; | |
2569 | else | |
2570 | { | |
2571 | SCM q = scm_i_mkbig (); | |
2572 | scm_t_inum rr; | |
2573 | /* Arrange for rr to initially be non-positive, | |
2574 | because that simplifies the test to see | |
2575 | if it is within the needed bounds. */ | |
2576 | if (yy > 0) | |
2577 | { | |
2578 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2579 | SCM_I_BIG_MPZ (x), yy); | |
2580 | scm_remember_upto_here_1 (x); | |
2581 | if (rr < -yy / 2) | |
2582 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2583 | SCM_I_BIG_MPZ (q), 1); | |
2584 | } | |
2585 | else | |
2586 | { | |
2587 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2588 | SCM_I_BIG_MPZ (x), -yy); | |
2589 | scm_remember_upto_here_1 (x); | |
2590 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2591 | if (rr < yy / 2) | |
2592 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2593 | SCM_I_BIG_MPZ (q), 1); | |
2594 | } | |
2595 | return scm_i_normbig (q); | |
2596 | } | |
2597 | } | |
2598 | else if (SCM_BIGP (y)) | |
2599 | return scm_i_bigint_centered_quotient (x, y); | |
2600 | else if (SCM_REALP (y)) | |
2601 | return scm_i_inexact_centered_quotient | |
2602 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2603 | else if (SCM_FRACTIONP (y)) | |
2604 | return scm_i_exact_rational_centered_quotient (x, y); | |
2605 | else | |
2606 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2607 | s_scm_centered_quotient); | |
2608 | } | |
2609 | else if (SCM_REALP (x)) | |
2610 | { | |
2611 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2612 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2613 | return scm_i_inexact_centered_quotient | |
2614 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2615 | else | |
2616 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2617 | s_scm_centered_quotient); | |
2618 | } | |
2619 | else if (SCM_FRACTIONP (x)) | |
2620 | { | |
2621 | if (SCM_REALP (y)) | |
2622 | return scm_i_inexact_centered_quotient | |
2623 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2624 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2625 | return scm_i_exact_rational_centered_quotient (x, y); | |
2626 | else | |
2627 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2628 | s_scm_centered_quotient); | |
2629 | } | |
2630 | else | |
2631 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
2632 | s_scm_centered_quotient); | |
2633 | } | |
2634 | #undef FUNC_NAME | |
2635 | ||
2636 | static SCM | |
2637 | scm_i_inexact_centered_quotient (double x, double y) | |
2638 | { | |
2639 | if (SCM_LIKELY (y > 0)) | |
2640 | return scm_from_double (floor (x/y + 0.5)); | |
2641 | else if (SCM_LIKELY (y < 0)) | |
2642 | return scm_from_double (ceil (x/y - 0.5)); | |
2643 | else if (y == 0) | |
2644 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
2645 | else | |
2646 | return scm_nan (); | |
2647 | } | |
2648 | ||
2649 | /* Assumes that both x and y are bigints, though | |
2650 | x might be able to fit into a fixnum. */ | |
2651 | static SCM | |
2652 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
2653 | { | |
2654 | SCM q, r, min_r; | |
2655 | ||
2656 | /* Note that x might be small enough to fit into a | |
2657 | fixnum, so we must not let it escape into the wild */ | |
2658 | q = scm_i_mkbig (); | |
2659 | r = scm_i_mkbig (); | |
2660 | ||
2661 | /* min_r will eventually become -abs(y)/2 */ | |
2662 | min_r = scm_i_mkbig (); | |
2663 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2664 | SCM_I_BIG_MPZ (y), 1); | |
2665 | ||
2666 | /* Arrange for rr to initially be non-positive, | |
2667 | because that simplifies the test to see | |
2668 | if it is within the needed bounds. */ | |
2669 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2670 | { | |
2671 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2672 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2673 | scm_remember_upto_here_2 (x, y); | |
2674 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2675 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2676 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2677 | SCM_I_BIG_MPZ (q), 1); | |
2678 | } | |
2679 | else | |
2680 | { | |
2681 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2682 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2683 | scm_remember_upto_here_2 (x, y); | |
2684 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2685 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2686 | SCM_I_BIG_MPZ (q), 1); | |
2687 | } | |
2688 | scm_remember_upto_here_2 (r, min_r); | |
2689 | return scm_i_normbig (q); | |
2690 | } | |
2691 | ||
2692 | static SCM | |
2693 | scm_i_exact_rational_centered_quotient (SCM x, SCM y) | |
2694 | { | |
2695 | return scm_centered_quotient | |
2696 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2697 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2698 | } | |
2699 | ||
2700 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
2701 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
2702 | static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y); | |
2703 | ||
2704 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
2705 | (SCM x, SCM y), | |
2706 | "Return the real number @var{r} such that\n" | |
2707 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
2708 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2709 | "for some integer @var{q}.\n" | |
2710 | "@lisp\n" | |
2711 | "(centered-remainder 123 10) @result{} 3\n" | |
2712 | "(centered-remainder 123 -10) @result{} 3\n" | |
2713 | "(centered-remainder -123 10) @result{} -3\n" | |
2714 | "(centered-remainder -123 -10) @result{} -3\n" | |
2715 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
2716 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
2717 | "@end lisp") | |
2718 | #define FUNC_NAME s_scm_centered_remainder | |
2719 | { | |
2720 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2721 | { | |
2722 | scm_t_inum xx = SCM_I_INUM (x); | |
2723 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2724 | { | |
2725 | scm_t_inum yy = SCM_I_INUM (y); | |
2726 | if (SCM_UNLIKELY (yy == 0)) | |
2727 | scm_num_overflow (s_scm_centered_remainder); | |
2728 | else | |
2729 | { | |
2730 | scm_t_inum rr = xx % yy; | |
2731 | if (SCM_LIKELY (xx > 0)) | |
2732 | { | |
2733 | if (SCM_LIKELY (yy > 0)) | |
2734 | { | |
2735 | if (rr >= (yy + 1) / 2) | |
2736 | rr -= yy; | |
2737 | } | |
2738 | else | |
2739 | { | |
2740 | if (rr >= (1 - yy) / 2) | |
2741 | rr += yy; | |
2742 | } | |
2743 | } | |
2744 | else | |
2745 | { | |
2746 | if (SCM_LIKELY (yy > 0)) | |
2747 | { | |
2748 | if (rr < -yy / 2) | |
2749 | rr += yy; | |
2750 | } | |
2751 | else | |
2752 | { | |
2753 | if (rr < yy / 2) | |
2754 | rr -= yy; | |
2755 | } | |
2756 | } | |
2757 | return SCM_I_MAKINUM (rr); | |
2758 | } | |
2759 | } | |
2760 | else if (SCM_BIGP (y)) | |
2761 | { | |
2762 | /* Pass a denormalized bignum version of x (even though it | |
2763 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
2764 | return scm_i_bigint_centered_remainder (scm_i_long2big (xx), y); | |
2765 | } | |
2766 | else if (SCM_REALP (y)) | |
2767 | return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y)); | |
2768 | else if (SCM_FRACTIONP (y)) | |
2769 | return scm_i_exact_rational_centered_remainder (x, y); | |
2770 | else | |
2771 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2772 | s_scm_centered_remainder); | |
2773 | } | |
2774 | else if (SCM_BIGP (x)) | |
2775 | { | |
2776 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2777 | { | |
2778 | scm_t_inum yy = SCM_I_INUM (y); | |
2779 | if (SCM_UNLIKELY (yy == 0)) | |
2780 | scm_num_overflow (s_scm_centered_remainder); | |
2781 | else | |
2782 | { | |
2783 | scm_t_inum rr; | |
2784 | /* Arrange for rr to initially be non-positive, | |
2785 | because that simplifies the test to see | |
2786 | if it is within the needed bounds. */ | |
2787 | if (yy > 0) | |
2788 | { | |
2789 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
2790 | scm_remember_upto_here_1 (x); | |
2791 | if (rr < -yy / 2) | |
2792 | rr += yy; | |
2793 | } | |
2794 | else | |
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 | return SCM_I_MAKINUM (rr); | |
2802 | } | |
2803 | } | |
2804 | else if (SCM_BIGP (y)) | |
2805 | return scm_i_bigint_centered_remainder (x, y); | |
2806 | else if (SCM_REALP (y)) | |
2807 | return scm_i_inexact_centered_remainder | |
2808 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2809 | else if (SCM_FRACTIONP (y)) | |
2810 | return scm_i_exact_rational_centered_remainder (x, y); | |
2811 | else | |
2812 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2813 | s_scm_centered_remainder); | |
2814 | } | |
2815 | else if (SCM_REALP (x)) | |
2816 | { | |
2817 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2818 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2819 | return scm_i_inexact_centered_remainder | |
2820 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2821 | else | |
2822 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2823 | s_scm_centered_remainder); | |
2824 | } | |
2825 | else if (SCM_FRACTIONP (x)) | |
2826 | { | |
2827 | if (SCM_REALP (y)) | |
2828 | return scm_i_inexact_centered_remainder | |
2829 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2830 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2831 | return scm_i_exact_rational_centered_remainder (x, y); | |
2832 | else | |
2833 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2834 | s_scm_centered_remainder); | |
2835 | } | |
2836 | else | |
2837 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
2838 | s_scm_centered_remainder); | |
2839 | } | |
2840 | #undef FUNC_NAME | |
2841 | ||
2842 | static SCM | |
2843 | scm_i_inexact_centered_remainder (double x, double y) | |
2844 | { | |
2845 | double q; | |
2846 | ||
2847 | /* Although it would be more efficient to use fmod here, we can't | |
2848 | because it would in some cases produce results inconsistent with | |
2849 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
2850 | close). In particular, when x-y/2 is very close to a multiple of | |
2851 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
2852 | two cases must correspond to different choices of q. If quotient | |
2853 | chooses one and remainder chooses the other, it would be bad. */ | |
2854 | if (SCM_LIKELY (y > 0)) | |
2855 | q = floor (x/y + 0.5); | |
2856 | else if (SCM_LIKELY (y < 0)) | |
2857 | q = ceil (x/y - 0.5); | |
2858 | else if (y == 0) | |
2859 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
2860 | else | |
2861 | return scm_nan (); | |
2862 | return scm_from_double (x - q * y); | |
2863 | } | |
2864 | ||
2865 | /* Assumes that both x and y are bigints, though | |
2866 | x might be able to fit into a fixnum. */ | |
2867 | static SCM | |
2868 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
2869 | { | |
2870 | SCM r, min_r; | |
2871 | ||
2872 | /* Note that x might be small enough to fit into a | |
2873 | fixnum, so we must not let it escape into the wild */ | |
2874 | r = scm_i_mkbig (); | |
2875 | ||
2876 | /* min_r will eventually become -abs(y)/2 */ | |
2877 | min_r = scm_i_mkbig (); | |
2878 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2879 | SCM_I_BIG_MPZ (y), 1); | |
2880 | ||
2881 | /* Arrange for rr to initially be non-positive, | |
2882 | because that simplifies the test to see | |
2883 | if it is within the needed bounds. */ | |
2884 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2885 | { | |
2886 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
2887 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2888 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2889 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2890 | mpz_add (SCM_I_BIG_MPZ (r), | |
2891 | SCM_I_BIG_MPZ (r), | |
2892 | SCM_I_BIG_MPZ (y)); | |
2893 | } | |
2894 | else | |
2895 | { | |
2896 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
2897 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2898 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2899 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2900 | SCM_I_BIG_MPZ (r), | |
2901 | SCM_I_BIG_MPZ (y)); | |
2902 | } | |
2903 | scm_remember_upto_here_2 (x, y); | |
2904 | return scm_i_normbig (r); | |
2905 | } | |
2906 | ||
2907 | static SCM | |
2908 | scm_i_exact_rational_centered_remainder (SCM x, SCM y) | |
2909 | { | |
2910 | SCM xd = scm_denominator (x); | |
2911 | SCM yd = scm_denominator (y); | |
2912 | SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd), | |
2913 | scm_product (scm_numerator (y), xd)); | |
2914 | return scm_divide (r1, scm_product (xd, yd)); | |
2915 | } | |
2916 | ||
2917 | ||
2918 | static void scm_i_inexact_centered_divide (double x, double y, | |
2919 | SCM *qp, SCM *rp); | |
2920 | static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
2921 | static void scm_i_exact_rational_centered_divide (SCM x, SCM y, | |
2922 | SCM *qp, SCM *rp); | |
2923 | ||
2924 | SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0, | |
2925 | (SCM x, SCM y), | |
2926 | "Return the integer @var{q} and the real number @var{r}\n" | |
2927 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2928 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2929 | "@lisp\n" | |
2930 | "(centered/ 123 10) @result{} 12 and 3\n" | |
2931 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
2932 | "(centered/ -123 10) @result{} -12 and -3\n" | |
2933 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
2934 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2935 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
2936 | "@end lisp") | |
2937 | #define FUNC_NAME s_scm_i_centered_divide | |
2938 | { | |
2939 | SCM q, r; | |
2940 | ||
2941 | scm_centered_divide(x, y, &q, &r); | |
2942 | return scm_values (scm_list_2 (q, r)); | |
2943 | } | |
2944 | #undef FUNC_NAME | |
2945 | ||
2946 | #define s_scm_centered_divide s_scm_i_centered_divide | |
2947 | #define g_scm_centered_divide g_scm_i_centered_divide | |
2948 | ||
2949 | void | |
2950 | scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2951 | { | |
2952 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2953 | { | |
2954 | scm_t_inum xx = SCM_I_INUM (x); | |
2955 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2956 | { | |
2957 | scm_t_inum yy = SCM_I_INUM (y); | |
2958 | if (SCM_UNLIKELY (yy == 0)) | |
2959 | scm_num_overflow (s_scm_centered_divide); | |
2960 | else | |
2961 | { | |
2962 | scm_t_inum qq = xx / yy; | |
2963 | scm_t_inum rr = xx % yy; | |
2964 | if (SCM_LIKELY (xx > 0)) | |
2965 | { | |
2966 | if (SCM_LIKELY (yy > 0)) | |
2967 | { | |
2968 | if (rr >= (yy + 1) / 2) | |
2969 | { qq++; rr -= yy; } | |
2970 | } | |
2971 | else | |
2972 | { | |
2973 | if (rr >= (1 - yy) / 2) | |
2974 | { qq--; rr += yy; } | |
2975 | } | |
2976 | } | |
2977 | else | |
2978 | { | |
2979 | if (SCM_LIKELY (yy > 0)) | |
2980 | { | |
2981 | if (rr < -yy / 2) | |
2982 | { qq--; rr += yy; } | |
2983 | } | |
2984 | else | |
2985 | { | |
2986 | if (rr < yy / 2) | |
2987 | { qq++; rr -= yy; } | |
2988 | } | |
2989 | } | |
2990 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2991 | *qp = SCM_I_MAKINUM (qq); | |
2992 | else | |
2993 | *qp = scm_i_inum2big (qq); | |
2994 | *rp = SCM_I_MAKINUM (rr); | |
2995 | } | |
2996 | return; | |
2997 | } | |
2998 | else if (SCM_BIGP (y)) | |
2999 | { | |
3000 | /* Pass a denormalized bignum version of x (even though it | |
3001 | can fit in a fixnum) to scm_i_bigint_centered_divide */ | |
3002 | return scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp); | |
3003 | } | |
3004 | else if (SCM_REALP (y)) | |
3005 | return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
3006 | else if (SCM_FRACTIONP (y)) | |
3007 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3008 | else | |
3009 | return two_valued_wta_dispatch_2 | |
3010 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3011 | s_scm_centered_divide, qp, rp); | |
3012 | } | |
3013 | else if (SCM_BIGP (x)) | |
3014 | { | |
3015 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3016 | { | |
3017 | scm_t_inum yy = SCM_I_INUM (y); | |
3018 | if (SCM_UNLIKELY (yy == 0)) | |
3019 | scm_num_overflow (s_scm_centered_divide); | |
3020 | else | |
3021 | { | |
3022 | SCM q = scm_i_mkbig (); | |
3023 | scm_t_inum rr; | |
3024 | /* Arrange for rr to initially be non-positive, | |
3025 | because that simplifies the test to see | |
3026 | if it is within the needed bounds. */ | |
3027 | if (yy > 0) | |
3028 | { | |
3029 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3030 | SCM_I_BIG_MPZ (x), yy); | |
3031 | scm_remember_upto_here_1 (x); | |
3032 | if (rr < -yy / 2) | |
3033 | { | |
3034 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3035 | SCM_I_BIG_MPZ (q), 1); | |
3036 | rr += yy; | |
3037 | } | |
3038 | } | |
3039 | else | |
3040 | { | |
3041 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3042 | SCM_I_BIG_MPZ (x), -yy); | |
3043 | scm_remember_upto_here_1 (x); | |
3044 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
3045 | if (rr < yy / 2) | |
3046 | { | |
3047 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3048 | SCM_I_BIG_MPZ (q), 1); | |
3049 | rr -= yy; | |
3050 | } | |
3051 | } | |
3052 | *qp = scm_i_normbig (q); | |
3053 | *rp = SCM_I_MAKINUM (rr); | |
3054 | } | |
3055 | return; | |
3056 | } | |
3057 | else if (SCM_BIGP (y)) | |
3058 | return scm_i_bigint_centered_divide (x, y, qp, rp); | |
3059 | else if (SCM_REALP (y)) | |
3060 | return scm_i_inexact_centered_divide | |
3061 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
3062 | else if (SCM_FRACTIONP (y)) | |
3063 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3064 | else | |
3065 | return two_valued_wta_dispatch_2 | |
3066 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3067 | s_scm_centered_divide, qp, rp); | |
3068 | } | |
3069 | else if (SCM_REALP (x)) | |
3070 | { | |
3071 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3072 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3073 | return scm_i_inexact_centered_divide | |
3074 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
3075 | else | |
3076 | return two_valued_wta_dispatch_2 | |
3077 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3078 | s_scm_centered_divide, qp, rp); | |
3079 | } | |
3080 | else if (SCM_FRACTIONP (x)) | |
3081 | { | |
3082 | if (SCM_REALP (y)) | |
3083 | return scm_i_inexact_centered_divide | |
3084 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
3085 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3086 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3087 | else | |
3088 | return two_valued_wta_dispatch_2 | |
3089 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3090 | s_scm_centered_divide, qp, rp); | |
3091 | } | |
3092 | else | |
3093 | return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1, | |
3094 | s_scm_centered_divide, qp, rp); | |
3095 | } | |
3096 | ||
3097 | static void | |
3098 | scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp) | |
3099 | { | |
3100 | double q, r; | |
3101 | ||
3102 | if (SCM_LIKELY (y > 0)) | |
3103 | q = floor (x/y + 0.5); | |
3104 | else if (SCM_LIKELY (y < 0)) | |
3105 | q = ceil (x/y - 0.5); | |
3106 | else if (y == 0) | |
3107 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ | |
3108 | else | |
3109 | q = guile_NaN; | |
3110 | r = x - q * y; | |
3111 | *qp = scm_from_double (q); | |
3112 | *rp = scm_from_double (r); | |
3113 | } | |
3114 | ||
3115 | /* Assumes that both x and y are bigints, though | |
3116 | x might be able to fit into a fixnum. */ | |
3117 | static void | |
3118 | scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3119 | { | |
3120 | SCM q, r, min_r; | |
3121 | ||
3122 | /* Note that x might be small enough to fit into a | |
3123 | fixnum, so we must not let it escape into the wild */ | |
3124 | q = scm_i_mkbig (); | |
3125 | r = scm_i_mkbig (); | |
3126 | ||
3127 | /* min_r will eventually become -abs(y/2) */ | |
3128 | min_r = scm_i_mkbig (); | |
3129 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3130 | SCM_I_BIG_MPZ (y), 1); | |
3131 | ||
3132 | /* Arrange for rr to initially be non-positive, | |
3133 | because that simplifies the test to see | |
3134 | if it is within the needed bounds. */ | |
3135 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3136 | { | |
3137 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3138 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3139 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3140 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3141 | { | |
3142 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3143 | SCM_I_BIG_MPZ (q), 1); | |
3144 | mpz_add (SCM_I_BIG_MPZ (r), | |
3145 | SCM_I_BIG_MPZ (r), | |
3146 | SCM_I_BIG_MPZ (y)); | |
3147 | } | |
3148 | } | |
3149 | else | |
3150 | { | |
3151 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3152 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3153 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3154 | { | |
3155 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3156 | SCM_I_BIG_MPZ (q), 1); | |
3157 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3158 | SCM_I_BIG_MPZ (r), | |
3159 | SCM_I_BIG_MPZ (y)); | |
3160 | } | |
3161 | } | |
3162 | scm_remember_upto_here_2 (x, y); | |
3163 | *qp = scm_i_normbig (q); | |
3164 | *rp = scm_i_normbig (r); | |
3165 | } | |
3166 | ||
3167 | static void | |
3168 | scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3169 | { | |
3170 | SCM r1; | |
3171 | SCM xd = scm_denominator (x); | |
3172 | SCM yd = scm_denominator (y); | |
3173 | ||
3174 | scm_centered_divide (scm_product (scm_numerator (x), yd), | |
3175 | scm_product (scm_numerator (y), xd), | |
3176 | qp, &r1); | |
3177 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
3178 | } | |
3179 | ||
3180 | static SCM scm_i_inexact_round_quotient (double x, double y); | |
3181 | static SCM scm_i_bigint_round_quotient (SCM x, SCM y); | |
3182 | static SCM scm_i_exact_rational_round_quotient (SCM x, SCM y); | |
3183 | ||
3184 | SCM_PRIMITIVE_GENERIC (scm_round_quotient, "round-quotient", 2, 0, 0, | |
ff62c168 | 3185 | (SCM x, SCM y), |
8f9da340 MW |
3186 | "Return @math{@var{x} / @var{y}} to the nearest integer,\n" |
3187 | "with ties going to the nearest even integer.\n" | |
ff62c168 | 3188 | "@lisp\n" |
8f9da340 MW |
3189 | "(round-quotient 123 10) @result{} 12\n" |
3190 | "(round-quotient 123 -10) @result{} -12\n" | |
3191 | "(round-quotient -123 10) @result{} -12\n" | |
3192 | "(round-quotient -123 -10) @result{} 12\n" | |
3193 | "(round-quotient 125 10) @result{} 12\n" | |
3194 | "(round-quotient 127 10) @result{} 13\n" | |
3195 | "(round-quotient 135 10) @result{} 14\n" | |
3196 | "(round-quotient -123.2 -63.5) @result{} 2.0\n" | |
3197 | "(round-quotient 16/3 -10/7) @result{} -4\n" | |
ff62c168 | 3198 | "@end lisp") |
8f9da340 | 3199 | #define FUNC_NAME s_scm_round_quotient |
ff62c168 MW |
3200 | { |
3201 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3202 | { | |
4a46bc2a | 3203 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3204 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3205 | { | |
3206 | scm_t_inum yy = SCM_I_INUM (y); | |
3207 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3208 | scm_num_overflow (s_scm_round_quotient); |
ff62c168 MW |
3209 | else |
3210 | { | |
ff62c168 | 3211 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3212 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3213 | scm_t_inum ay = yy; |
3214 | scm_t_inum r2 = 2 * rr; | |
3215 | ||
3216 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3217 | { |
8f9da340 MW |
3218 | ay = -ay; |
3219 | r2 = -r2; | |
3220 | } | |
3221 | ||
3222 | if (qq & 1L) | |
3223 | { | |
3224 | if (r2 >= ay) | |
3225 | qq++; | |
3226 | else if (r2 <= -ay) | |
3227 | qq--; | |
ff62c168 MW |
3228 | } |
3229 | else | |
3230 | { | |
8f9da340 MW |
3231 | if (r2 > ay) |
3232 | qq++; | |
3233 | else if (r2 < -ay) | |
3234 | qq--; | |
ff62c168 | 3235 | } |
4a46bc2a MW |
3236 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
3237 | return SCM_I_MAKINUM (qq); | |
3238 | else | |
3239 | return scm_i_inum2big (qq); | |
ff62c168 MW |
3240 | } |
3241 | } | |
3242 | else if (SCM_BIGP (y)) | |
3243 | { | |
3244 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3245 | can fit in a fixnum) to scm_i_bigint_round_quotient */ |
3246 | return scm_i_bigint_round_quotient (scm_i_long2big (xx), y); | |
ff62c168 MW |
3247 | } |
3248 | else if (SCM_REALP (y)) | |
8f9da340 | 3249 | return scm_i_inexact_round_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3250 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3251 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3252 | else |
8f9da340 MW |
3253 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3254 | s_scm_round_quotient); | |
ff62c168 MW |
3255 | } |
3256 | else if (SCM_BIGP (x)) | |
3257 | { | |
3258 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3259 | { | |
3260 | scm_t_inum yy = SCM_I_INUM (y); | |
3261 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3262 | scm_num_overflow (s_scm_round_quotient); |
4a46bc2a MW |
3263 | else if (SCM_UNLIKELY (yy == 1)) |
3264 | return x; | |
ff62c168 MW |
3265 | else |
3266 | { | |
3267 | SCM q = scm_i_mkbig (); | |
3268 | scm_t_inum rr; | |
8f9da340 MW |
3269 | int needs_adjustment; |
3270 | ||
ff62c168 MW |
3271 | if (yy > 0) |
3272 | { | |
8f9da340 MW |
3273 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3274 | SCM_I_BIG_MPZ (x), yy); | |
3275 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3276 | needs_adjustment = (2*rr >= yy); | |
3277 | else | |
3278 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3279 | } |
3280 | else | |
3281 | { | |
3282 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3283 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3284 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3285 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3286 | needs_adjustment = (2*rr <= yy); | |
3287 | else | |
3288 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3289 | } |
8f9da340 MW |
3290 | scm_remember_upto_here_1 (x); |
3291 | if (needs_adjustment) | |
3292 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
ff62c168 MW |
3293 | return scm_i_normbig (q); |
3294 | } | |
3295 | } | |
3296 | else if (SCM_BIGP (y)) | |
8f9da340 | 3297 | return scm_i_bigint_round_quotient (x, y); |
ff62c168 | 3298 | else if (SCM_REALP (y)) |
8f9da340 | 3299 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3300 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3301 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3302 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3303 | else |
8f9da340 MW |
3304 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3305 | s_scm_round_quotient); | |
ff62c168 MW |
3306 | } |
3307 | else if (SCM_REALP (x)) | |
3308 | { | |
3309 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3310 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3311 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3312 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3313 | else | |
8f9da340 MW |
3314 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3315 | s_scm_round_quotient); | |
ff62c168 MW |
3316 | } |
3317 | else if (SCM_FRACTIONP (x)) | |
3318 | { | |
3319 | if (SCM_REALP (y)) | |
8f9da340 | 3320 | return scm_i_inexact_round_quotient |
ff62c168 | 3321 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3322 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3323 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3324 | else |
8f9da340 MW |
3325 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3326 | s_scm_round_quotient); | |
ff62c168 MW |
3327 | } |
3328 | else | |
8f9da340 MW |
3329 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG1, |
3330 | s_scm_round_quotient); | |
ff62c168 MW |
3331 | } |
3332 | #undef FUNC_NAME | |
3333 | ||
3334 | static SCM | |
8f9da340 | 3335 | scm_i_inexact_round_quotient (double x, double y) |
ff62c168 | 3336 | { |
8f9da340 MW |
3337 | if (SCM_UNLIKELY (y == 0)) |
3338 | scm_num_overflow (s_scm_round_quotient); /* or return a NaN? */ | |
ff62c168 | 3339 | else |
8f9da340 | 3340 | return scm_from_double (scm_c_round (x / y)); |
ff62c168 MW |
3341 | } |
3342 | ||
3343 | /* Assumes that both x and y are bigints, though | |
3344 | x might be able to fit into a fixnum. */ | |
3345 | static SCM | |
8f9da340 | 3346 | scm_i_bigint_round_quotient (SCM x, SCM y) |
ff62c168 | 3347 | { |
8f9da340 MW |
3348 | SCM q, r, r2; |
3349 | int cmp, needs_adjustment; | |
ff62c168 MW |
3350 | |
3351 | /* Note that x might be small enough to fit into a | |
3352 | fixnum, so we must not let it escape into the wild */ | |
3353 | q = scm_i_mkbig (); | |
3354 | r = scm_i_mkbig (); | |
8f9da340 | 3355 | r2 = scm_i_mkbig (); |
ff62c168 | 3356 | |
8f9da340 MW |
3357 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3358 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3359 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
3360 | scm_remember_upto_here_2 (x, r); | |
ff62c168 | 3361 | |
8f9da340 MW |
3362 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3363 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3364 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3365 | else |
8f9da340 MW |
3366 | needs_adjustment = (cmp > 0); |
3367 | scm_remember_upto_here_2 (r2, y); | |
3368 | ||
3369 | if (needs_adjustment) | |
3370 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3371 | ||
ff62c168 MW |
3372 | return scm_i_normbig (q); |
3373 | } | |
3374 | ||
ff62c168 | 3375 | static SCM |
8f9da340 | 3376 | scm_i_exact_rational_round_quotient (SCM x, SCM y) |
ff62c168 | 3377 | { |
8f9da340 | 3378 | return scm_round_quotient |
03ddd15b MW |
3379 | (scm_product (scm_numerator (x), scm_denominator (y)), |
3380 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
3381 | } |
3382 | ||
8f9da340 MW |
3383 | static SCM scm_i_inexact_round_remainder (double x, double y); |
3384 | static SCM scm_i_bigint_round_remainder (SCM x, SCM y); | |
3385 | static SCM scm_i_exact_rational_round_remainder (SCM x, SCM y); | |
ff62c168 | 3386 | |
8f9da340 | 3387 | SCM_PRIMITIVE_GENERIC (scm_round_remainder, "round-remainder", 2, 0, 0, |
ff62c168 MW |
3388 | (SCM x, SCM y), |
3389 | "Return the real number @var{r} such that\n" | |
8f9da340 MW |
3390 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}, where\n" |
3391 | "@var{q} is @math{@var{x} / @var{y}} rounded to the\n" | |
3392 | "nearest integer, with ties going to the nearest\n" | |
3393 | "even integer.\n" | |
ff62c168 | 3394 | "@lisp\n" |
8f9da340 MW |
3395 | "(round-remainder 123 10) @result{} 3\n" |
3396 | "(round-remainder 123 -10) @result{} 3\n" | |
3397 | "(round-remainder -123 10) @result{} -3\n" | |
3398 | "(round-remainder -123 -10) @result{} -3\n" | |
3399 | "(round-remainder 125 10) @result{} 5\n" | |
3400 | "(round-remainder 127 10) @result{} -3\n" | |
3401 | "(round-remainder 135 10) @result{} -5\n" | |
3402 | "(round-remainder -123.2 -63.5) @result{} 3.8\n" | |
3403 | "(round-remainder 16/3 -10/7) @result{} -8/21\n" | |
ff62c168 | 3404 | "@end lisp") |
8f9da340 | 3405 | #define FUNC_NAME s_scm_round_remainder |
ff62c168 MW |
3406 | { |
3407 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3408 | { | |
4a46bc2a | 3409 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3410 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3411 | { | |
3412 | scm_t_inum yy = SCM_I_INUM (y); | |
3413 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3414 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3415 | else |
3416 | { | |
8f9da340 | 3417 | scm_t_inum qq = xx / yy; |
ff62c168 | 3418 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3419 | scm_t_inum ay = yy; |
3420 | scm_t_inum r2 = 2 * rr; | |
3421 | ||
3422 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3423 | { |
8f9da340 MW |
3424 | ay = -ay; |
3425 | r2 = -r2; | |
3426 | } | |
3427 | ||
3428 | if (qq & 1L) | |
3429 | { | |
3430 | if (r2 >= ay) | |
3431 | rr -= yy; | |
3432 | else if (r2 <= -ay) | |
3433 | rr += yy; | |
ff62c168 MW |
3434 | } |
3435 | else | |
3436 | { | |
8f9da340 MW |
3437 | if (r2 > ay) |
3438 | rr -= yy; | |
3439 | else if (r2 < -ay) | |
3440 | rr += yy; | |
ff62c168 MW |
3441 | } |
3442 | return SCM_I_MAKINUM (rr); | |
3443 | } | |
3444 | } | |
3445 | else if (SCM_BIGP (y)) | |
3446 | { | |
3447 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3448 | can fit in a fixnum) to scm_i_bigint_round_remainder */ |
3449 | return scm_i_bigint_round_remainder | |
3450 | (scm_i_long2big (xx), y); | |
ff62c168 MW |
3451 | } |
3452 | else if (SCM_REALP (y)) | |
8f9da340 | 3453 | return scm_i_inexact_round_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3454 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3455 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3456 | else |
8f9da340 MW |
3457 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3458 | s_scm_round_remainder); | |
ff62c168 MW |
3459 | } |
3460 | else if (SCM_BIGP (x)) | |
3461 | { | |
3462 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3463 | { | |
3464 | scm_t_inum yy = SCM_I_INUM (y); | |
3465 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3466 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3467 | else |
3468 | { | |
8f9da340 | 3469 | SCM q = scm_i_mkbig (); |
ff62c168 | 3470 | scm_t_inum rr; |
8f9da340 MW |
3471 | int needs_adjustment; |
3472 | ||
ff62c168 MW |
3473 | if (yy > 0) |
3474 | { | |
8f9da340 MW |
3475 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3476 | SCM_I_BIG_MPZ (x), yy); | |
3477 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3478 | needs_adjustment = (2*rr >= yy); | |
3479 | else | |
3480 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3481 | } |
3482 | else | |
3483 | { | |
8f9da340 MW |
3484 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
3485 | SCM_I_BIG_MPZ (x), -yy); | |
3486 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3487 | needs_adjustment = (2*rr <= yy); | |
3488 | else | |
3489 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3490 | } |
8f9da340 MW |
3491 | scm_remember_upto_here_2 (x, q); |
3492 | if (needs_adjustment) | |
3493 | rr -= yy; | |
ff62c168 MW |
3494 | return SCM_I_MAKINUM (rr); |
3495 | } | |
3496 | } | |
3497 | else if (SCM_BIGP (y)) | |
8f9da340 | 3498 | return scm_i_bigint_round_remainder (x, y); |
ff62c168 | 3499 | else if (SCM_REALP (y)) |
8f9da340 | 3500 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3501 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3502 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3503 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3504 | else |
8f9da340 MW |
3505 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3506 | s_scm_round_remainder); | |
ff62c168 MW |
3507 | } |
3508 | else if (SCM_REALP (x)) | |
3509 | { | |
3510 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3511 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3512 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3513 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3514 | else | |
8f9da340 MW |
3515 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3516 | s_scm_round_remainder); | |
ff62c168 MW |
3517 | } |
3518 | else if (SCM_FRACTIONP (x)) | |
3519 | { | |
3520 | if (SCM_REALP (y)) | |
8f9da340 | 3521 | return scm_i_inexact_round_remainder |
ff62c168 | 3522 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3523 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3524 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3525 | else |
8f9da340 MW |
3526 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3527 | s_scm_round_remainder); | |
ff62c168 MW |
3528 | } |
3529 | else | |
8f9da340 MW |
3530 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG1, |
3531 | s_scm_round_remainder); | |
ff62c168 MW |
3532 | } |
3533 | #undef FUNC_NAME | |
3534 | ||
3535 | static SCM | |
8f9da340 | 3536 | scm_i_inexact_round_remainder (double x, double y) |
ff62c168 | 3537 | { |
ff62c168 MW |
3538 | /* Although it would be more efficient to use fmod here, we can't |
3539 | because it would in some cases produce results inconsistent with | |
8f9da340 | 3540 | scm_i_inexact_round_quotient, such that x != r + q * y (not even |
ff62c168 | 3541 | close). In particular, when x-y/2 is very close to a multiple of |
8f9da340 MW |
3542 | y, then r might be either -abs(y/2) or abs(y/2), but those two |
3543 | cases must correspond to different choices of q. If quotient | |
ff62c168 | 3544 | chooses one and remainder chooses the other, it would be bad. */ |
8f9da340 MW |
3545 | |
3546 | if (SCM_UNLIKELY (y == 0)) | |
3547 | scm_num_overflow (s_scm_round_remainder); /* or return a NaN? */ | |
ff62c168 | 3548 | else |
8f9da340 MW |
3549 | { |
3550 | double q = scm_c_round (x / y); | |
3551 | return scm_from_double (x - q * y); | |
3552 | } | |
ff62c168 MW |
3553 | } |
3554 | ||
3555 | /* Assumes that both x and y are bigints, though | |
3556 | x might be able to fit into a fixnum. */ | |
3557 | static SCM | |
8f9da340 | 3558 | scm_i_bigint_round_remainder (SCM x, SCM y) |
ff62c168 | 3559 | { |
8f9da340 MW |
3560 | SCM q, r, r2; |
3561 | int cmp, needs_adjustment; | |
ff62c168 MW |
3562 | |
3563 | /* Note that x might be small enough to fit into a | |
3564 | fixnum, so we must not let it escape into the wild */ | |
8f9da340 | 3565 | q = scm_i_mkbig (); |
ff62c168 | 3566 | r = scm_i_mkbig (); |
8f9da340 | 3567 | r2 = scm_i_mkbig (); |
ff62c168 | 3568 | |
8f9da340 MW |
3569 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3570 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3571 | scm_remember_upto_here_1 (x); | |
3572 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3573 | |
8f9da340 MW |
3574 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3575 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3576 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3577 | else |
8f9da340 MW |
3578 | needs_adjustment = (cmp > 0); |
3579 | scm_remember_upto_here_2 (q, r2); | |
3580 | ||
3581 | if (needs_adjustment) | |
3582 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
3583 | ||
3584 | scm_remember_upto_here_1 (y); | |
ff62c168 MW |
3585 | return scm_i_normbig (r); |
3586 | } | |
3587 | ||
ff62c168 | 3588 | static SCM |
8f9da340 | 3589 | scm_i_exact_rational_round_remainder (SCM x, SCM y) |
ff62c168 | 3590 | { |
03ddd15b MW |
3591 | SCM xd = scm_denominator (x); |
3592 | SCM yd = scm_denominator (y); | |
8f9da340 MW |
3593 | SCM r1 = scm_round_remainder (scm_product (scm_numerator (x), yd), |
3594 | scm_product (scm_numerator (y), xd)); | |
03ddd15b | 3595 | return scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3596 | } |
3597 | ||
3598 | ||
8f9da340 MW |
3599 | static void scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp); |
3600 | static void scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3601 | static void scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
ff62c168 | 3602 | |
8f9da340 | 3603 | SCM_PRIMITIVE_GENERIC (scm_i_round_divide, "round/", 2, 0, 0, |
ff62c168 MW |
3604 | (SCM x, SCM y), |
3605 | "Return the integer @var{q} and the real number @var{r}\n" | |
3606 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
8f9da340 MW |
3607 | "and @var{q} is @math{@var{x} / @var{y}} rounded to the\n" |
3608 | "nearest integer, with ties going to the nearest even integer.\n" | |
ff62c168 | 3609 | "@lisp\n" |
8f9da340 MW |
3610 | "(round/ 123 10) @result{} 12 and 3\n" |
3611 | "(round/ 123 -10) @result{} -12 and 3\n" | |
3612 | "(round/ -123 10) @result{} -12 and -3\n" | |
3613 | "(round/ -123 -10) @result{} 12 and -3\n" | |
3614 | "(round/ 125 10) @result{} 12 and 5\n" | |
3615 | "(round/ 127 10) @result{} 13 and -3\n" | |
3616 | "(round/ 135 10) @result{} 14 and -5\n" | |
3617 | "(round/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3618 | "(round/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
ff62c168 | 3619 | "@end lisp") |
8f9da340 | 3620 | #define FUNC_NAME s_scm_i_round_divide |
5fbf680b MW |
3621 | { |
3622 | SCM q, r; | |
3623 | ||
8f9da340 | 3624 | scm_round_divide(x, y, &q, &r); |
5fbf680b MW |
3625 | return scm_values (scm_list_2 (q, r)); |
3626 | } | |
3627 | #undef FUNC_NAME | |
3628 | ||
8f9da340 MW |
3629 | #define s_scm_round_divide s_scm_i_round_divide |
3630 | #define g_scm_round_divide g_scm_i_round_divide | |
5fbf680b MW |
3631 | |
3632 | void | |
8f9da340 | 3633 | scm_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 MW |
3634 | { |
3635 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3636 | { | |
4a46bc2a | 3637 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3638 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3639 | { | |
3640 | scm_t_inum yy = SCM_I_INUM (y); | |
3641 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3642 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3643 | else |
3644 | { | |
ff62c168 | 3645 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3646 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3647 | scm_t_inum ay = yy; |
3648 | scm_t_inum r2 = 2 * rr; | |
3649 | ||
3650 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3651 | { |
8f9da340 MW |
3652 | ay = -ay; |
3653 | r2 = -r2; | |
3654 | } | |
3655 | ||
3656 | if (qq & 1L) | |
3657 | { | |
3658 | if (r2 >= ay) | |
3659 | { qq++; rr -= yy; } | |
3660 | else if (r2 <= -ay) | |
3661 | { qq--; rr += yy; } | |
ff62c168 MW |
3662 | } |
3663 | else | |
3664 | { | |
8f9da340 MW |
3665 | if (r2 > ay) |
3666 | { qq++; rr -= yy; } | |
3667 | else if (r2 < -ay) | |
3668 | { qq--; rr += yy; } | |
ff62c168 | 3669 | } |
4a46bc2a | 3670 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 3671 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 3672 | else |
5fbf680b MW |
3673 | *qp = scm_i_inum2big (qq); |
3674 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3675 | } |
5fbf680b | 3676 | return; |
ff62c168 MW |
3677 | } |
3678 | else if (SCM_BIGP (y)) | |
3679 | { | |
3680 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3681 | can fit in a fixnum) to scm_i_bigint_round_divide */ |
3682 | return scm_i_bigint_round_divide | |
3683 | (scm_i_long2big (SCM_I_INUM (x)), y, qp, rp); | |
ff62c168 MW |
3684 | } |
3685 | else if (SCM_REALP (y)) | |
8f9da340 | 3686 | return scm_i_inexact_round_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3687 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3688 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3689 | else |
8f9da340 MW |
3690 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3691 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3692 | } |
3693 | else if (SCM_BIGP (x)) | |
3694 | { | |
3695 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3696 | { | |
3697 | scm_t_inum yy = SCM_I_INUM (y); | |
3698 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3699 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3700 | else |
3701 | { | |
3702 | SCM q = scm_i_mkbig (); | |
3703 | scm_t_inum rr; | |
8f9da340 MW |
3704 | int needs_adjustment; |
3705 | ||
ff62c168 MW |
3706 | if (yy > 0) |
3707 | { | |
8f9da340 MW |
3708 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3709 | SCM_I_BIG_MPZ (x), yy); | |
3710 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3711 | needs_adjustment = (2*rr >= yy); | |
3712 | else | |
3713 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3714 | } |
3715 | else | |
3716 | { | |
3717 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3718 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3719 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3720 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3721 | needs_adjustment = (2*rr <= yy); | |
3722 | else | |
3723 | needs_adjustment = (2*rr < yy); | |
3724 | } | |
3725 | scm_remember_upto_here_1 (x); | |
3726 | if (needs_adjustment) | |
3727 | { | |
3728 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3729 | rr -= yy; | |
ff62c168 | 3730 | } |
5fbf680b MW |
3731 | *qp = scm_i_normbig (q); |
3732 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3733 | } |
5fbf680b | 3734 | return; |
ff62c168 MW |
3735 | } |
3736 | else if (SCM_BIGP (y)) | |
8f9da340 | 3737 | return scm_i_bigint_round_divide (x, y, qp, rp); |
ff62c168 | 3738 | else if (SCM_REALP (y)) |
8f9da340 | 3739 | return scm_i_inexact_round_divide |
5fbf680b | 3740 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3741 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3742 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3743 | else |
8f9da340 MW |
3744 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3745 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3746 | } |
3747 | else if (SCM_REALP (x)) | |
3748 | { | |
3749 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3750 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3751 | return scm_i_inexact_round_divide |
5fbf680b | 3752 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
03ddd15b | 3753 | else |
8f9da340 MW |
3754 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3755 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3756 | } |
3757 | else if (SCM_FRACTIONP (x)) | |
3758 | { | |
3759 | if (SCM_REALP (y)) | |
8f9da340 | 3760 | return scm_i_inexact_round_divide |
5fbf680b | 3761 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b | 3762 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3763 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3764 | else |
8f9da340 MW |
3765 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3766 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3767 | } |
3768 | else | |
8f9da340 MW |
3769 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG1, |
3770 | s_scm_round_divide, qp, rp); | |
ff62c168 | 3771 | } |
ff62c168 | 3772 | |
5fbf680b | 3773 | static void |
8f9da340 | 3774 | scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp) |
ff62c168 | 3775 | { |
8f9da340 MW |
3776 | if (SCM_UNLIKELY (y == 0)) |
3777 | scm_num_overflow (s_scm_round_divide); /* or return a NaN? */ | |
ff62c168 | 3778 | else |
8f9da340 MW |
3779 | { |
3780 | double q = scm_c_round (x / y); | |
3781 | double r = x - q * y; | |
3782 | *qp = scm_from_double (q); | |
3783 | *rp = scm_from_double (r); | |
3784 | } | |
ff62c168 MW |
3785 | } |
3786 | ||
3787 | /* Assumes that both x and y are bigints, though | |
3788 | x might be able to fit into a fixnum. */ | |
5fbf680b | 3789 | static void |
8f9da340 | 3790 | scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3791 | { |
8f9da340 MW |
3792 | SCM q, r, r2; |
3793 | int cmp, needs_adjustment; | |
ff62c168 MW |
3794 | |
3795 | /* Note that x might be small enough to fit into a | |
3796 | fixnum, so we must not let it escape into the wild */ | |
3797 | q = scm_i_mkbig (); | |
3798 | r = scm_i_mkbig (); | |
8f9da340 | 3799 | r2 = scm_i_mkbig (); |
ff62c168 | 3800 | |
8f9da340 MW |
3801 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3802 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3803 | scm_remember_upto_here_1 (x); | |
3804 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3805 | |
8f9da340 MW |
3806 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3807 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3808 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3809 | else |
8f9da340 MW |
3810 | needs_adjustment = (cmp > 0); |
3811 | ||
3812 | if (needs_adjustment) | |
ff62c168 | 3813 | { |
8f9da340 MW |
3814 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
3815 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
ff62c168 | 3816 | } |
8f9da340 MW |
3817 | |
3818 | scm_remember_upto_here_2 (r2, y); | |
5fbf680b MW |
3819 | *qp = scm_i_normbig (q); |
3820 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
3821 | } |
3822 | ||
5fbf680b | 3823 | static void |
8f9da340 | 3824 | scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3825 | { |
03ddd15b MW |
3826 | SCM r1; |
3827 | SCM xd = scm_denominator (x); | |
3828 | SCM yd = scm_denominator (y); | |
3829 | ||
8f9da340 MW |
3830 | scm_round_divide (scm_product (scm_numerator (x), yd), |
3831 | scm_product (scm_numerator (y), xd), | |
3832 | qp, &r1); | |
03ddd15b | 3833 | *rp = scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3834 | } |
3835 | ||
3836 | ||
78d3deb1 AW |
3837 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
3838 | (SCM x, SCM y, SCM rest), | |
3839 | "Return the greatest common divisor of all parameter values.\n" | |
3840 | "If called without arguments, 0 is returned.") | |
3841 | #define FUNC_NAME s_scm_i_gcd | |
3842 | { | |
3843 | while (!scm_is_null (rest)) | |
3844 | { x = scm_gcd (x, y); | |
3845 | y = scm_car (rest); | |
3846 | rest = scm_cdr (rest); | |
3847 | } | |
3848 | return scm_gcd (x, y); | |
3849 | } | |
3850 | #undef FUNC_NAME | |
3851 | ||
3852 | #define s_gcd s_scm_i_gcd | |
3853 | #define g_gcd g_scm_i_gcd | |
3854 | ||
0f2d19dd | 3855 | SCM |
6e8d25a6 | 3856 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 3857 | { |
ca46fb90 | 3858 | if (SCM_UNBNDP (y)) |
1dd79792 | 3859 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 3860 | |
e11e83f3 | 3861 | if (SCM_I_INUMP (x)) |
ca46fb90 | 3862 | { |
e11e83f3 | 3863 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3864 | { |
e25f3727 AW |
3865 | scm_t_inum xx = SCM_I_INUM (x); |
3866 | scm_t_inum yy = SCM_I_INUM (y); | |
3867 | scm_t_inum u = xx < 0 ? -xx : xx; | |
3868 | scm_t_inum v = yy < 0 ? -yy : yy; | |
3869 | scm_t_inum result; | |
0aacf84e MD |
3870 | if (xx == 0) |
3871 | result = v; | |
3872 | else if (yy == 0) | |
3873 | result = u; | |
3874 | else | |
3875 | { | |
e25f3727 AW |
3876 | scm_t_inum k = 1; |
3877 | scm_t_inum t; | |
0aacf84e MD |
3878 | /* Determine a common factor 2^k */ |
3879 | while (!(1 & (u | v))) | |
3880 | { | |
3881 | k <<= 1; | |
3882 | u >>= 1; | |
3883 | v >>= 1; | |
3884 | } | |
3885 | /* Now, any factor 2^n can be eliminated */ | |
3886 | if (u & 1) | |
3887 | t = -v; | |
3888 | else | |
3889 | { | |
3890 | t = u; | |
3891 | b3: | |
3892 | t = SCM_SRS (t, 1); | |
3893 | } | |
3894 | if (!(1 & t)) | |
3895 | goto b3; | |
3896 | if (t > 0) | |
3897 | u = t; | |
3898 | else | |
3899 | v = -t; | |
3900 | t = u - v; | |
3901 | if (t != 0) | |
3902 | goto b3; | |
3903 | result = u * k; | |
3904 | } | |
3905 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 3906 | ? SCM_I_MAKINUM (result) |
e25f3727 | 3907 | : scm_i_inum2big (result)); |
ca46fb90 RB |
3908 | } |
3909 | else if (SCM_BIGP (y)) | |
3910 | { | |
0bff4dce KR |
3911 | SCM_SWAP (x, y); |
3912 | goto big_inum; | |
ca46fb90 RB |
3913 | } |
3914 | else | |
3915 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 3916 | } |
ca46fb90 RB |
3917 | else if (SCM_BIGP (x)) |
3918 | { | |
e11e83f3 | 3919 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3920 | { |
e25f3727 AW |
3921 | scm_t_bits result; |
3922 | scm_t_inum yy; | |
0bff4dce | 3923 | big_inum: |
e11e83f3 | 3924 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
3925 | if (yy == 0) |
3926 | return scm_abs (x); | |
0aacf84e MD |
3927 | if (yy < 0) |
3928 | yy = -yy; | |
ca46fb90 RB |
3929 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
3930 | scm_remember_upto_here_1 (x); | |
0aacf84e | 3931 | return (SCM_POSFIXABLE (result) |
d956fa6f | 3932 | ? SCM_I_MAKINUM (result) |
e25f3727 | 3933 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
3934 | } |
3935 | else if (SCM_BIGP (y)) | |
3936 | { | |
3937 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
3938 | mpz_gcd (SCM_I_BIG_MPZ (result), |
3939 | SCM_I_BIG_MPZ (x), | |
3940 | SCM_I_BIG_MPZ (y)); | |
3941 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
3942 | return scm_i_normbig (result); |
3943 | } | |
3944 | else | |
3945 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 3946 | } |
ca46fb90 | 3947 | else |
09fb7599 | 3948 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
3949 | } |
3950 | ||
78d3deb1 AW |
3951 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
3952 | (SCM x, SCM y, SCM rest), | |
3953 | "Return the least common multiple of the arguments.\n" | |
3954 | "If called without arguments, 1 is returned.") | |
3955 | #define FUNC_NAME s_scm_i_lcm | |
3956 | { | |
3957 | while (!scm_is_null (rest)) | |
3958 | { x = scm_lcm (x, y); | |
3959 | y = scm_car (rest); | |
3960 | rest = scm_cdr (rest); | |
3961 | } | |
3962 | return scm_lcm (x, y); | |
3963 | } | |
3964 | #undef FUNC_NAME | |
3965 | ||
3966 | #define s_lcm s_scm_i_lcm | |
3967 | #define g_lcm g_scm_i_lcm | |
3968 | ||
0f2d19dd | 3969 | SCM |
6e8d25a6 | 3970 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 3971 | { |
ca46fb90 RB |
3972 | if (SCM_UNBNDP (n2)) |
3973 | { | |
3974 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
3975 | return SCM_I_MAKINUM (1L); |
3976 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 3977 | } |
09fb7599 | 3978 | |
e11e83f3 | 3979 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 3980 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 3981 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 3982 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 3983 | |
e11e83f3 | 3984 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 3985 | { |
e11e83f3 | 3986 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
3987 | { |
3988 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 3989 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
3990 | return d; |
3991 | else | |
3992 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
3993 | } | |
3994 | else | |
3995 | { | |
3996 | /* inum n1, big n2 */ | |
3997 | inumbig: | |
3998 | { | |
3999 | SCM result = scm_i_mkbig (); | |
e25f3727 | 4000 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
4001 | if (nn1 == 0) return SCM_INUM0; |
4002 | if (nn1 < 0) nn1 = - nn1; | |
4003 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
4004 | scm_remember_upto_here_1 (n2); | |
4005 | return result; | |
4006 | } | |
4007 | } | |
4008 | } | |
4009 | else | |
4010 | { | |
4011 | /* big n1 */ | |
e11e83f3 | 4012 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4013 | { |
4014 | SCM_SWAP (n1, n2); | |
4015 | goto inumbig; | |
4016 | } | |
4017 | else | |
4018 | { | |
4019 | SCM result = scm_i_mkbig (); | |
4020 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
4021 | SCM_I_BIG_MPZ (n1), | |
4022 | SCM_I_BIG_MPZ (n2)); | |
4023 | scm_remember_upto_here_2(n1, n2); | |
4024 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
4025 | return result; | |
4026 | } | |
f872b822 | 4027 | } |
0f2d19dd JB |
4028 | } |
4029 | ||
8a525303 GB |
4030 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
4031 | ||
4032 | Logand: | |
4033 | X Y Result Method: | |
4034 | (len) | |
4035 | + + + x (map digit:logand X Y) | |
4036 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
4037 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
4038 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
4039 | ||
4040 | Logior: | |
4041 | X Y Result Method: | |
4042 | ||
4043 | + + + (map digit:logior X Y) | |
4044 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
4045 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
4046 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
4047 | ||
4048 | Logxor: | |
4049 | X Y Result Method: | |
4050 | ||
4051 | + + + (map digit:logxor X Y) | |
4052 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
4053 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
4054 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
4055 | ||
4056 | Logtest: | |
4057 | X Y Result | |
4058 | ||
4059 | + + (any digit:logand X Y) | |
4060 | + - (any digit:logand X (lognot (+ -1 Y))) | |
4061 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
4062 | - - #t | |
4063 | ||
4064 | */ | |
4065 | ||
78d3deb1 AW |
4066 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
4067 | (SCM x, SCM y, SCM rest), | |
4068 | "Return the bitwise AND of the integer arguments.\n\n" | |
4069 | "@lisp\n" | |
4070 | "(logand) @result{} -1\n" | |
4071 | "(logand 7) @result{} 7\n" | |
4072 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
4073 | "@end lisp") | |
4074 | #define FUNC_NAME s_scm_i_logand | |
4075 | { | |
4076 | while (!scm_is_null (rest)) | |
4077 | { x = scm_logand (x, y); | |
4078 | y = scm_car (rest); | |
4079 | rest = scm_cdr (rest); | |
4080 | } | |
4081 | return scm_logand (x, y); | |
4082 | } | |
4083 | #undef FUNC_NAME | |
4084 | ||
4085 | #define s_scm_logand s_scm_i_logand | |
4086 | ||
4087 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 4088 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 4089 | { |
e25f3727 | 4090 | scm_t_inum nn1; |
9a00c9fc | 4091 | |
0aacf84e MD |
4092 | if (SCM_UNBNDP (n2)) |
4093 | { | |
4094 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 4095 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
4096 | else if (!SCM_NUMBERP (n1)) |
4097 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
4098 | else if (SCM_NUMBERP (n1)) | |
4099 | return n1; | |
4100 | else | |
4101 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4102 | } |
09fb7599 | 4103 | |
e11e83f3 | 4104 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4105 | { |
e11e83f3 MV |
4106 | nn1 = SCM_I_INUM (n1); |
4107 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4108 | { |
e25f3727 | 4109 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4110 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
4111 | } |
4112 | else if SCM_BIGP (n2) | |
4113 | { | |
4114 | intbig: | |
4115 | if (n1 == 0) | |
4116 | return SCM_INUM0; | |
4117 | { | |
4118 | SCM result_z = scm_i_mkbig (); | |
4119 | mpz_t nn1_z; | |
4120 | mpz_init_set_si (nn1_z, nn1); | |
4121 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4122 | scm_remember_upto_here_1 (n2); | |
4123 | mpz_clear (nn1_z); | |
4124 | return scm_i_normbig (result_z); | |
4125 | } | |
4126 | } | |
4127 | else | |
4128 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4129 | } | |
4130 | else if (SCM_BIGP (n1)) | |
4131 | { | |
e11e83f3 | 4132 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4133 | { |
4134 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4135 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4136 | goto intbig; |
4137 | } | |
4138 | else if (SCM_BIGP (n2)) | |
4139 | { | |
4140 | SCM result_z = scm_i_mkbig (); | |
4141 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
4142 | SCM_I_BIG_MPZ (n1), | |
4143 | SCM_I_BIG_MPZ (n2)); | |
4144 | scm_remember_upto_here_2 (n1, n2); | |
4145 | return scm_i_normbig (result_z); | |
4146 | } | |
4147 | else | |
4148 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4149 | } |
0aacf84e | 4150 | else |
09fb7599 | 4151 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4152 | } |
1bbd0b84 | 4153 | #undef FUNC_NAME |
0f2d19dd | 4154 | |
09fb7599 | 4155 | |
78d3deb1 AW |
4156 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
4157 | (SCM x, SCM y, SCM rest), | |
4158 | "Return the bitwise OR of the integer arguments.\n\n" | |
4159 | "@lisp\n" | |
4160 | "(logior) @result{} 0\n" | |
4161 | "(logior 7) @result{} 7\n" | |
4162 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
4163 | "@end lisp") | |
4164 | #define FUNC_NAME s_scm_i_logior | |
4165 | { | |
4166 | while (!scm_is_null (rest)) | |
4167 | { x = scm_logior (x, y); | |
4168 | y = scm_car (rest); | |
4169 | rest = scm_cdr (rest); | |
4170 | } | |
4171 | return scm_logior (x, y); | |
4172 | } | |
4173 | #undef FUNC_NAME | |
4174 | ||
4175 | #define s_scm_logior s_scm_i_logior | |
4176 | ||
4177 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 4178 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 4179 | { |
e25f3727 | 4180 | scm_t_inum nn1; |
9a00c9fc | 4181 | |
0aacf84e MD |
4182 | if (SCM_UNBNDP (n2)) |
4183 | { | |
4184 | if (SCM_UNBNDP (n1)) | |
4185 | return SCM_INUM0; | |
4186 | else if (SCM_NUMBERP (n1)) | |
4187 | return n1; | |
4188 | else | |
4189 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4190 | } |
09fb7599 | 4191 | |
e11e83f3 | 4192 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4193 | { |
e11e83f3 MV |
4194 | nn1 = SCM_I_INUM (n1); |
4195 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4196 | { |
e11e83f3 | 4197 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 4198 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
4199 | } |
4200 | else if (SCM_BIGP (n2)) | |
4201 | { | |
4202 | intbig: | |
4203 | if (nn1 == 0) | |
4204 | return n2; | |
4205 | { | |
4206 | SCM result_z = scm_i_mkbig (); | |
4207 | mpz_t nn1_z; | |
4208 | mpz_init_set_si (nn1_z, nn1); | |
4209 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4210 | scm_remember_upto_here_1 (n2); | |
4211 | mpz_clear (nn1_z); | |
9806de0d | 4212 | return scm_i_normbig (result_z); |
0aacf84e MD |
4213 | } |
4214 | } | |
4215 | else | |
4216 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4217 | } | |
4218 | else if (SCM_BIGP (n1)) | |
4219 | { | |
e11e83f3 | 4220 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4221 | { |
4222 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4223 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4224 | goto intbig; |
4225 | } | |
4226 | else if (SCM_BIGP (n2)) | |
4227 | { | |
4228 | SCM result_z = scm_i_mkbig (); | |
4229 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
4230 | SCM_I_BIG_MPZ (n1), | |
4231 | SCM_I_BIG_MPZ (n2)); | |
4232 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 4233 | return scm_i_normbig (result_z); |
0aacf84e MD |
4234 | } |
4235 | else | |
4236 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4237 | } |
0aacf84e | 4238 | else |
09fb7599 | 4239 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4240 | } |
1bbd0b84 | 4241 | #undef FUNC_NAME |
0f2d19dd | 4242 | |
09fb7599 | 4243 | |
78d3deb1 AW |
4244 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
4245 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
4246 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
4247 | "set in the result if it is set in an odd number of arguments.\n" | |
4248 | "@lisp\n" | |
4249 | "(logxor) @result{} 0\n" | |
4250 | "(logxor 7) @result{} 7\n" | |
4251 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
4252 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 4253 | "@end lisp") |
78d3deb1 AW |
4254 | #define FUNC_NAME s_scm_i_logxor |
4255 | { | |
4256 | while (!scm_is_null (rest)) | |
4257 | { x = scm_logxor (x, y); | |
4258 | y = scm_car (rest); | |
4259 | rest = scm_cdr (rest); | |
4260 | } | |
4261 | return scm_logxor (x, y); | |
4262 | } | |
4263 | #undef FUNC_NAME | |
4264 | ||
4265 | #define s_scm_logxor s_scm_i_logxor | |
4266 | ||
4267 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 4268 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 4269 | { |
e25f3727 | 4270 | scm_t_inum nn1; |
9a00c9fc | 4271 | |
0aacf84e MD |
4272 | if (SCM_UNBNDP (n2)) |
4273 | { | |
4274 | if (SCM_UNBNDP (n1)) | |
4275 | return SCM_INUM0; | |
4276 | else if (SCM_NUMBERP (n1)) | |
4277 | return n1; | |
4278 | else | |
4279 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4280 | } |
09fb7599 | 4281 | |
e11e83f3 | 4282 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4283 | { |
e11e83f3 MV |
4284 | nn1 = SCM_I_INUM (n1); |
4285 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4286 | { |
e25f3727 | 4287 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4288 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
4289 | } |
4290 | else if (SCM_BIGP (n2)) | |
4291 | { | |
4292 | intbig: | |
4293 | { | |
4294 | SCM result_z = scm_i_mkbig (); | |
4295 | mpz_t nn1_z; | |
4296 | mpz_init_set_si (nn1_z, nn1); | |
4297 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4298 | scm_remember_upto_here_1 (n2); | |
4299 | mpz_clear (nn1_z); | |
4300 | return scm_i_normbig (result_z); | |
4301 | } | |
4302 | } | |
4303 | else | |
4304 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4305 | } | |
4306 | else if (SCM_BIGP (n1)) | |
4307 | { | |
e11e83f3 | 4308 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4309 | { |
4310 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4311 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4312 | goto intbig; |
4313 | } | |
4314 | else if (SCM_BIGP (n2)) | |
4315 | { | |
4316 | SCM result_z = scm_i_mkbig (); | |
4317 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
4318 | SCM_I_BIG_MPZ (n1), | |
4319 | SCM_I_BIG_MPZ (n2)); | |
4320 | scm_remember_upto_here_2 (n1, n2); | |
4321 | return scm_i_normbig (result_z); | |
4322 | } | |
4323 | else | |
4324 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4325 | } |
0aacf84e | 4326 | else |
09fb7599 | 4327 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4328 | } |
1bbd0b84 | 4329 | #undef FUNC_NAME |
0f2d19dd | 4330 | |
09fb7599 | 4331 | |
a1ec6916 | 4332 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 4333 | (SCM j, SCM k), |
ba6e7231 KR |
4334 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
4335 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
4336 | "without actually calculating the @code{logand}, just testing\n" | |
4337 | "for non-zero.\n" | |
4338 | "\n" | |
1e6808ea | 4339 | "@lisp\n" |
b380b885 MD |
4340 | "(logtest #b0100 #b1011) @result{} #f\n" |
4341 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 4342 | "@end lisp") |
1bbd0b84 | 4343 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 4344 | { |
e25f3727 | 4345 | scm_t_inum nj; |
9a00c9fc | 4346 | |
e11e83f3 | 4347 | if (SCM_I_INUMP (j)) |
0aacf84e | 4348 | { |
e11e83f3 MV |
4349 | nj = SCM_I_INUM (j); |
4350 | if (SCM_I_INUMP (k)) | |
0aacf84e | 4351 | { |
e25f3727 | 4352 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 4353 | return scm_from_bool (nj & nk); |
0aacf84e MD |
4354 | } |
4355 | else if (SCM_BIGP (k)) | |
4356 | { | |
4357 | intbig: | |
4358 | if (nj == 0) | |
4359 | return SCM_BOOL_F; | |
4360 | { | |
4361 | SCM result; | |
4362 | mpz_t nj_z; | |
4363 | mpz_init_set_si (nj_z, nj); | |
4364 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
4365 | scm_remember_upto_here_1 (k); | |
73e4de09 | 4366 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
4367 | mpz_clear (nj_z); |
4368 | return result; | |
4369 | } | |
4370 | } | |
4371 | else | |
4372 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4373 | } | |
4374 | else if (SCM_BIGP (j)) | |
4375 | { | |
e11e83f3 | 4376 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
4377 | { |
4378 | SCM_SWAP (j, k); | |
e11e83f3 | 4379 | nj = SCM_I_INUM (j); |
0aacf84e MD |
4380 | goto intbig; |
4381 | } | |
4382 | else if (SCM_BIGP (k)) | |
4383 | { | |
4384 | SCM result; | |
4385 | mpz_t result_z; | |
4386 | mpz_init (result_z); | |
4387 | mpz_and (result_z, | |
4388 | SCM_I_BIG_MPZ (j), | |
4389 | SCM_I_BIG_MPZ (k)); | |
4390 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 4391 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
4392 | mpz_clear (result_z); |
4393 | return result; | |
4394 | } | |
4395 | else | |
4396 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4397 | } | |
4398 | else | |
4399 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 4400 | } |
1bbd0b84 | 4401 | #undef FUNC_NAME |
0f2d19dd | 4402 | |
c1bfcf60 | 4403 | |
a1ec6916 | 4404 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 4405 | (SCM index, SCM j), |
ba6e7231 KR |
4406 | "Test whether bit number @var{index} in @var{j} is set.\n" |
4407 | "@var{index} starts from 0 for the least significant bit.\n" | |
4408 | "\n" | |
1e6808ea | 4409 | "@lisp\n" |
b380b885 MD |
4410 | "(logbit? 0 #b1101) @result{} #t\n" |
4411 | "(logbit? 1 #b1101) @result{} #f\n" | |
4412 | "(logbit? 2 #b1101) @result{} #t\n" | |
4413 | "(logbit? 3 #b1101) @result{} #t\n" | |
4414 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 4415 | "@end lisp") |
1bbd0b84 | 4416 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 4417 | { |
78166ad5 | 4418 | unsigned long int iindex; |
5efd3c7d | 4419 | iindex = scm_to_ulong (index); |
78166ad5 | 4420 | |
e11e83f3 | 4421 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
4422 | { |
4423 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 4424 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 4425 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 4426 | } |
0aacf84e MD |
4427 | else if (SCM_BIGP (j)) |
4428 | { | |
4429 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
4430 | scm_remember_upto_here_1 (j); | |
73e4de09 | 4431 | return scm_from_bool (val); |
0aacf84e MD |
4432 | } |
4433 | else | |
78166ad5 | 4434 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 4435 | } |
1bbd0b84 | 4436 | #undef FUNC_NAME |
0f2d19dd | 4437 | |
78166ad5 | 4438 | |
a1ec6916 | 4439 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 4440 | (SCM n), |
4d814788 | 4441 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
4442 | "argument.\n" |
4443 | "\n" | |
b380b885 MD |
4444 | "@lisp\n" |
4445 | "(number->string (lognot #b10000000) 2)\n" | |
4446 | " @result{} \"-10000001\"\n" | |
4447 | "(number->string (lognot #b0) 2)\n" | |
4448 | " @result{} \"-1\"\n" | |
1e6808ea | 4449 | "@end lisp") |
1bbd0b84 | 4450 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 4451 | { |
e11e83f3 | 4452 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
4453 | /* No overflow here, just need to toggle all the bits making up the inum. |
4454 | Enhancement: No need to strip the tag and add it back, could just xor | |
4455 | a block of 1 bits, if that worked with the various debug versions of | |
4456 | the SCM typedef. */ | |
e11e83f3 | 4457 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
4458 | |
4459 | } else if (SCM_BIGP (n)) { | |
4460 | SCM result = scm_i_mkbig (); | |
4461 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
4462 | scm_remember_upto_here_1 (n); | |
4463 | return result; | |
4464 | ||
4465 | } else { | |
4466 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4467 | } | |
0f2d19dd | 4468 | } |
1bbd0b84 | 4469 | #undef FUNC_NAME |
0f2d19dd | 4470 | |
518b7508 KR |
4471 | /* returns 0 if IN is not an integer. OUT must already be |
4472 | initialized. */ | |
4473 | static int | |
4474 | coerce_to_big (SCM in, mpz_t out) | |
4475 | { | |
4476 | if (SCM_BIGP (in)) | |
4477 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
4478 | else if (SCM_I_INUMP (in)) |
4479 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
4480 | else |
4481 | return 0; | |
4482 | ||
4483 | return 1; | |
4484 | } | |
4485 | ||
d885e204 | 4486 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
4487 | (SCM n, SCM k, SCM m), |
4488 | "Return @var{n} raised to the integer exponent\n" | |
4489 | "@var{k}, modulo @var{m}.\n" | |
4490 | "\n" | |
4491 | "@lisp\n" | |
4492 | "(modulo-expt 2 3 5)\n" | |
4493 | " @result{} 3\n" | |
4494 | "@end lisp") | |
d885e204 | 4495 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
4496 | { |
4497 | mpz_t n_tmp; | |
4498 | mpz_t k_tmp; | |
4499 | mpz_t m_tmp; | |
4500 | ||
4501 | /* There are two classes of error we might encounter -- | |
4502 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
4503 | and | |
4504 | 2) wrong-type errors, which of course we'll report by calling | |
4505 | SCM_WRONG_TYPE_ARG. | |
4506 | We don't report those errors immediately, however; instead we do | |
4507 | some cleanup first. These variables tell us which error (if | |
4508 | any) we should report after cleaning up. | |
4509 | */ | |
4510 | int report_overflow = 0; | |
4511 | ||
4512 | int position_of_wrong_type = 0; | |
4513 | SCM value_of_wrong_type = SCM_INUM0; | |
4514 | ||
4515 | SCM result = SCM_UNDEFINED; | |
4516 | ||
4517 | mpz_init (n_tmp); | |
4518 | mpz_init (k_tmp); | |
4519 | mpz_init (m_tmp); | |
4520 | ||
bc36d050 | 4521 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
4522 | { |
4523 | report_overflow = 1; | |
4524 | goto cleanup; | |
4525 | } | |
4526 | ||
4527 | if (!coerce_to_big (n, n_tmp)) | |
4528 | { | |
4529 | value_of_wrong_type = n; | |
4530 | position_of_wrong_type = 1; | |
4531 | goto cleanup; | |
4532 | } | |
4533 | ||
4534 | if (!coerce_to_big (k, k_tmp)) | |
4535 | { | |
4536 | value_of_wrong_type = k; | |
4537 | position_of_wrong_type = 2; | |
4538 | goto cleanup; | |
4539 | } | |
4540 | ||
4541 | if (!coerce_to_big (m, m_tmp)) | |
4542 | { | |
4543 | value_of_wrong_type = m; | |
4544 | position_of_wrong_type = 3; | |
4545 | goto cleanup; | |
4546 | } | |
4547 | ||
4548 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
4549 | will get a divide-by-zero exception when an inverse 1/n mod m | |
4550 | doesn't exist (or is not unique). Since exceptions are hard to | |
4551 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
4552 | a simple failure code, which is easy to handle. */ | |
4553 | ||
4554 | if (-1 == mpz_sgn (k_tmp)) | |
4555 | { | |
4556 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
4557 | { | |
4558 | report_overflow = 1; | |
4559 | goto cleanup; | |
4560 | } | |
4561 | mpz_neg (k_tmp, k_tmp); | |
4562 | } | |
4563 | ||
4564 | result = scm_i_mkbig (); | |
4565 | mpz_powm (SCM_I_BIG_MPZ (result), | |
4566 | n_tmp, | |
4567 | k_tmp, | |
4568 | m_tmp); | |
b7b8c575 KR |
4569 | |
4570 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
4571 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
4572 | ||
518b7508 KR |
4573 | cleanup: |
4574 | mpz_clear (m_tmp); | |
4575 | mpz_clear (k_tmp); | |
4576 | mpz_clear (n_tmp); | |
4577 | ||
4578 | if (report_overflow) | |
4579 | scm_num_overflow (FUNC_NAME); | |
4580 | ||
4581 | if (position_of_wrong_type) | |
4582 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
4583 | value_of_wrong_type); | |
4584 | ||
4585 | return scm_i_normbig (result); | |
4586 | } | |
4587 | #undef FUNC_NAME | |
4588 | ||
a1ec6916 | 4589 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 4590 | (SCM n, SCM k), |
ba6e7231 KR |
4591 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
4592 | "exact integer, @var{n} can be any number.\n" | |
4593 | "\n" | |
2519490c MW |
4594 | "Negative @var{k} is supported, and results in\n" |
4595 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
4596 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 4597 | "includes @math{0^0} is 1.\n" |
1e6808ea | 4598 | "\n" |
b380b885 | 4599 | "@lisp\n" |
ba6e7231 KR |
4600 | "(integer-expt 2 5) @result{} 32\n" |
4601 | "(integer-expt -3 3) @result{} -27\n" | |
4602 | "(integer-expt 5 -3) @result{} 1/125\n" | |
4603 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 4604 | "@end lisp") |
1bbd0b84 | 4605 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 4606 | { |
e25f3727 | 4607 | scm_t_inum i2 = 0; |
1c35cb19 RB |
4608 | SCM z_i2 = SCM_BOOL_F; |
4609 | int i2_is_big = 0; | |
d956fa6f | 4610 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 4611 | |
bfe1f03a MW |
4612 | /* Specifically refrain from checking the type of the first argument. |
4613 | This allows us to exponentiate any object that can be multiplied. | |
4614 | If we must raise to a negative power, we must also be able to | |
4615 | take its reciprocal. */ | |
4616 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 4617 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 4618 | |
bfe1f03a MW |
4619 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
4620 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
4621 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
4622 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
4623 | /* The next check is necessary only because R6RS specifies different | |
4624 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
4625 | we simply skip this case and move on. */ | |
4626 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
4627 | { | |
4628 | /* k cannot be 0 at this point, because we | |
4629 | have already checked for that case above */ | |
4630 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
4631 | return n; |
4632 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
4633 | return scm_nan (); | |
4634 | } | |
ca46fb90 | 4635 | |
e11e83f3 MV |
4636 | if (SCM_I_INUMP (k)) |
4637 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
4638 | else if (SCM_BIGP (k)) |
4639 | { | |
4640 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
4641 | scm_remember_upto_here_1 (k); |
4642 | i2_is_big = 1; | |
4643 | } | |
2830fd91 | 4644 | else |
ca46fb90 RB |
4645 | SCM_WRONG_TYPE_ARG (2, k); |
4646 | ||
4647 | if (i2_is_big) | |
f872b822 | 4648 | { |
ca46fb90 RB |
4649 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
4650 | { | |
4651 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
4652 | n = scm_divide (n, SCM_UNDEFINED); | |
4653 | } | |
4654 | while (1) | |
4655 | { | |
4656 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
4657 | { | |
ca46fb90 RB |
4658 | return acc; |
4659 | } | |
4660 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
4661 | { | |
ca46fb90 RB |
4662 | return scm_product (acc, n); |
4663 | } | |
4664 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
4665 | acc = scm_product (acc, n); | |
4666 | n = scm_product (n, n); | |
4667 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
4668 | } | |
f872b822 | 4669 | } |
ca46fb90 | 4670 | else |
f872b822 | 4671 | { |
ca46fb90 RB |
4672 | if (i2 < 0) |
4673 | { | |
4674 | i2 = -i2; | |
4675 | n = scm_divide (n, SCM_UNDEFINED); | |
4676 | } | |
4677 | while (1) | |
4678 | { | |
4679 | if (0 == i2) | |
4680 | return acc; | |
4681 | if (1 == i2) | |
4682 | return scm_product (acc, n); | |
4683 | if (i2 & 1) | |
4684 | acc = scm_product (acc, n); | |
4685 | n = scm_product (n, n); | |
4686 | i2 >>= 1; | |
4687 | } | |
f872b822 | 4688 | } |
0f2d19dd | 4689 | } |
1bbd0b84 | 4690 | #undef FUNC_NAME |
0f2d19dd | 4691 | |
a1ec6916 | 4692 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 4693 | (SCM n, SCM cnt), |
32f19569 KR |
4694 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
4695 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 4696 | "\n" |
e7644cb2 | 4697 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
4698 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
4699 | "infinity. (Note that this is not the same rounding as\n" | |
4700 | "@code{quotient} does.)\n" | |
4701 | "\n" | |
4702 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
4703 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
4704 | "shift dropping bits.\n" | |
1e6808ea | 4705 | "\n" |
b380b885 | 4706 | "@lisp\n" |
1e6808ea MG |
4707 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
4708 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
4709 | "\n" |
4710 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
4711 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 4712 | "@end lisp") |
1bbd0b84 | 4713 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 4714 | { |
3ab9f56e | 4715 | long bits_to_shift; |
5efd3c7d | 4716 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 4717 | |
788aca27 KR |
4718 | if (SCM_I_INUMP (n)) |
4719 | { | |
e25f3727 | 4720 | scm_t_inum nn = SCM_I_INUM (n); |
788aca27 KR |
4721 | |
4722 | if (bits_to_shift > 0) | |
4723 | { | |
4724 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
4725 | overflow a non-zero fixnum. For smaller shifts we check the | |
4726 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
4727 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
4728 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
4729 | bits_to_shift)". */ | |
4730 | ||
4731 | if (nn == 0) | |
4732 | return n; | |
4733 | ||
4734 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4735 | && ((scm_t_bits) |
788aca27 KR |
4736 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) |
4737 | <= 1)) | |
4738 | { | |
4739 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
4740 | } | |
4741 | else | |
4742 | { | |
e25f3727 | 4743 | SCM result = scm_i_inum2big (nn); |
788aca27 KR |
4744 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
4745 | bits_to_shift); | |
4746 | return result; | |
4747 | } | |
4748 | } | |
4749 | else | |
4750 | { | |
4751 | bits_to_shift = -bits_to_shift; | |
4752 | if (bits_to_shift >= SCM_LONG_BIT) | |
cff5fa33 | 4753 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1)); |
788aca27 KR |
4754 | else |
4755 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
4756 | } | |
4757 | ||
4758 | } | |
4759 | else if (SCM_BIGP (n)) | |
ca46fb90 | 4760 | { |
788aca27 KR |
4761 | SCM result; |
4762 | ||
4763 | if (bits_to_shift == 0) | |
4764 | return n; | |
4765 | ||
4766 | result = scm_i_mkbig (); | |
4767 | if (bits_to_shift >= 0) | |
4768 | { | |
4769 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
4770 | bits_to_shift); | |
4771 | return result; | |
4772 | } | |
ca46fb90 | 4773 | else |
788aca27 KR |
4774 | { |
4775 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
4776 | we have to allocate a bignum even if the result is going to be a | |
4777 | fixnum. */ | |
4778 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
4779 | -bits_to_shift); | |
4780 | return scm_i_normbig (result); | |
4781 | } | |
4782 | ||
ca46fb90 RB |
4783 | } |
4784 | else | |
788aca27 KR |
4785 | { |
4786 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4787 | } | |
0f2d19dd | 4788 | } |
1bbd0b84 | 4789 | #undef FUNC_NAME |
0f2d19dd | 4790 | |
3c9f20f8 | 4791 | |
a1ec6916 | 4792 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 4793 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
4794 | "Return the integer composed of the @var{start} (inclusive)\n" |
4795 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
4796 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
4797 | "\n" | |
b380b885 MD |
4798 | "@lisp\n" |
4799 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
4800 | " @result{} \"1010\"\n" | |
4801 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
4802 | " @result{} \"10110\"\n" | |
4803 | "@end lisp") | |
1bbd0b84 | 4804 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 4805 | { |
7f848242 | 4806 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
4807 | istart = scm_to_ulong (start); |
4808 | iend = scm_to_ulong (end); | |
c1bfcf60 | 4809 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 4810 | |
7f848242 KR |
4811 | /* how many bits to keep */ |
4812 | bits = iend - istart; | |
4813 | ||
e11e83f3 | 4814 | if (SCM_I_INUMP (n)) |
0aacf84e | 4815 | { |
e25f3727 | 4816 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
4817 | |
4818 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 4819 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 4820 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 4821 | |
0aacf84e MD |
4822 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
4823 | { | |
4824 | /* Since we emulate two's complement encoded numbers, this | |
4825 | * special case requires us to produce a result that has | |
7f848242 | 4826 | * more bits than can be stored in a fixnum. |
0aacf84e | 4827 | */ |
e25f3727 | 4828 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
4829 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
4830 | bits); | |
4831 | return result; | |
0aacf84e | 4832 | } |
ac0c002c | 4833 | |
7f848242 | 4834 | /* mask down to requisite bits */ |
857ae6af | 4835 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 4836 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
4837 | } |
4838 | else if (SCM_BIGP (n)) | |
ac0c002c | 4839 | { |
7f848242 KR |
4840 | SCM result; |
4841 | if (bits == 1) | |
4842 | { | |
d956fa6f | 4843 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
4844 | } |
4845 | else | |
4846 | { | |
4847 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
4848 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
4849 | such bits into a ulong. */ | |
4850 | result = scm_i_mkbig (); | |
4851 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
4852 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
4853 | result = scm_i_normbig (result); | |
4854 | } | |
4855 | scm_remember_upto_here_1 (n); | |
4856 | return result; | |
ac0c002c | 4857 | } |
0aacf84e | 4858 | else |
78166ad5 | 4859 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 4860 | } |
1bbd0b84 | 4861 | #undef FUNC_NAME |
0f2d19dd | 4862 | |
7f848242 | 4863 | |
e4755e5c JB |
4864 | static const char scm_logtab[] = { |
4865 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
4866 | }; | |
1cc91f1b | 4867 | |
a1ec6916 | 4868 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 4869 | (SCM n), |
1e6808ea MG |
4870 | "Return the number of bits in integer @var{n}. If integer is\n" |
4871 | "positive, the 1-bits in its binary representation are counted.\n" | |
4872 | "If negative, the 0-bits in its two's-complement binary\n" | |
4873 | "representation are counted. If 0, 0 is returned.\n" | |
4874 | "\n" | |
b380b885 MD |
4875 | "@lisp\n" |
4876 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
4877 | " @result{} 4\n" |
4878 | "(logcount 0)\n" | |
4879 | " @result{} 0\n" | |
4880 | "(logcount -2)\n" | |
4881 | " @result{} 1\n" | |
4882 | "@end lisp") | |
4883 | #define FUNC_NAME s_scm_logcount | |
4884 | { | |
e11e83f3 | 4885 | if (SCM_I_INUMP (n)) |
f872b822 | 4886 | { |
e25f3727 AW |
4887 | unsigned long c = 0; |
4888 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
4889 | if (nn < 0) |
4890 | nn = -1 - nn; | |
4891 | while (nn) | |
4892 | { | |
4893 | c += scm_logtab[15 & nn]; | |
4894 | nn >>= 4; | |
4895 | } | |
d956fa6f | 4896 | return SCM_I_MAKINUM (c); |
f872b822 | 4897 | } |
ca46fb90 | 4898 | else if (SCM_BIGP (n)) |
f872b822 | 4899 | { |
ca46fb90 | 4900 | unsigned long count; |
713a4259 KR |
4901 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
4902 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 4903 | else |
713a4259 KR |
4904 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
4905 | scm_remember_upto_here_1 (n); | |
d956fa6f | 4906 | return SCM_I_MAKINUM (count); |
f872b822 | 4907 | } |
ca46fb90 RB |
4908 | else |
4909 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 4910 | } |
ca46fb90 | 4911 | #undef FUNC_NAME |
0f2d19dd JB |
4912 | |
4913 | ||
ca46fb90 RB |
4914 | static const char scm_ilentab[] = { |
4915 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
4916 | }; | |
4917 | ||
0f2d19dd | 4918 | |
ca46fb90 RB |
4919 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
4920 | (SCM n), | |
4921 | "Return the number of bits necessary to represent @var{n}.\n" | |
4922 | "\n" | |
4923 | "@lisp\n" | |
4924 | "(integer-length #b10101010)\n" | |
4925 | " @result{} 8\n" | |
4926 | "(integer-length 0)\n" | |
4927 | " @result{} 0\n" | |
4928 | "(integer-length #b1111)\n" | |
4929 | " @result{} 4\n" | |
4930 | "@end lisp") | |
4931 | #define FUNC_NAME s_scm_integer_length | |
4932 | { | |
e11e83f3 | 4933 | if (SCM_I_INUMP (n)) |
0aacf84e | 4934 | { |
e25f3727 | 4935 | unsigned long c = 0; |
0aacf84e | 4936 | unsigned int l = 4; |
e25f3727 | 4937 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
4938 | if (nn < 0) |
4939 | nn = -1 - nn; | |
4940 | while (nn) | |
4941 | { | |
4942 | c += 4; | |
4943 | l = scm_ilentab [15 & nn]; | |
4944 | nn >>= 4; | |
4945 | } | |
d956fa6f | 4946 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
4947 | } |
4948 | else if (SCM_BIGP (n)) | |
4949 | { | |
4950 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
4951 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
4952 | 1 too big, so check for that and adjust. */ | |
4953 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
4954 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
4955 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
4956 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
4957 | size--; | |
4958 | scm_remember_upto_here_1 (n); | |
d956fa6f | 4959 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
4960 | } |
4961 | else | |
ca46fb90 | 4962 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
4963 | } |
4964 | #undef FUNC_NAME | |
0f2d19dd JB |
4965 | |
4966 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
4967 | #define SCM_MAX_DBL_PREC 60 |
4968 | #define SCM_MAX_DBL_RADIX 36 | |
4969 | ||
4970 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
4971 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
4972 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
4973 | ||
4974 | static | |
4975 | void init_dblprec(int *prec, int radix) { | |
4976 | /* determine floating point precision by adding successively | |
4977 | smaller increments to 1.0 until it is considered == 1.0 */ | |
4978 | double f = ((double)1.0)/radix; | |
4979 | double fsum = 1.0 + f; | |
4980 | ||
4981 | *prec = 0; | |
4982 | while (fsum != 1.0) | |
4983 | { | |
4984 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
4985 | fsum = 1.0; | |
4986 | else | |
4987 | { | |
4988 | f /= radix; | |
4989 | fsum = f + 1.0; | |
4990 | } | |
4991 | } | |
4992 | (*prec) -= 1; | |
4993 | } | |
4994 | ||
4995 | static | |
4996 | void init_fx_radix(double *fx_list, int radix) | |
4997 | { | |
4998 | /* initialize a per-radix list of tolerances. When added | |
4999 | to a number < 1.0, we can determine if we should raund | |
5000 | up and quit converting a number to a string. */ | |
5001 | int i; | |
5002 | fx_list[0] = 0.0; | |
5003 | fx_list[1] = 0.5; | |
5004 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
5005 | fx_list[i] = (fx_list[i-1] / radix); | |
5006 | } | |
5007 | ||
5008 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 5009 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 5010 | |
1be6b49c | 5011 | static size_t |
0b799eea | 5012 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 5013 | { |
0b799eea MV |
5014 | int efmt, dpt, d, i, wp; |
5015 | double *fx; | |
5016 | #ifdef DBL_MIN_10_EXP | |
5017 | double f_cpy; | |
5018 | int exp_cpy; | |
5019 | #endif /* DBL_MIN_10_EXP */ | |
5020 | size_t ch = 0; | |
5021 | int exp = 0; | |
5022 | ||
5023 | if(radix < 2 || | |
5024 | radix > SCM_MAX_DBL_RADIX) | |
5025 | { | |
5026 | /* revert to existing behavior */ | |
5027 | radix = 10; | |
5028 | } | |
5029 | ||
5030 | wp = scm_dblprec[radix-2]; | |
5031 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 5032 | |
f872b822 | 5033 | if (f == 0.0) |
abb7e44d MV |
5034 | { |
5035 | #ifdef HAVE_COPYSIGN | |
5036 | double sgn = copysign (1.0, f); | |
5037 | ||
5038 | if (sgn < 0.0) | |
5039 | a[ch++] = '-'; | |
5040 | #endif | |
abb7e44d MV |
5041 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
5042 | } | |
7351e207 | 5043 | |
2e65b52f | 5044 | if (isinf (f)) |
7351e207 MV |
5045 | { |
5046 | if (f < 0) | |
5047 | strcpy (a, "-inf.0"); | |
5048 | else | |
5049 | strcpy (a, "+inf.0"); | |
5050 | return ch+6; | |
5051 | } | |
2e65b52f | 5052 | else if (isnan (f)) |
7351e207 MV |
5053 | { |
5054 | strcpy (a, "+nan.0"); | |
5055 | return ch+6; | |
5056 | } | |
5057 | ||
f872b822 MD |
5058 | if (f < 0.0) |
5059 | { | |
5060 | f = -f; | |
5061 | a[ch++] = '-'; | |
5062 | } | |
7351e207 | 5063 | |
f872b822 MD |
5064 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
5065 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
5066 | /* just do the checking...if it passes, we do the conversion for our |
5067 | radix again below */ | |
5068 | f_cpy = f; | |
5069 | exp_cpy = exp; | |
5070 | ||
5071 | while (f_cpy < 1.0) | |
f872b822 | 5072 | { |
0b799eea MV |
5073 | f_cpy *= 10.0; |
5074 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
5075 | { |
5076 | a[ch++] = '#'; | |
5077 | a[ch++] = '.'; | |
5078 | a[ch++] = '#'; | |
5079 | return ch; | |
5080 | } | |
f872b822 | 5081 | } |
0b799eea | 5082 | while (f_cpy > 10.0) |
f872b822 | 5083 | { |
0b799eea MV |
5084 | f_cpy *= 0.10; |
5085 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
5086 | { |
5087 | a[ch++] = '#'; | |
5088 | a[ch++] = '.'; | |
5089 | a[ch++] = '#'; | |
5090 | return ch; | |
5091 | } | |
f872b822 | 5092 | } |
0b799eea MV |
5093 | #endif |
5094 | ||
f872b822 MD |
5095 | while (f < 1.0) |
5096 | { | |
0b799eea | 5097 | f *= radix; |
f872b822 MD |
5098 | exp--; |
5099 | } | |
0b799eea | 5100 | while (f > radix) |
f872b822 | 5101 | { |
0b799eea | 5102 | f /= radix; |
f872b822 MD |
5103 | exp++; |
5104 | } | |
0b799eea MV |
5105 | |
5106 | if (f + fx[wp] >= radix) | |
f872b822 MD |
5107 | { |
5108 | f = 1.0; | |
5109 | exp++; | |
5110 | } | |
0f2d19dd | 5111 | zero: |
0b799eea MV |
5112 | #ifdef ENGNOT |
5113 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 5114 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
5115 | exp -= dpt++; |
5116 | efmt = 1; | |
f872b822 MD |
5117 | #else |
5118 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 5119 | if (!efmt) |
cda139a7 MD |
5120 | { |
5121 | if (exp < 0) | |
5122 | { | |
5123 | a[ch++] = '0'; | |
5124 | a[ch++] = '.'; | |
5125 | dpt = exp; | |
f872b822 MD |
5126 | while (++dpt) |
5127 | a[ch++] = '0'; | |
cda139a7 MD |
5128 | } |
5129 | else | |
f872b822 | 5130 | dpt = exp + 1; |
cda139a7 | 5131 | } |
0f2d19dd JB |
5132 | else |
5133 | dpt = 1; | |
f872b822 MD |
5134 | #endif |
5135 | ||
5136 | do | |
5137 | { | |
5138 | d = f; | |
5139 | f -= d; | |
0b799eea | 5140 | a[ch++] = number_chars[d]; |
f872b822 MD |
5141 | if (f < fx[wp]) |
5142 | break; | |
5143 | if (f + fx[wp] >= 1.0) | |
5144 | { | |
0b799eea | 5145 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
5146 | break; |
5147 | } | |
0b799eea | 5148 | f *= radix; |
f872b822 MD |
5149 | if (!(--dpt)) |
5150 | a[ch++] = '.'; | |
0f2d19dd | 5151 | } |
f872b822 | 5152 | while (wp--); |
0f2d19dd JB |
5153 | |
5154 | if (dpt > 0) | |
cda139a7 | 5155 | { |
f872b822 | 5156 | #ifndef ENGNOT |
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 | |
f872b822 | 5166 | #endif |
cda139a7 | 5167 | { |
f872b822 MD |
5168 | while (--dpt) |
5169 | a[ch++] = '0'; | |
cda139a7 MD |
5170 | a[ch++] = '.'; |
5171 | } | |
5172 | } | |
f872b822 MD |
5173 | if (a[ch - 1] == '.') |
5174 | a[ch++] = '0'; /* trailing zero */ | |
5175 | if (efmt && exp) | |
5176 | { | |
5177 | a[ch++] = 'e'; | |
5178 | if (exp < 0) | |
5179 | { | |
5180 | exp = -exp; | |
5181 | a[ch++] = '-'; | |
5182 | } | |
0b799eea MV |
5183 | for (i = radix; i <= exp; i *= radix); |
5184 | for (i /= radix; i; i /= radix) | |
f872b822 | 5185 | { |
0b799eea | 5186 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
5187 | exp %= i; |
5188 | } | |
0f2d19dd | 5189 | } |
0f2d19dd JB |
5190 | return ch; |
5191 | } | |
5192 | ||
7a1aba42 MV |
5193 | |
5194 | static size_t | |
5195 | icmplx2str (double real, double imag, char *str, int radix) | |
5196 | { | |
5197 | size_t i; | |
c7218482 | 5198 | double sgn; |
7a1aba42 MV |
5199 | |
5200 | i = idbl2str (real, str, radix); | |
c7218482 MW |
5201 | #ifdef HAVE_COPYSIGN |
5202 | sgn = copysign (1.0, imag); | |
5203 | #else | |
5204 | sgn = imag; | |
5205 | #endif | |
5206 | /* Don't output a '+' for negative numbers or for Inf and | |
5207 | NaN. They will provide their own sign. */ | |
5208 | if (sgn >= 0 && DOUBLE_IS_FINITE (imag)) | |
5209 | str[i++] = '+'; | |
5210 | i += idbl2str (imag, &str[i], radix); | |
5211 | str[i++] = 'i'; | |
7a1aba42 MV |
5212 | return i; |
5213 | } | |
5214 | ||
1be6b49c | 5215 | static size_t |
0b799eea | 5216 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 5217 | { |
1be6b49c | 5218 | size_t i; |
3c9a524f | 5219 | if (SCM_REALP (flt)) |
0b799eea | 5220 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 5221 | else |
7a1aba42 MV |
5222 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
5223 | str, radix); | |
0f2d19dd JB |
5224 | return i; |
5225 | } | |
0f2d19dd | 5226 | |
2881e77b | 5227 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
5228 | characters in the result. |
5229 | rad is output base | |
5230 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 5231 | size_t |
2881e77b MV |
5232 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
5233 | { | |
5234 | if (num < 0) | |
5235 | { | |
5236 | *p++ = '-'; | |
5237 | return scm_iuint2str (-num, rad, p) + 1; | |
5238 | } | |
5239 | else | |
5240 | return scm_iuint2str (num, rad, p); | |
5241 | } | |
5242 | ||
5243 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
5244 | characters in the result. | |
5245 | rad is output base | |
5246 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
5247 | size_t | |
5248 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 5249 | { |
1be6b49c ML |
5250 | size_t j = 1; |
5251 | size_t i; | |
2881e77b | 5252 | scm_t_uintmax n = num; |
5c11cc9d | 5253 | |
a6f3af16 AW |
5254 | if (rad < 2 || rad > 36) |
5255 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
5256 | ||
f872b822 | 5257 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
5258 | j++; |
5259 | ||
5260 | i = j; | |
2881e77b | 5261 | n = num; |
f872b822 MD |
5262 | while (i--) |
5263 | { | |
5c11cc9d GH |
5264 | int d = n % rad; |
5265 | ||
f872b822 | 5266 | n /= rad; |
a6f3af16 | 5267 | p[i] = number_chars[d]; |
f872b822 | 5268 | } |
0f2d19dd JB |
5269 | return j; |
5270 | } | |
5271 | ||
a1ec6916 | 5272 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
5273 | (SCM n, SCM radix), |
5274 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
5275 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
5276 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 5277 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 5278 | { |
1bbd0b84 | 5279 | int base; |
98cb6e75 | 5280 | |
0aacf84e | 5281 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 5282 | base = 10; |
0aacf84e | 5283 | else |
5efd3c7d | 5284 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 5285 | |
e11e83f3 | 5286 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
5287 | { |
5288 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 5289 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 5290 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
5291 | } |
5292 | else if (SCM_BIGP (n)) | |
5293 | { | |
5294 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
5295 | scm_remember_upto_here_1 (n); | |
cc95e00a | 5296 | return scm_take_locale_string (str); |
0aacf84e | 5297 | } |
f92e85f7 MV |
5298 | else if (SCM_FRACTIONP (n)) |
5299 | { | |
f92e85f7 | 5300 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 5301 | scm_from_locale_string ("/"), |
f92e85f7 MV |
5302 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
5303 | } | |
0aacf84e MD |
5304 | else if (SCM_INEXACTP (n)) |
5305 | { | |
5306 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 5307 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
5308 | } |
5309 | else | |
bb628794 | 5310 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 5311 | } |
1bbd0b84 | 5312 | #undef FUNC_NAME |
0f2d19dd JB |
5313 | |
5314 | ||
ca46fb90 RB |
5315 | /* These print routines used to be stubbed here so that scm_repl.c |
5316 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 5317 | |
0f2d19dd | 5318 | int |
e81d98ec | 5319 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5320 | { |
56e55ac7 | 5321 | char num_buf[FLOBUFLEN]; |
0b799eea | 5322 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
5323 | return !0; |
5324 | } | |
5325 | ||
b479fe9a MV |
5326 | void |
5327 | scm_i_print_double (double val, SCM port) | |
5328 | { | |
5329 | char num_buf[FLOBUFLEN]; | |
5330 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
5331 | } | |
5332 | ||
f3ae5d60 | 5333 | int |
e81d98ec | 5334 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 5335 | |
f3ae5d60 | 5336 | { |
56e55ac7 | 5337 | char num_buf[FLOBUFLEN]; |
0b799eea | 5338 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
5339 | return !0; |
5340 | } | |
1cc91f1b | 5341 | |
7a1aba42 MV |
5342 | void |
5343 | scm_i_print_complex (double real, double imag, SCM port) | |
5344 | { | |
5345 | char num_buf[FLOBUFLEN]; | |
5346 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
5347 | } | |
5348 | ||
f92e85f7 MV |
5349 | int |
5350 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
5351 | { | |
5352 | SCM str; | |
f92e85f7 | 5353 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 5354 | scm_display (str, port); |
f92e85f7 MV |
5355 | scm_remember_upto_here_1 (str); |
5356 | return !0; | |
5357 | } | |
5358 | ||
0f2d19dd | 5359 | int |
e81d98ec | 5360 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5361 | { |
ca46fb90 RB |
5362 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
5363 | scm_remember_upto_here_1 (exp); | |
5364 | scm_lfwrite (str, (size_t) strlen (str), port); | |
5365 | free (str); | |
0f2d19dd JB |
5366 | return !0; |
5367 | } | |
5368 | /*** END nums->strs ***/ | |
5369 | ||
3c9a524f | 5370 | |
0f2d19dd | 5371 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 5372 | |
3c9a524f DH |
5373 | /* The following functions implement the conversion from strings to numbers. |
5374 | * The implementation somehow follows the grammar for numbers as it is given | |
5375 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
5376 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
5377 | * points should be noted about the implementation: | |
bc3d34f5 | 5378 | * |
3c9a524f DH |
5379 | * * Each function keeps a local index variable 'idx' that points at the |
5380 | * current position within the parsed string. The global index is only | |
5381 | * updated if the function could parse the corresponding syntactic unit | |
5382 | * successfully. | |
bc3d34f5 | 5383 | * |
3c9a524f | 5384 | * * Similarly, the functions keep track of indicators of inexactness ('#', |
bc3d34f5 MW |
5385 | * '.' or exponents) using local variables ('hash_seen', 'x'). |
5386 | * | |
3c9a524f DH |
5387 | * * Sequences of digits are parsed into temporary variables holding fixnums. |
5388 | * Only if these fixnums would overflow, the result variables are updated | |
5389 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
5390 | * the temporary variables holding the fixnums are cleared, and the process | |
5391 | * starts over again. If for example fixnums were able to store five decimal | |
5392 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
5393 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
5394 | * only every five digits two bignum operations were performed. | |
bc3d34f5 MW |
5395 | * |
5396 | * Notes on the handling of exactness specifiers: | |
5397 | * | |
5398 | * When parsing non-real complex numbers, we apply exactness specifiers on | |
5399 | * per-component basis, as is done in PLT Scheme. For complex numbers | |
5400 | * written in rectangular form, exactness specifiers are applied to the | |
5401 | * real and imaginary parts before calling scm_make_rectangular. For | |
5402 | * complex numbers written in polar form, exactness specifiers are applied | |
5403 | * to the magnitude and angle before calling scm_make_polar. | |
5404 | * | |
5405 | * There are two kinds of exactness specifiers: forced and implicit. A | |
5406 | * forced exactness specifier is a "#e" or "#i" prefix at the beginning of | |
5407 | * the entire number, and applies to both components of a complex number. | |
5408 | * "#e" causes each component to be made exact, and "#i" causes each | |
5409 | * component to be made inexact. If no forced exactness specifier is | |
5410 | * present, then the exactness of each component is determined | |
5411 | * independently by the presence or absence of a decimal point or hash mark | |
5412 | * within that component. If a decimal point or hash mark is present, the | |
5413 | * component is made inexact, otherwise it is made exact. | |
5414 | * | |
5415 | * After the exactness specifiers have been applied to each component, they | |
5416 | * are passed to either scm_make_rectangular or scm_make_polar to produce | |
5417 | * the final result. Note that this will result in a real number if the | |
5418 | * imaginary part, magnitude, or angle is an exact 0. | |
5419 | * | |
5420 | * For example, (string->number "#i5.0+0i") does the equivalent of: | |
5421 | * | |
5422 | * (make-rectangular (exact->inexact 5) (exact->inexact 0)) | |
3c9a524f DH |
5423 | */ |
5424 | ||
5425 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
5426 | ||
5427 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
5428 | ||
a6f3af16 AW |
5429 | /* Caller is responsible for checking that the return value is in range |
5430 | for the given radix, which should be <= 36. */ | |
5431 | static unsigned int | |
5432 | char_decimal_value (scm_t_uint32 c) | |
5433 | { | |
5434 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
5435 | that's certainly above any valid decimal, so we take advantage of | |
5436 | that to elide some tests. */ | |
5437 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
5438 | ||
5439 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
5440 | hexadecimals. */ | |
5441 | if (d >= 10U) | |
5442 | { | |
5443 | c = uc_tolower (c); | |
5444 | if (c >= (scm_t_uint32) 'a') | |
5445 | d = c - (scm_t_uint32)'a' + 10U; | |
5446 | } | |
5447 | return d; | |
5448 | } | |
3c9a524f | 5449 | |
2a8fecee | 5450 | static SCM |
3f47e526 | 5451 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 5452 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 5453 | { |
3c9a524f DH |
5454 | unsigned int idx = *p_idx; |
5455 | unsigned int hash_seen = 0; | |
5456 | scm_t_bits shift = 1; | |
5457 | scm_t_bits add = 0; | |
5458 | unsigned int digit_value; | |
5459 | SCM result; | |
5460 | char c; | |
3f47e526 | 5461 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5462 | |
5463 | if (idx == len) | |
5464 | return SCM_BOOL_F; | |
2a8fecee | 5465 | |
3f47e526 | 5466 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5467 | digit_value = char_decimal_value (c); |
3c9a524f DH |
5468 | if (digit_value >= radix) |
5469 | return SCM_BOOL_F; | |
5470 | ||
5471 | idx++; | |
d956fa6f | 5472 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 5473 | while (idx != len) |
f872b822 | 5474 | { |
3f47e526 | 5475 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5476 | if (c == '#') |
3c9a524f DH |
5477 | { |
5478 | hash_seen = 1; | |
5479 | digit_value = 0; | |
5480 | } | |
a6f3af16 AW |
5481 | else if (hash_seen) |
5482 | break; | |
3c9a524f | 5483 | else |
a6f3af16 AW |
5484 | { |
5485 | digit_value = char_decimal_value (c); | |
5486 | /* This check catches non-decimals in addition to out-of-range | |
5487 | decimals. */ | |
5488 | if (digit_value >= radix) | |
5489 | break; | |
5490 | } | |
3c9a524f DH |
5491 | |
5492 | idx++; | |
5493 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
5494 | { | |
d956fa6f | 5495 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5496 | if (add > 0) |
d956fa6f | 5497 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5498 | |
5499 | shift = radix; | |
5500 | add = digit_value; | |
5501 | } | |
5502 | else | |
5503 | { | |
5504 | shift = shift * radix; | |
5505 | add = add * radix + digit_value; | |
5506 | } | |
5507 | }; | |
5508 | ||
5509 | if (shift > 1) | |
d956fa6f | 5510 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5511 | if (add > 0) |
d956fa6f | 5512 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5513 | |
5514 | *p_idx = idx; | |
5515 | if (hash_seen) | |
5516 | *p_exactness = INEXACT; | |
5517 | ||
5518 | return result; | |
2a8fecee JB |
5519 | } |
5520 | ||
5521 | ||
3c9a524f DH |
5522 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
5523 | * covers the parts of the rules that start at a potential point. The value | |
5524 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
5525 | * in variable result. The content of *p_exactness indicates, whether a hash |
5526 | * has already been seen in the digits before the point. | |
3c9a524f | 5527 | */ |
1cc91f1b | 5528 | |
3f47e526 | 5529 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
5530 | |
5531 | static SCM | |
3f47e526 | 5532 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 5533 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 5534 | { |
3c9a524f DH |
5535 | unsigned int idx = *p_idx; |
5536 | enum t_exactness x = *p_exactness; | |
3f47e526 | 5537 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5538 | |
5539 | if (idx == len) | |
79d34f68 | 5540 | return result; |
3c9a524f | 5541 | |
3f47e526 | 5542 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5543 | { |
5544 | scm_t_bits shift = 1; | |
5545 | scm_t_bits add = 0; | |
5546 | unsigned int digit_value; | |
cff5fa33 | 5547 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
5548 | |
5549 | idx++; | |
5550 | while (idx != len) | |
5551 | { | |
3f47e526 MG |
5552 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5553 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5554 | { |
5555 | if (x == INEXACT) | |
5556 | return SCM_BOOL_F; | |
5557 | else | |
5558 | digit_value = DIGIT2UINT (c); | |
5559 | } | |
5560 | else if (c == '#') | |
5561 | { | |
5562 | x = INEXACT; | |
5563 | digit_value = 0; | |
5564 | } | |
5565 | else | |
5566 | break; | |
5567 | ||
5568 | idx++; | |
5569 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
5570 | { | |
d956fa6f MV |
5571 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5572 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 5573 | if (add > 0) |
d956fa6f | 5574 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5575 | |
5576 | shift = 10; | |
5577 | add = digit_value; | |
5578 | } | |
5579 | else | |
5580 | { | |
5581 | shift = shift * 10; | |
5582 | add = add * 10 + digit_value; | |
5583 | } | |
5584 | }; | |
5585 | ||
5586 | if (add > 0) | |
5587 | { | |
d956fa6f MV |
5588 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5589 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
5590 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
5591 | } |
5592 | ||
d8592269 | 5593 | result = scm_divide (result, big_shift); |
79d34f68 | 5594 | |
3c9a524f DH |
5595 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
5596 | x = INEXACT; | |
f872b822 | 5597 | } |
3c9a524f | 5598 | |
3c9a524f | 5599 | if (idx != len) |
f872b822 | 5600 | { |
3c9a524f DH |
5601 | int sign = 1; |
5602 | unsigned int start; | |
3f47e526 | 5603 | scm_t_wchar c; |
3c9a524f DH |
5604 | int exponent; |
5605 | SCM e; | |
5606 | ||
5607 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
5608 | ||
3f47e526 | 5609 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 5610 | { |
3c9a524f DH |
5611 | case 'd': case 'D': |
5612 | case 'e': case 'E': | |
5613 | case 'f': case 'F': | |
5614 | case 'l': case 'L': | |
5615 | case 's': case 'S': | |
5616 | idx++; | |
ee0ddd21 AW |
5617 | if (idx == len) |
5618 | return SCM_BOOL_F; | |
5619 | ||
3c9a524f | 5620 | start = idx; |
3f47e526 | 5621 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5622 | if (c == '-') |
5623 | { | |
5624 | idx++; | |
ee0ddd21 AW |
5625 | if (idx == len) |
5626 | return SCM_BOOL_F; | |
5627 | ||
3c9a524f | 5628 | sign = -1; |
3f47e526 | 5629 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5630 | } |
5631 | else if (c == '+') | |
5632 | { | |
5633 | idx++; | |
ee0ddd21 AW |
5634 | if (idx == len) |
5635 | return SCM_BOOL_F; | |
5636 | ||
3c9a524f | 5637 | sign = 1; |
3f47e526 | 5638 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5639 | } |
5640 | else | |
5641 | sign = 1; | |
5642 | ||
3f47e526 | 5643 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
5644 | return SCM_BOOL_F; |
5645 | ||
5646 | idx++; | |
5647 | exponent = DIGIT2UINT (c); | |
5648 | while (idx != len) | |
f872b822 | 5649 | { |
3f47e526 MG |
5650 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5651 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5652 | { |
5653 | idx++; | |
5654 | if (exponent <= SCM_MAXEXP) | |
5655 | exponent = exponent * 10 + DIGIT2UINT (c); | |
5656 | } | |
5657 | else | |
5658 | break; | |
f872b822 | 5659 | } |
3c9a524f DH |
5660 | |
5661 | if (exponent > SCM_MAXEXP) | |
f872b822 | 5662 | { |
3c9a524f | 5663 | size_t exp_len = idx - start; |
3f47e526 | 5664 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
5665 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
5666 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 5667 | } |
3c9a524f | 5668 | |
d956fa6f | 5669 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
5670 | if (sign == 1) |
5671 | result = scm_product (result, e); | |
5672 | else | |
6ebecdeb | 5673 | result = scm_divide (result, e); |
3c9a524f DH |
5674 | |
5675 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
5676 | x = INEXACT; | |
5677 | ||
f872b822 | 5678 | break; |
3c9a524f | 5679 | |
f872b822 | 5680 | default: |
3c9a524f | 5681 | break; |
f872b822 | 5682 | } |
0f2d19dd | 5683 | } |
3c9a524f DH |
5684 | |
5685 | *p_idx = idx; | |
5686 | if (x == INEXACT) | |
5687 | *p_exactness = x; | |
5688 | ||
5689 | return result; | |
0f2d19dd | 5690 | } |
0f2d19dd | 5691 | |
3c9a524f DH |
5692 | |
5693 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
5694 | ||
5695 | static SCM | |
3f47e526 | 5696 | mem2ureal (SCM mem, unsigned int *p_idx, |
9d427b2c | 5697 | unsigned int radix, enum t_exactness forced_x) |
0f2d19dd | 5698 | { |
3c9a524f | 5699 | unsigned int idx = *p_idx; |
164d2481 | 5700 | SCM result; |
3f47e526 | 5701 | size_t len = scm_i_string_length (mem); |
3c9a524f | 5702 | |
40f89215 NJ |
5703 | /* Start off believing that the number will be exact. This changes |
5704 | to INEXACT if we see a decimal point or a hash. */ | |
9d427b2c | 5705 | enum t_exactness implicit_x = EXACT; |
40f89215 | 5706 | |
3c9a524f DH |
5707 | if (idx == len) |
5708 | return SCM_BOOL_F; | |
5709 | ||
3f47e526 | 5710 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
5711 | { |
5712 | *p_idx = idx+5; | |
5713 | return scm_inf (); | |
5714 | } | |
5715 | ||
3f47e526 | 5716 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 5717 | { |
d8592269 MV |
5718 | /* Cobble up the fractional part. We might want to set the |
5719 | NaN's mantissa from it. */ | |
7351e207 | 5720 | idx += 4; |
9d427b2c | 5721 | mem2uinteger (mem, &idx, 10, &implicit_x); |
7351e207 MV |
5722 | *p_idx = idx; |
5723 | return scm_nan (); | |
5724 | } | |
5725 | ||
3f47e526 | 5726 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5727 | { |
5728 | if (radix != 10) | |
5729 | return SCM_BOOL_F; | |
5730 | else if (idx + 1 == len) | |
5731 | return SCM_BOOL_F; | |
3f47e526 | 5732 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
5733 | return SCM_BOOL_F; |
5734 | else | |
cff5fa33 | 5735 | result = mem2decimal_from_point (SCM_INUM0, mem, |
9d427b2c | 5736 | p_idx, &implicit_x); |
f872b822 | 5737 | } |
3c9a524f DH |
5738 | else |
5739 | { | |
3c9a524f | 5740 | SCM uinteger; |
3c9a524f | 5741 | |
9d427b2c | 5742 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 5743 | if (scm_is_false (uinteger)) |
3c9a524f DH |
5744 | return SCM_BOOL_F; |
5745 | ||
5746 | if (idx == len) | |
5747 | result = uinteger; | |
3f47e526 | 5748 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 5749 | { |
3c9a524f DH |
5750 | SCM divisor; |
5751 | ||
5752 | idx++; | |
ee0ddd21 AW |
5753 | if (idx == len) |
5754 | return SCM_BOOL_F; | |
3c9a524f | 5755 | |
9d427b2c | 5756 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 5757 | if (scm_is_false (divisor)) |
3c9a524f DH |
5758 | return SCM_BOOL_F; |
5759 | ||
f92e85f7 | 5760 | /* both are int/big here, I assume */ |
cba42c93 | 5761 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 5762 | } |
3c9a524f DH |
5763 | else if (radix == 10) |
5764 | { | |
9d427b2c | 5765 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
73e4de09 | 5766 | if (scm_is_false (result)) |
3c9a524f DH |
5767 | return SCM_BOOL_F; |
5768 | } | |
5769 | else | |
5770 | result = uinteger; | |
5771 | ||
5772 | *p_idx = idx; | |
f872b822 | 5773 | } |
164d2481 | 5774 | |
9d427b2c MW |
5775 | switch (forced_x) |
5776 | { | |
5777 | case EXACT: | |
5778 | if (SCM_INEXACTP (result)) | |
5779 | return scm_inexact_to_exact (result); | |
5780 | else | |
5781 | return result; | |
5782 | case INEXACT: | |
5783 | if (SCM_INEXACTP (result)) | |
5784 | return result; | |
5785 | else | |
5786 | return scm_exact_to_inexact (result); | |
5787 | case NO_EXACTNESS: | |
5788 | if (implicit_x == INEXACT) | |
5789 | { | |
5790 | if (SCM_INEXACTP (result)) | |
5791 | return result; | |
5792 | else | |
5793 | return scm_exact_to_inexact (result); | |
5794 | } | |
5795 | else | |
5796 | return result; | |
5797 | } | |
164d2481 | 5798 | |
9d427b2c MW |
5799 | /* We should never get here */ |
5800 | scm_syserror ("mem2ureal"); | |
3c9a524f | 5801 | } |
0f2d19dd | 5802 | |
0f2d19dd | 5803 | |
3c9a524f | 5804 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 5805 | |
3c9a524f | 5806 | static SCM |
3f47e526 | 5807 | mem2complex (SCM mem, unsigned int idx, |
9d427b2c | 5808 | unsigned int radix, enum t_exactness forced_x) |
3c9a524f | 5809 | { |
3f47e526 | 5810 | scm_t_wchar c; |
3c9a524f DH |
5811 | int sign = 0; |
5812 | SCM ureal; | |
3f47e526 | 5813 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5814 | |
5815 | if (idx == len) | |
5816 | return SCM_BOOL_F; | |
5817 | ||
3f47e526 | 5818 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5819 | if (c == '+') |
5820 | { | |
5821 | idx++; | |
5822 | sign = 1; | |
5823 | } | |
5824 | else if (c == '-') | |
5825 | { | |
5826 | idx++; | |
5827 | sign = -1; | |
0f2d19dd | 5828 | } |
0f2d19dd | 5829 | |
3c9a524f DH |
5830 | if (idx == len) |
5831 | return SCM_BOOL_F; | |
5832 | ||
9d427b2c | 5833 | ureal = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 5834 | if (scm_is_false (ureal)) |
f872b822 | 5835 | { |
3c9a524f DH |
5836 | /* input must be either +i or -i */ |
5837 | ||
5838 | if (sign == 0) | |
5839 | return SCM_BOOL_F; | |
5840 | ||
3f47e526 MG |
5841 | if (scm_i_string_ref (mem, idx) == 'i' |
5842 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 5843 | { |
3c9a524f DH |
5844 | idx++; |
5845 | if (idx != len) | |
5846 | return SCM_BOOL_F; | |
5847 | ||
cff5fa33 | 5848 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 5849 | } |
3c9a524f DH |
5850 | else |
5851 | return SCM_BOOL_F; | |
0f2d19dd | 5852 | } |
3c9a524f DH |
5853 | else |
5854 | { | |
73e4de09 | 5855 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 5856 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 5857 | |
3c9a524f DH |
5858 | if (idx == len) |
5859 | return ureal; | |
5860 | ||
3f47e526 | 5861 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 5862 | switch (c) |
f872b822 | 5863 | { |
3c9a524f DH |
5864 | case 'i': case 'I': |
5865 | /* either +<ureal>i or -<ureal>i */ | |
5866 | ||
5867 | idx++; | |
5868 | if (sign == 0) | |
5869 | return SCM_BOOL_F; | |
5870 | if (idx != len) | |
5871 | return SCM_BOOL_F; | |
cff5fa33 | 5872 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
5873 | |
5874 | case '@': | |
5875 | /* polar input: <real>@<real>. */ | |
5876 | ||
5877 | idx++; | |
5878 | if (idx == len) | |
5879 | return SCM_BOOL_F; | |
5880 | else | |
f872b822 | 5881 | { |
3c9a524f DH |
5882 | int sign; |
5883 | SCM angle; | |
5884 | SCM result; | |
5885 | ||
3f47e526 | 5886 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5887 | if (c == '+') |
5888 | { | |
5889 | idx++; | |
ee0ddd21 AW |
5890 | if (idx == len) |
5891 | return SCM_BOOL_F; | |
3c9a524f DH |
5892 | sign = 1; |
5893 | } | |
5894 | else if (c == '-') | |
5895 | { | |
5896 | idx++; | |
ee0ddd21 AW |
5897 | if (idx == len) |
5898 | return SCM_BOOL_F; | |
3c9a524f DH |
5899 | sign = -1; |
5900 | } | |
5901 | else | |
5902 | sign = 1; | |
5903 | ||
9d427b2c | 5904 | angle = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 5905 | if (scm_is_false (angle)) |
3c9a524f DH |
5906 | return SCM_BOOL_F; |
5907 | if (idx != len) | |
5908 | return SCM_BOOL_F; | |
5909 | ||
73e4de09 | 5910 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
5911 | angle = scm_difference (angle, SCM_UNDEFINED); |
5912 | ||
5913 | result = scm_make_polar (ureal, angle); | |
5914 | return result; | |
f872b822 | 5915 | } |
3c9a524f DH |
5916 | case '+': |
5917 | case '-': | |
5918 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 5919 | |
3c9a524f DH |
5920 | idx++; |
5921 | if (idx == len) | |
5922 | return SCM_BOOL_F; | |
5923 | else | |
5924 | { | |
5925 | int sign = (c == '+') ? 1 : -1; | |
9d427b2c | 5926 | SCM imag = mem2ureal (mem, &idx, radix, forced_x); |
0f2d19dd | 5927 | |
73e4de09 | 5928 | if (scm_is_false (imag)) |
d956fa6f | 5929 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 5930 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 5931 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 5932 | |
3c9a524f DH |
5933 | if (idx == len) |
5934 | return SCM_BOOL_F; | |
3f47e526 MG |
5935 | if (scm_i_string_ref (mem, idx) != 'i' |
5936 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 5937 | return SCM_BOOL_F; |
0f2d19dd | 5938 | |
3c9a524f DH |
5939 | idx++; |
5940 | if (idx != len) | |
5941 | return SCM_BOOL_F; | |
0f2d19dd | 5942 | |
1fe5e088 | 5943 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
5944 | } |
5945 | default: | |
5946 | return SCM_BOOL_F; | |
5947 | } | |
5948 | } | |
0f2d19dd | 5949 | } |
0f2d19dd JB |
5950 | |
5951 | ||
3c9a524f DH |
5952 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
5953 | ||
5954 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 5955 | |
0f2d19dd | 5956 | SCM |
3f47e526 | 5957 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 5958 | { |
3c9a524f DH |
5959 | unsigned int idx = 0; |
5960 | unsigned int radix = NO_RADIX; | |
5961 | enum t_exactness forced_x = NO_EXACTNESS; | |
3f47e526 | 5962 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5963 | |
5964 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 5965 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 5966 | { |
3f47e526 | 5967 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
5968 | { |
5969 | case 'b': case 'B': | |
5970 | if (radix != NO_RADIX) | |
5971 | return SCM_BOOL_F; | |
5972 | radix = DUAL; | |
5973 | break; | |
5974 | case 'd': case 'D': | |
5975 | if (radix != NO_RADIX) | |
5976 | return SCM_BOOL_F; | |
5977 | radix = DEC; | |
5978 | break; | |
5979 | case 'i': case 'I': | |
5980 | if (forced_x != NO_EXACTNESS) | |
5981 | return SCM_BOOL_F; | |
5982 | forced_x = INEXACT; | |
5983 | break; | |
5984 | case 'e': case 'E': | |
5985 | if (forced_x != NO_EXACTNESS) | |
5986 | return SCM_BOOL_F; | |
5987 | forced_x = EXACT; | |
5988 | break; | |
5989 | case 'o': case 'O': | |
5990 | if (radix != NO_RADIX) | |
5991 | return SCM_BOOL_F; | |
5992 | radix = OCT; | |
5993 | break; | |
5994 | case 'x': case 'X': | |
5995 | if (radix != NO_RADIX) | |
5996 | return SCM_BOOL_F; | |
5997 | radix = HEX; | |
5998 | break; | |
5999 | default: | |
f872b822 | 6000 | return SCM_BOOL_F; |
3c9a524f DH |
6001 | } |
6002 | idx += 2; | |
6003 | } | |
6004 | ||
6005 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
6006 | if (radix == NO_RADIX) | |
9d427b2c | 6007 | radix = default_radix; |
f872b822 | 6008 | |
9d427b2c | 6009 | return mem2complex (mem, idx, radix, forced_x); |
0f2d19dd JB |
6010 | } |
6011 | ||
3f47e526 MG |
6012 | SCM |
6013 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
6014 | unsigned int default_radix) | |
6015 | { | |
6016 | SCM str = scm_from_locale_stringn (mem, len); | |
6017 | ||
6018 | return scm_i_string_to_number (str, default_radix); | |
6019 | } | |
6020 | ||
0f2d19dd | 6021 | |
a1ec6916 | 6022 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 6023 | (SCM string, SCM radix), |
1e6808ea | 6024 | "Return a number of the maximally precise representation\n" |
942e5b91 | 6025 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
6026 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
6027 | "is a default radix that may be overridden by an explicit radix\n" | |
6028 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
6029 | "supplied, then the default radix is 10. If string is not a\n" | |
6030 | "syntactically valid notation for a number, then\n" | |
6031 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 6032 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
6033 | { |
6034 | SCM answer; | |
5efd3c7d | 6035 | unsigned int base; |
a6d9e5ab | 6036 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
6037 | |
6038 | if (SCM_UNBNDP (radix)) | |
6039 | base = 10; | |
6040 | else | |
6041 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
6042 | ||
3f47e526 | 6043 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
6044 | scm_remember_upto_here_1 (string); |
6045 | return answer; | |
0f2d19dd | 6046 | } |
1bbd0b84 | 6047 | #undef FUNC_NAME |
3c9a524f DH |
6048 | |
6049 | ||
0f2d19dd JB |
6050 | /*** END strs->nums ***/ |
6051 | ||
5986c47d | 6052 | |
8507ec80 MV |
6053 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
6054 | (SCM x), | |
6055 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
6056 | "otherwise.") | |
6057 | #define FUNC_NAME s_scm_number_p | |
6058 | { | |
6059 | return scm_from_bool (SCM_NUMBERP (x)); | |
6060 | } | |
6061 | #undef FUNC_NAME | |
6062 | ||
6063 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 6064 | (SCM x), |
942e5b91 | 6065 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 6066 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
6067 | "values form subsets of the set of complex numbers, i. e. the\n" |
6068 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
6069 | "rational or integer number.") | |
8507ec80 | 6070 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 6071 | { |
8507ec80 MV |
6072 | /* all numbers are complex. */ |
6073 | return scm_number_p (x); | |
0f2d19dd | 6074 | } |
1bbd0b84 | 6075 | #undef FUNC_NAME |
0f2d19dd | 6076 | |
f92e85f7 MV |
6077 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
6078 | (SCM x), | |
6079 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
6080 | "otherwise. Note that the set of integer values forms a subset of\n" | |
6081 | "the set of real numbers, i. e. the predicate will also be\n" | |
6082 | "fulfilled if @var{x} is an integer number.") | |
6083 | #define FUNC_NAME s_scm_real_p | |
6084 | { | |
c960e556 MW |
6085 | return scm_from_bool |
6086 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
6087 | } |
6088 | #undef FUNC_NAME | |
6089 | ||
6090 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 6091 | (SCM x), |
942e5b91 | 6092 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 6093 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 6094 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
6095 | "fulfilled if @var{x} is an integer number.") |
6096 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 6097 | { |
c960e556 | 6098 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
6099 | return SCM_BOOL_T; |
6100 | else if (SCM_REALP (x)) | |
c960e556 MW |
6101 | /* due to their limited precision, finite floating point numbers are |
6102 | rational as well. (finite means neither infinity nor a NaN) */ | |
6103 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 6104 | else |
bb628794 | 6105 | return SCM_BOOL_F; |
0f2d19dd | 6106 | } |
1bbd0b84 | 6107 | #undef FUNC_NAME |
0f2d19dd | 6108 | |
a1ec6916 | 6109 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 6110 | (SCM x), |
942e5b91 MG |
6111 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
6112 | "else.") | |
1bbd0b84 | 6113 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 6114 | { |
c960e556 | 6115 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 6116 | return SCM_BOOL_T; |
c960e556 MW |
6117 | else if (SCM_REALP (x)) |
6118 | { | |
6119 | double val = SCM_REAL_VALUE (x); | |
6120 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
6121 | } | |
6122 | else | |
8e43ed5d | 6123 | return SCM_BOOL_F; |
0f2d19dd | 6124 | } |
1bbd0b84 | 6125 | #undef FUNC_NAME |
0f2d19dd JB |
6126 | |
6127 | ||
8a1f4f98 AW |
6128 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
6129 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
6130 | (SCM x, SCM y, SCM rest), | |
6131 | "Return @code{#t} if all parameters are numerically equal.") | |
6132 | #define FUNC_NAME s_scm_i_num_eq_p | |
6133 | { | |
6134 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6135 | return SCM_BOOL_T; | |
6136 | while (!scm_is_null (rest)) | |
6137 | { | |
6138 | if (scm_is_false (scm_num_eq_p (x, y))) | |
6139 | return SCM_BOOL_F; | |
6140 | x = y; | |
6141 | y = scm_car (rest); | |
6142 | rest = scm_cdr (rest); | |
6143 | } | |
6144 | return scm_num_eq_p (x, y); | |
6145 | } | |
6146 | #undef FUNC_NAME | |
0f2d19dd | 6147 | SCM |
6e8d25a6 | 6148 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 6149 | { |
d8b95e27 | 6150 | again: |
e11e83f3 | 6151 | if (SCM_I_INUMP (x)) |
0aacf84e | 6152 | { |
e25f3727 | 6153 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 6154 | if (SCM_I_INUMP (y)) |
0aacf84e | 6155 | { |
e25f3727 | 6156 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 6157 | return scm_from_bool (xx == yy); |
0aacf84e MD |
6158 | } |
6159 | else if (SCM_BIGP (y)) | |
6160 | return SCM_BOOL_F; | |
6161 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
6162 | { |
6163 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
6164 | to a double and compare. | |
6165 | ||
6166 | But on a 64-bit system an inum is bigger than a double and | |
6167 | casting it to a double (call that dxx) will round. dxx is at | |
6168 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
6169 | an integer and fits a long. So we cast yy to a long and | |
6170 | compare with plain xx. | |
6171 | ||
6172 | An alternative (for any size system actually) would be to check | |
6173 | yy is an integer (with floor) and is in range of an inum | |
6174 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
6175 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
6176 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
6177 | |
6178 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
6179 | return scm_from_bool ((double) xx == yy |
6180 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6181 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 6182 | } |
0aacf84e | 6183 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6184 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6185 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
6186 | else if (SCM_FRACTIONP (y)) |
6187 | return SCM_BOOL_F; | |
0aacf84e | 6188 | else |
8a1f4f98 | 6189 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6190 | } |
0aacf84e MD |
6191 | else if (SCM_BIGP (x)) |
6192 | { | |
e11e83f3 | 6193 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6194 | return SCM_BOOL_F; |
6195 | else if (SCM_BIGP (y)) | |
6196 | { | |
6197 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6198 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6199 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6200 | } |
6201 | else if (SCM_REALP (y)) | |
6202 | { | |
6203 | int cmp; | |
2e65b52f | 6204 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6205 | return SCM_BOOL_F; |
6206 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6207 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6208 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6209 | } |
6210 | else if (SCM_COMPLEXP (y)) | |
6211 | { | |
6212 | int cmp; | |
6213 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
6214 | return SCM_BOOL_F; | |
2e65b52f | 6215 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
6216 | return SCM_BOOL_F; |
6217 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
6218 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6219 | return scm_from_bool (0 == cmp); |
0aacf84e | 6220 | } |
f92e85f7 MV |
6221 | else if (SCM_FRACTIONP (y)) |
6222 | return SCM_BOOL_F; | |
0aacf84e | 6223 | else |
8a1f4f98 | 6224 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6225 | } |
0aacf84e MD |
6226 | else if (SCM_REALP (x)) |
6227 | { | |
e8c5b1f2 | 6228 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 6229 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
6230 | { |
6231 | /* see comments with inum/real above */ | |
e25f3727 | 6232 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
6233 | return scm_from_bool (xx == (double) yy |
6234 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6235 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 6236 | } |
0aacf84e MD |
6237 | else if (SCM_BIGP (y)) |
6238 | { | |
6239 | int cmp; | |
2e65b52f | 6240 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6241 | return SCM_BOOL_F; |
6242 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6243 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6244 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6245 | } |
6246 | else if (SCM_REALP (y)) | |
73e4de09 | 6247 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 6248 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6249 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6250 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6251 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6252 | { |
6253 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6254 | if (isnan (xx)) |
d8b95e27 | 6255 | return SCM_BOOL_F; |
2e65b52f | 6256 | if (isinf (xx)) |
73e4de09 | 6257 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6258 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6259 | goto again; | |
6260 | } | |
0aacf84e | 6261 | else |
8a1f4f98 | 6262 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6263 | } |
0aacf84e MD |
6264 | else if (SCM_COMPLEXP (x)) |
6265 | { | |
e11e83f3 MV |
6266 | if (SCM_I_INUMP (y)) |
6267 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
6268 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6269 | else if (SCM_BIGP (y)) | |
6270 | { | |
6271 | int cmp; | |
6272 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
6273 | return SCM_BOOL_F; | |
2e65b52f | 6274 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
6275 | return SCM_BOOL_F; |
6276 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
6277 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6278 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6279 | } |
6280 | else if (SCM_REALP (y)) | |
73e4de09 | 6281 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
6282 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6283 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 6284 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6285 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6286 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6287 | { |
6288 | double xx; | |
6289 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
6290 | return SCM_BOOL_F; | |
6291 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 6292 | if (isnan (xx)) |
d8b95e27 | 6293 | return SCM_BOOL_F; |
2e65b52f | 6294 | if (isinf (xx)) |
73e4de09 | 6295 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6296 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6297 | goto again; | |
6298 | } | |
f92e85f7 | 6299 | else |
8a1f4f98 | 6300 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
6301 | } |
6302 | else if (SCM_FRACTIONP (x)) | |
6303 | { | |
e11e83f3 | 6304 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
6305 | return SCM_BOOL_F; |
6306 | else if (SCM_BIGP (y)) | |
6307 | return SCM_BOOL_F; | |
6308 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
6309 | { |
6310 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6311 | if (isnan (yy)) |
d8b95e27 | 6312 | return SCM_BOOL_F; |
2e65b52f | 6313 | if (isinf (yy)) |
73e4de09 | 6314 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6315 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6316 | goto again; | |
6317 | } | |
f92e85f7 | 6318 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
6319 | { |
6320 | double yy; | |
6321 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
6322 | return SCM_BOOL_F; | |
6323 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 6324 | if (isnan (yy)) |
d8b95e27 | 6325 | return SCM_BOOL_F; |
2e65b52f | 6326 | if (isinf (yy)) |
73e4de09 | 6327 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6328 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6329 | goto again; | |
6330 | } | |
f92e85f7 MV |
6331 | else if (SCM_FRACTIONP (y)) |
6332 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 6333 | else |
8a1f4f98 | 6334 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6335 | } |
0aacf84e | 6336 | else |
8a1f4f98 | 6337 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
6338 | } |
6339 | ||
6340 | ||
a5f0b599 KR |
6341 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
6342 | done are good for inums, but for bignums an answer can almost always be | |
6343 | had by just examining a few high bits of the operands, as done by GMP in | |
6344 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
6345 | of the float exponent to take into account. */ | |
6346 | ||
8c93b597 | 6347 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
6348 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
6349 | (SCM x, SCM y, SCM rest), | |
6350 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6351 | "increasing.") | |
6352 | #define FUNC_NAME s_scm_i_num_less_p | |
6353 | { | |
6354 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6355 | return SCM_BOOL_T; | |
6356 | while (!scm_is_null (rest)) | |
6357 | { | |
6358 | if (scm_is_false (scm_less_p (x, y))) | |
6359 | return SCM_BOOL_F; | |
6360 | x = y; | |
6361 | y = scm_car (rest); | |
6362 | rest = scm_cdr (rest); | |
6363 | } | |
6364 | return scm_less_p (x, y); | |
6365 | } | |
6366 | #undef FUNC_NAME | |
0f2d19dd | 6367 | SCM |
6e8d25a6 | 6368 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 6369 | { |
a5f0b599 | 6370 | again: |
e11e83f3 | 6371 | if (SCM_I_INUMP (x)) |
0aacf84e | 6372 | { |
e25f3727 | 6373 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6374 | if (SCM_I_INUMP (y)) |
0aacf84e | 6375 | { |
e25f3727 | 6376 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 6377 | return scm_from_bool (xx < yy); |
0aacf84e MD |
6378 | } |
6379 | else if (SCM_BIGP (y)) | |
6380 | { | |
6381 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6382 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6383 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6384 | } |
6385 | else if (SCM_REALP (y)) | |
73e4de09 | 6386 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 6387 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6388 | { |
6389 | /* "x < a/b" becomes "x*b < a" */ | |
6390 | int_frac: | |
6391 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
6392 | y = SCM_FRACTION_NUMERATOR (y); | |
6393 | goto again; | |
6394 | } | |
0aacf84e | 6395 | else |
8a1f4f98 | 6396 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6397 | } |
0aacf84e MD |
6398 | else if (SCM_BIGP (x)) |
6399 | { | |
e11e83f3 | 6400 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6401 | { |
6402 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6403 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6404 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6405 | } |
6406 | else if (SCM_BIGP (y)) | |
6407 | { | |
6408 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6409 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6410 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
6411 | } |
6412 | else if (SCM_REALP (y)) | |
6413 | { | |
6414 | int cmp; | |
2e65b52f | 6415 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6416 | return SCM_BOOL_F; |
6417 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6418 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6419 | return scm_from_bool (cmp < 0); |
0aacf84e | 6420 | } |
f92e85f7 | 6421 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 6422 | goto int_frac; |
0aacf84e | 6423 | else |
8a1f4f98 | 6424 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 6425 | } |
0aacf84e MD |
6426 | else if (SCM_REALP (x)) |
6427 | { | |
e11e83f3 MV |
6428 | if (SCM_I_INUMP (y)) |
6429 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
6430 | else if (SCM_BIGP (y)) |
6431 | { | |
6432 | int cmp; | |
2e65b52f | 6433 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6434 | return SCM_BOOL_F; |
6435 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6436 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6437 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
6438 | } |
6439 | else if (SCM_REALP (y)) | |
73e4de09 | 6440 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 6441 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6442 | { |
6443 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6444 | if (isnan (xx)) |
a5f0b599 | 6445 | return SCM_BOOL_F; |
2e65b52f | 6446 | if (isinf (xx)) |
73e4de09 | 6447 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
6448 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6449 | goto again; | |
6450 | } | |
f92e85f7 | 6451 | else |
8a1f4f98 | 6452 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
6453 | } |
6454 | else if (SCM_FRACTIONP (x)) | |
6455 | { | |
e11e83f3 | 6456 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
6457 | { |
6458 | /* "a/b < y" becomes "a < y*b" */ | |
6459 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
6460 | x = SCM_FRACTION_NUMERATOR (x); | |
6461 | goto again; | |
6462 | } | |
f92e85f7 | 6463 | else if (SCM_REALP (y)) |
a5f0b599 KR |
6464 | { |
6465 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6466 | if (isnan (yy)) |
a5f0b599 | 6467 | return SCM_BOOL_F; |
2e65b52f | 6468 | if (isinf (yy)) |
73e4de09 | 6469 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
6470 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6471 | goto again; | |
6472 | } | |
f92e85f7 | 6473 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6474 | { |
6475 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
6476 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
6477 | SCM_FRACTION_DENOMINATOR (y)); | |
6478 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
6479 | SCM_FRACTION_DENOMINATOR (x)); | |
6480 | x = new_x; | |
6481 | y = new_y; | |
6482 | goto again; | |
6483 | } | |
0aacf84e | 6484 | else |
8a1f4f98 | 6485 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6486 | } |
0aacf84e | 6487 | else |
8a1f4f98 | 6488 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
6489 | } |
6490 | ||
6491 | ||
8a1f4f98 AW |
6492 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
6493 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
6494 | (SCM x, SCM y, SCM rest), | |
6495 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6496 | "decreasing.") | |
6497 | #define FUNC_NAME s_scm_i_num_gr_p | |
6498 | { | |
6499 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6500 | return SCM_BOOL_T; | |
6501 | while (!scm_is_null (rest)) | |
6502 | { | |
6503 | if (scm_is_false (scm_gr_p (x, y))) | |
6504 | return SCM_BOOL_F; | |
6505 | x = y; | |
6506 | y = scm_car (rest); | |
6507 | rest = scm_cdr (rest); | |
6508 | } | |
6509 | return scm_gr_p (x, y); | |
6510 | } | |
6511 | #undef FUNC_NAME | |
6512 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
6513 | SCM |
6514 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 6515 | { |
c76b1eaf | 6516 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6517 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6518 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6519 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
6520 | else |
6521 | return scm_less_p (y, x); | |
0f2d19dd | 6522 | } |
1bbd0b84 | 6523 | #undef FUNC_NAME |
0f2d19dd JB |
6524 | |
6525 | ||
8a1f4f98 AW |
6526 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
6527 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
6528 | (SCM x, SCM y, SCM rest), | |
6529 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6530 | "non-decreasing.") | |
6531 | #define FUNC_NAME s_scm_i_num_leq_p | |
6532 | { | |
6533 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6534 | return SCM_BOOL_T; | |
6535 | while (!scm_is_null (rest)) | |
6536 | { | |
6537 | if (scm_is_false (scm_leq_p (x, y))) | |
6538 | return SCM_BOOL_F; | |
6539 | x = y; | |
6540 | y = scm_car (rest); | |
6541 | rest = scm_cdr (rest); | |
6542 | } | |
6543 | return scm_leq_p (x, y); | |
6544 | } | |
6545 | #undef FUNC_NAME | |
6546 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
6547 | SCM |
6548 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 6549 | { |
c76b1eaf | 6550 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6551 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6552 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6553 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6554 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6555 | return SCM_BOOL_F; |
c76b1eaf | 6556 | else |
73e4de09 | 6557 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 6558 | } |
1bbd0b84 | 6559 | #undef FUNC_NAME |
0f2d19dd JB |
6560 | |
6561 | ||
8a1f4f98 AW |
6562 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
6563 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
6564 | (SCM x, SCM y, SCM rest), | |
6565 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6566 | "non-increasing.") | |
6567 | #define FUNC_NAME s_scm_i_num_geq_p | |
6568 | { | |
6569 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6570 | return SCM_BOOL_T; | |
6571 | while (!scm_is_null (rest)) | |
6572 | { | |
6573 | if (scm_is_false (scm_geq_p (x, y))) | |
6574 | return SCM_BOOL_F; | |
6575 | x = y; | |
6576 | y = scm_car (rest); | |
6577 | rest = scm_cdr (rest); | |
6578 | } | |
6579 | return scm_geq_p (x, y); | |
6580 | } | |
6581 | #undef FUNC_NAME | |
6582 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
6583 | SCM |
6584 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 6585 | { |
c76b1eaf | 6586 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6587 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6588 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6589 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6590 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6591 | return SCM_BOOL_F; |
c76b1eaf | 6592 | else |
73e4de09 | 6593 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 6594 | } |
1bbd0b84 | 6595 | #undef FUNC_NAME |
0f2d19dd JB |
6596 | |
6597 | ||
2519490c MW |
6598 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
6599 | (SCM z), | |
6600 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
6601 | "zero.") | |
6602 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 6603 | { |
e11e83f3 | 6604 | if (SCM_I_INUMP (z)) |
bc36d050 | 6605 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 6606 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 6607 | return SCM_BOOL_F; |
0aacf84e | 6608 | else if (SCM_REALP (z)) |
73e4de09 | 6609 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 6610 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 6611 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 6612 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
6613 | else if (SCM_FRACTIONP (z)) |
6614 | return SCM_BOOL_F; | |
0aacf84e | 6615 | else |
2519490c | 6616 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 6617 | } |
2519490c | 6618 | #undef FUNC_NAME |
0f2d19dd JB |
6619 | |
6620 | ||
2519490c MW |
6621 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
6622 | (SCM x), | |
6623 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
6624 | "zero.") | |
6625 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 6626 | { |
e11e83f3 MV |
6627 | if (SCM_I_INUMP (x)) |
6628 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
6629 | else if (SCM_BIGP (x)) |
6630 | { | |
6631 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6632 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6633 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6634 | } |
6635 | else if (SCM_REALP (x)) | |
73e4de09 | 6636 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
6637 | else if (SCM_FRACTIONP (x)) |
6638 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6639 | else |
2519490c | 6640 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 6641 | } |
2519490c | 6642 | #undef FUNC_NAME |
0f2d19dd JB |
6643 | |
6644 | ||
2519490c MW |
6645 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
6646 | (SCM x), | |
6647 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
6648 | "zero.") | |
6649 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 6650 | { |
e11e83f3 MV |
6651 | if (SCM_I_INUMP (x)) |
6652 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
6653 | else if (SCM_BIGP (x)) |
6654 | { | |
6655 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6656 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6657 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6658 | } |
6659 | else if (SCM_REALP (x)) | |
73e4de09 | 6660 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
6661 | else if (SCM_FRACTIONP (x)) |
6662 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6663 | else |
2519490c | 6664 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 6665 | } |
2519490c | 6666 | #undef FUNC_NAME |
0f2d19dd JB |
6667 | |
6668 | ||
2a06f791 KR |
6669 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
6670 | required by r5rs. On that basis, for exact/inexact combinations the | |
6671 | exact is converted to inexact to compare and possibly return. This is | |
6672 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
6673 | its test, such trouble is not required for min and max. */ | |
6674 | ||
78d3deb1 AW |
6675 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
6676 | (SCM x, SCM y, SCM rest), | |
6677 | "Return the maximum of all parameter values.") | |
6678 | #define FUNC_NAME s_scm_i_max | |
6679 | { | |
6680 | while (!scm_is_null (rest)) | |
6681 | { x = scm_max (x, y); | |
6682 | y = scm_car (rest); | |
6683 | rest = scm_cdr (rest); | |
6684 | } | |
6685 | return scm_max (x, y); | |
6686 | } | |
6687 | #undef FUNC_NAME | |
6688 | ||
6689 | #define s_max s_scm_i_max | |
6690 | #define g_max g_scm_i_max | |
6691 | ||
0f2d19dd | 6692 | SCM |
6e8d25a6 | 6693 | scm_max (SCM x, SCM y) |
0f2d19dd | 6694 | { |
0aacf84e MD |
6695 | if (SCM_UNBNDP (y)) |
6696 | { | |
6697 | if (SCM_UNBNDP (x)) | |
6698 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 6699 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
6700 | return x; |
6701 | else | |
6702 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 6703 | } |
f4c627b3 | 6704 | |
e11e83f3 | 6705 | if (SCM_I_INUMP (x)) |
0aacf84e | 6706 | { |
e25f3727 | 6707 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6708 | if (SCM_I_INUMP (y)) |
0aacf84e | 6709 | { |
e25f3727 | 6710 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6711 | return (xx < yy) ? y : x; |
6712 | } | |
6713 | else if (SCM_BIGP (y)) | |
6714 | { | |
6715 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6716 | scm_remember_upto_here_1 (y); | |
6717 | return (sgn < 0) ? x : y; | |
6718 | } | |
6719 | else if (SCM_REALP (y)) | |
6720 | { | |
2e274311 MW |
6721 | double xxd = xx; |
6722 | double yyd = SCM_REAL_VALUE (y); | |
6723 | ||
6724 | if (xxd > yyd) | |
6725 | return scm_from_double (xxd); | |
6726 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
6727 | else if (SCM_LIKELY (!(xxd == yyd))) | |
6728 | return y; | |
6729 | /* Handle signed zeroes properly */ | |
6730 | else if (xx == 0) | |
6731 | return flo0; | |
6732 | else | |
6733 | return y; | |
0aacf84e | 6734 | } |
f92e85f7 MV |
6735 | else if (SCM_FRACTIONP (y)) |
6736 | { | |
e4bc5d6c | 6737 | use_less: |
73e4de09 | 6738 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 6739 | } |
0aacf84e MD |
6740 | else |
6741 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 6742 | } |
0aacf84e MD |
6743 | else if (SCM_BIGP (x)) |
6744 | { | |
e11e83f3 | 6745 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6746 | { |
6747 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6748 | scm_remember_upto_here_1 (x); | |
6749 | return (sgn < 0) ? y : x; | |
6750 | } | |
6751 | else if (SCM_BIGP (y)) | |
6752 | { | |
6753 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6754 | scm_remember_upto_here_2 (x, y); | |
6755 | return (cmp > 0) ? x : y; | |
6756 | } | |
6757 | else if (SCM_REALP (y)) | |
6758 | { | |
2a06f791 KR |
6759 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
6760 | double xx, yy; | |
6761 | big_real: | |
6762 | xx = scm_i_big2dbl (x); | |
6763 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 6764 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 6765 | } |
f92e85f7 MV |
6766 | else if (SCM_FRACTIONP (y)) |
6767 | { | |
e4bc5d6c | 6768 | goto use_less; |
f92e85f7 | 6769 | } |
0aacf84e MD |
6770 | else |
6771 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 6772 | } |
0aacf84e MD |
6773 | else if (SCM_REALP (x)) |
6774 | { | |
e11e83f3 | 6775 | if (SCM_I_INUMP (y)) |
0aacf84e | 6776 | { |
2e274311 MW |
6777 | scm_t_inum yy = SCM_I_INUM (y); |
6778 | double xxd = SCM_REAL_VALUE (x); | |
6779 | double yyd = yy; | |
6780 | ||
6781 | if (yyd > xxd) | |
6782 | return scm_from_double (yyd); | |
6783 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
6784 | else if (SCM_LIKELY (!(xxd == yyd))) | |
6785 | return x; | |
6786 | /* Handle signed zeroes properly */ | |
6787 | else if (yy == 0) | |
6788 | return flo0; | |
6789 | else | |
6790 | return x; | |
0aacf84e MD |
6791 | } |
6792 | else if (SCM_BIGP (y)) | |
6793 | { | |
b6f8f763 | 6794 | SCM_SWAP (x, y); |
2a06f791 | 6795 | goto big_real; |
0aacf84e MD |
6796 | } |
6797 | else if (SCM_REALP (y)) | |
6798 | { | |
0aacf84e | 6799 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
6800 | double yy = SCM_REAL_VALUE (y); |
6801 | ||
6802 | /* For purposes of max: +inf.0 > nan > everything else, per R6RS */ | |
6803 | if (xx > yy) | |
6804 | return x; | |
6805 | else if (SCM_LIKELY (xx < yy)) | |
6806 | return y; | |
6807 | /* If neither (xx > yy) nor (xx < yy), then | |
6808 | either they're equal or one is a NaN */ | |
6809 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 6810 | return DOUBLE_IS_POSITIVE_INFINITY (yy) ? y : x; |
2e274311 | 6811 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 6812 | return DOUBLE_IS_POSITIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
6813 | /* xx == yy, but handle signed zeroes properly */ |
6814 | else if (double_is_non_negative_zero (yy)) | |
6815 | return y; | |
6816 | else | |
6817 | return x; | |
0aacf84e | 6818 | } |
f92e85f7 MV |
6819 | else if (SCM_FRACTIONP (y)) |
6820 | { | |
6821 | double yy = scm_i_fraction2double (y); | |
6822 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 6823 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
6824 | } |
6825 | else | |
6826 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
6827 | } | |
6828 | else if (SCM_FRACTIONP (x)) | |
6829 | { | |
e11e83f3 | 6830 | if (SCM_I_INUMP (y)) |
f92e85f7 | 6831 | { |
e4bc5d6c | 6832 | goto use_less; |
f92e85f7 MV |
6833 | } |
6834 | else if (SCM_BIGP (y)) | |
6835 | { | |
e4bc5d6c | 6836 | goto use_less; |
f92e85f7 MV |
6837 | } |
6838 | else if (SCM_REALP (y)) | |
6839 | { | |
6840 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
6841 | /* if y==NaN then ">" is false, so we return the NaN y */ |
6842 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
6843 | } |
6844 | else if (SCM_FRACTIONP (y)) | |
6845 | { | |
e4bc5d6c | 6846 | goto use_less; |
f92e85f7 | 6847 | } |
0aacf84e MD |
6848 | else |
6849 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 6850 | } |
0aacf84e | 6851 | else |
f4c627b3 | 6852 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
6853 | } |
6854 | ||
6855 | ||
78d3deb1 AW |
6856 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
6857 | (SCM x, SCM y, SCM rest), | |
6858 | "Return the minimum of all parameter values.") | |
6859 | #define FUNC_NAME s_scm_i_min | |
6860 | { | |
6861 | while (!scm_is_null (rest)) | |
6862 | { x = scm_min (x, y); | |
6863 | y = scm_car (rest); | |
6864 | rest = scm_cdr (rest); | |
6865 | } | |
6866 | return scm_min (x, y); | |
6867 | } | |
6868 | #undef FUNC_NAME | |
6869 | ||
6870 | #define s_min s_scm_i_min | |
6871 | #define g_min g_scm_i_min | |
6872 | ||
0f2d19dd | 6873 | SCM |
6e8d25a6 | 6874 | scm_min (SCM x, SCM y) |
0f2d19dd | 6875 | { |
0aacf84e MD |
6876 | if (SCM_UNBNDP (y)) |
6877 | { | |
6878 | if (SCM_UNBNDP (x)) | |
6879 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 6880 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
6881 | return x; |
6882 | else | |
6883 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 6884 | } |
f4c627b3 | 6885 | |
e11e83f3 | 6886 | if (SCM_I_INUMP (x)) |
0aacf84e | 6887 | { |
e25f3727 | 6888 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6889 | if (SCM_I_INUMP (y)) |
0aacf84e | 6890 | { |
e25f3727 | 6891 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6892 | return (xx < yy) ? x : y; |
6893 | } | |
6894 | else if (SCM_BIGP (y)) | |
6895 | { | |
6896 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6897 | scm_remember_upto_here_1 (y); | |
6898 | return (sgn < 0) ? y : x; | |
6899 | } | |
6900 | else if (SCM_REALP (y)) | |
6901 | { | |
6902 | double z = xx; | |
6903 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 6904 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 6905 | } |
f92e85f7 MV |
6906 | else if (SCM_FRACTIONP (y)) |
6907 | { | |
e4bc5d6c | 6908 | use_less: |
73e4de09 | 6909 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 6910 | } |
0aacf84e MD |
6911 | else |
6912 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 6913 | } |
0aacf84e MD |
6914 | else if (SCM_BIGP (x)) |
6915 | { | |
e11e83f3 | 6916 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6917 | { |
6918 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6919 | scm_remember_upto_here_1 (x); | |
6920 | return (sgn < 0) ? x : y; | |
6921 | } | |
6922 | else if (SCM_BIGP (y)) | |
6923 | { | |
6924 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6925 | scm_remember_upto_here_2 (x, y); | |
6926 | return (cmp > 0) ? y : x; | |
6927 | } | |
6928 | else if (SCM_REALP (y)) | |
6929 | { | |
2a06f791 KR |
6930 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
6931 | double xx, yy; | |
6932 | big_real: | |
6933 | xx = scm_i_big2dbl (x); | |
6934 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 6935 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 6936 | } |
f92e85f7 MV |
6937 | else if (SCM_FRACTIONP (y)) |
6938 | { | |
e4bc5d6c | 6939 | goto use_less; |
f92e85f7 | 6940 | } |
0aacf84e MD |
6941 | else |
6942 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 6943 | } |
0aacf84e MD |
6944 | else if (SCM_REALP (x)) |
6945 | { | |
e11e83f3 | 6946 | if (SCM_I_INUMP (y)) |
0aacf84e | 6947 | { |
e11e83f3 | 6948 | double z = SCM_I_INUM (y); |
0aacf84e | 6949 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 6950 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
6951 | } |
6952 | else if (SCM_BIGP (y)) | |
6953 | { | |
b6f8f763 | 6954 | SCM_SWAP (x, y); |
2a06f791 | 6955 | goto big_real; |
0aacf84e MD |
6956 | } |
6957 | else if (SCM_REALP (y)) | |
6958 | { | |
0aacf84e | 6959 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
6960 | double yy = SCM_REAL_VALUE (y); |
6961 | ||
6962 | /* For purposes of min: -inf.0 < nan < everything else, per R6RS */ | |
6963 | if (xx < yy) | |
6964 | return x; | |
6965 | else if (SCM_LIKELY (xx > yy)) | |
6966 | return y; | |
6967 | /* If neither (xx < yy) nor (xx > yy), then | |
6968 | either they're equal or one is a NaN */ | |
6969 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 6970 | return DOUBLE_IS_NEGATIVE_INFINITY (yy) ? y : x; |
2e274311 | 6971 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 6972 | return DOUBLE_IS_NEGATIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
6973 | /* xx == yy, but handle signed zeroes properly */ |
6974 | else if (double_is_non_negative_zero (xx)) | |
6975 | return y; | |
6976 | else | |
6977 | return x; | |
0aacf84e | 6978 | } |
f92e85f7 MV |
6979 | else if (SCM_FRACTIONP (y)) |
6980 | { | |
6981 | double yy = scm_i_fraction2double (y); | |
6982 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 6983 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 6984 | } |
0aacf84e MD |
6985 | else |
6986 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 6987 | } |
f92e85f7 MV |
6988 | else if (SCM_FRACTIONP (x)) |
6989 | { | |
e11e83f3 | 6990 | if (SCM_I_INUMP (y)) |
f92e85f7 | 6991 | { |
e4bc5d6c | 6992 | goto use_less; |
f92e85f7 MV |
6993 | } |
6994 | else if (SCM_BIGP (y)) | |
6995 | { | |
e4bc5d6c | 6996 | goto use_less; |
f92e85f7 MV |
6997 | } |
6998 | else if (SCM_REALP (y)) | |
6999 | { | |
7000 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
7001 | /* if y==NaN then "<" is false, so we return the NaN y */ |
7002 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
7003 | } |
7004 | else if (SCM_FRACTIONP (y)) | |
7005 | { | |
e4bc5d6c | 7006 | goto use_less; |
f92e85f7 MV |
7007 | } |
7008 | else | |
78d3deb1 | 7009 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 7010 | } |
0aacf84e | 7011 | else |
f4c627b3 | 7012 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
7013 | } |
7014 | ||
7015 | ||
8ccd24f7 AW |
7016 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
7017 | (SCM x, SCM y, SCM rest), | |
7018 | "Return the sum of all parameter values. Return 0 if called without\n" | |
7019 | "any parameters." ) | |
7020 | #define FUNC_NAME s_scm_i_sum | |
7021 | { | |
7022 | while (!scm_is_null (rest)) | |
7023 | { x = scm_sum (x, y); | |
7024 | y = scm_car (rest); | |
7025 | rest = scm_cdr (rest); | |
7026 | } | |
7027 | return scm_sum (x, y); | |
7028 | } | |
7029 | #undef FUNC_NAME | |
7030 | ||
7031 | #define s_sum s_scm_i_sum | |
7032 | #define g_sum g_scm_i_sum | |
7033 | ||
0f2d19dd | 7034 | SCM |
6e8d25a6 | 7035 | scm_sum (SCM x, SCM y) |
0f2d19dd | 7036 | { |
9cc37597 | 7037 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7038 | { |
7039 | if (SCM_NUMBERP (x)) return x; | |
7040 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 7041 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 7042 | } |
c209c88e | 7043 | |
9cc37597 | 7044 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 7045 | { |
9cc37597 | 7046 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 7047 | { |
e25f3727 AW |
7048 | scm_t_inum xx = SCM_I_INUM (x); |
7049 | scm_t_inum yy = SCM_I_INUM (y); | |
7050 | scm_t_inum z = xx + yy; | |
7051 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
7052 | } |
7053 | else if (SCM_BIGP (y)) | |
7054 | { | |
7055 | SCM_SWAP (x, y); | |
7056 | goto add_big_inum; | |
7057 | } | |
7058 | else if (SCM_REALP (y)) | |
7059 | { | |
e25f3727 | 7060 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 7061 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
7062 | } |
7063 | else if (SCM_COMPLEXP (y)) | |
7064 | { | |
e25f3727 | 7065 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 7066 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
7067 | SCM_COMPLEX_IMAG (y)); |
7068 | } | |
f92e85f7 | 7069 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7070 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7071 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7072 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
7073 | else |
7074 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
7075 | } else if (SCM_BIGP (x)) |
7076 | { | |
e11e83f3 | 7077 | if (SCM_I_INUMP (y)) |
0aacf84e | 7078 | { |
e25f3727 | 7079 | scm_t_inum inum; |
0aacf84e MD |
7080 | int bigsgn; |
7081 | add_big_inum: | |
e11e83f3 | 7082 | inum = SCM_I_INUM (y); |
0aacf84e MD |
7083 | if (inum == 0) |
7084 | return x; | |
7085 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7086 | if (inum < 0) | |
7087 | { | |
7088 | SCM result = scm_i_mkbig (); | |
7089 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
7090 | scm_remember_upto_here_1 (x); | |
7091 | /* we know the result will have to be a bignum */ | |
7092 | if (bigsgn == -1) | |
7093 | return result; | |
7094 | return scm_i_normbig (result); | |
7095 | } | |
7096 | else | |
7097 | { | |
7098 | SCM result = scm_i_mkbig (); | |
7099 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
7100 | scm_remember_upto_here_1 (x); | |
7101 | /* we know the result will have to be a bignum */ | |
7102 | if (bigsgn == 1) | |
7103 | return result; | |
7104 | return scm_i_normbig (result); | |
7105 | } | |
7106 | } | |
7107 | else if (SCM_BIGP (y)) | |
7108 | { | |
7109 | SCM result = scm_i_mkbig (); | |
7110 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7111 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7112 | mpz_add (SCM_I_BIG_MPZ (result), | |
7113 | SCM_I_BIG_MPZ (x), | |
7114 | SCM_I_BIG_MPZ (y)); | |
7115 | scm_remember_upto_here_2 (x, y); | |
7116 | /* we know the result will have to be a bignum */ | |
7117 | if (sgn_x == sgn_y) | |
7118 | return result; | |
7119 | return scm_i_normbig (result); | |
7120 | } | |
7121 | else if (SCM_REALP (y)) | |
7122 | { | |
7123 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
7124 | scm_remember_upto_here_1 (x); | |
55f26379 | 7125 | return scm_from_double (result); |
0aacf84e MD |
7126 | } |
7127 | else if (SCM_COMPLEXP (y)) | |
7128 | { | |
7129 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7130 | + SCM_COMPLEX_REAL (y)); | |
7131 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7132 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7133 | } |
f92e85f7 | 7134 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7135 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7136 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7137 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7138 | else |
7139 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 7140 | } |
0aacf84e MD |
7141 | else if (SCM_REALP (x)) |
7142 | { | |
e11e83f3 | 7143 | if (SCM_I_INUMP (y)) |
55f26379 | 7144 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
7145 | else if (SCM_BIGP (y)) |
7146 | { | |
7147 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
7148 | scm_remember_upto_here_1 (y); | |
55f26379 | 7149 | return scm_from_double (result); |
0aacf84e MD |
7150 | } |
7151 | else if (SCM_REALP (y)) | |
55f26379 | 7152 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 7153 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7154 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7155 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7156 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7157 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
7158 | else |
7159 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 7160 | } |
0aacf84e MD |
7161 | else if (SCM_COMPLEXP (x)) |
7162 | { | |
e11e83f3 | 7163 | if (SCM_I_INUMP (y)) |
8507ec80 | 7164 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
7165 | SCM_COMPLEX_IMAG (x)); |
7166 | else if (SCM_BIGP (y)) | |
7167 | { | |
7168 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
7169 | + SCM_COMPLEX_REAL (x)); | |
7170 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7171 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7172 | } |
7173 | else if (SCM_REALP (y)) | |
8507ec80 | 7174 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
7175 | SCM_COMPLEX_IMAG (x)); |
7176 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7177 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7178 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7179 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7180 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
7181 | SCM_COMPLEX_IMAG (x)); |
7182 | else | |
7183 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
7184 | } | |
7185 | else if (SCM_FRACTIONP (x)) | |
7186 | { | |
e11e83f3 | 7187 | if (SCM_I_INUMP (y)) |
cba42c93 | 7188 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7189 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7190 | SCM_FRACTION_DENOMINATOR (x)); | |
7191 | else if (SCM_BIGP (y)) | |
cba42c93 | 7192 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7193 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7194 | SCM_FRACTION_DENOMINATOR (x)); | |
7195 | else if (SCM_REALP (y)) | |
55f26379 | 7196 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 7197 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7198 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
7199 | SCM_COMPLEX_IMAG (y)); |
7200 | else if (SCM_FRACTIONP (y)) | |
7201 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 7202 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7203 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7204 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7205 | else |
7206 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 7207 | } |
0aacf84e | 7208 | else |
98cb6e75 | 7209 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
7210 | } |
7211 | ||
7212 | ||
40882e3d KR |
7213 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
7214 | (SCM x), | |
7215 | "Return @math{@var{x}+1}.") | |
7216 | #define FUNC_NAME s_scm_oneplus | |
7217 | { | |
cff5fa33 | 7218 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
7219 | } |
7220 | #undef FUNC_NAME | |
7221 | ||
7222 | ||
78d3deb1 AW |
7223 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
7224 | (SCM x, SCM y, SCM rest), | |
7225 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
7226 | "the sum of all but the first argument are subtracted from the first\n" | |
7227 | "argument.") | |
7228 | #define FUNC_NAME s_scm_i_difference | |
7229 | { | |
7230 | while (!scm_is_null (rest)) | |
7231 | { x = scm_difference (x, y); | |
7232 | y = scm_car (rest); | |
7233 | rest = scm_cdr (rest); | |
7234 | } | |
7235 | return scm_difference (x, y); | |
7236 | } | |
7237 | #undef FUNC_NAME | |
7238 | ||
7239 | #define s_difference s_scm_i_difference | |
7240 | #define g_difference g_scm_i_difference | |
7241 | ||
0f2d19dd | 7242 | SCM |
6e8d25a6 | 7243 | scm_difference (SCM x, SCM y) |
78d3deb1 | 7244 | #define FUNC_NAME s_difference |
0f2d19dd | 7245 | { |
9cc37597 | 7246 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7247 | { |
7248 | if (SCM_UNBNDP (x)) | |
7249 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
7250 | else | |
e11e83f3 | 7251 | if (SCM_I_INUMP (x)) |
ca46fb90 | 7252 | { |
e25f3727 | 7253 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 7254 | if (SCM_FIXABLE (xx)) |
d956fa6f | 7255 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 7256 | else |
e25f3727 | 7257 | return scm_i_inum2big (xx); |
ca46fb90 RB |
7258 | } |
7259 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
7260 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
7261 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
7262 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
7263 | else if (SCM_REALP (x)) | |
55f26379 | 7264 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 7265 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 7266 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 7267 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 7268 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 7269 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 7270 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
7271 | else |
7272 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 7273 | } |
ca46fb90 | 7274 | |
9cc37597 | 7275 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7276 | { |
9cc37597 | 7277 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7278 | { |
e25f3727 AW |
7279 | scm_t_inum xx = SCM_I_INUM (x); |
7280 | scm_t_inum yy = SCM_I_INUM (y); | |
7281 | scm_t_inum z = xx - yy; | |
0aacf84e | 7282 | if (SCM_FIXABLE (z)) |
d956fa6f | 7283 | return SCM_I_MAKINUM (z); |
0aacf84e | 7284 | else |
e25f3727 | 7285 | return scm_i_inum2big (z); |
0aacf84e MD |
7286 | } |
7287 | else if (SCM_BIGP (y)) | |
7288 | { | |
7289 | /* inum-x - big-y */ | |
e25f3727 | 7290 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 7291 | |
0aacf84e | 7292 | if (xx == 0) |
b5c40589 MW |
7293 | { |
7294 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
7295 | bignum, but negating that gives a fixnum. */ | |
7296 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
7297 | } | |
0aacf84e MD |
7298 | else |
7299 | { | |
7300 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7301 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7302 | |
0aacf84e MD |
7303 | if (xx >= 0) |
7304 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
7305 | else | |
7306 | { | |
7307 | /* x - y == -(y + -x) */ | |
7308 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
7309 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7310 | } | |
7311 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 7312 | |
0aacf84e MD |
7313 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
7314 | /* we know the result will have to be a bignum */ | |
7315 | return result; | |
7316 | else | |
7317 | return scm_i_normbig (result); | |
7318 | } | |
7319 | } | |
7320 | else if (SCM_REALP (y)) | |
7321 | { | |
e25f3727 | 7322 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7323 | |
7324 | /* | |
7325 | * We need to handle x == exact 0 | |
7326 | * specially because R6RS states that: | |
7327 | * (- 0.0) ==> -0.0 and | |
7328 | * (- 0.0 0.0) ==> 0.0 | |
7329 | * and the scheme compiler changes | |
7330 | * (- 0.0) into (- 0 0.0) | |
7331 | * So we need to treat (- 0 0.0) like (- 0.0). | |
7332 | * At the C level, (-x) is different than (0.0 - x). | |
7333 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
7334 | */ | |
7335 | if (xx == 0) | |
7336 | return scm_from_double (- SCM_REAL_VALUE (y)); | |
7337 | else | |
7338 | return scm_from_double (xx - SCM_REAL_VALUE (y)); | |
0aacf84e MD |
7339 | } |
7340 | else if (SCM_COMPLEXP (y)) | |
7341 | { | |
e25f3727 | 7342 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7343 | |
7344 | /* We need to handle x == exact 0 specially. | |
7345 | See the comment above (for SCM_REALP (y)) */ | |
7346 | if (xx == 0) | |
7347 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
7348 | - SCM_COMPLEX_IMAG (y)); | |
7349 | else | |
7350 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
7351 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 7352 | } |
f92e85f7 MV |
7353 | else if (SCM_FRACTIONP (y)) |
7354 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 7355 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7356 | SCM_FRACTION_NUMERATOR (y)), |
7357 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7358 | else |
7359 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 7360 | } |
0aacf84e MD |
7361 | else if (SCM_BIGP (x)) |
7362 | { | |
e11e83f3 | 7363 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7364 | { |
7365 | /* big-x - inum-y */ | |
e25f3727 | 7366 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 7367 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 7368 | |
0aacf84e MD |
7369 | scm_remember_upto_here_1 (x); |
7370 | if (sgn_x == 0) | |
c71b0706 | 7371 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 7372 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
7373 | else |
7374 | { | |
7375 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7376 | |
708f22c6 KR |
7377 | if (yy >= 0) |
7378 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
7379 | else | |
7380 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 7381 | scm_remember_upto_here_1 (x); |
ca46fb90 | 7382 | |
0aacf84e MD |
7383 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
7384 | /* we know the result will have to be a bignum */ | |
7385 | return result; | |
7386 | else | |
7387 | return scm_i_normbig (result); | |
7388 | } | |
7389 | } | |
7390 | else if (SCM_BIGP (y)) | |
7391 | { | |
7392 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7393 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7394 | SCM result = scm_i_mkbig (); | |
7395 | mpz_sub (SCM_I_BIG_MPZ (result), | |
7396 | SCM_I_BIG_MPZ (x), | |
7397 | SCM_I_BIG_MPZ (y)); | |
7398 | scm_remember_upto_here_2 (x, y); | |
7399 | /* we know the result will have to be a bignum */ | |
7400 | if ((sgn_x == 1) && (sgn_y == -1)) | |
7401 | return result; | |
7402 | if ((sgn_x == -1) && (sgn_y == 1)) | |
7403 | return result; | |
7404 | return scm_i_normbig (result); | |
7405 | } | |
7406 | else if (SCM_REALP (y)) | |
7407 | { | |
7408 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
7409 | scm_remember_upto_here_1 (x); | |
55f26379 | 7410 | return scm_from_double (result); |
0aacf84e MD |
7411 | } |
7412 | else if (SCM_COMPLEXP (y)) | |
7413 | { | |
7414 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7415 | - SCM_COMPLEX_REAL (y)); | |
7416 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7417 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7418 | } |
f92e85f7 | 7419 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7420 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7421 | SCM_FRACTION_NUMERATOR (y)), |
7422 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 7423 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 7424 | } |
0aacf84e MD |
7425 | else if (SCM_REALP (x)) |
7426 | { | |
e11e83f3 | 7427 | if (SCM_I_INUMP (y)) |
55f26379 | 7428 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
7429 | else if (SCM_BIGP (y)) |
7430 | { | |
7431 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7432 | scm_remember_upto_here_1 (x); | |
55f26379 | 7433 | return scm_from_double (result); |
0aacf84e MD |
7434 | } |
7435 | else if (SCM_REALP (y)) | |
55f26379 | 7436 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 7437 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7438 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7439 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7440 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7441 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
7442 | else |
7443 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7444 | } |
0aacf84e MD |
7445 | else if (SCM_COMPLEXP (x)) |
7446 | { | |
e11e83f3 | 7447 | if (SCM_I_INUMP (y)) |
8507ec80 | 7448 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
7449 | SCM_COMPLEX_IMAG (x)); |
7450 | else if (SCM_BIGP (y)) | |
7451 | { | |
7452 | double real_part = (SCM_COMPLEX_REAL (x) | |
7453 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
7454 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7455 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
7456 | } |
7457 | else if (SCM_REALP (y)) | |
8507ec80 | 7458 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
7459 | SCM_COMPLEX_IMAG (x)); |
7460 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7461 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7462 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7463 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7464 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
7465 | SCM_COMPLEX_IMAG (x)); |
7466 | else | |
7467 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
7468 | } | |
7469 | else if (SCM_FRACTIONP (x)) | |
7470 | { | |
e11e83f3 | 7471 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7472 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 7473 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7474 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7475 | SCM_FRACTION_DENOMINATOR (x)); | |
7476 | else if (SCM_BIGP (y)) | |
cba42c93 | 7477 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7478 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7479 | SCM_FRACTION_DENOMINATOR (x)); | |
7480 | else if (SCM_REALP (y)) | |
55f26379 | 7481 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 7482 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7483 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7484 | -SCM_COMPLEX_IMAG (y)); |
7485 | else if (SCM_FRACTIONP (y)) | |
7486 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 7487 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7488 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7489 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7490 | else |
7491 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7492 | } |
0aacf84e | 7493 | else |
98cb6e75 | 7494 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 7495 | } |
c05e97b7 | 7496 | #undef FUNC_NAME |
0f2d19dd | 7497 | |
ca46fb90 | 7498 | |
40882e3d KR |
7499 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
7500 | (SCM x), | |
7501 | "Return @math{@var{x}-1}.") | |
7502 | #define FUNC_NAME s_scm_oneminus | |
7503 | { | |
cff5fa33 | 7504 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
7505 | } |
7506 | #undef FUNC_NAME | |
7507 | ||
7508 | ||
78d3deb1 AW |
7509 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
7510 | (SCM x, SCM y, SCM rest), | |
7511 | "Return the product of all arguments. If called without arguments,\n" | |
7512 | "1 is returned.") | |
7513 | #define FUNC_NAME s_scm_i_product | |
7514 | { | |
7515 | while (!scm_is_null (rest)) | |
7516 | { x = scm_product (x, y); | |
7517 | y = scm_car (rest); | |
7518 | rest = scm_cdr (rest); | |
7519 | } | |
7520 | return scm_product (x, y); | |
7521 | } | |
7522 | #undef FUNC_NAME | |
7523 | ||
7524 | #define s_product s_scm_i_product | |
7525 | #define g_product g_scm_i_product | |
7526 | ||
0f2d19dd | 7527 | SCM |
6e8d25a6 | 7528 | scm_product (SCM x, SCM y) |
0f2d19dd | 7529 | { |
9cc37597 | 7530 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7531 | { |
7532 | if (SCM_UNBNDP (x)) | |
d956fa6f | 7533 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
7534 | else if (SCM_NUMBERP (x)) |
7535 | return x; | |
7536 | else | |
7537 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 7538 | } |
ca46fb90 | 7539 | |
9cc37597 | 7540 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7541 | { |
e25f3727 | 7542 | scm_t_inum xx; |
f4c627b3 | 7543 | |
5e791807 | 7544 | xinum: |
e11e83f3 | 7545 | xx = SCM_I_INUM (x); |
f4c627b3 | 7546 | |
0aacf84e MD |
7547 | switch (xx) |
7548 | { | |
5e791807 MW |
7549 | case 1: |
7550 | /* exact1 is the universal multiplicative identity */ | |
7551 | return y; | |
7552 | break; | |
7553 | case 0: | |
7554 | /* exact0 times a fixnum is exact0: optimize this case */ | |
7555 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
7556 | return SCM_INUM0; | |
7557 | /* if the other argument is inexact, the result is inexact, | |
7558 | and we must do the multiplication in order to handle | |
7559 | infinities and NaNs properly. */ | |
7560 | else if (SCM_REALP (y)) | |
7561 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
7562 | else if (SCM_COMPLEXP (y)) | |
7563 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
7564 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
7565 | /* we've already handled inexact numbers, | |
7566 | so y must be exact, and we return exact0 */ | |
7567 | else if (SCM_NUMP (y)) | |
7568 | return SCM_INUM0; | |
7569 | else | |
7570 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
7571 | break; | |
7572 | case -1: | |
b5c40589 | 7573 | /* |
5e791807 MW |
7574 | * This case is important for more than just optimization. |
7575 | * It handles the case of negating | |
b5c40589 MW |
7576 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
7577 | * which is a bignum that must be changed back into a fixnum. | |
7578 | * Failure to do so will cause the following to return #f: | |
7579 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
7580 | */ | |
b5c40589 MW |
7581 | return scm_difference(y, SCM_UNDEFINED); |
7582 | break; | |
0aacf84e | 7583 | } |
f4c627b3 | 7584 | |
9cc37597 | 7585 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7586 | { |
e25f3727 AW |
7587 | scm_t_inum yy = SCM_I_INUM (y); |
7588 | scm_t_inum kk = xx * yy; | |
d956fa6f | 7589 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 7590 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
7591 | return k; |
7592 | else | |
7593 | { | |
e25f3727 | 7594 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
7595 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
7596 | return scm_i_normbig (result); | |
7597 | } | |
7598 | } | |
7599 | else if (SCM_BIGP (y)) | |
7600 | { | |
7601 | SCM result = scm_i_mkbig (); | |
7602 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
7603 | scm_remember_upto_here_1 (y); | |
7604 | return result; | |
7605 | } | |
7606 | else if (SCM_REALP (y)) | |
55f26379 | 7607 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 7608 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7609 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 7610 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7611 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7612 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7613 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7614 | else |
7615 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7616 | } |
0aacf84e MD |
7617 | else if (SCM_BIGP (x)) |
7618 | { | |
e11e83f3 | 7619 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7620 | { |
7621 | SCM_SWAP (x, y); | |
5e791807 | 7622 | goto xinum; |
0aacf84e MD |
7623 | } |
7624 | else if (SCM_BIGP (y)) | |
7625 | { | |
7626 | SCM result = scm_i_mkbig (); | |
7627 | mpz_mul (SCM_I_BIG_MPZ (result), | |
7628 | SCM_I_BIG_MPZ (x), | |
7629 | SCM_I_BIG_MPZ (y)); | |
7630 | scm_remember_upto_here_2 (x, y); | |
7631 | return result; | |
7632 | } | |
7633 | else if (SCM_REALP (y)) | |
7634 | { | |
7635 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
7636 | scm_remember_upto_here_1 (x); | |
55f26379 | 7637 | return scm_from_double (result); |
0aacf84e MD |
7638 | } |
7639 | else if (SCM_COMPLEXP (y)) | |
7640 | { | |
7641 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
7642 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7643 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
7644 | z * SCM_COMPLEX_IMAG (y)); |
7645 | } | |
f92e85f7 | 7646 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7647 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7648 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7649 | else |
7650 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7651 | } |
0aacf84e MD |
7652 | else if (SCM_REALP (x)) |
7653 | { | |
e11e83f3 | 7654 | if (SCM_I_INUMP (y)) |
5e791807 MW |
7655 | { |
7656 | SCM_SWAP (x, y); | |
7657 | goto xinum; | |
7658 | } | |
0aacf84e MD |
7659 | else if (SCM_BIGP (y)) |
7660 | { | |
7661 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
7662 | scm_remember_upto_here_1 (y); | |
55f26379 | 7663 | return scm_from_double (result); |
0aacf84e MD |
7664 | } |
7665 | else if (SCM_REALP (y)) | |
55f26379 | 7666 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 7667 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7668 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 7669 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7670 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7671 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
7672 | else |
7673 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7674 | } |
0aacf84e MD |
7675 | else if (SCM_COMPLEXP (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 z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7685 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7686 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 7687 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7688 | } |
7689 | else if (SCM_REALP (y)) | |
8507ec80 | 7690 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
7691 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
7692 | else if (SCM_COMPLEXP (y)) | |
7693 | { | |
8507ec80 | 7694 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
7695 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
7696 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
7697 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
7698 | } | |
f92e85f7 MV |
7699 | else if (SCM_FRACTIONP (y)) |
7700 | { | |
7701 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 7702 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
7703 | yy * SCM_COMPLEX_IMAG (x)); |
7704 | } | |
7705 | else | |
7706 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
7707 | } | |
7708 | else if (SCM_FRACTIONP (x)) | |
7709 | { | |
e11e83f3 | 7710 | if (SCM_I_INUMP (y)) |
cba42c93 | 7711 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
7712 | SCM_FRACTION_DENOMINATOR (x)); |
7713 | else if (SCM_BIGP (y)) | |
cba42c93 | 7714 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
7715 | SCM_FRACTION_DENOMINATOR (x)); |
7716 | else if (SCM_REALP (y)) | |
55f26379 | 7717 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
7718 | else if (SCM_COMPLEXP (y)) |
7719 | { | |
7720 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 7721 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7722 | xx * SCM_COMPLEX_IMAG (y)); |
7723 | } | |
7724 | else if (SCM_FRACTIONP (y)) | |
7725 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 7726 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7727 | SCM_FRACTION_NUMERATOR (y)), |
7728 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
7729 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7730 | else |
7731 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7732 | } |
0aacf84e | 7733 | else |
f4c627b3 | 7734 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
7735 | } |
7736 | ||
7351e207 MV |
7737 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
7738 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
7739 | #define ALLOW_DIVIDE_BY_ZERO | |
7740 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
7741 | #endif | |
0f2d19dd | 7742 | |
ba74ef4e MV |
7743 | /* The code below for complex division is adapted from the GNU |
7744 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
7745 | this copyright: */ | |
7746 | ||
7747 | /**************************************************************** | |
7748 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
7749 | ||
7750 | Permission to use, copy, modify, and distribute this software | |
7751 | and its documentation for any purpose and without fee is hereby | |
7752 | granted, provided that the above copyright notice appear in all | |
7753 | copies and that both that the copyright notice and this | |
7754 | permission notice and warranty disclaimer appear in supporting | |
7755 | documentation, and that the names of AT&T Bell Laboratories or | |
7756 | Bellcore or any of their entities not be used in advertising or | |
7757 | publicity pertaining to distribution of the software without | |
7758 | specific, written prior permission. | |
7759 | ||
7760 | AT&T and Bellcore disclaim all warranties with regard to this | |
7761 | software, including all implied warranties of merchantability | |
7762 | and fitness. In no event shall AT&T or Bellcore be liable for | |
7763 | any special, indirect or consequential damages or any damages | |
7764 | whatsoever resulting from loss of use, data or profits, whether | |
7765 | in an action of contract, negligence or other tortious action, | |
7766 | arising out of or in connection with the use or performance of | |
7767 | this software. | |
7768 | ****************************************************************/ | |
7769 | ||
78d3deb1 AW |
7770 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
7771 | (SCM x, SCM y, SCM rest), | |
7772 | "Divide the first argument by the product of the remaining\n" | |
7773 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
7774 | "returned.") | |
7775 | #define FUNC_NAME s_scm_i_divide | |
7776 | { | |
7777 | while (!scm_is_null (rest)) | |
7778 | { x = scm_divide (x, y); | |
7779 | y = scm_car (rest); | |
7780 | rest = scm_cdr (rest); | |
7781 | } | |
7782 | return scm_divide (x, y); | |
7783 | } | |
7784 | #undef FUNC_NAME | |
7785 | ||
7786 | #define s_divide s_scm_i_divide | |
7787 | #define g_divide g_scm_i_divide | |
7788 | ||
f92e85f7 | 7789 | static SCM |
78d3deb1 AW |
7790 | do_divide (SCM x, SCM y, int inexact) |
7791 | #define FUNC_NAME s_divide | |
0f2d19dd | 7792 | { |
f8de44c1 DH |
7793 | double a; |
7794 | ||
9cc37597 | 7795 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7796 | { |
7797 | if (SCM_UNBNDP (x)) | |
7798 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 7799 | else if (SCM_I_INUMP (x)) |
0aacf84e | 7800 | { |
e25f3727 | 7801 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
7802 | if (xx == 1 || xx == -1) |
7803 | return x; | |
7351e207 | 7804 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
7805 | else if (xx == 0) |
7806 | scm_num_overflow (s_divide); | |
7351e207 | 7807 | #endif |
0aacf84e | 7808 | else |
f92e85f7 MV |
7809 | { |
7810 | if (inexact) | |
55f26379 | 7811 | return scm_from_double (1.0 / (double) xx); |
cff5fa33 | 7812 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 7813 | } |
0aacf84e MD |
7814 | } |
7815 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
7816 | { |
7817 | if (inexact) | |
55f26379 | 7818 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cff5fa33 | 7819 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 7820 | } |
0aacf84e MD |
7821 | else if (SCM_REALP (x)) |
7822 | { | |
7823 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 7824 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
7825 | if (xx == 0.0) |
7826 | scm_num_overflow (s_divide); | |
7827 | else | |
7351e207 | 7828 | #endif |
55f26379 | 7829 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
7830 | } |
7831 | else if (SCM_COMPLEXP (x)) | |
7832 | { | |
7833 | double r = SCM_COMPLEX_REAL (x); | |
7834 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 7835 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
7836 | { |
7837 | double t = r / i; | |
7838 | double d = i * (1.0 + t * t); | |
8507ec80 | 7839 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
7840 | } |
7841 | else | |
7842 | { | |
7843 | double t = i / r; | |
7844 | double d = r * (1.0 + t * t); | |
8507ec80 | 7845 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
7846 | } |
7847 | } | |
f92e85f7 | 7848 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 7849 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 7850 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
7851 | else |
7852 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 7853 | } |
f8de44c1 | 7854 | |
9cc37597 | 7855 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7856 | { |
e25f3727 | 7857 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 7858 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7859 | { |
e25f3727 | 7860 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7861 | if (yy == 0) |
7862 | { | |
7351e207 | 7863 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 7864 | scm_num_overflow (s_divide); |
7351e207 | 7865 | #else |
55f26379 | 7866 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 7867 | #endif |
0aacf84e MD |
7868 | } |
7869 | else if (xx % yy != 0) | |
f92e85f7 MV |
7870 | { |
7871 | if (inexact) | |
55f26379 | 7872 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 7873 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 7874 | } |
0aacf84e MD |
7875 | else |
7876 | { | |
e25f3727 | 7877 | scm_t_inum z = xx / yy; |
0aacf84e | 7878 | if (SCM_FIXABLE (z)) |
d956fa6f | 7879 | return SCM_I_MAKINUM (z); |
0aacf84e | 7880 | else |
e25f3727 | 7881 | return scm_i_inum2big (z); |
0aacf84e | 7882 | } |
f872b822 | 7883 | } |
0aacf84e | 7884 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
7885 | { |
7886 | if (inexact) | |
55f26379 | 7887 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 7888 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 7889 | } |
0aacf84e MD |
7890 | else if (SCM_REALP (y)) |
7891 | { | |
7892 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 7893 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
7894 | if (yy == 0.0) |
7895 | scm_num_overflow (s_divide); | |
7896 | else | |
7351e207 | 7897 | #endif |
55f26379 | 7898 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 7899 | } |
0aacf84e MD |
7900 | else if (SCM_COMPLEXP (y)) |
7901 | { | |
7902 | a = xx; | |
7903 | complex_div: /* y _must_ be a complex number */ | |
7904 | { | |
7905 | double r = SCM_COMPLEX_REAL (y); | |
7906 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 7907 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
7908 | { |
7909 | double t = r / i; | |
7910 | double d = i * (1.0 + t * t); | |
8507ec80 | 7911 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
7912 | } |
7913 | else | |
7914 | { | |
7915 | double t = i / r; | |
7916 | double d = r * (1.0 + t * t); | |
8507ec80 | 7917 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
7918 | } |
7919 | } | |
7920 | } | |
f92e85f7 MV |
7921 | else if (SCM_FRACTIONP (y)) |
7922 | /* a / b/c = ac / b */ | |
cba42c93 | 7923 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 7924 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
7925 | else |
7926 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 7927 | } |
0aacf84e MD |
7928 | else if (SCM_BIGP (x)) |
7929 | { | |
e11e83f3 | 7930 | if (SCM_I_INUMP (y)) |
0aacf84e | 7931 | { |
e25f3727 | 7932 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7933 | if (yy == 0) |
7934 | { | |
7351e207 | 7935 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 7936 | scm_num_overflow (s_divide); |
7351e207 | 7937 | #else |
0aacf84e MD |
7938 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
7939 | scm_remember_upto_here_1 (x); | |
7940 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 7941 | #endif |
0aacf84e MD |
7942 | } |
7943 | else if (yy == 1) | |
7944 | return x; | |
7945 | else | |
7946 | { | |
7947 | /* FIXME: HMM, what are the relative performance issues here? | |
7948 | We need to test. Is it faster on average to test | |
7949 | divisible_p, then perform whichever operation, or is it | |
7950 | faster to perform the integer div opportunistically and | |
7951 | switch to real if there's a remainder? For now we take the | |
7952 | middle ground: test, then if divisible, use the faster div | |
7953 | func. */ | |
7954 | ||
e25f3727 | 7955 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
7956 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
7957 | ||
7958 | if (divisible_p) | |
7959 | { | |
7960 | SCM result = scm_i_mkbig (); | |
7961 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
7962 | scm_remember_upto_here_1 (x); | |
7963 | if (yy < 0) | |
7964 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7965 | return scm_i_normbig (result); | |
7966 | } | |
7967 | else | |
f92e85f7 MV |
7968 | { |
7969 | if (inexact) | |
55f26379 | 7970 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 7971 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 7972 | } |
0aacf84e MD |
7973 | } |
7974 | } | |
7975 | else if (SCM_BIGP (y)) | |
7976 | { | |
a4955a04 MW |
7977 | /* big_x / big_y */ |
7978 | if (inexact) | |
0aacf84e | 7979 | { |
a4955a04 MW |
7980 | /* It's easily possible for the ratio x/y to fit a double |
7981 | but one or both x and y be too big to fit a double, | |
7982 | hence the use of mpq_get_d rather than converting and | |
7983 | dividing. */ | |
7984 | mpq_t q; | |
7985 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
7986 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
7987 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
7988 | } |
7989 | else | |
7990 | { | |
a4955a04 MW |
7991 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
7992 | SCM_I_BIG_MPZ (y)); | |
7993 | if (divisible_p) | |
7994 | { | |
7995 | SCM result = scm_i_mkbig (); | |
7996 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
7997 | SCM_I_BIG_MPZ (x), | |
7998 | SCM_I_BIG_MPZ (y)); | |
7999 | scm_remember_upto_here_2 (x, y); | |
8000 | return scm_i_normbig (result); | |
8001 | } | |
8002 | else | |
8003 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
8004 | } |
8005 | } | |
8006 | else if (SCM_REALP (y)) | |
8007 | { | |
8008 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8009 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8010 | if (yy == 0.0) |
8011 | scm_num_overflow (s_divide); | |
8012 | else | |
7351e207 | 8013 | #endif |
55f26379 | 8014 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
8015 | } |
8016 | else if (SCM_COMPLEXP (y)) | |
8017 | { | |
8018 | a = scm_i_big2dbl (x); | |
8019 | goto complex_div; | |
8020 | } | |
f92e85f7 | 8021 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8022 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 8023 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
8024 | else |
8025 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8026 | } |
0aacf84e MD |
8027 | else if (SCM_REALP (x)) |
8028 | { | |
8029 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 8030 | if (SCM_I_INUMP (y)) |
0aacf84e | 8031 | { |
e25f3727 | 8032 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8033 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8034 | if (yy == 0) |
8035 | scm_num_overflow (s_divide); | |
8036 | else | |
7351e207 | 8037 | #endif |
55f26379 | 8038 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
8039 | } |
8040 | else if (SCM_BIGP (y)) | |
8041 | { | |
8042 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8043 | scm_remember_upto_here_1 (y); | |
55f26379 | 8044 | return scm_from_double (rx / dby); |
0aacf84e MD |
8045 | } |
8046 | else if (SCM_REALP (y)) | |
8047 | { | |
8048 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8049 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8050 | if (yy == 0.0) |
8051 | scm_num_overflow (s_divide); | |
8052 | else | |
7351e207 | 8053 | #endif |
55f26379 | 8054 | return scm_from_double (rx / yy); |
0aacf84e MD |
8055 | } |
8056 | else if (SCM_COMPLEXP (y)) | |
8057 | { | |
8058 | a = rx; | |
8059 | goto complex_div; | |
8060 | } | |
f92e85f7 | 8061 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8062 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
8063 | else |
8064 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8065 | } |
0aacf84e MD |
8066 | else if (SCM_COMPLEXP (x)) |
8067 | { | |
8068 | double rx = SCM_COMPLEX_REAL (x); | |
8069 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 8070 | if (SCM_I_INUMP (y)) |
0aacf84e | 8071 | { |
e25f3727 | 8072 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8073 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8074 | if (yy == 0) |
8075 | scm_num_overflow (s_divide); | |
8076 | else | |
7351e207 | 8077 | #endif |
0aacf84e MD |
8078 | { |
8079 | double d = yy; | |
8507ec80 | 8080 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
8081 | } |
8082 | } | |
8083 | else if (SCM_BIGP (y)) | |
8084 | { | |
8085 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8086 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8087 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
8088 | } |
8089 | else if (SCM_REALP (y)) | |
8090 | { | |
8091 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8092 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8093 | if (yy == 0.0) |
8094 | scm_num_overflow (s_divide); | |
8095 | else | |
7351e207 | 8096 | #endif |
8507ec80 | 8097 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
8098 | } |
8099 | else if (SCM_COMPLEXP (y)) | |
8100 | { | |
8101 | double ry = SCM_COMPLEX_REAL (y); | |
8102 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8103 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
8104 | { |
8105 | double t = ry / iy; | |
8106 | double d = iy * (1.0 + t * t); | |
8507ec80 | 8107 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
8108 | } |
8109 | else | |
8110 | { | |
8111 | double t = iy / ry; | |
8112 | double d = ry * (1.0 + t * t); | |
8507ec80 | 8113 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
8114 | } |
8115 | } | |
f92e85f7 MV |
8116 | else if (SCM_FRACTIONP (y)) |
8117 | { | |
8118 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 8119 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 8120 | } |
0aacf84e MD |
8121 | else |
8122 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 8123 | } |
f92e85f7 MV |
8124 | else if (SCM_FRACTIONP (x)) |
8125 | { | |
e11e83f3 | 8126 | if (SCM_I_INUMP (y)) |
f92e85f7 | 8127 | { |
e25f3727 | 8128 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
8129 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
8130 | if (yy == 0) | |
8131 | scm_num_overflow (s_divide); | |
8132 | else | |
8133 | #endif | |
cba42c93 | 8134 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8135 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8136 | } | |
8137 | else if (SCM_BIGP (y)) | |
8138 | { | |
cba42c93 | 8139 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8140 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8141 | } | |
8142 | else if (SCM_REALP (y)) | |
8143 | { | |
8144 | double yy = SCM_REAL_VALUE (y); | |
8145 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8146 | if (yy == 0.0) | |
8147 | scm_num_overflow (s_divide); | |
8148 | else | |
8149 | #endif | |
55f26379 | 8150 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
8151 | } |
8152 | else if (SCM_COMPLEXP (y)) | |
8153 | { | |
8154 | a = scm_i_fraction2double (x); | |
8155 | goto complex_div; | |
8156 | } | |
8157 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 8158 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
8159 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
8160 | else | |
8161 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
8162 | } | |
0aacf84e | 8163 | else |
f8de44c1 | 8164 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 8165 | } |
f92e85f7 MV |
8166 | |
8167 | SCM | |
8168 | scm_divide (SCM x, SCM y) | |
8169 | { | |
78d3deb1 | 8170 | return do_divide (x, y, 0); |
f92e85f7 MV |
8171 | } |
8172 | ||
8173 | static SCM scm_divide2real (SCM x, SCM y) | |
8174 | { | |
78d3deb1 | 8175 | return do_divide (x, y, 1); |
f92e85f7 | 8176 | } |
c05e97b7 | 8177 | #undef FUNC_NAME |
0f2d19dd | 8178 | |
fa605590 | 8179 | |
0f2d19dd | 8180 | double |
3101f40f | 8181 | scm_c_truncate (double x) |
0f2d19dd | 8182 | { |
fa605590 | 8183 | return trunc (x); |
0f2d19dd | 8184 | } |
0f2d19dd | 8185 | |
3101f40f MV |
8186 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
8187 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
8188 | Then half-way cases are identified and adjusted down if the | |
8189 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
8190 | |
8191 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
8192 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
8193 | ||
8194 | An odd "result" value is identified with result/2 != floor(result/2). | |
8195 | This is done with plus_half, since that value is ready for use sooner in | |
8196 | a pipelined cpu, and we're already requiring plus_half == result. | |
8197 | ||
8198 | Note however that we need to be careful when x is big and already an | |
8199 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
8200 | us to return such a value, incorrectly. For instance if the hardware is | |
8201 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
8202 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
8203 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
8204 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
8205 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
8206 | ||
8207 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
8208 | x is already an integer. If it is then clearly that's the desired result | |
8209 | already. And if it's not then the exponent must be small enough to allow | |
8210 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
8211 | ||
0f2d19dd | 8212 | double |
3101f40f | 8213 | scm_c_round (double x) |
0f2d19dd | 8214 | { |
6187f48b KR |
8215 | double plus_half, result; |
8216 | ||
8217 | if (x == floor (x)) | |
8218 | return x; | |
8219 | ||
8220 | plus_half = x + 0.5; | |
8221 | result = floor (plus_half); | |
3101f40f | 8222 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
8223 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
8224 | ? result - 1 | |
8225 | : result); | |
0f2d19dd JB |
8226 | } |
8227 | ||
8b56bcec MW |
8228 | SCM_PRIMITIVE_GENERIC (scm_truncate_number, "truncate", 1, 0, 0, |
8229 | (SCM x), | |
8230 | "Round the number @var{x} towards zero.") | |
f92e85f7 MV |
8231 | #define FUNC_NAME s_scm_truncate_number |
8232 | { | |
8b56bcec MW |
8233 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
8234 | return x; | |
8235 | else if (SCM_REALP (x)) | |
c251ab63 | 8236 | return scm_from_double (trunc (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8237 | else if (SCM_FRACTIONP (x)) |
8238 | return scm_truncate_quotient (SCM_FRACTION_NUMERATOR (x), | |
8239 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8240 | else |
8b56bcec MW |
8241 | SCM_WTA_DISPATCH_1 (g_scm_truncate_number, x, SCM_ARG1, |
8242 | s_scm_truncate_number); | |
f92e85f7 MV |
8243 | } |
8244 | #undef FUNC_NAME | |
8245 | ||
8b56bcec MW |
8246 | SCM_PRIMITIVE_GENERIC (scm_round_number, "round", 1, 0, 0, |
8247 | (SCM x), | |
8248 | "Round the number @var{x} towards the nearest integer. " | |
8249 | "When it is exactly halfway between two integers, " | |
8250 | "round towards the even one.") | |
f92e85f7 MV |
8251 | #define FUNC_NAME s_scm_round_number |
8252 | { | |
e11e83f3 | 8253 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
8254 | return x; |
8255 | else if (SCM_REALP (x)) | |
3101f40f | 8256 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8257 | else if (SCM_FRACTIONP (x)) |
8258 | return scm_round_quotient (SCM_FRACTION_NUMERATOR (x), | |
8259 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8260 | else |
8b56bcec MW |
8261 | SCM_WTA_DISPATCH_1 (g_scm_round_number, x, SCM_ARG1, |
8262 | s_scm_round_number); | |
f92e85f7 MV |
8263 | } |
8264 | #undef FUNC_NAME | |
8265 | ||
8266 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
8267 | (SCM x), | |
8268 | "Round the number @var{x} towards minus infinity.") | |
8269 | #define FUNC_NAME s_scm_floor | |
8270 | { | |
e11e83f3 | 8271 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8272 | return x; |
8273 | else if (SCM_REALP (x)) | |
55f26379 | 8274 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 | 8275 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8276 | return scm_floor_quotient (SCM_FRACTION_NUMERATOR (x), |
8277 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8278 | else |
8279 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
8280 | } | |
8281 | #undef FUNC_NAME | |
8282 | ||
8283 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
8284 | (SCM x), | |
8285 | "Round the number @var{x} towards infinity.") | |
8286 | #define FUNC_NAME s_scm_ceiling | |
8287 | { | |
e11e83f3 | 8288 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8289 | return x; |
8290 | else if (SCM_REALP (x)) | |
55f26379 | 8291 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 | 8292 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8293 | return scm_ceiling_quotient (SCM_FRACTION_NUMERATOR (x), |
8294 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8295 | else |
8296 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
8297 | } | |
8298 | #undef FUNC_NAME | |
0f2d19dd | 8299 | |
2519490c MW |
8300 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
8301 | (SCM x, SCM y), | |
8302 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 8303 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 8304 | { |
01c7284a MW |
8305 | if (scm_is_integer (y)) |
8306 | { | |
8307 | if (scm_is_true (scm_exact_p (y))) | |
8308 | return scm_integer_expt (x, y); | |
8309 | else | |
8310 | { | |
8311 | /* Here we handle the case where the exponent is an inexact | |
8312 | integer. We make the exponent exact in order to use | |
8313 | scm_integer_expt, and thus avoid the spurious imaginary | |
8314 | parts that may result from round-off errors in the general | |
8315 | e^(y log x) method below (for example when squaring a large | |
8316 | negative number). In this case, we must return an inexact | |
8317 | result for correctness. We also make the base inexact so | |
8318 | that scm_integer_expt will use fast inexact arithmetic | |
8319 | internally. Note that making the base inexact is not | |
8320 | sufficient to guarantee an inexact result, because | |
8321 | scm_integer_expt will return an exact 1 when the exponent | |
8322 | is 0, even if the base is inexact. */ | |
8323 | return scm_exact_to_inexact | |
8324 | (scm_integer_expt (scm_exact_to_inexact (x), | |
8325 | scm_inexact_to_exact (y))); | |
8326 | } | |
8327 | } | |
6fc4d012 AW |
8328 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
8329 | { | |
8330 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
8331 | } | |
2519490c | 8332 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 8333 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c MW |
8334 | else if (scm_is_complex (x)) |
8335 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); | |
8336 | else | |
8337 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); | |
0f2d19dd | 8338 | } |
1bbd0b84 | 8339 | #undef FUNC_NAME |
0f2d19dd | 8340 | |
7f41099e MW |
8341 | /* sin/cos/tan/asin/acos/atan |
8342 | sinh/cosh/tanh/asinh/acosh/atanh | |
8343 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
8344 | Written by Jerry D. Hedden, (C) FSF. | |
8345 | See the file `COPYING' for terms applying to this program. */ | |
8346 | ||
ad79736c AW |
8347 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
8348 | (SCM z), | |
8349 | "Compute the sine of @var{z}.") | |
8350 | #define FUNC_NAME s_scm_sin | |
8351 | { | |
8deddc94 MW |
8352 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8353 | return z; /* sin(exact0) = exact0 */ | |
8354 | else if (scm_is_real (z)) | |
ad79736c AW |
8355 | return scm_from_double (sin (scm_to_double (z))); |
8356 | else if (SCM_COMPLEXP (z)) | |
8357 | { double x, y; | |
8358 | x = SCM_COMPLEX_REAL (z); | |
8359 | y = SCM_COMPLEX_IMAG (z); | |
8360 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
8361 | cos (x) * sinh (y)); | |
8362 | } | |
8363 | else | |
8364 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
8365 | } | |
8366 | #undef FUNC_NAME | |
0f2d19dd | 8367 | |
ad79736c AW |
8368 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
8369 | (SCM z), | |
8370 | "Compute the cosine of @var{z}.") | |
8371 | #define FUNC_NAME s_scm_cos | |
8372 | { | |
8deddc94 MW |
8373 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8374 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
8375 | else if (scm_is_real (z)) | |
ad79736c AW |
8376 | return scm_from_double (cos (scm_to_double (z))); |
8377 | else if (SCM_COMPLEXP (z)) | |
8378 | { double x, y; | |
8379 | x = SCM_COMPLEX_REAL (z); | |
8380 | y = SCM_COMPLEX_IMAG (z); | |
8381 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
8382 | -sin (x) * sinh (y)); | |
8383 | } | |
8384 | else | |
8385 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
8386 | } | |
8387 | #undef FUNC_NAME | |
8388 | ||
8389 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
8390 | (SCM z), | |
8391 | "Compute the tangent of @var{z}.") | |
8392 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 8393 | { |
8deddc94 MW |
8394 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8395 | return z; /* tan(exact0) = exact0 */ | |
8396 | else if (scm_is_real (z)) | |
ad79736c AW |
8397 | return scm_from_double (tan (scm_to_double (z))); |
8398 | else if (SCM_COMPLEXP (z)) | |
8399 | { double x, y, w; | |
8400 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8401 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8402 | w = cos (x) + cosh (y); | |
8403 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8404 | if (w == 0.0) | |
8405 | scm_num_overflow (s_scm_tan); | |
8406 | #endif | |
8407 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
8408 | } | |
8409 | else | |
8410 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
8411 | } | |
8412 | #undef FUNC_NAME | |
8413 | ||
8414 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
8415 | (SCM z), | |
8416 | "Compute the hyperbolic sine of @var{z}.") | |
8417 | #define FUNC_NAME s_scm_sinh | |
8418 | { | |
8deddc94 MW |
8419 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8420 | return z; /* sinh(exact0) = exact0 */ | |
8421 | else if (scm_is_real (z)) | |
ad79736c AW |
8422 | return scm_from_double (sinh (scm_to_double (z))); |
8423 | else if (SCM_COMPLEXP (z)) | |
8424 | { double x, y; | |
8425 | x = SCM_COMPLEX_REAL (z); | |
8426 | y = SCM_COMPLEX_IMAG (z); | |
8427 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
8428 | cosh (x) * sin (y)); | |
8429 | } | |
8430 | else | |
8431 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
8432 | } | |
8433 | #undef FUNC_NAME | |
8434 | ||
8435 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
8436 | (SCM z), | |
8437 | "Compute the hyperbolic cosine of @var{z}.") | |
8438 | #define FUNC_NAME s_scm_cosh | |
8439 | { | |
8deddc94 MW |
8440 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8441 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
8442 | else if (scm_is_real (z)) | |
ad79736c AW |
8443 | return scm_from_double (cosh (scm_to_double (z))); |
8444 | else if (SCM_COMPLEXP (z)) | |
8445 | { double x, y; | |
8446 | x = SCM_COMPLEX_REAL (z); | |
8447 | y = SCM_COMPLEX_IMAG (z); | |
8448 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
8449 | sinh (x) * sin (y)); | |
8450 | } | |
8451 | else | |
8452 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
8453 | } | |
8454 | #undef FUNC_NAME | |
8455 | ||
8456 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
8457 | (SCM z), | |
8458 | "Compute the hyperbolic tangent of @var{z}.") | |
8459 | #define FUNC_NAME s_scm_tanh | |
8460 | { | |
8deddc94 MW |
8461 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8462 | return z; /* tanh(exact0) = exact0 */ | |
8463 | else if (scm_is_real (z)) | |
ad79736c AW |
8464 | return scm_from_double (tanh (scm_to_double (z))); |
8465 | else if (SCM_COMPLEXP (z)) | |
8466 | { double x, y, w; | |
8467 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8468 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8469 | w = cosh (x) + cos (y); | |
8470 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8471 | if (w == 0.0) | |
8472 | scm_num_overflow (s_scm_tanh); | |
8473 | #endif | |
8474 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
8475 | } | |
8476 | else | |
8477 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
8478 | } | |
8479 | #undef FUNC_NAME | |
8480 | ||
8481 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
8482 | (SCM z), | |
8483 | "Compute the arc sine of @var{z}.") | |
8484 | #define FUNC_NAME s_scm_asin | |
8485 | { | |
8deddc94 MW |
8486 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8487 | return z; /* asin(exact0) = exact0 */ | |
8488 | else if (scm_is_real (z)) | |
ad79736c AW |
8489 | { |
8490 | double w = scm_to_double (z); | |
8491 | if (w >= -1.0 && w <= 1.0) | |
8492 | return scm_from_double (asin (w)); | |
8493 | else | |
8494 | return scm_product (scm_c_make_rectangular (0, -1), | |
8495 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
8496 | } | |
8497 | else if (SCM_COMPLEXP (z)) | |
8498 | { double x, y; | |
8499 | x = SCM_COMPLEX_REAL (z); | |
8500 | y = SCM_COMPLEX_IMAG (z); | |
8501 | return scm_product (scm_c_make_rectangular (0, -1), | |
8502 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
8503 | } | |
8504 | else | |
8505 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
8506 | } | |
8507 | #undef FUNC_NAME | |
8508 | ||
8509 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
8510 | (SCM z), | |
8511 | "Compute the arc cosine of @var{z}.") | |
8512 | #define FUNC_NAME s_scm_acos | |
8513 | { | |
8deddc94 MW |
8514 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8515 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
8516 | else if (scm_is_real (z)) | |
ad79736c AW |
8517 | { |
8518 | double w = scm_to_double (z); | |
8519 | if (w >= -1.0 && w <= 1.0) | |
8520 | return scm_from_double (acos (w)); | |
8521 | else | |
8522 | return scm_sum (scm_from_double (acos (0.0)), | |
8523 | scm_product (scm_c_make_rectangular (0, 1), | |
8524 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
8525 | } | |
8526 | else if (SCM_COMPLEXP (z)) | |
8527 | { double x, y; | |
8528 | x = SCM_COMPLEX_REAL (z); | |
8529 | y = SCM_COMPLEX_IMAG (z); | |
8530 | return scm_sum (scm_from_double (acos (0.0)), | |
8531 | scm_product (scm_c_make_rectangular (0, 1), | |
8532 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
8533 | } | |
8534 | else | |
8535 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
8536 | } | |
8537 | #undef FUNC_NAME | |
8538 | ||
8539 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
8540 | (SCM z, SCM y), | |
8541 | "With one argument, compute the arc tangent of @var{z}.\n" | |
8542 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
8543 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
8544 | #define FUNC_NAME s_scm_atan | |
8545 | { | |
8546 | if (SCM_UNBNDP (y)) | |
8547 | { | |
8deddc94 MW |
8548 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8549 | return z; /* atan(exact0) = exact0 */ | |
8550 | else if (scm_is_real (z)) | |
ad79736c AW |
8551 | return scm_from_double (atan (scm_to_double (z))); |
8552 | else if (SCM_COMPLEXP (z)) | |
8553 | { | |
8554 | double v, w; | |
8555 | v = SCM_COMPLEX_REAL (z); | |
8556 | w = SCM_COMPLEX_IMAG (z); | |
8557 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
8558 | scm_c_make_rectangular (v, w + 1.0))), | |
8559 | scm_c_make_rectangular (0, 2)); | |
8560 | } | |
8561 | else | |
18104cac | 8562 | SCM_WTA_DISPATCH_1 (g_scm_atan, z, SCM_ARG1, s_scm_atan); |
ad79736c AW |
8563 | } |
8564 | else if (scm_is_real (z)) | |
8565 | { | |
8566 | if (scm_is_real (y)) | |
8567 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
8568 | else | |
8569 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
8570 | } | |
8571 | else | |
8572 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
8573 | } | |
8574 | #undef FUNC_NAME | |
8575 | ||
8576 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
8577 | (SCM z), | |
8578 | "Compute the inverse hyperbolic sine of @var{z}.") | |
8579 | #define FUNC_NAME s_scm_sys_asinh | |
8580 | { | |
8deddc94 MW |
8581 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8582 | return z; /* asinh(exact0) = exact0 */ | |
8583 | else if (scm_is_real (z)) | |
ad79736c AW |
8584 | return scm_from_double (asinh (scm_to_double (z))); |
8585 | else if (scm_is_number (z)) | |
8586 | return scm_log (scm_sum (z, | |
8587 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 8588 | SCM_INUM1)))); |
ad79736c AW |
8589 | else |
8590 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
8591 | } | |
8592 | #undef FUNC_NAME | |
8593 | ||
8594 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
8595 | (SCM z), | |
8596 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
8597 | #define FUNC_NAME s_scm_sys_acosh | |
8598 | { | |
8deddc94 MW |
8599 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8600 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
8601 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
8602 | return scm_from_double (acosh (scm_to_double (z))); |
8603 | else if (scm_is_number (z)) | |
8604 | return scm_log (scm_sum (z, | |
8605 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 8606 | SCM_INUM1)))); |
ad79736c AW |
8607 | else |
8608 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
8609 | } | |
8610 | #undef FUNC_NAME | |
8611 | ||
8612 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
8613 | (SCM z), | |
8614 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
8615 | #define FUNC_NAME s_scm_sys_atanh | |
8616 | { | |
8deddc94 MW |
8617 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8618 | return z; /* atanh(exact0) = exact0 */ | |
8619 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
8620 | return scm_from_double (atanh (scm_to_double (z))); |
8621 | else if (scm_is_number (z)) | |
cff5fa33 MW |
8622 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
8623 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
8624 | SCM_I_MAKINUM (2)); |
8625 | else | |
8626 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 8627 | } |
1bbd0b84 | 8628 | #undef FUNC_NAME |
0f2d19dd | 8629 | |
8507ec80 MV |
8630 | SCM |
8631 | scm_c_make_rectangular (double re, double im) | |
8632 | { | |
c7218482 | 8633 | SCM z; |
03604fcf | 8634 | |
c7218482 MW |
8635 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
8636 | "complex")); | |
8637 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); | |
8638 | SCM_COMPLEX_REAL (z) = re; | |
8639 | SCM_COMPLEX_IMAG (z) = im; | |
8640 | return z; | |
8507ec80 | 8641 | } |
0f2d19dd | 8642 | |
a1ec6916 | 8643 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
8644 | (SCM real_part, SCM imaginary_part), |
8645 | "Return a complex number constructed of the given @var{real-part} " | |
8646 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 8647 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 8648 | { |
ad79736c AW |
8649 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
8650 | SCM_ARG1, FUNC_NAME, "real"); | |
8651 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
8652 | SCM_ARG2, FUNC_NAME, "real"); | |
c7218482 MW |
8653 | |
8654 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ | |
8655 | if (scm_is_eq (imaginary_part, SCM_INUM0)) | |
8656 | return real_part; | |
8657 | else | |
8658 | return scm_c_make_rectangular (scm_to_double (real_part), | |
8659 | scm_to_double (imaginary_part)); | |
0f2d19dd | 8660 | } |
1bbd0b84 | 8661 | #undef FUNC_NAME |
0f2d19dd | 8662 | |
8507ec80 MV |
8663 | SCM |
8664 | scm_c_make_polar (double mag, double ang) | |
8665 | { | |
8666 | double s, c; | |
5e647d08 LC |
8667 | |
8668 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
8669 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
8670 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
8671 | details. */ | |
8672 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
8673 | sincos (ang, &s, &c); |
8674 | #else | |
8675 | s = sin (ang); | |
8676 | c = cos (ang); | |
8677 | #endif | |
9d427b2c MW |
8678 | |
8679 | /* If s and c are NaNs, this indicates that the angle is a NaN, | |
8680 | infinite, or perhaps simply too large to determine its value | |
8681 | mod 2*pi. However, we know something that the floating-point | |
8682 | implementation doesn't know: We know that s and c are finite. | |
8683 | Therefore, if the magnitude is zero, return a complex zero. | |
8684 | ||
8685 | The reason we check for the NaNs instead of using this case | |
8686 | whenever mag == 0.0 is because when the angle is known, we'd | |
8687 | like to return the correct kind of non-real complex zero: | |
8688 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending | |
8689 | on which quadrant the angle is in. | |
8690 | */ | |
8691 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) | |
8692 | return scm_c_make_rectangular (0.0, 0.0); | |
8693 | else | |
8694 | return scm_c_make_rectangular (mag * c, mag * s); | |
8507ec80 | 8695 | } |
0f2d19dd | 8696 | |
a1ec6916 | 8697 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
c7218482 MW |
8698 | (SCM mag, SCM ang), |
8699 | "Return the complex number @var{mag} * e^(i * @var{ang}).") | |
1bbd0b84 | 8700 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 8701 | { |
c7218482 MW |
8702 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
8703 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); | |
8704 | ||
8705 | /* If mag is exact0, return exact0 */ | |
8706 | if (scm_is_eq (mag, SCM_INUM0)) | |
8707 | return SCM_INUM0; | |
8708 | /* Return a real if ang is exact0 */ | |
8709 | else if (scm_is_eq (ang, SCM_INUM0)) | |
8710 | return mag; | |
8711 | else | |
8712 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); | |
0f2d19dd | 8713 | } |
1bbd0b84 | 8714 | #undef FUNC_NAME |
0f2d19dd JB |
8715 | |
8716 | ||
2519490c MW |
8717 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
8718 | (SCM z), | |
8719 | "Return the real part of the number @var{z}.") | |
8720 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 8721 | { |
2519490c | 8722 | if (SCM_COMPLEXP (z)) |
55f26379 | 8723 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 8724 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 8725 | return z; |
0aacf84e | 8726 | else |
2519490c | 8727 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 8728 | } |
2519490c | 8729 | #undef FUNC_NAME |
0f2d19dd JB |
8730 | |
8731 | ||
2519490c MW |
8732 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
8733 | (SCM z), | |
8734 | "Return the imaginary part of the number @var{z}.") | |
8735 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 8736 | { |
2519490c MW |
8737 | if (SCM_COMPLEXP (z)) |
8738 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
c7218482 | 8739 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 8740 | return SCM_INUM0; |
0aacf84e | 8741 | else |
2519490c | 8742 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 8743 | } |
2519490c | 8744 | #undef FUNC_NAME |
0f2d19dd | 8745 | |
2519490c MW |
8746 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
8747 | (SCM z), | |
8748 | "Return the numerator of the number @var{z}.") | |
8749 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 8750 | { |
2519490c | 8751 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
8752 | return z; |
8753 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 8754 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
8755 | else if (SCM_REALP (z)) |
8756 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
8757 | else | |
2519490c | 8758 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 8759 | } |
2519490c | 8760 | #undef FUNC_NAME |
f92e85f7 MV |
8761 | |
8762 | ||
2519490c MW |
8763 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
8764 | (SCM z), | |
8765 | "Return the denominator of the number @var{z}.") | |
8766 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 8767 | { |
2519490c | 8768 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 8769 | return SCM_INUM1; |
f92e85f7 | 8770 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 8771 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
8772 | else if (SCM_REALP (z)) |
8773 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
8774 | else | |
2519490c | 8775 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
f92e85f7 | 8776 | } |
2519490c | 8777 | #undef FUNC_NAME |
0f2d19dd | 8778 | |
2519490c MW |
8779 | |
8780 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
8781 | (SCM z), | |
8782 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
8783 | "@code{abs} for real arguments, but also allows complex numbers.") | |
8784 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 8785 | { |
e11e83f3 | 8786 | if (SCM_I_INUMP (z)) |
0aacf84e | 8787 | { |
e25f3727 | 8788 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
8789 | if (zz >= 0) |
8790 | return z; | |
8791 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 8792 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 8793 | else |
e25f3727 | 8794 | return scm_i_inum2big (-zz); |
5986c47d | 8795 | } |
0aacf84e MD |
8796 | else if (SCM_BIGP (z)) |
8797 | { | |
8798 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
8799 | scm_remember_upto_here_1 (z); | |
8800 | if (sgn < 0) | |
8801 | return scm_i_clonebig (z, 0); | |
8802 | else | |
8803 | return z; | |
5986c47d | 8804 | } |
0aacf84e | 8805 | else if (SCM_REALP (z)) |
55f26379 | 8806 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 8807 | else if (SCM_COMPLEXP (z)) |
55f26379 | 8808 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
8809 | else if (SCM_FRACTIONP (z)) |
8810 | { | |
73e4de09 | 8811 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 8812 | return z; |
cba42c93 | 8813 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
8814 | SCM_FRACTION_DENOMINATOR (z)); |
8815 | } | |
0aacf84e | 8816 | else |
2519490c | 8817 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
0f2d19dd | 8818 | } |
2519490c | 8819 | #undef FUNC_NAME |
0f2d19dd JB |
8820 | |
8821 | ||
2519490c MW |
8822 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
8823 | (SCM z), | |
8824 | "Return the angle of the complex number @var{z}.") | |
8825 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 8826 | { |
c8ae173e | 8827 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 8828 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
8829 | But if atan2 follows the floating point rounding mode, then the value |
8830 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 8831 | if (SCM_I_INUMP (z)) |
0aacf84e | 8832 | { |
e11e83f3 | 8833 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 8834 | return flo0; |
0aacf84e | 8835 | else |
55f26379 | 8836 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 8837 | } |
0aacf84e MD |
8838 | else if (SCM_BIGP (z)) |
8839 | { | |
8840 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
8841 | scm_remember_upto_here_1 (z); | |
8842 | if (sgn < 0) | |
55f26379 | 8843 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 8844 | else |
e7efe8e7 | 8845 | return flo0; |
0f2d19dd | 8846 | } |
0aacf84e | 8847 | else if (SCM_REALP (z)) |
c8ae173e KR |
8848 | { |
8849 | if (SCM_REAL_VALUE (z) >= 0) | |
e7efe8e7 | 8850 | return flo0; |
c8ae173e | 8851 | else |
55f26379 | 8852 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 8853 | } |
0aacf84e | 8854 | else if (SCM_COMPLEXP (z)) |
55f26379 | 8855 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
8856 | else if (SCM_FRACTIONP (z)) |
8857 | { | |
73e4de09 | 8858 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 8859 | return flo0; |
55f26379 | 8860 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 8861 | } |
0aacf84e | 8862 | else |
2519490c | 8863 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 8864 | } |
2519490c | 8865 | #undef FUNC_NAME |
0f2d19dd JB |
8866 | |
8867 | ||
2519490c MW |
8868 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
8869 | (SCM z), | |
8870 | "Convert the number @var{z} to its inexact representation.\n") | |
8871 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 8872 | { |
e11e83f3 | 8873 | if (SCM_I_INUMP (z)) |
55f26379 | 8874 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 8875 | else if (SCM_BIGP (z)) |
55f26379 | 8876 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 8877 | else if (SCM_FRACTIONP (z)) |
55f26379 | 8878 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
8879 | else if (SCM_INEXACTP (z)) |
8880 | return z; | |
8881 | else | |
2519490c | 8882 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
3c9a524f | 8883 | } |
2519490c | 8884 | #undef FUNC_NAME |
3c9a524f DH |
8885 | |
8886 | ||
2519490c MW |
8887 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
8888 | (SCM z), | |
8889 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 8890 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 8891 | { |
c7218482 | 8892 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f872b822 | 8893 | return z; |
c7218482 | 8894 | else |
0aacf84e | 8895 | { |
c7218482 MW |
8896 | double val; |
8897 | ||
8898 | if (SCM_REALP (z)) | |
8899 | val = SCM_REAL_VALUE (z); | |
8900 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) | |
8901 | val = SCM_COMPLEX_REAL (z); | |
8902 | else | |
8903 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); | |
8904 | ||
8905 | if (!SCM_LIKELY (DOUBLE_IS_FINITE (val))) | |
f92e85f7 | 8906 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 8907 | else |
f92e85f7 MV |
8908 | { |
8909 | mpq_t frac; | |
8910 | SCM q; | |
8911 | ||
8912 | mpq_init (frac); | |
c7218482 | 8913 | mpq_set_d (frac, val); |
cba42c93 | 8914 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
c7218482 | 8915 | scm_i_mpz2num (mpq_denref (frac))); |
f92e85f7 | 8916 | |
cba42c93 | 8917 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
8918 | for frac... |
8919 | */ | |
8920 | mpq_clear (frac); | |
8921 | return q; | |
8922 | } | |
c2ff8ab0 | 8923 | } |
0f2d19dd | 8924 | } |
1bbd0b84 | 8925 | #undef FUNC_NAME |
0f2d19dd | 8926 | |
f92e85f7 | 8927 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
8928 | (SCM x, SCM eps), |
8929 | "Returns the @emph{simplest} rational number differing\n" | |
8930 | "from @var{x} by no more than @var{eps}.\n" | |
8931 | "\n" | |
8932 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
8933 | "exact result when both its arguments are exact. Thus, you might need\n" | |
8934 | "to use @code{inexact->exact} on the arguments.\n" | |
8935 | "\n" | |
8936 | "@lisp\n" | |
8937 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
8938 | "@result{} 6/5\n" | |
8939 | "@end lisp") | |
f92e85f7 MV |
8940 | #define FUNC_NAME s_scm_rationalize |
8941 | { | |
605f6980 MW |
8942 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
8943 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
8944 | eps = scm_abs (eps); | |
8945 | if (scm_is_false (scm_positive_p (eps))) | |
8946 | { | |
8947 | /* eps is either zero or a NaN */ | |
8948 | if (scm_is_true (scm_nan_p (eps))) | |
8949 | return scm_nan (); | |
8950 | else if (SCM_INEXACTP (eps)) | |
8951 | return scm_exact_to_inexact (x); | |
8952 | else | |
8953 | return x; | |
8954 | } | |
8955 | else if (scm_is_false (scm_finite_p (eps))) | |
8956 | { | |
8957 | if (scm_is_true (scm_finite_p (x))) | |
8958 | return flo0; | |
8959 | else | |
8960 | return scm_nan (); | |
8961 | } | |
8962 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 8963 | return x; |
605f6980 MW |
8964 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
8965 | scm_ceiling (scm_difference (x, eps))))) | |
8966 | { | |
8967 | /* There's an integer within range; we want the one closest to zero */ | |
8968 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
8969 | { | |
8970 | /* zero is within range */ | |
8971 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
8972 | return flo0; | |
8973 | else | |
8974 | return SCM_INUM0; | |
8975 | } | |
8976 | else if (scm_is_true (scm_positive_p (x))) | |
8977 | return scm_ceiling (scm_difference (x, eps)); | |
8978 | else | |
8979 | return scm_floor (scm_sum (x, eps)); | |
8980 | } | |
8981 | else | |
f92e85f7 MV |
8982 | { |
8983 | /* Use continued fractions to find closest ratio. All | |
8984 | arithmetic is done with exact numbers. | |
8985 | */ | |
8986 | ||
8987 | SCM ex = scm_inexact_to_exact (x); | |
8988 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
8989 | SCM tt = SCM_INUM1; |
8990 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
8991 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
8992 | SCM rx; |
8993 | int i = 0; | |
8994 | ||
f92e85f7 MV |
8995 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
8996 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
8997 | ||
8998 | /* We stop after a million iterations just to be absolutely sure | |
8999 | that we don't go into an infinite loop. The process normally | |
9000 | converges after less than a dozen iterations. | |
9001 | */ | |
9002 | ||
f92e85f7 MV |
9003 | while (++i < 1000000) |
9004 | { | |
9005 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
9006 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
9007 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
9008 | scm_is_false | |
f92e85f7 | 9009 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 9010 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
9011 | { |
9012 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 9013 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
9014 | return scm_exact_to_inexact (res); |
9015 | else | |
9016 | return res; | |
9017 | } | |
f92e85f7 MV |
9018 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
9019 | SCM_UNDEFINED); | |
9020 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
9021 | a2 = a1; | |
9022 | b2 = b1; | |
9023 | a1 = a; | |
9024 | b1 = b; | |
9025 | } | |
9026 | scm_num_overflow (s_scm_rationalize); | |
9027 | } | |
f92e85f7 MV |
9028 | } |
9029 | #undef FUNC_NAME | |
9030 | ||
73e4de09 MV |
9031 | /* conversion functions */ |
9032 | ||
9033 | int | |
9034 | scm_is_integer (SCM val) | |
9035 | { | |
9036 | return scm_is_true (scm_integer_p (val)); | |
9037 | } | |
9038 | ||
9039 | int | |
9040 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
9041 | { | |
e11e83f3 | 9042 | if (SCM_I_INUMP (val)) |
73e4de09 | 9043 | { |
e11e83f3 | 9044 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9045 | return n >= min && n <= max; |
9046 | } | |
9047 | else if (SCM_BIGP (val)) | |
9048 | { | |
9049 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
9050 | return 0; | |
9051 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
9052 | { |
9053 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
9054 | { | |
9055 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
9056 | return n >= min && n <= max; | |
9057 | } | |
9058 | else | |
9059 | return 0; | |
9060 | } | |
73e4de09 MV |
9061 | else |
9062 | { | |
d956fa6f MV |
9063 | scm_t_intmax n; |
9064 | size_t count; | |
73e4de09 | 9065 | |
d956fa6f MV |
9066 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9067 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
9068 | return 0; | |
9069 | ||
9070 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9071 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9072 | |
d956fa6f | 9073 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 9074 | { |
d956fa6f MV |
9075 | if (n < 0) |
9076 | return 0; | |
73e4de09 | 9077 | } |
73e4de09 MV |
9078 | else |
9079 | { | |
d956fa6f MV |
9080 | n = -n; |
9081 | if (n >= 0) | |
9082 | return 0; | |
73e4de09 | 9083 | } |
d956fa6f MV |
9084 | |
9085 | return n >= min && n <= max; | |
73e4de09 MV |
9086 | } |
9087 | } | |
73e4de09 MV |
9088 | else |
9089 | return 0; | |
9090 | } | |
9091 | ||
9092 | int | |
9093 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
9094 | { | |
e11e83f3 | 9095 | if (SCM_I_INUMP (val)) |
73e4de09 | 9096 | { |
e11e83f3 | 9097 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9098 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
9099 | } | |
9100 | else if (SCM_BIGP (val)) | |
9101 | { | |
9102 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
9103 | return 0; | |
9104 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
9105 | { |
9106 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
9107 | { | |
9108 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
9109 | return n >= min && n <= max; | |
9110 | } | |
9111 | else | |
9112 | return 0; | |
9113 | } | |
73e4de09 MV |
9114 | else |
9115 | { | |
d956fa6f MV |
9116 | scm_t_uintmax n; |
9117 | size_t count; | |
73e4de09 | 9118 | |
d956fa6f MV |
9119 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
9120 | return 0; | |
73e4de09 | 9121 | |
d956fa6f MV |
9122 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9123 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 9124 | return 0; |
d956fa6f MV |
9125 | |
9126 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9127 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9128 | |
d956fa6f | 9129 | return n >= min && n <= max; |
73e4de09 MV |
9130 | } |
9131 | } | |
73e4de09 MV |
9132 | else |
9133 | return 0; | |
9134 | } | |
9135 | ||
1713d319 MV |
9136 | static void |
9137 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
9138 | { | |
9139 | scm_error (scm_out_of_range_key, | |
9140 | NULL, | |
9141 | "Value out of range ~S to ~S: ~S", | |
9142 | scm_list_3 (min, max, bad_val), | |
9143 | scm_list_1 (bad_val)); | |
9144 | } | |
9145 | ||
bfd7932e MV |
9146 | #define TYPE scm_t_intmax |
9147 | #define TYPE_MIN min | |
9148 | #define TYPE_MAX max | |
9149 | #define SIZEOF_TYPE 0 | |
9150 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
9151 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
9152 | #include "libguile/conv-integer.i.c" | |
9153 | ||
9154 | #define TYPE scm_t_uintmax | |
9155 | #define TYPE_MIN min | |
9156 | #define TYPE_MAX max | |
9157 | #define SIZEOF_TYPE 0 | |
9158 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
9159 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
9160 | #include "libguile/conv-uinteger.i.c" | |
9161 | ||
9162 | #define TYPE scm_t_int8 | |
9163 | #define TYPE_MIN SCM_T_INT8_MIN | |
9164 | #define TYPE_MAX SCM_T_INT8_MAX | |
9165 | #define SIZEOF_TYPE 1 | |
9166 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
9167 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
9168 | #include "libguile/conv-integer.i.c" | |
9169 | ||
9170 | #define TYPE scm_t_uint8 | |
9171 | #define TYPE_MIN 0 | |
9172 | #define TYPE_MAX SCM_T_UINT8_MAX | |
9173 | #define SIZEOF_TYPE 1 | |
9174 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
9175 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
9176 | #include "libguile/conv-uinteger.i.c" | |
9177 | ||
9178 | #define TYPE scm_t_int16 | |
9179 | #define TYPE_MIN SCM_T_INT16_MIN | |
9180 | #define TYPE_MAX SCM_T_INT16_MAX | |
9181 | #define SIZEOF_TYPE 2 | |
9182 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
9183 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
9184 | #include "libguile/conv-integer.i.c" | |
9185 | ||
9186 | #define TYPE scm_t_uint16 | |
9187 | #define TYPE_MIN 0 | |
9188 | #define TYPE_MAX SCM_T_UINT16_MAX | |
9189 | #define SIZEOF_TYPE 2 | |
9190 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
9191 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
9192 | #include "libguile/conv-uinteger.i.c" | |
9193 | ||
9194 | #define TYPE scm_t_int32 | |
9195 | #define TYPE_MIN SCM_T_INT32_MIN | |
9196 | #define TYPE_MAX SCM_T_INT32_MAX | |
9197 | #define SIZEOF_TYPE 4 | |
9198 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
9199 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
9200 | #include "libguile/conv-integer.i.c" | |
9201 | ||
9202 | #define TYPE scm_t_uint32 | |
9203 | #define TYPE_MIN 0 | |
9204 | #define TYPE_MAX SCM_T_UINT32_MAX | |
9205 | #define SIZEOF_TYPE 4 | |
9206 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
9207 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
9208 | #include "libguile/conv-uinteger.i.c" | |
9209 | ||
904a78f1 MG |
9210 | #define TYPE scm_t_wchar |
9211 | #define TYPE_MIN (scm_t_int32)-1 | |
9212 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
9213 | #define SIZEOF_TYPE 4 | |
9214 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
9215 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
9216 | #include "libguile/conv-integer.i.c" | |
9217 | ||
bfd7932e MV |
9218 | #define TYPE scm_t_int64 |
9219 | #define TYPE_MIN SCM_T_INT64_MIN | |
9220 | #define TYPE_MAX SCM_T_INT64_MAX | |
9221 | #define SIZEOF_TYPE 8 | |
9222 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
9223 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
9224 | #include "libguile/conv-integer.i.c" | |
9225 | ||
9226 | #define TYPE scm_t_uint64 | |
9227 | #define TYPE_MIN 0 | |
9228 | #define TYPE_MAX SCM_T_UINT64_MAX | |
9229 | #define SIZEOF_TYPE 8 | |
9230 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
9231 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
9232 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 9233 | |
cd036260 MV |
9234 | void |
9235 | scm_to_mpz (SCM val, mpz_t rop) | |
9236 | { | |
9237 | if (SCM_I_INUMP (val)) | |
9238 | mpz_set_si (rop, SCM_I_INUM (val)); | |
9239 | else if (SCM_BIGP (val)) | |
9240 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
9241 | else | |
9242 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
9243 | } | |
9244 | ||
9245 | SCM | |
9246 | scm_from_mpz (mpz_t val) | |
9247 | { | |
9248 | return scm_i_mpz2num (val); | |
9249 | } | |
9250 | ||
73e4de09 MV |
9251 | int |
9252 | scm_is_real (SCM val) | |
9253 | { | |
9254 | return scm_is_true (scm_real_p (val)); | |
9255 | } | |
9256 | ||
55f26379 MV |
9257 | int |
9258 | scm_is_rational (SCM val) | |
9259 | { | |
9260 | return scm_is_true (scm_rational_p (val)); | |
9261 | } | |
9262 | ||
73e4de09 MV |
9263 | double |
9264 | scm_to_double (SCM val) | |
9265 | { | |
55f26379 MV |
9266 | if (SCM_I_INUMP (val)) |
9267 | return SCM_I_INUM (val); | |
9268 | else if (SCM_BIGP (val)) | |
9269 | return scm_i_big2dbl (val); | |
9270 | else if (SCM_FRACTIONP (val)) | |
9271 | return scm_i_fraction2double (val); | |
9272 | else if (SCM_REALP (val)) | |
9273 | return SCM_REAL_VALUE (val); | |
9274 | else | |
7a1aba42 | 9275 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
9276 | } |
9277 | ||
9278 | SCM | |
9279 | scm_from_double (double val) | |
9280 | { | |
978c52d1 LC |
9281 | SCM z; |
9282 | ||
9283 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
9284 | ||
9285 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 9286 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 9287 | |
55f26379 | 9288 | return z; |
73e4de09 MV |
9289 | } |
9290 | ||
220058a8 | 9291 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
9292 | |
9293 | float | |
e25f3727 | 9294 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9295 | { |
220058a8 AW |
9296 | scm_c_issue_deprecation_warning |
9297 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
9298 | ||
55f26379 MV |
9299 | if (SCM_BIGP (num)) |
9300 | { | |
9301 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9302 | if (!isinf (res)) |
55f26379 MV |
9303 | return res; |
9304 | else | |
9305 | scm_out_of_range (NULL, num); | |
9306 | } | |
9307 | else | |
9308 | return scm_to_double (num); | |
9309 | } | |
9310 | ||
9311 | double | |
e25f3727 | 9312 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9313 | { |
220058a8 AW |
9314 | scm_c_issue_deprecation_warning |
9315 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
9316 | ||
55f26379 MV |
9317 | if (SCM_BIGP (num)) |
9318 | { | |
9319 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9320 | if (!isinf (res)) |
55f26379 MV |
9321 | return res; |
9322 | else | |
9323 | scm_out_of_range (NULL, num); | |
9324 | } | |
9325 | else | |
9326 | return scm_to_double (num); | |
9327 | } | |
9328 | ||
9329 | #endif | |
9330 | ||
8507ec80 MV |
9331 | int |
9332 | scm_is_complex (SCM val) | |
9333 | { | |
9334 | return scm_is_true (scm_complex_p (val)); | |
9335 | } | |
9336 | ||
9337 | double | |
9338 | scm_c_real_part (SCM z) | |
9339 | { | |
9340 | if (SCM_COMPLEXP (z)) | |
9341 | return SCM_COMPLEX_REAL (z); | |
9342 | else | |
9343 | { | |
9344 | /* Use the scm_real_part to get proper error checking and | |
9345 | dispatching. | |
9346 | */ | |
9347 | return scm_to_double (scm_real_part (z)); | |
9348 | } | |
9349 | } | |
9350 | ||
9351 | double | |
9352 | scm_c_imag_part (SCM z) | |
9353 | { | |
9354 | if (SCM_COMPLEXP (z)) | |
9355 | return SCM_COMPLEX_IMAG (z); | |
9356 | else | |
9357 | { | |
9358 | /* Use the scm_imag_part to get proper error checking and | |
9359 | dispatching. The result will almost always be 0.0, but not | |
9360 | always. | |
9361 | */ | |
9362 | return scm_to_double (scm_imag_part (z)); | |
9363 | } | |
9364 | } | |
9365 | ||
9366 | double | |
9367 | scm_c_magnitude (SCM z) | |
9368 | { | |
9369 | return scm_to_double (scm_magnitude (z)); | |
9370 | } | |
9371 | ||
9372 | double | |
9373 | scm_c_angle (SCM z) | |
9374 | { | |
9375 | return scm_to_double (scm_angle (z)); | |
9376 | } | |
9377 | ||
9378 | int | |
9379 | scm_is_number (SCM z) | |
9380 | { | |
9381 | return scm_is_true (scm_number_p (z)); | |
9382 | } | |
9383 | ||
8ab3d8a0 | 9384 | |
a5f6b751 MW |
9385 | /* Returns log(x * 2^shift) */ |
9386 | static SCM | |
9387 | log_of_shifted_double (double x, long shift) | |
9388 | { | |
9389 | double ans = log (fabs (x)) + shift * M_LN2; | |
9390 | ||
9391 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
9392 | return scm_from_double (ans); | |
9393 | else | |
9394 | return scm_c_make_rectangular (ans, M_PI); | |
9395 | } | |
9396 | ||
9397 | /* Returns log(n), for exact integer n of integer-length size */ | |
9398 | static SCM | |
9399 | log_of_exact_integer_with_size (SCM n, long size) | |
9400 | { | |
9401 | long shift = size - 2 * scm_dblprec[0]; | |
9402 | ||
9403 | if (shift > 0) | |
9404 | return log_of_shifted_double | |
9405 | (scm_to_double (scm_ash (n, scm_from_long(-shift))), | |
9406 | shift); | |
9407 | else | |
9408 | return log_of_shifted_double (scm_to_double (n), 0); | |
9409 | } | |
9410 | ||
85bdb6ac | 9411 | /* Returns log(n), for exact integer n */ |
a5f6b751 MW |
9412 | static SCM |
9413 | log_of_exact_integer (SCM n) | |
9414 | { | |
9415 | return log_of_exact_integer_with_size | |
9416 | (n, scm_to_long (scm_integer_length (n))); | |
9417 | } | |
9418 | ||
9419 | /* Returns log(n/d), for exact non-zero integers n and d */ | |
9420 | static SCM | |
9421 | log_of_fraction (SCM n, SCM d) | |
9422 | { | |
9423 | long n_size = scm_to_long (scm_integer_length (n)); | |
9424 | long d_size = scm_to_long (scm_integer_length (d)); | |
9425 | ||
9426 | if (abs (n_size - d_size) > 1) | |
9427 | return (scm_difference (log_of_exact_integer_with_size (n, n_size), | |
9428 | log_of_exact_integer_with_size (d, d_size))); | |
9429 | else if (scm_is_false (scm_negative_p (n))) | |
9430 | return scm_from_double | |
9431 | (log1p (scm_to_double (scm_divide2real (scm_difference (n, d), d)))); | |
9432 | else | |
9433 | return scm_c_make_rectangular | |
9434 | (log1p (scm_to_double (scm_divide2real | |
9435 | (scm_difference (scm_abs (n), d), | |
9436 | d))), | |
9437 | M_PI); | |
9438 | } | |
9439 | ||
9440 | ||
8ab3d8a0 KR |
9441 | /* In the following functions we dispatch to the real-arg funcs like log() |
9442 | when we know the arg is real, instead of just handing everything to | |
9443 | clog() for instance. This is in case clog() doesn't optimize for a | |
9444 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
9445 | well use it to go straight to the applicable C func. */ | |
9446 | ||
2519490c MW |
9447 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
9448 | (SCM z), | |
9449 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
9450 | #define FUNC_NAME s_scm_log |
9451 | { | |
9452 | if (SCM_COMPLEXP (z)) | |
9453 | { | |
03976fee AW |
9454 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG \ |
9455 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
9456 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
9457 | #else | |
9458 | double re = SCM_COMPLEX_REAL (z); | |
9459 | double im = SCM_COMPLEX_IMAG (z); | |
9460 | return scm_c_make_rectangular (log (hypot (re, im)), | |
9461 | atan2 (im, re)); | |
9462 | #endif | |
9463 | } | |
a5f6b751 MW |
9464 | else if (SCM_REALP (z)) |
9465 | return log_of_shifted_double (SCM_REAL_VALUE (z), 0); | |
9466 | else if (SCM_I_INUMP (z)) | |
8ab3d8a0 | 9467 | { |
a5f6b751 MW |
9468 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9469 | if (scm_is_eq (z, SCM_INUM0)) | |
9470 | scm_num_overflow (s_scm_log); | |
9471 | #endif | |
9472 | return log_of_shifted_double (SCM_I_INUM (z), 0); | |
8ab3d8a0 | 9473 | } |
a5f6b751 MW |
9474 | else if (SCM_BIGP (z)) |
9475 | return log_of_exact_integer (z); | |
9476 | else if (SCM_FRACTIONP (z)) | |
9477 | return log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9478 | SCM_FRACTION_DENOMINATOR (z)); | |
2519490c MW |
9479 | else |
9480 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); | |
8ab3d8a0 KR |
9481 | } |
9482 | #undef FUNC_NAME | |
9483 | ||
9484 | ||
2519490c MW |
9485 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
9486 | (SCM z), | |
9487 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
9488 | #define FUNC_NAME s_scm_log10 |
9489 | { | |
9490 | if (SCM_COMPLEXP (z)) | |
9491 | { | |
9492 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
9493 | clog() and a multiply by M_LOG10E, rather than the fallback | |
9494 | log10+hypot+atan2.) */ | |
f328f862 LC |
9495 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
9496 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
9497 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
9498 | #else | |
9499 | double re = SCM_COMPLEX_REAL (z); | |
9500 | double im = SCM_COMPLEX_IMAG (z); | |
9501 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
9502 | M_LOG10E * atan2 (im, re)); | |
9503 | #endif | |
9504 | } | |
a5f6b751 | 9505 | else if (SCM_REALP (z) || SCM_I_INUMP (z)) |
8ab3d8a0 | 9506 | { |
a5f6b751 MW |
9507 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9508 | if (scm_is_eq (z, SCM_INUM0)) | |
9509 | scm_num_overflow (s_scm_log10); | |
9510 | #endif | |
9511 | { | |
9512 | double re = scm_to_double (z); | |
9513 | double l = log10 (fabs (re)); | |
9514 | if (re > 0.0 || double_is_non_negative_zero (re)) | |
9515 | return scm_from_double (l); | |
9516 | else | |
9517 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
9518 | } | |
8ab3d8a0 | 9519 | } |
a5f6b751 MW |
9520 | else if (SCM_BIGP (z)) |
9521 | return scm_product (flo_log10e, log_of_exact_integer (z)); | |
9522 | else if (SCM_FRACTIONP (z)) | |
9523 | return scm_product (flo_log10e, | |
9524 | log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9525 | SCM_FRACTION_DENOMINATOR (z))); | |
2519490c MW |
9526 | else |
9527 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); | |
8ab3d8a0 KR |
9528 | } |
9529 | #undef FUNC_NAME | |
9530 | ||
9531 | ||
2519490c MW |
9532 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
9533 | (SCM z), | |
9534 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
9535 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
9536 | #define FUNC_NAME s_scm_exp |
9537 | { | |
9538 | if (SCM_COMPLEXP (z)) | |
9539 | { | |
03976fee AW |
9540 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CEXP \ |
9541 | && defined (SCM_COMPLEX_VALUE) | |
8ab3d8a0 KR |
9542 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
9543 | #else | |
9544 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
9545 | SCM_COMPLEX_IMAG (z)); | |
9546 | #endif | |
9547 | } | |
2519490c | 9548 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
9549 | { |
9550 | /* When z is a negative bignum the conversion to double overflows, | |
9551 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
9552 | return scm_from_double (exp (scm_to_double (z))); | |
9553 | } | |
2519490c MW |
9554 | else |
9555 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); | |
8ab3d8a0 KR |
9556 | } |
9557 | #undef FUNC_NAME | |
9558 | ||
9559 | ||
882c8963 MW |
9560 | SCM_DEFINE (scm_i_exact_integer_sqrt, "exact-integer-sqrt", 1, 0, 0, |
9561 | (SCM k), | |
9562 | "Return two exact non-negative integers @var{s} and @var{r}\n" | |
9563 | "such that @math{@var{k} = @var{s}^2 + @var{r}} and\n" | |
9564 | "@math{@var{s}^2 <= @var{k} < (@var{s} + 1)^2}.\n" | |
9565 | "An error is raised if @var{k} is not an exact non-negative integer.\n" | |
9566 | "\n" | |
9567 | "@lisp\n" | |
9568 | "(exact-integer-sqrt 10) @result{} 3 and 1\n" | |
9569 | "@end lisp") | |
9570 | #define FUNC_NAME s_scm_i_exact_integer_sqrt | |
9571 | { | |
9572 | SCM s, r; | |
9573 | ||
9574 | scm_exact_integer_sqrt (k, &s, &r); | |
9575 | return scm_values (scm_list_2 (s, r)); | |
9576 | } | |
9577 | #undef FUNC_NAME | |
9578 | ||
9579 | void | |
9580 | scm_exact_integer_sqrt (SCM k, SCM *sp, SCM *rp) | |
9581 | { | |
9582 | if (SCM_LIKELY (SCM_I_INUMP (k))) | |
9583 | { | |
9584 | scm_t_inum kk = SCM_I_INUM (k); | |
9585 | scm_t_inum uu = kk; | |
9586 | scm_t_inum ss; | |
9587 | ||
9588 | if (SCM_LIKELY (kk > 0)) | |
9589 | { | |
9590 | do | |
9591 | { | |
9592 | ss = uu; | |
9593 | uu = (ss + kk/ss) / 2; | |
9594 | } while (uu < ss); | |
9595 | *sp = SCM_I_MAKINUM (ss); | |
9596 | *rp = SCM_I_MAKINUM (kk - ss*ss); | |
9597 | } | |
9598 | else if (SCM_LIKELY (kk == 0)) | |
9599 | *sp = *rp = SCM_INUM0; | |
9600 | else | |
9601 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9602 | "exact non-negative integer"); | |
9603 | } | |
9604 | else if (SCM_LIKELY (SCM_BIGP (k))) | |
9605 | { | |
9606 | SCM s, r; | |
9607 | ||
9608 | if (mpz_sgn (SCM_I_BIG_MPZ (k)) < 0) | |
9609 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9610 | "exact non-negative integer"); | |
9611 | s = scm_i_mkbig (); | |
9612 | r = scm_i_mkbig (); | |
9613 | mpz_sqrtrem (SCM_I_BIG_MPZ (s), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (k)); | |
9614 | scm_remember_upto_here_1 (k); | |
9615 | *sp = scm_i_normbig (s); | |
9616 | *rp = scm_i_normbig (r); | |
9617 | } | |
9618 | else | |
9619 | scm_wrong_type_arg_msg ("exact-integer-sqrt", SCM_ARG1, k, | |
9620 | "exact non-negative integer"); | |
9621 | } | |
9622 | ||
9623 | ||
2519490c MW |
9624 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
9625 | (SCM z), | |
9626 | "Return the square root of @var{z}. Of the two possible roots\n" | |
ffb62a43 | 9627 | "(positive and negative), the one with positive real part\n" |
2519490c MW |
9628 | "is returned, or if that's zero then a positive imaginary part.\n" |
9629 | "Thus,\n" | |
9630 | "\n" | |
9631 | "@example\n" | |
9632 | "(sqrt 9.0) @result{} 3.0\n" | |
9633 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
9634 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
9635 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
9636 | "@end example") | |
8ab3d8a0 KR |
9637 | #define FUNC_NAME s_scm_sqrt |
9638 | { | |
2519490c | 9639 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 9640 | { |
f328f862 LC |
9641 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
9642 | && defined SCM_COMPLEX_VALUE | |
2519490c | 9643 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 9644 | #else |
2519490c MW |
9645 | double re = SCM_COMPLEX_REAL (z); |
9646 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
9647 | return scm_c_make_polar (sqrt (hypot (re, im)), |
9648 | 0.5 * atan2 (im, re)); | |
9649 | #endif | |
9650 | } | |
2519490c | 9651 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 9652 | { |
2519490c | 9653 | double xx = scm_to_double (z); |
8ab3d8a0 KR |
9654 | if (xx < 0) |
9655 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
9656 | else | |
9657 | return scm_from_double (sqrt (xx)); | |
9658 | } | |
2519490c MW |
9659 | else |
9660 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); | |
8ab3d8a0 KR |
9661 | } |
9662 | #undef FUNC_NAME | |
9663 | ||
9664 | ||
9665 | ||
0f2d19dd JB |
9666 | void |
9667 | scm_init_numbers () | |
0f2d19dd | 9668 | { |
0b799eea MV |
9669 | int i; |
9670 | ||
713a4259 KR |
9671 | mpz_init_set_si (z_negative_one, -1); |
9672 | ||
a261c0e9 DH |
9673 | /* It may be possible to tune the performance of some algorithms by using |
9674 | * the following constants to avoid the creation of bignums. Please, before | |
9675 | * using these values, remember the two rules of program optimization: | |
9676 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 9677 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 9678 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 9679 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 9680 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 9681 | |
f3ae5d60 MD |
9682 | scm_add_feature ("complex"); |
9683 | scm_add_feature ("inexact"); | |
e7efe8e7 | 9684 | flo0 = scm_from_double (0.0); |
a5f6b751 | 9685 | flo_log10e = scm_from_double (M_LOG10E); |
0b799eea MV |
9686 | |
9687 | /* determine floating point precision */ | |
55f26379 | 9688 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
9689 | { |
9690 | init_dblprec(&scm_dblprec[i-2],i); | |
9691 | init_fx_radix(fx_per_radix[i-2],i); | |
9692 | } | |
f872b822 | 9693 | #ifdef DBL_DIG |
0b799eea | 9694 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 9695 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 9696 | #endif |
1be6b49c | 9697 | |
cff5fa33 | 9698 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 9699 | #include "libguile/numbers.x" |
0f2d19dd | 9700 | } |
89e00824 ML |
9701 | |
9702 | /* | |
9703 | Local Variables: | |
9704 | c-file-style: "gnu" | |
9705 | End: | |
9706 | */ |