Commit | Line | Data |
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8c93b597 | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006, 2007, 2008, 2009, 2010 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 RB |
24 | /* General assumptions: |
25 | * All objects satisfying SCM_COMPLEXP() have a non-zero complex component. | |
26 | * All objects satisfying SCM_BIGP() are too large to fit in a fixnum. | |
27 | * If an object satisfies integer?, it's either an inum, a bignum, or a real. | |
28 | * If floor (r) == r, r is an int, and mpz_set_d will DTRT. | |
f92e85f7 | 29 | * All objects satisfying SCM_FRACTIONP are never an integer. |
ca46fb90 RB |
30 | */ |
31 | ||
32 | /* TODO: | |
33 | ||
34 | - see if special casing bignums and reals in integer-exponent when | |
35 | possible (to use mpz_pow and mpf_pow_ui) is faster. | |
36 | ||
37 | - look in to better short-circuiting of common cases in | |
38 | integer-expt and elsewhere. | |
39 | ||
40 | - see if direct mpz operations can help in ash and elsewhere. | |
41 | ||
42 | */ | |
0f2d19dd | 43 | |
dbb605f5 | 44 | #ifdef HAVE_CONFIG_H |
ee33d62a RB |
45 | # include <config.h> |
46 | #endif | |
47 | ||
0f2d19dd | 48 | #include <math.h> |
fc194577 | 49 | #include <string.h> |
3f47e526 MG |
50 | #include <unicase.h> |
51 | #include <unictype.h> | |
f92e85f7 | 52 | |
8ab3d8a0 KR |
53 | #if HAVE_COMPLEX_H |
54 | #include <complex.h> | |
55 | #endif | |
56 | ||
a0599745 | 57 | #include "libguile/_scm.h" |
a0599745 MD |
58 | #include "libguile/feature.h" |
59 | #include "libguile/ports.h" | |
60 | #include "libguile/root.h" | |
61 | #include "libguile/smob.h" | |
62 | #include "libguile/strings.h" | |
864e7d42 | 63 | #include "libguile/bdw-gc.h" |
a0599745 MD |
64 | |
65 | #include "libguile/validate.h" | |
66 | #include "libguile/numbers.h" | |
1be6b49c | 67 | #include "libguile/deprecation.h" |
f4c627b3 | 68 | |
f92e85f7 MV |
69 | #include "libguile/eq.h" |
70 | ||
8ab3d8a0 KR |
71 | /* values per glibc, if not already defined */ |
72 | #ifndef M_LOG10E | |
73 | #define M_LOG10E 0.43429448190325182765 | |
74 | #endif | |
75 | #ifndef M_PI | |
76 | #define M_PI 3.14159265358979323846 | |
77 | #endif | |
78 | ||
0f2d19dd | 79 | \f |
f4c627b3 | 80 | |
ca46fb90 RB |
81 | /* |
82 | Wonder if this might be faster for some of our code? A switch on | |
83 | the numtag would jump directly to the right case, and the | |
84 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
85 | ||
86 | #define SCM_I_NUMTAG_NOTNUM 0 | |
87 | #define SCM_I_NUMTAG_INUM 1 | |
88 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
89 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
90 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
91 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 92 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 93 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 94 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
95 | : SCM_I_NUMTAG_NOTNUM))) |
96 | */ | |
f92e85f7 | 97 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
98 | |
99 | ||
e7efe8e7 AW |
100 | static SCM flo0; |
101 | ||
34d19ef6 | 102 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 103 | |
56e55ac7 | 104 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
105 | * printed or scm_string representation of an inexact number. |
106 | */ | |
0b799eea | 107 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 108 | |
b127c712 | 109 | |
ad79736c AW |
110 | #if !defined (HAVE_ASINH) |
111 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } | |
112 | #endif | |
113 | #if !defined (HAVE_ACOSH) | |
114 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } | |
115 | #endif | |
116 | #if !defined (HAVE_ATANH) | |
117 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } | |
118 | #endif | |
119 | ||
f8a8200b KR |
120 | /* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses |
121 | an explicit check. In some future gmp (don't know what version number), | |
122 | mpz_cmp_d is supposed to do this itself. */ | |
123 | #if 1 | |
b127c712 | 124 | #define xmpz_cmp_d(z, d) \ |
2e65b52f | 125 | (isinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) |
b127c712 KR |
126 | #else |
127 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
128 | #endif | |
129 | ||
f92e85f7 | 130 | |
4b26c03e | 131 | #if defined (GUILE_I) |
bca69a9f | 132 | #if HAVE_COMPLEX_DOUBLE |
8ab3d8a0 KR |
133 | |
134 | /* For an SCM object Z which is a complex number (ie. satisfies | |
135 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
136 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 137 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 138 | |
7a35784c | 139 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
8ab3d8a0 KR |
140 | |
141 | /* Convert a C "complex double" to an SCM value. */ | |
7a35784c | 142 | static inline SCM |
8ab3d8a0 KR |
143 | scm_from_complex_double (complex double z) |
144 | { | |
145 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
146 | } | |
bca69a9f | 147 | |
8ab3d8a0 | 148 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 149 | #endif /* GUILE_I */ |
8ab3d8a0 | 150 | |
0f2d19dd JB |
151 | \f |
152 | ||
713a4259 | 153 | static mpz_t z_negative_one; |
ac0c002c DH |
154 | |
155 | \f | |
864e7d42 LC |
156 | /* Clear the `mpz_t' embedded in bignum PTR. */ |
157 | static void | |
158 | finalize_bignum (GC_PTR ptr, GC_PTR data) | |
159 | { | |
160 | SCM bignum; | |
161 | ||
162 | bignum = PTR2SCM (ptr); | |
163 | mpz_clear (SCM_I_BIG_MPZ (bignum)); | |
164 | } | |
165 | ||
d017fcdf LC |
166 | /* Return a new uninitialized bignum. */ |
167 | static inline SCM | |
168 | make_bignum (void) | |
169 | { | |
170 | scm_t_bits *p; | |
864e7d42 LC |
171 | GC_finalization_proc prev_finalizer; |
172 | GC_PTR prev_finalizer_data; | |
d017fcdf LC |
173 | |
174 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ | |
175 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), | |
176 | "bignum"); | |
177 | p[0] = scm_tc16_big; | |
178 | ||
864e7d42 LC |
179 | GC_REGISTER_FINALIZER_NO_ORDER (p, finalize_bignum, NULL, |
180 | &prev_finalizer, | |
181 | &prev_finalizer_data); | |
182 | ||
d017fcdf LC |
183 | return SCM_PACK (p); |
184 | } | |
ac0c002c | 185 | |
864e7d42 | 186 | |
189171c5 | 187 | SCM |
ca46fb90 RB |
188 | scm_i_mkbig () |
189 | { | |
190 | /* Return a newly created bignum. */ | |
d017fcdf | 191 | SCM z = make_bignum (); |
ca46fb90 RB |
192 | mpz_init (SCM_I_BIG_MPZ (z)); |
193 | return z; | |
194 | } | |
195 | ||
189171c5 | 196 | SCM |
c71b0706 MV |
197 | scm_i_long2big (long x) |
198 | { | |
199 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 200 | SCM z = make_bignum (); |
c71b0706 MV |
201 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
202 | return z; | |
203 | } | |
204 | ||
189171c5 | 205 | SCM |
c71b0706 MV |
206 | scm_i_ulong2big (unsigned long x) |
207 | { | |
208 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 209 | SCM z = make_bignum (); |
c71b0706 MV |
210 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
211 | return z; | |
212 | } | |
213 | ||
189171c5 | 214 | SCM |
ca46fb90 RB |
215 | scm_i_clonebig (SCM src_big, int same_sign_p) |
216 | { | |
217 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
d017fcdf | 218 | SCM z = make_bignum (); |
ca46fb90 | 219 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
0aacf84e MD |
220 | if (!same_sign_p) |
221 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
222 | return z; |
223 | } | |
224 | ||
189171c5 | 225 | int |
ca46fb90 RB |
226 | scm_i_bigcmp (SCM x, SCM y) |
227 | { | |
228 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
229 | /* presume we already know x and y are bignums */ | |
230 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
231 | scm_remember_upto_here_2 (x, y); | |
232 | return result; | |
233 | } | |
234 | ||
189171c5 | 235 | SCM |
ca46fb90 RB |
236 | scm_i_dbl2big (double d) |
237 | { | |
238 | /* results are only defined if d is an integer */ | |
d017fcdf | 239 | SCM z = make_bignum (); |
ca46fb90 RB |
240 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
241 | return z; | |
242 | } | |
243 | ||
f92e85f7 MV |
244 | /* Convert a integer in double representation to a SCM number. */ |
245 | ||
189171c5 | 246 | SCM |
f92e85f7 MV |
247 | scm_i_dbl2num (double u) |
248 | { | |
249 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
250 | powers of 2, so there's no rounding when making "double" values | |
251 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
252 | get rounded on a 64-bit machine, hence the "+1". | |
253 | ||
254 | The use of floor() to force to an integer value ensures we get a | |
255 | "numerically closest" value without depending on how a | |
256 | double->long cast or how mpz_set_d will round. For reference, | |
257 | double->long probably follows the hardware rounding mode, | |
258 | mpz_set_d truncates towards zero. */ | |
259 | ||
260 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
261 | representable as a double? */ | |
262 | ||
263 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
264 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
d956fa6f | 265 | return SCM_I_MAKINUM ((long) u); |
f92e85f7 MV |
266 | else |
267 | return scm_i_dbl2big (u); | |
268 | } | |
269 | ||
089c9a59 KR |
270 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
271 | with R5RS exact->inexact. | |
272 | ||
273 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
274 | (ie. truncate towards zero), then adjust to get the closest double by |
275 | examining the next lower bit and adding 1 (to the absolute value) if | |
276 | necessary. | |
277 | ||
278 | Bignums exactly half way between representable doubles are rounded to the | |
279 | next higher absolute value (ie. away from zero). This seems like an | |
280 | adequate interpretation of R5RS "numerically closest", and it's easier | |
281 | and faster than a full "nearest-even" style. | |
282 | ||
283 | The bit test must be done on the absolute value of the mpz_t, which means | |
284 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
285 | negatives as twos complement. | |
286 | ||
287 | In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up | |
288 | following the hardware rounding mode, but applied to the absolute value | |
289 | of the mpz_t operand. This is not what we want so we put the high | |
290 | DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when, | |
291 | mpz_get_d is supposed to always truncate towards zero. | |
292 | ||
293 | ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3 | |
294 | is a slowdown. It'd be faster to pick out the relevant high bits with | |
295 | mpz_getlimbn if we could be bothered coding that, and if the new | |
296 | truncating gmp doesn't come out. */ | |
089c9a59 KR |
297 | |
298 | double | |
ca46fb90 RB |
299 | scm_i_big2dbl (SCM b) |
300 | { | |
089c9a59 KR |
301 | double result; |
302 | size_t bits; | |
303 | ||
304 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
305 | ||
f8a8200b | 306 | #if 1 |
089c9a59 | 307 | { |
f8a8200b | 308 | /* Current GMP, eg. 4.1.3, force truncation towards zero */ |
089c9a59 KR |
309 | mpz_t tmp; |
310 | if (bits > DBL_MANT_DIG) | |
311 | { | |
312 | size_t shift = bits - DBL_MANT_DIG; | |
313 | mpz_init2 (tmp, DBL_MANT_DIG); | |
314 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
315 | result = ldexp (mpz_get_d (tmp), shift); | |
316 | mpz_clear (tmp); | |
317 | } | |
318 | else | |
319 | { | |
320 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
321 | } | |
322 | } | |
323 | #else | |
f8a8200b | 324 | /* Future GMP */ |
089c9a59 KR |
325 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
326 | #endif | |
327 | ||
328 | if (bits > DBL_MANT_DIG) | |
329 | { | |
330 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
331 | /* test bit number "pos" in absolute value */ | |
332 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
333 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
334 | { | |
335 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
336 | } | |
337 | } | |
338 | ||
ca46fb90 RB |
339 | scm_remember_upto_here_1 (b); |
340 | return result; | |
341 | } | |
342 | ||
189171c5 | 343 | SCM |
ca46fb90 RB |
344 | scm_i_normbig (SCM b) |
345 | { | |
346 | /* convert a big back to a fixnum if it'll fit */ | |
347 | /* presume b is a bignum */ | |
348 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
349 | { | |
350 | long val = mpz_get_si (SCM_I_BIG_MPZ (b)); | |
351 | if (SCM_FIXABLE (val)) | |
d956fa6f | 352 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
353 | } |
354 | return b; | |
355 | } | |
f872b822 | 356 | |
f92e85f7 MV |
357 | static SCM_C_INLINE_KEYWORD SCM |
358 | scm_i_mpz2num (mpz_t b) | |
359 | { | |
360 | /* convert a mpz number to a SCM number. */ | |
361 | if (mpz_fits_slong_p (b)) | |
362 | { | |
363 | long val = mpz_get_si (b); | |
364 | if (SCM_FIXABLE (val)) | |
d956fa6f | 365 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
366 | } |
367 | ||
368 | { | |
d017fcdf | 369 | SCM z = make_bignum (); |
f92e85f7 MV |
370 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
371 | return z; | |
372 | } | |
373 | } | |
374 | ||
375 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
376 | static SCM scm_divide2real (SCM x, SCM y); | |
377 | ||
cba42c93 MV |
378 | static SCM |
379 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 380 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 381 | { |
c60e130c MV |
382 | /* First make sure the arguments are proper. |
383 | */ | |
e11e83f3 | 384 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 385 | { |
bc36d050 | 386 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 387 | scm_num_overflow ("make-ratio"); |
bc36d050 | 388 | if (scm_is_eq (denominator, SCM_I_MAKINUM(1))) |
f92e85f7 MV |
389 | return numerator; |
390 | } | |
391 | else | |
392 | { | |
393 | if (!(SCM_BIGP(denominator))) | |
394 | SCM_WRONG_TYPE_ARG (2, denominator); | |
395 | } | |
e11e83f3 | 396 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
397 | SCM_WRONG_TYPE_ARG (1, numerator); |
398 | ||
399 | /* Then flip signs so that the denominator is positive. | |
400 | */ | |
73e4de09 | 401 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
402 | { |
403 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
404 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
405 | } | |
406 | ||
407 | /* Now consider for each of the four fixnum/bignum combinations | |
408 | whether the rational number is really an integer. | |
409 | */ | |
e11e83f3 | 410 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 411 | { |
e11e83f3 | 412 | long x = SCM_I_INUM (numerator); |
bc36d050 | 413 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 414 | return SCM_INUM0; |
e11e83f3 | 415 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 416 | { |
dd5130ca | 417 | long y; |
e11e83f3 | 418 | y = SCM_I_INUM (denominator); |
f92e85f7 | 419 | if (x == y) |
d956fa6f | 420 | return SCM_I_MAKINUM(1); |
f92e85f7 | 421 | if ((x % y) == 0) |
d956fa6f | 422 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 423 | } |
dd5130ca KR |
424 | else |
425 | { | |
426 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
427 | of that value for the denominator, as a bignum. Apart from |
428 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
429 | integer. */ | |
430 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
431 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
432 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 433 | return SCM_I_MAKINUM(-1); |
dd5130ca | 434 | } |
f92e85f7 | 435 | } |
c60e130c | 436 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 437 | { |
e11e83f3 | 438 | if (SCM_I_INUMP (denominator)) |
c60e130c | 439 | { |
e11e83f3 | 440 | long yy = SCM_I_INUM (denominator); |
c60e130c MV |
441 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
442 | return scm_divide (numerator, denominator); | |
443 | } | |
444 | else | |
f92e85f7 | 445 | { |
bc36d050 | 446 | if (scm_is_eq (numerator, denominator)) |
d956fa6f | 447 | return SCM_I_MAKINUM(1); |
c60e130c MV |
448 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
449 | SCM_I_BIG_MPZ (denominator))) | |
450 | return scm_divide(numerator, denominator); | |
f92e85f7 | 451 | } |
f92e85f7 | 452 | } |
c60e130c MV |
453 | |
454 | /* No, it's a proper fraction. | |
455 | */ | |
e2bf3b19 HWN |
456 | { |
457 | SCM divisor = scm_gcd (numerator, denominator); | |
458 | if (!(scm_is_eq (divisor, SCM_I_MAKINUM(1)))) | |
459 | { | |
460 | numerator = scm_divide (numerator, divisor); | |
461 | denominator = scm_divide (denominator, divisor); | |
462 | } | |
463 | ||
464 | return scm_double_cell (scm_tc16_fraction, | |
465 | SCM_UNPACK (numerator), | |
466 | SCM_UNPACK (denominator), 0); | |
467 | } | |
f92e85f7 | 468 | } |
c60e130c | 469 | #undef FUNC_NAME |
f92e85f7 | 470 | |
f92e85f7 MV |
471 | double |
472 | scm_i_fraction2double (SCM z) | |
473 | { | |
55f26379 MV |
474 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
475 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
476 | } |
477 | ||
a1ec6916 | 478 | SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0, |
1bbd0b84 | 479 | (SCM x), |
942e5b91 MG |
480 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
481 | "otherwise.") | |
1bbd0b84 | 482 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 483 | { |
e11e83f3 | 484 | if (SCM_I_INUMP (x)) |
0aacf84e MD |
485 | return SCM_BOOL_T; |
486 | if (SCM_BIGP (x)) | |
487 | return SCM_BOOL_T; | |
f92e85f7 MV |
488 | if (SCM_FRACTIONP (x)) |
489 | return SCM_BOOL_T; | |
eb927cb9 MV |
490 | if (SCM_NUMBERP (x)) |
491 | return SCM_BOOL_F; | |
492 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 493 | } |
1bbd0b84 | 494 | #undef FUNC_NAME |
0f2d19dd | 495 | |
4219f20d | 496 | |
a1ec6916 | 497 | SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 498 | (SCM n), |
942e5b91 MG |
499 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
500 | "otherwise.") | |
1bbd0b84 | 501 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 502 | { |
e11e83f3 | 503 | if (SCM_I_INUMP (n)) |
0aacf84e | 504 | { |
e11e83f3 | 505 | long val = SCM_I_INUM (n); |
73e4de09 | 506 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
507 | } |
508 | else if (SCM_BIGP (n)) | |
509 | { | |
510 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
511 | scm_remember_upto_here_1 (n); | |
73e4de09 | 512 | return scm_from_bool (odd_p); |
0aacf84e | 513 | } |
73e4de09 | 514 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 515 | return SCM_BOOL_T; |
f92e85f7 MV |
516 | else if (SCM_REALP (n)) |
517 | { | |
518 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
519 | if (rem == 1.0) | |
520 | return SCM_BOOL_T; | |
521 | else if (rem == 0.0) | |
522 | return SCM_BOOL_F; | |
523 | else | |
524 | SCM_WRONG_TYPE_ARG (1, n); | |
525 | } | |
0aacf84e | 526 | else |
a1a33b0f | 527 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 528 | } |
1bbd0b84 | 529 | #undef FUNC_NAME |
0f2d19dd | 530 | |
4219f20d | 531 | |
a1ec6916 | 532 | SCM_DEFINE (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 533 | (SCM n), |
942e5b91 MG |
534 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
535 | "otherwise.") | |
1bbd0b84 | 536 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 537 | { |
e11e83f3 | 538 | if (SCM_I_INUMP (n)) |
0aacf84e | 539 | { |
e11e83f3 | 540 | long val = SCM_I_INUM (n); |
73e4de09 | 541 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
542 | } |
543 | else if (SCM_BIGP (n)) | |
544 | { | |
545 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
546 | scm_remember_upto_here_1 (n); | |
73e4de09 | 547 | return scm_from_bool (even_p); |
0aacf84e | 548 | } |
73e4de09 | 549 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 550 | return SCM_BOOL_T; |
f92e85f7 MV |
551 | else if (SCM_REALP (n)) |
552 | { | |
553 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
554 | if (rem == 1.0) | |
555 | return SCM_BOOL_F; | |
556 | else if (rem == 0.0) | |
557 | return SCM_BOOL_T; | |
558 | else | |
559 | SCM_WRONG_TYPE_ARG (1, n); | |
560 | } | |
0aacf84e | 561 | else |
a1a33b0f | 562 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 563 | } |
1bbd0b84 | 564 | #undef FUNC_NAME |
0f2d19dd | 565 | |
7351e207 | 566 | SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0, |
b1092b3a MV |
567 | (SCM x), |
568 | "Return @code{#t} if @var{x} is either @samp{+inf.0}\n" | |
569 | "or @samp{-inf.0}, @code{#f} otherwise.") | |
7351e207 MV |
570 | #define FUNC_NAME s_scm_inf_p |
571 | { | |
b1092b3a | 572 | if (SCM_REALP (x)) |
2e65b52f | 573 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
b1092b3a | 574 | else if (SCM_COMPLEXP (x)) |
2e65b52f LC |
575 | return scm_from_bool (isinf (SCM_COMPLEX_REAL (x)) |
576 | || isinf (SCM_COMPLEX_IMAG (x))); | |
0aacf84e | 577 | else |
7351e207 | 578 | return SCM_BOOL_F; |
7351e207 MV |
579 | } |
580 | #undef FUNC_NAME | |
581 | ||
582 | SCM_DEFINE (scm_nan_p, "nan?", 1, 0, 0, | |
583 | (SCM n), | |
584 | "Return @code{#t} if @var{n} is a NaN, @code{#f}\n" | |
585 | "otherwise.") | |
586 | #define FUNC_NAME s_scm_nan_p | |
587 | { | |
0aacf84e | 588 | if (SCM_REALP (n)) |
2e65b52f | 589 | return scm_from_bool (isnan (SCM_REAL_VALUE (n))); |
0aacf84e | 590 | else if (SCM_COMPLEXP (n)) |
2e65b52f LC |
591 | return scm_from_bool (isnan (SCM_COMPLEX_REAL (n)) |
592 | || isnan (SCM_COMPLEX_IMAG (n))); | |
0aacf84e | 593 | else |
7351e207 | 594 | return SCM_BOOL_F; |
7351e207 MV |
595 | } |
596 | #undef FUNC_NAME | |
597 | ||
598 | /* Guile's idea of infinity. */ | |
599 | static double guile_Inf; | |
600 | ||
601 | /* Guile's idea of not a number. */ | |
602 | static double guile_NaN; | |
603 | ||
604 | static void | |
605 | guile_ieee_init (void) | |
606 | { | |
7351e207 MV |
607 | /* Some version of gcc on some old version of Linux used to crash when |
608 | trying to make Inf and NaN. */ | |
609 | ||
240a27d2 KR |
610 | #ifdef INFINITY |
611 | /* C99 INFINITY, when available. | |
612 | FIXME: The standard allows for INFINITY to be something that overflows | |
613 | at compile time. We ought to have a configure test to check for that | |
614 | before trying to use it. (But in practice we believe this is not a | |
615 | problem on any system guile is likely to target.) */ | |
616 | guile_Inf = INFINITY; | |
56a3dcd4 | 617 | #elif defined HAVE_DINFINITY |
240a27d2 | 618 | /* OSF */ |
7351e207 | 619 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 620 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
621 | #else |
622 | double tmp = 1e+10; | |
623 | guile_Inf = tmp; | |
624 | for (;;) | |
625 | { | |
626 | guile_Inf *= 1e+10; | |
627 | if (guile_Inf == tmp) | |
628 | break; | |
629 | tmp = guile_Inf; | |
630 | } | |
631 | #endif | |
632 | ||
240a27d2 KR |
633 | #ifdef NAN |
634 | /* C99 NAN, when available */ | |
635 | guile_NaN = NAN; | |
56a3dcd4 | 636 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
637 | { |
638 | /* OSF */ | |
639 | extern unsigned int DQNAN[2]; | |
640 | guile_NaN = (*((double *)(DQNAN))); | |
641 | } | |
7351e207 MV |
642 | #else |
643 | guile_NaN = guile_Inf / guile_Inf; | |
644 | #endif | |
7351e207 MV |
645 | } |
646 | ||
647 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
648 | (void), | |
649 | "Return Inf.") | |
650 | #define FUNC_NAME s_scm_inf | |
651 | { | |
652 | static int initialized = 0; | |
653 | if (! initialized) | |
654 | { | |
655 | guile_ieee_init (); | |
656 | initialized = 1; | |
657 | } | |
55f26379 | 658 | return scm_from_double (guile_Inf); |
7351e207 MV |
659 | } |
660 | #undef FUNC_NAME | |
661 | ||
662 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
663 | (void), | |
664 | "Return NaN.") | |
665 | #define FUNC_NAME s_scm_nan | |
666 | { | |
667 | static int initialized = 0; | |
0aacf84e | 668 | if (!initialized) |
7351e207 MV |
669 | { |
670 | guile_ieee_init (); | |
671 | initialized = 1; | |
672 | } | |
55f26379 | 673 | return scm_from_double (guile_NaN); |
7351e207 MV |
674 | } |
675 | #undef FUNC_NAME | |
676 | ||
4219f20d | 677 | |
a48d60b1 MD |
678 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
679 | (SCM x), | |
680 | "Return the absolute value of @var{x}.") | |
681 | #define FUNC_NAME | |
0f2d19dd | 682 | { |
e11e83f3 | 683 | if (SCM_I_INUMP (x)) |
0aacf84e | 684 | { |
e11e83f3 | 685 | long int xx = SCM_I_INUM (x); |
0aacf84e MD |
686 | if (xx >= 0) |
687 | return x; | |
688 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 689 | return SCM_I_MAKINUM (-xx); |
0aacf84e MD |
690 | else |
691 | return scm_i_long2big (-xx); | |
4219f20d | 692 | } |
0aacf84e MD |
693 | else if (SCM_BIGP (x)) |
694 | { | |
695 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
696 | if (sgn < 0) | |
697 | return scm_i_clonebig (x, 0); | |
698 | else | |
699 | return x; | |
4219f20d | 700 | } |
0aacf84e | 701 | else if (SCM_REALP (x)) |
ae38324d KR |
702 | { |
703 | /* note that if x is a NaN then xx<0 is false so we return x unchanged */ | |
704 | double xx = SCM_REAL_VALUE (x); | |
705 | if (xx < 0.0) | |
55f26379 | 706 | return scm_from_double (-xx); |
ae38324d KR |
707 | else |
708 | return x; | |
709 | } | |
f92e85f7 MV |
710 | else if (SCM_FRACTIONP (x)) |
711 | { | |
73e4de09 | 712 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 713 | return x; |
cba42c93 | 714 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
715 | SCM_FRACTION_DENOMINATOR (x)); |
716 | } | |
0aacf84e | 717 | else |
a48d60b1 | 718 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 719 | } |
a48d60b1 | 720 | #undef FUNC_NAME |
0f2d19dd | 721 | |
4219f20d | 722 | |
9de33deb | 723 | SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); |
942e5b91 MG |
724 | /* "Return the quotient of the numbers @var{x} and @var{y}." |
725 | */ | |
0f2d19dd | 726 | SCM |
6e8d25a6 | 727 | scm_quotient (SCM x, SCM y) |
0f2d19dd | 728 | { |
e11e83f3 | 729 | if (SCM_I_INUMP (x)) |
0aacf84e | 730 | { |
e11e83f3 MV |
731 | long xx = SCM_I_INUM (x); |
732 | if (SCM_I_INUMP (y)) | |
0aacf84e | 733 | { |
e11e83f3 | 734 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
735 | if (yy == 0) |
736 | scm_num_overflow (s_quotient); | |
737 | else | |
738 | { | |
739 | long z = xx / yy; | |
740 | if (SCM_FIXABLE (z)) | |
d956fa6f | 741 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
742 | else |
743 | return scm_i_long2big (z); | |
744 | } | |
828865c3 | 745 | } |
0aacf84e | 746 | else if (SCM_BIGP (y)) |
ac0c002c | 747 | { |
e11e83f3 | 748 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
749 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
750 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
751 | { | |
752 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
753 | scm_remember_upto_here_1 (y); | |
d956fa6f | 754 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 755 | } |
0aacf84e | 756 | else |
d956fa6f | 757 | return SCM_I_MAKINUM (0); |
ac0c002c DH |
758 | } |
759 | else | |
0aacf84e | 760 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); |
828865c3 | 761 | } |
0aacf84e MD |
762 | else if (SCM_BIGP (x)) |
763 | { | |
e11e83f3 | 764 | if (SCM_I_INUMP (y)) |
0aacf84e | 765 | { |
e11e83f3 | 766 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
767 | if (yy == 0) |
768 | scm_num_overflow (s_quotient); | |
769 | else if (yy == 1) | |
770 | return x; | |
771 | else | |
772 | { | |
773 | SCM result = scm_i_mkbig (); | |
774 | if (yy < 0) | |
775 | { | |
776 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
777 | SCM_I_BIG_MPZ (x), | |
778 | - yy); | |
779 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
780 | } | |
781 | else | |
782 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
783 | scm_remember_upto_here_1 (x); | |
784 | return scm_i_normbig (result); | |
785 | } | |
786 | } | |
787 | else if (SCM_BIGP (y)) | |
788 | { | |
789 | SCM result = scm_i_mkbig (); | |
790 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
791 | SCM_I_BIG_MPZ (x), | |
792 | SCM_I_BIG_MPZ (y)); | |
793 | scm_remember_upto_here_2 (x, y); | |
794 | return scm_i_normbig (result); | |
795 | } | |
796 | else | |
797 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); | |
f872b822 | 798 | } |
0aacf84e | 799 | else |
89a7e495 | 800 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient); |
0f2d19dd JB |
801 | } |
802 | ||
9de33deb | 803 | SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); |
942e5b91 MG |
804 | /* "Return the remainder of the numbers @var{x} and @var{y}.\n" |
805 | * "@lisp\n" | |
806 | * "(remainder 13 4) @result{} 1\n" | |
807 | * "(remainder -13 4) @result{} -1\n" | |
808 | * "@end lisp" | |
809 | */ | |
0f2d19dd | 810 | SCM |
6e8d25a6 | 811 | scm_remainder (SCM x, SCM y) |
0f2d19dd | 812 | { |
e11e83f3 | 813 | if (SCM_I_INUMP (x)) |
0aacf84e | 814 | { |
e11e83f3 | 815 | if (SCM_I_INUMP (y)) |
0aacf84e | 816 | { |
e11e83f3 | 817 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
818 | if (yy == 0) |
819 | scm_num_overflow (s_remainder); | |
820 | else | |
821 | { | |
e11e83f3 | 822 | long z = SCM_I_INUM (x) % yy; |
d956fa6f | 823 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
824 | } |
825 | } | |
826 | else if (SCM_BIGP (y)) | |
ac0c002c | 827 | { |
e11e83f3 | 828 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
829 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
830 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
831 | { | |
832 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
833 | scm_remember_upto_here_1 (y); | |
d956fa6f | 834 | return SCM_I_MAKINUM (0); |
4dc09ee4 | 835 | } |
0aacf84e MD |
836 | else |
837 | return x; | |
ac0c002c DH |
838 | } |
839 | else | |
0aacf84e | 840 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); |
89a7e495 | 841 | } |
0aacf84e MD |
842 | else if (SCM_BIGP (x)) |
843 | { | |
e11e83f3 | 844 | if (SCM_I_INUMP (y)) |
0aacf84e | 845 | { |
e11e83f3 | 846 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
847 | if (yy == 0) |
848 | scm_num_overflow (s_remainder); | |
849 | else | |
850 | { | |
851 | SCM result = scm_i_mkbig (); | |
852 | if (yy < 0) | |
853 | yy = - yy; | |
854 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
855 | scm_remember_upto_here_1 (x); | |
856 | return scm_i_normbig (result); | |
857 | } | |
858 | } | |
859 | else if (SCM_BIGP (y)) | |
860 | { | |
861 | SCM result = scm_i_mkbig (); | |
862 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
863 | SCM_I_BIG_MPZ (x), | |
864 | SCM_I_BIG_MPZ (y)); | |
865 | scm_remember_upto_here_2 (x, y); | |
866 | return scm_i_normbig (result); | |
867 | } | |
868 | else | |
869 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); | |
f872b822 | 870 | } |
0aacf84e | 871 | else |
89a7e495 | 872 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder); |
0f2d19dd JB |
873 | } |
874 | ||
89a7e495 | 875 | |
9de33deb | 876 | SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); |
942e5b91 MG |
877 | /* "Return the modulo of the numbers @var{x} and @var{y}.\n" |
878 | * "@lisp\n" | |
879 | * "(modulo 13 4) @result{} 1\n" | |
880 | * "(modulo -13 4) @result{} 3\n" | |
881 | * "@end lisp" | |
882 | */ | |
0f2d19dd | 883 | SCM |
6e8d25a6 | 884 | scm_modulo (SCM x, SCM y) |
0f2d19dd | 885 | { |
e11e83f3 | 886 | if (SCM_I_INUMP (x)) |
0aacf84e | 887 | { |
e11e83f3 MV |
888 | long xx = SCM_I_INUM (x); |
889 | if (SCM_I_INUMP (y)) | |
0aacf84e | 890 | { |
e11e83f3 | 891 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
892 | if (yy == 0) |
893 | scm_num_overflow (s_modulo); | |
894 | else | |
895 | { | |
66b1c775 KR |
896 | /* C99 specifies that "%" is the remainder corresponding to a |
897 | quotient rounded towards zero, and that's also traditional | |
898 | for machine division, so z here should be well defined. */ | |
0aacf84e MD |
899 | long z = xx % yy; |
900 | long result; | |
901 | ||
902 | if (yy < 0) | |
903 | { | |
904 | if (z > 0) | |
905 | result = z + yy; | |
906 | else | |
907 | result = z; | |
908 | } | |
909 | else | |
910 | { | |
911 | if (z < 0) | |
912 | result = z + yy; | |
913 | else | |
914 | result = z; | |
915 | } | |
d956fa6f | 916 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
917 | } |
918 | } | |
919 | else if (SCM_BIGP (y)) | |
920 | { | |
921 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
922 | { |
923 | mpz_t z_x; | |
924 | SCM result; | |
925 | ||
926 | if (sgn_y < 0) | |
927 | { | |
928 | SCM pos_y = scm_i_clonebig (y, 0); | |
929 | /* do this after the last scm_op */ | |
930 | mpz_init_set_si (z_x, xx); | |
931 | result = pos_y; /* re-use this bignum */ | |
932 | mpz_mod (SCM_I_BIG_MPZ (result), | |
933 | z_x, | |
934 | SCM_I_BIG_MPZ (pos_y)); | |
935 | scm_remember_upto_here_1 (pos_y); | |
936 | } | |
937 | else | |
938 | { | |
939 | result = scm_i_mkbig (); | |
940 | /* do this after the last scm_op */ | |
941 | mpz_init_set_si (z_x, xx); | |
942 | mpz_mod (SCM_I_BIG_MPZ (result), | |
943 | z_x, | |
944 | SCM_I_BIG_MPZ (y)); | |
945 | scm_remember_upto_here_1 (y); | |
946 | } | |
ca46fb90 | 947 | |
0aacf84e MD |
948 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
949 | mpz_add (SCM_I_BIG_MPZ (result), | |
950 | SCM_I_BIG_MPZ (y), | |
951 | SCM_I_BIG_MPZ (result)); | |
952 | scm_remember_upto_here_1 (y); | |
953 | /* and do this before the next one */ | |
954 | mpz_clear (z_x); | |
955 | return scm_i_normbig (result); | |
956 | } | |
957 | } | |
958 | else | |
959 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
f872b822 | 960 | } |
0aacf84e MD |
961 | else if (SCM_BIGP (x)) |
962 | { | |
e11e83f3 | 963 | if (SCM_I_INUMP (y)) |
0aacf84e | 964 | { |
e11e83f3 | 965 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
966 | if (yy == 0) |
967 | scm_num_overflow (s_modulo); | |
968 | else | |
969 | { | |
970 | SCM result = scm_i_mkbig (); | |
971 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
972 | SCM_I_BIG_MPZ (x), | |
973 | (yy < 0) ? - yy : yy); | |
974 | scm_remember_upto_here_1 (x); | |
975 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
976 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
977 | SCM_I_BIG_MPZ (result), | |
978 | - yy); | |
979 | return scm_i_normbig (result); | |
980 | } | |
981 | } | |
982 | else if (SCM_BIGP (y)) | |
983 | { | |
0aacf84e MD |
984 | { |
985 | SCM result = scm_i_mkbig (); | |
986 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
987 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
988 | mpz_mod (SCM_I_BIG_MPZ (result), | |
989 | SCM_I_BIG_MPZ (x), | |
990 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 991 | |
0aacf84e MD |
992 | scm_remember_upto_here_1 (x); |
993 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
994 | mpz_add (SCM_I_BIG_MPZ (result), | |
995 | SCM_I_BIG_MPZ (y), | |
996 | SCM_I_BIG_MPZ (result)); | |
997 | scm_remember_upto_here_2 (y, pos_y); | |
998 | return scm_i_normbig (result); | |
999 | } | |
1000 | } | |
1001 | else | |
1002 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
828865c3 | 1003 | } |
0aacf84e | 1004 | else |
09fb7599 | 1005 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); |
0f2d19dd JB |
1006 | } |
1007 | ||
78d3deb1 AW |
1008 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
1009 | (SCM x, SCM y, SCM rest), | |
1010 | "Return the greatest common divisor of all parameter values.\n" | |
1011 | "If called without arguments, 0 is returned.") | |
1012 | #define FUNC_NAME s_scm_i_gcd | |
1013 | { | |
1014 | while (!scm_is_null (rest)) | |
1015 | { x = scm_gcd (x, y); | |
1016 | y = scm_car (rest); | |
1017 | rest = scm_cdr (rest); | |
1018 | } | |
1019 | return scm_gcd (x, y); | |
1020 | } | |
1021 | #undef FUNC_NAME | |
1022 | ||
1023 | #define s_gcd s_scm_i_gcd | |
1024 | #define g_gcd g_scm_i_gcd | |
1025 | ||
0f2d19dd | 1026 | SCM |
6e8d25a6 | 1027 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 1028 | { |
ca46fb90 | 1029 | if (SCM_UNBNDP (y)) |
1dd79792 | 1030 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 1031 | |
e11e83f3 | 1032 | if (SCM_I_INUMP (x)) |
ca46fb90 | 1033 | { |
e11e83f3 | 1034 | if (SCM_I_INUMP (y)) |
ca46fb90 | 1035 | { |
e11e83f3 MV |
1036 | long xx = SCM_I_INUM (x); |
1037 | long yy = SCM_I_INUM (y); | |
ca46fb90 RB |
1038 | long u = xx < 0 ? -xx : xx; |
1039 | long v = yy < 0 ? -yy : yy; | |
1040 | long result; | |
0aacf84e MD |
1041 | if (xx == 0) |
1042 | result = v; | |
1043 | else if (yy == 0) | |
1044 | result = u; | |
1045 | else | |
1046 | { | |
1047 | long k = 1; | |
1048 | long t; | |
1049 | /* Determine a common factor 2^k */ | |
1050 | while (!(1 & (u | v))) | |
1051 | { | |
1052 | k <<= 1; | |
1053 | u >>= 1; | |
1054 | v >>= 1; | |
1055 | } | |
1056 | /* Now, any factor 2^n can be eliminated */ | |
1057 | if (u & 1) | |
1058 | t = -v; | |
1059 | else | |
1060 | { | |
1061 | t = u; | |
1062 | b3: | |
1063 | t = SCM_SRS (t, 1); | |
1064 | } | |
1065 | if (!(1 & t)) | |
1066 | goto b3; | |
1067 | if (t > 0) | |
1068 | u = t; | |
1069 | else | |
1070 | v = -t; | |
1071 | t = u - v; | |
1072 | if (t != 0) | |
1073 | goto b3; | |
1074 | result = u * k; | |
1075 | } | |
1076 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 1077 | ? SCM_I_MAKINUM (result) |
0aacf84e | 1078 | : scm_i_long2big (result)); |
ca46fb90 RB |
1079 | } |
1080 | else if (SCM_BIGP (y)) | |
1081 | { | |
0bff4dce KR |
1082 | SCM_SWAP (x, y); |
1083 | goto big_inum; | |
ca46fb90 RB |
1084 | } |
1085 | else | |
1086 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 1087 | } |
ca46fb90 RB |
1088 | else if (SCM_BIGP (x)) |
1089 | { | |
e11e83f3 | 1090 | if (SCM_I_INUMP (y)) |
ca46fb90 RB |
1091 | { |
1092 | unsigned long result; | |
0bff4dce KR |
1093 | long yy; |
1094 | big_inum: | |
e11e83f3 | 1095 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
1096 | if (yy == 0) |
1097 | return scm_abs (x); | |
0aacf84e MD |
1098 | if (yy < 0) |
1099 | yy = -yy; | |
ca46fb90 RB |
1100 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
1101 | scm_remember_upto_here_1 (x); | |
0aacf84e | 1102 | return (SCM_POSFIXABLE (result) |
d956fa6f | 1103 | ? SCM_I_MAKINUM (result) |
c71b0706 | 1104 | : scm_from_ulong (result)); |
ca46fb90 RB |
1105 | } |
1106 | else if (SCM_BIGP (y)) | |
1107 | { | |
1108 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
1109 | mpz_gcd (SCM_I_BIG_MPZ (result), |
1110 | SCM_I_BIG_MPZ (x), | |
1111 | SCM_I_BIG_MPZ (y)); | |
1112 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
1113 | return scm_i_normbig (result); |
1114 | } | |
1115 | else | |
1116 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 1117 | } |
ca46fb90 | 1118 | else |
09fb7599 | 1119 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
1120 | } |
1121 | ||
78d3deb1 AW |
1122 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
1123 | (SCM x, SCM y, SCM rest), | |
1124 | "Return the least common multiple of the arguments.\n" | |
1125 | "If called without arguments, 1 is returned.") | |
1126 | #define FUNC_NAME s_scm_i_lcm | |
1127 | { | |
1128 | while (!scm_is_null (rest)) | |
1129 | { x = scm_lcm (x, y); | |
1130 | y = scm_car (rest); | |
1131 | rest = scm_cdr (rest); | |
1132 | } | |
1133 | return scm_lcm (x, y); | |
1134 | } | |
1135 | #undef FUNC_NAME | |
1136 | ||
1137 | #define s_lcm s_scm_i_lcm | |
1138 | #define g_lcm g_scm_i_lcm | |
1139 | ||
0f2d19dd | 1140 | SCM |
6e8d25a6 | 1141 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 1142 | { |
ca46fb90 RB |
1143 | if (SCM_UNBNDP (n2)) |
1144 | { | |
1145 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
1146 | return SCM_I_MAKINUM (1L); |
1147 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 1148 | } |
09fb7599 | 1149 | |
e11e83f3 | 1150 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 1151 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 1152 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 1153 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 1154 | |
e11e83f3 | 1155 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 1156 | { |
e11e83f3 | 1157 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1158 | { |
1159 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 1160 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
1161 | return d; |
1162 | else | |
1163 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
1164 | } | |
1165 | else | |
1166 | { | |
1167 | /* inum n1, big n2 */ | |
1168 | inumbig: | |
1169 | { | |
1170 | SCM result = scm_i_mkbig (); | |
e11e83f3 | 1171 | long nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
1172 | if (nn1 == 0) return SCM_INUM0; |
1173 | if (nn1 < 0) nn1 = - nn1; | |
1174 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
1175 | scm_remember_upto_here_1 (n2); | |
1176 | return result; | |
1177 | } | |
1178 | } | |
1179 | } | |
1180 | else | |
1181 | { | |
1182 | /* big n1 */ | |
e11e83f3 | 1183 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1184 | { |
1185 | SCM_SWAP (n1, n2); | |
1186 | goto inumbig; | |
1187 | } | |
1188 | else | |
1189 | { | |
1190 | SCM result = scm_i_mkbig (); | |
1191 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
1192 | SCM_I_BIG_MPZ (n1), | |
1193 | SCM_I_BIG_MPZ (n2)); | |
1194 | scm_remember_upto_here_2(n1, n2); | |
1195 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
1196 | return result; | |
1197 | } | |
f872b822 | 1198 | } |
0f2d19dd JB |
1199 | } |
1200 | ||
8a525303 GB |
1201 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
1202 | ||
1203 | Logand: | |
1204 | X Y Result Method: | |
1205 | (len) | |
1206 | + + + x (map digit:logand X Y) | |
1207 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
1208 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
1209 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
1210 | ||
1211 | Logior: | |
1212 | X Y Result Method: | |
1213 | ||
1214 | + + + (map digit:logior X Y) | |
1215 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
1216 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
1217 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
1218 | ||
1219 | Logxor: | |
1220 | X Y Result Method: | |
1221 | ||
1222 | + + + (map digit:logxor X Y) | |
1223 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
1224 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
1225 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
1226 | ||
1227 | Logtest: | |
1228 | X Y Result | |
1229 | ||
1230 | + + (any digit:logand X Y) | |
1231 | + - (any digit:logand X (lognot (+ -1 Y))) | |
1232 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
1233 | - - #t | |
1234 | ||
1235 | */ | |
1236 | ||
78d3deb1 AW |
1237 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
1238 | (SCM x, SCM y, SCM rest), | |
1239 | "Return the bitwise AND of the integer arguments.\n\n" | |
1240 | "@lisp\n" | |
1241 | "(logand) @result{} -1\n" | |
1242 | "(logand 7) @result{} 7\n" | |
1243 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
1244 | "@end lisp") | |
1245 | #define FUNC_NAME s_scm_i_logand | |
1246 | { | |
1247 | while (!scm_is_null (rest)) | |
1248 | { x = scm_logand (x, y); | |
1249 | y = scm_car (rest); | |
1250 | rest = scm_cdr (rest); | |
1251 | } | |
1252 | return scm_logand (x, y); | |
1253 | } | |
1254 | #undef FUNC_NAME | |
1255 | ||
1256 | #define s_scm_logand s_scm_i_logand | |
1257 | ||
1258 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 1259 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 1260 | { |
9a00c9fc DH |
1261 | long int nn1; |
1262 | ||
0aacf84e MD |
1263 | if (SCM_UNBNDP (n2)) |
1264 | { | |
1265 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 1266 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
1267 | else if (!SCM_NUMBERP (n1)) |
1268 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1269 | else if (SCM_NUMBERP (n1)) | |
1270 | return n1; | |
1271 | else | |
1272 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1273 | } |
09fb7599 | 1274 | |
e11e83f3 | 1275 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1276 | { |
e11e83f3 MV |
1277 | nn1 = SCM_I_INUM (n1); |
1278 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1279 | { |
e11e83f3 | 1280 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1281 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
1282 | } |
1283 | else if SCM_BIGP (n2) | |
1284 | { | |
1285 | intbig: | |
1286 | if (n1 == 0) | |
1287 | return SCM_INUM0; | |
1288 | { | |
1289 | SCM result_z = scm_i_mkbig (); | |
1290 | mpz_t nn1_z; | |
1291 | mpz_init_set_si (nn1_z, nn1); | |
1292 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1293 | scm_remember_upto_here_1 (n2); | |
1294 | mpz_clear (nn1_z); | |
1295 | return scm_i_normbig (result_z); | |
1296 | } | |
1297 | } | |
1298 | else | |
1299 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1300 | } | |
1301 | else if (SCM_BIGP (n1)) | |
1302 | { | |
e11e83f3 | 1303 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1304 | { |
1305 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1306 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1307 | goto intbig; |
1308 | } | |
1309 | else if (SCM_BIGP (n2)) | |
1310 | { | |
1311 | SCM result_z = scm_i_mkbig (); | |
1312 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
1313 | SCM_I_BIG_MPZ (n1), | |
1314 | SCM_I_BIG_MPZ (n2)); | |
1315 | scm_remember_upto_here_2 (n1, n2); | |
1316 | return scm_i_normbig (result_z); | |
1317 | } | |
1318 | else | |
1319 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1320 | } |
0aacf84e | 1321 | else |
09fb7599 | 1322 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1323 | } |
1bbd0b84 | 1324 | #undef FUNC_NAME |
0f2d19dd | 1325 | |
09fb7599 | 1326 | |
78d3deb1 AW |
1327 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
1328 | (SCM x, SCM y, SCM rest), | |
1329 | "Return the bitwise OR of the integer arguments.\n\n" | |
1330 | "@lisp\n" | |
1331 | "(logior) @result{} 0\n" | |
1332 | "(logior 7) @result{} 7\n" | |
1333 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1334 | "@end lisp") | |
1335 | #define FUNC_NAME s_scm_i_logior | |
1336 | { | |
1337 | while (!scm_is_null (rest)) | |
1338 | { x = scm_logior (x, y); | |
1339 | y = scm_car (rest); | |
1340 | rest = scm_cdr (rest); | |
1341 | } | |
1342 | return scm_logior (x, y); | |
1343 | } | |
1344 | #undef FUNC_NAME | |
1345 | ||
1346 | #define s_scm_logior s_scm_i_logior | |
1347 | ||
1348 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 1349 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 1350 | { |
9a00c9fc DH |
1351 | long int nn1; |
1352 | ||
0aacf84e MD |
1353 | if (SCM_UNBNDP (n2)) |
1354 | { | |
1355 | if (SCM_UNBNDP (n1)) | |
1356 | return SCM_INUM0; | |
1357 | else if (SCM_NUMBERP (n1)) | |
1358 | return n1; | |
1359 | else | |
1360 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1361 | } |
09fb7599 | 1362 | |
e11e83f3 | 1363 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1364 | { |
e11e83f3 MV |
1365 | nn1 = SCM_I_INUM (n1); |
1366 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1367 | { |
e11e83f3 | 1368 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1369 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
1370 | } |
1371 | else if (SCM_BIGP (n2)) | |
1372 | { | |
1373 | intbig: | |
1374 | if (nn1 == 0) | |
1375 | return n2; | |
1376 | { | |
1377 | SCM result_z = scm_i_mkbig (); | |
1378 | mpz_t nn1_z; | |
1379 | mpz_init_set_si (nn1_z, nn1); | |
1380 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1381 | scm_remember_upto_here_1 (n2); | |
1382 | mpz_clear (nn1_z); | |
9806de0d | 1383 | return scm_i_normbig (result_z); |
0aacf84e MD |
1384 | } |
1385 | } | |
1386 | else | |
1387 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1388 | } | |
1389 | else if (SCM_BIGP (n1)) | |
1390 | { | |
e11e83f3 | 1391 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1392 | { |
1393 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1394 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1395 | goto intbig; |
1396 | } | |
1397 | else if (SCM_BIGP (n2)) | |
1398 | { | |
1399 | SCM result_z = scm_i_mkbig (); | |
1400 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
1401 | SCM_I_BIG_MPZ (n1), | |
1402 | SCM_I_BIG_MPZ (n2)); | |
1403 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 1404 | return scm_i_normbig (result_z); |
0aacf84e MD |
1405 | } |
1406 | else | |
1407 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1408 | } |
0aacf84e | 1409 | else |
09fb7599 | 1410 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1411 | } |
1bbd0b84 | 1412 | #undef FUNC_NAME |
0f2d19dd | 1413 | |
09fb7599 | 1414 | |
78d3deb1 AW |
1415 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
1416 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
1417 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1418 | "set in the result if it is set in an odd number of arguments.\n" | |
1419 | "@lisp\n" | |
1420 | "(logxor) @result{} 0\n" | |
1421 | "(logxor 7) @result{} 7\n" | |
1422 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1423 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1424 | "@end lisp") |
78d3deb1 AW |
1425 | #define FUNC_NAME s_scm_i_logxor |
1426 | { | |
1427 | while (!scm_is_null (rest)) | |
1428 | { x = scm_logxor (x, y); | |
1429 | y = scm_car (rest); | |
1430 | rest = scm_cdr (rest); | |
1431 | } | |
1432 | return scm_logxor (x, y); | |
1433 | } | |
1434 | #undef FUNC_NAME | |
1435 | ||
1436 | #define s_scm_logxor s_scm_i_logxor | |
1437 | ||
1438 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 1439 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1440 | { |
9a00c9fc DH |
1441 | long int nn1; |
1442 | ||
0aacf84e MD |
1443 | if (SCM_UNBNDP (n2)) |
1444 | { | |
1445 | if (SCM_UNBNDP (n1)) | |
1446 | return SCM_INUM0; | |
1447 | else if (SCM_NUMBERP (n1)) | |
1448 | return n1; | |
1449 | else | |
1450 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1451 | } |
09fb7599 | 1452 | |
e11e83f3 | 1453 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1454 | { |
e11e83f3 MV |
1455 | nn1 = SCM_I_INUM (n1); |
1456 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1457 | { |
e11e83f3 | 1458 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1459 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
1460 | } |
1461 | else if (SCM_BIGP (n2)) | |
1462 | { | |
1463 | intbig: | |
1464 | { | |
1465 | SCM result_z = scm_i_mkbig (); | |
1466 | mpz_t nn1_z; | |
1467 | mpz_init_set_si (nn1_z, nn1); | |
1468 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1469 | scm_remember_upto_here_1 (n2); | |
1470 | mpz_clear (nn1_z); | |
1471 | return scm_i_normbig (result_z); | |
1472 | } | |
1473 | } | |
1474 | else | |
1475 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1476 | } | |
1477 | else if (SCM_BIGP (n1)) | |
1478 | { | |
e11e83f3 | 1479 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1480 | { |
1481 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1482 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1483 | goto intbig; |
1484 | } | |
1485 | else if (SCM_BIGP (n2)) | |
1486 | { | |
1487 | SCM result_z = scm_i_mkbig (); | |
1488 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
1489 | SCM_I_BIG_MPZ (n1), | |
1490 | SCM_I_BIG_MPZ (n2)); | |
1491 | scm_remember_upto_here_2 (n1, n2); | |
1492 | return scm_i_normbig (result_z); | |
1493 | } | |
1494 | else | |
1495 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1496 | } |
0aacf84e | 1497 | else |
09fb7599 | 1498 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1499 | } |
1bbd0b84 | 1500 | #undef FUNC_NAME |
0f2d19dd | 1501 | |
09fb7599 | 1502 | |
a1ec6916 | 1503 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 1504 | (SCM j, SCM k), |
ba6e7231 KR |
1505 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
1506 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
1507 | "without actually calculating the @code{logand}, just testing\n" | |
1508 | "for non-zero.\n" | |
1509 | "\n" | |
1e6808ea | 1510 | "@lisp\n" |
b380b885 MD |
1511 | "(logtest #b0100 #b1011) @result{} #f\n" |
1512 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1513 | "@end lisp") |
1bbd0b84 | 1514 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1515 | { |
1e6808ea | 1516 | long int nj; |
9a00c9fc | 1517 | |
e11e83f3 | 1518 | if (SCM_I_INUMP (j)) |
0aacf84e | 1519 | { |
e11e83f3 MV |
1520 | nj = SCM_I_INUM (j); |
1521 | if (SCM_I_INUMP (k)) | |
0aacf84e | 1522 | { |
e11e83f3 | 1523 | long nk = SCM_I_INUM (k); |
73e4de09 | 1524 | return scm_from_bool (nj & nk); |
0aacf84e MD |
1525 | } |
1526 | else if (SCM_BIGP (k)) | |
1527 | { | |
1528 | intbig: | |
1529 | if (nj == 0) | |
1530 | return SCM_BOOL_F; | |
1531 | { | |
1532 | SCM result; | |
1533 | mpz_t nj_z; | |
1534 | mpz_init_set_si (nj_z, nj); | |
1535 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
1536 | scm_remember_upto_here_1 (k); | |
73e4de09 | 1537 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
1538 | mpz_clear (nj_z); |
1539 | return result; | |
1540 | } | |
1541 | } | |
1542 | else | |
1543 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1544 | } | |
1545 | else if (SCM_BIGP (j)) | |
1546 | { | |
e11e83f3 | 1547 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
1548 | { |
1549 | SCM_SWAP (j, k); | |
e11e83f3 | 1550 | nj = SCM_I_INUM (j); |
0aacf84e MD |
1551 | goto intbig; |
1552 | } | |
1553 | else if (SCM_BIGP (k)) | |
1554 | { | |
1555 | SCM result; | |
1556 | mpz_t result_z; | |
1557 | mpz_init (result_z); | |
1558 | mpz_and (result_z, | |
1559 | SCM_I_BIG_MPZ (j), | |
1560 | SCM_I_BIG_MPZ (k)); | |
1561 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 1562 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
1563 | mpz_clear (result_z); |
1564 | return result; | |
1565 | } | |
1566 | else | |
1567 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1568 | } | |
1569 | else | |
1570 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 1571 | } |
1bbd0b84 | 1572 | #undef FUNC_NAME |
0f2d19dd | 1573 | |
c1bfcf60 | 1574 | |
a1ec6916 | 1575 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1576 | (SCM index, SCM j), |
ba6e7231 KR |
1577 | "Test whether bit number @var{index} in @var{j} is set.\n" |
1578 | "@var{index} starts from 0 for the least significant bit.\n" | |
1579 | "\n" | |
1e6808ea | 1580 | "@lisp\n" |
b380b885 MD |
1581 | "(logbit? 0 #b1101) @result{} #t\n" |
1582 | "(logbit? 1 #b1101) @result{} #f\n" | |
1583 | "(logbit? 2 #b1101) @result{} #t\n" | |
1584 | "(logbit? 3 #b1101) @result{} #t\n" | |
1585 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1586 | "@end lisp") |
1bbd0b84 | 1587 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1588 | { |
78166ad5 | 1589 | unsigned long int iindex; |
5efd3c7d | 1590 | iindex = scm_to_ulong (index); |
78166ad5 | 1591 | |
e11e83f3 | 1592 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
1593 | { |
1594 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 1595 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 1596 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 1597 | } |
0aacf84e MD |
1598 | else if (SCM_BIGP (j)) |
1599 | { | |
1600 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
1601 | scm_remember_upto_here_1 (j); | |
73e4de09 | 1602 | return scm_from_bool (val); |
0aacf84e MD |
1603 | } |
1604 | else | |
78166ad5 | 1605 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 1606 | } |
1bbd0b84 | 1607 | #undef FUNC_NAME |
0f2d19dd | 1608 | |
78166ad5 | 1609 | |
a1ec6916 | 1610 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1611 | (SCM n), |
4d814788 | 1612 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
1613 | "argument.\n" |
1614 | "\n" | |
b380b885 MD |
1615 | "@lisp\n" |
1616 | "(number->string (lognot #b10000000) 2)\n" | |
1617 | " @result{} \"-10000001\"\n" | |
1618 | "(number->string (lognot #b0) 2)\n" | |
1619 | " @result{} \"-1\"\n" | |
1e6808ea | 1620 | "@end lisp") |
1bbd0b84 | 1621 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1622 | { |
e11e83f3 | 1623 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
1624 | /* No overflow here, just need to toggle all the bits making up the inum. |
1625 | Enhancement: No need to strip the tag and add it back, could just xor | |
1626 | a block of 1 bits, if that worked with the various debug versions of | |
1627 | the SCM typedef. */ | |
e11e83f3 | 1628 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
1629 | |
1630 | } else if (SCM_BIGP (n)) { | |
1631 | SCM result = scm_i_mkbig (); | |
1632 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
1633 | scm_remember_upto_here_1 (n); | |
1634 | return result; | |
1635 | ||
1636 | } else { | |
1637 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1638 | } | |
0f2d19dd | 1639 | } |
1bbd0b84 | 1640 | #undef FUNC_NAME |
0f2d19dd | 1641 | |
518b7508 KR |
1642 | /* returns 0 if IN is not an integer. OUT must already be |
1643 | initialized. */ | |
1644 | static int | |
1645 | coerce_to_big (SCM in, mpz_t out) | |
1646 | { | |
1647 | if (SCM_BIGP (in)) | |
1648 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
1649 | else if (SCM_I_INUMP (in)) |
1650 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
1651 | else |
1652 | return 0; | |
1653 | ||
1654 | return 1; | |
1655 | } | |
1656 | ||
d885e204 | 1657 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
1658 | (SCM n, SCM k, SCM m), |
1659 | "Return @var{n} raised to the integer exponent\n" | |
1660 | "@var{k}, modulo @var{m}.\n" | |
1661 | "\n" | |
1662 | "@lisp\n" | |
1663 | "(modulo-expt 2 3 5)\n" | |
1664 | " @result{} 3\n" | |
1665 | "@end lisp") | |
d885e204 | 1666 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
1667 | { |
1668 | mpz_t n_tmp; | |
1669 | mpz_t k_tmp; | |
1670 | mpz_t m_tmp; | |
1671 | ||
1672 | /* There are two classes of error we might encounter -- | |
1673 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
1674 | and | |
1675 | 2) wrong-type errors, which of course we'll report by calling | |
1676 | SCM_WRONG_TYPE_ARG. | |
1677 | We don't report those errors immediately, however; instead we do | |
1678 | some cleanup first. These variables tell us which error (if | |
1679 | any) we should report after cleaning up. | |
1680 | */ | |
1681 | int report_overflow = 0; | |
1682 | ||
1683 | int position_of_wrong_type = 0; | |
1684 | SCM value_of_wrong_type = SCM_INUM0; | |
1685 | ||
1686 | SCM result = SCM_UNDEFINED; | |
1687 | ||
1688 | mpz_init (n_tmp); | |
1689 | mpz_init (k_tmp); | |
1690 | mpz_init (m_tmp); | |
1691 | ||
bc36d050 | 1692 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
1693 | { |
1694 | report_overflow = 1; | |
1695 | goto cleanup; | |
1696 | } | |
1697 | ||
1698 | if (!coerce_to_big (n, n_tmp)) | |
1699 | { | |
1700 | value_of_wrong_type = n; | |
1701 | position_of_wrong_type = 1; | |
1702 | goto cleanup; | |
1703 | } | |
1704 | ||
1705 | if (!coerce_to_big (k, k_tmp)) | |
1706 | { | |
1707 | value_of_wrong_type = k; | |
1708 | position_of_wrong_type = 2; | |
1709 | goto cleanup; | |
1710 | } | |
1711 | ||
1712 | if (!coerce_to_big (m, m_tmp)) | |
1713 | { | |
1714 | value_of_wrong_type = m; | |
1715 | position_of_wrong_type = 3; | |
1716 | goto cleanup; | |
1717 | } | |
1718 | ||
1719 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
1720 | will get a divide-by-zero exception when an inverse 1/n mod m | |
1721 | doesn't exist (or is not unique). Since exceptions are hard to | |
1722 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
1723 | a simple failure code, which is easy to handle. */ | |
1724 | ||
1725 | if (-1 == mpz_sgn (k_tmp)) | |
1726 | { | |
1727 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
1728 | { | |
1729 | report_overflow = 1; | |
1730 | goto cleanup; | |
1731 | } | |
1732 | mpz_neg (k_tmp, k_tmp); | |
1733 | } | |
1734 | ||
1735 | result = scm_i_mkbig (); | |
1736 | mpz_powm (SCM_I_BIG_MPZ (result), | |
1737 | n_tmp, | |
1738 | k_tmp, | |
1739 | m_tmp); | |
b7b8c575 KR |
1740 | |
1741 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
1742 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
1743 | ||
518b7508 KR |
1744 | cleanup: |
1745 | mpz_clear (m_tmp); | |
1746 | mpz_clear (k_tmp); | |
1747 | mpz_clear (n_tmp); | |
1748 | ||
1749 | if (report_overflow) | |
1750 | scm_num_overflow (FUNC_NAME); | |
1751 | ||
1752 | if (position_of_wrong_type) | |
1753 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
1754 | value_of_wrong_type); | |
1755 | ||
1756 | return scm_i_normbig (result); | |
1757 | } | |
1758 | #undef FUNC_NAME | |
1759 | ||
a1ec6916 | 1760 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1761 | (SCM n, SCM k), |
ba6e7231 KR |
1762 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
1763 | "exact integer, @var{n} can be any number.\n" | |
1764 | "\n" | |
1765 | "Negative @var{k} is supported, and results in @math{1/n^abs(k)}\n" | |
1766 | "in the usual way. @math{@var{n}^0} is 1, as usual, and that\n" | |
1767 | "includes @math{0^0} is 1.\n" | |
1e6808ea | 1768 | "\n" |
b380b885 | 1769 | "@lisp\n" |
ba6e7231 KR |
1770 | "(integer-expt 2 5) @result{} 32\n" |
1771 | "(integer-expt -3 3) @result{} -27\n" | |
1772 | "(integer-expt 5 -3) @result{} 1/125\n" | |
1773 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 1774 | "@end lisp") |
1bbd0b84 | 1775 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1776 | { |
1c35cb19 RB |
1777 | long i2 = 0; |
1778 | SCM z_i2 = SCM_BOOL_F; | |
1779 | int i2_is_big = 0; | |
d956fa6f | 1780 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 1781 | |
5a8fc758 AW |
1782 | SCM_VALIDATE_NUMBER (SCM_ARG1, n); |
1783 | ||
d57ed702 | 1784 | /* 0^0 == 1 according to R5RS */ |
bc36d050 | 1785 | if (scm_is_eq (n, SCM_INUM0) || scm_is_eq (n, acc)) |
73e4de09 | 1786 | return scm_is_false (scm_zero_p(k)) ? n : acc; |
bc36d050 | 1787 | else if (scm_is_eq (n, SCM_I_MAKINUM (-1L))) |
73e4de09 | 1788 | return scm_is_false (scm_even_p (k)) ? n : acc; |
ca46fb90 | 1789 | |
e11e83f3 MV |
1790 | if (SCM_I_INUMP (k)) |
1791 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
1792 | else if (SCM_BIGP (k)) |
1793 | { | |
1794 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
1795 | scm_remember_upto_here_1 (k); |
1796 | i2_is_big = 1; | |
1797 | } | |
2830fd91 | 1798 | else |
ca46fb90 RB |
1799 | SCM_WRONG_TYPE_ARG (2, k); |
1800 | ||
1801 | if (i2_is_big) | |
f872b822 | 1802 | { |
ca46fb90 RB |
1803 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
1804 | { | |
1805 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
1806 | n = scm_divide (n, SCM_UNDEFINED); | |
1807 | } | |
1808 | while (1) | |
1809 | { | |
1810 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
1811 | { | |
ca46fb90 RB |
1812 | return acc; |
1813 | } | |
1814 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
1815 | { | |
ca46fb90 RB |
1816 | return scm_product (acc, n); |
1817 | } | |
1818 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
1819 | acc = scm_product (acc, n); | |
1820 | n = scm_product (n, n); | |
1821 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
1822 | } | |
f872b822 | 1823 | } |
ca46fb90 | 1824 | else |
f872b822 | 1825 | { |
ca46fb90 RB |
1826 | if (i2 < 0) |
1827 | { | |
1828 | i2 = -i2; | |
1829 | n = scm_divide (n, SCM_UNDEFINED); | |
1830 | } | |
1831 | while (1) | |
1832 | { | |
1833 | if (0 == i2) | |
1834 | return acc; | |
1835 | if (1 == i2) | |
1836 | return scm_product (acc, n); | |
1837 | if (i2 & 1) | |
1838 | acc = scm_product (acc, n); | |
1839 | n = scm_product (n, n); | |
1840 | i2 >>= 1; | |
1841 | } | |
f872b822 | 1842 | } |
0f2d19dd | 1843 | } |
1bbd0b84 | 1844 | #undef FUNC_NAME |
0f2d19dd | 1845 | |
a1ec6916 | 1846 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1847 | (SCM n, SCM cnt), |
32f19569 KR |
1848 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
1849 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 1850 | "\n" |
e7644cb2 | 1851 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
1852 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
1853 | "infinity. (Note that this is not the same rounding as\n" | |
1854 | "@code{quotient} does.)\n" | |
1855 | "\n" | |
1856 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
1857 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
1858 | "shift dropping bits.\n" | |
1e6808ea | 1859 | "\n" |
b380b885 | 1860 | "@lisp\n" |
1e6808ea MG |
1861 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1862 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
1863 | "\n" |
1864 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
1865 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 1866 | "@end lisp") |
1bbd0b84 | 1867 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1868 | { |
3ab9f56e | 1869 | long bits_to_shift; |
5efd3c7d | 1870 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 1871 | |
788aca27 KR |
1872 | if (SCM_I_INUMP (n)) |
1873 | { | |
1874 | long nn = SCM_I_INUM (n); | |
1875 | ||
1876 | if (bits_to_shift > 0) | |
1877 | { | |
1878 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
1879 | overflow a non-zero fixnum. For smaller shifts we check the | |
1880 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
1881 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
1882 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
1883 | bits_to_shift)". */ | |
1884 | ||
1885 | if (nn == 0) | |
1886 | return n; | |
1887 | ||
1888 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
1889 | && ((unsigned long) | |
1890 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) | |
1891 | <= 1)) | |
1892 | { | |
1893 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
1894 | } | |
1895 | else | |
1896 | { | |
1897 | SCM result = scm_i_long2big (nn); | |
1898 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1899 | bits_to_shift); | |
1900 | return result; | |
1901 | } | |
1902 | } | |
1903 | else | |
1904 | { | |
1905 | bits_to_shift = -bits_to_shift; | |
1906 | if (bits_to_shift >= SCM_LONG_BIT) | |
1907 | return (nn >= 0 ? SCM_I_MAKINUM (0) : SCM_I_MAKINUM(-1)); | |
1908 | else | |
1909 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
1910 | } | |
1911 | ||
1912 | } | |
1913 | else if (SCM_BIGP (n)) | |
ca46fb90 | 1914 | { |
788aca27 KR |
1915 | SCM result; |
1916 | ||
1917 | if (bits_to_shift == 0) | |
1918 | return n; | |
1919 | ||
1920 | result = scm_i_mkbig (); | |
1921 | if (bits_to_shift >= 0) | |
1922 | { | |
1923 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1924 | bits_to_shift); | |
1925 | return result; | |
1926 | } | |
ca46fb90 | 1927 | else |
788aca27 KR |
1928 | { |
1929 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
1930 | we have to allocate a bignum even if the result is going to be a | |
1931 | fixnum. */ | |
1932 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1933 | -bits_to_shift); | |
1934 | return scm_i_normbig (result); | |
1935 | } | |
1936 | ||
ca46fb90 RB |
1937 | } |
1938 | else | |
788aca27 KR |
1939 | { |
1940 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1941 | } | |
0f2d19dd | 1942 | } |
1bbd0b84 | 1943 | #undef FUNC_NAME |
0f2d19dd | 1944 | |
3c9f20f8 | 1945 | |
a1ec6916 | 1946 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 1947 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
1948 | "Return the integer composed of the @var{start} (inclusive)\n" |
1949 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
1950 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
1951 | "\n" | |
b380b885 MD |
1952 | "@lisp\n" |
1953 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
1954 | " @result{} \"1010\"\n" | |
1955 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
1956 | " @result{} \"10110\"\n" | |
1957 | "@end lisp") | |
1bbd0b84 | 1958 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 1959 | { |
7f848242 | 1960 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
1961 | istart = scm_to_ulong (start); |
1962 | iend = scm_to_ulong (end); | |
c1bfcf60 | 1963 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 1964 | |
7f848242 KR |
1965 | /* how many bits to keep */ |
1966 | bits = iend - istart; | |
1967 | ||
e11e83f3 | 1968 | if (SCM_I_INUMP (n)) |
0aacf84e | 1969 | { |
e11e83f3 | 1970 | long int in = SCM_I_INUM (n); |
7f848242 KR |
1971 | |
1972 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 1973 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 1974 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 1975 | |
0aacf84e MD |
1976 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
1977 | { | |
1978 | /* Since we emulate two's complement encoded numbers, this | |
1979 | * special case requires us to produce a result that has | |
7f848242 | 1980 | * more bits than can be stored in a fixnum. |
0aacf84e | 1981 | */ |
7f848242 KR |
1982 | SCM result = scm_i_long2big (in); |
1983 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1984 | bits); | |
1985 | return result; | |
0aacf84e | 1986 | } |
ac0c002c | 1987 | |
7f848242 | 1988 | /* mask down to requisite bits */ |
857ae6af | 1989 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 1990 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
1991 | } |
1992 | else if (SCM_BIGP (n)) | |
ac0c002c | 1993 | { |
7f848242 KR |
1994 | SCM result; |
1995 | if (bits == 1) | |
1996 | { | |
d956fa6f | 1997 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
1998 | } |
1999 | else | |
2000 | { | |
2001 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
2002 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
2003 | such bits into a ulong. */ | |
2004 | result = scm_i_mkbig (); | |
2005 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
2006 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
2007 | result = scm_i_normbig (result); | |
2008 | } | |
2009 | scm_remember_upto_here_1 (n); | |
2010 | return result; | |
ac0c002c | 2011 | } |
0aacf84e | 2012 | else |
78166ad5 | 2013 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 2014 | } |
1bbd0b84 | 2015 | #undef FUNC_NAME |
0f2d19dd | 2016 | |
7f848242 | 2017 | |
e4755e5c JB |
2018 | static const char scm_logtab[] = { |
2019 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
2020 | }; | |
1cc91f1b | 2021 | |
a1ec6916 | 2022 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 2023 | (SCM n), |
1e6808ea MG |
2024 | "Return the number of bits in integer @var{n}. If integer is\n" |
2025 | "positive, the 1-bits in its binary representation are counted.\n" | |
2026 | "If negative, the 0-bits in its two's-complement binary\n" | |
2027 | "representation are counted. If 0, 0 is returned.\n" | |
2028 | "\n" | |
b380b885 MD |
2029 | "@lisp\n" |
2030 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
2031 | " @result{} 4\n" |
2032 | "(logcount 0)\n" | |
2033 | " @result{} 0\n" | |
2034 | "(logcount -2)\n" | |
2035 | " @result{} 1\n" | |
2036 | "@end lisp") | |
2037 | #define FUNC_NAME s_scm_logcount | |
2038 | { | |
e11e83f3 | 2039 | if (SCM_I_INUMP (n)) |
f872b822 | 2040 | { |
ca46fb90 | 2041 | unsigned long int c = 0; |
e11e83f3 | 2042 | long int nn = SCM_I_INUM (n); |
ca46fb90 RB |
2043 | if (nn < 0) |
2044 | nn = -1 - nn; | |
2045 | while (nn) | |
2046 | { | |
2047 | c += scm_logtab[15 & nn]; | |
2048 | nn >>= 4; | |
2049 | } | |
d956fa6f | 2050 | return SCM_I_MAKINUM (c); |
f872b822 | 2051 | } |
ca46fb90 | 2052 | else if (SCM_BIGP (n)) |
f872b822 | 2053 | { |
ca46fb90 | 2054 | unsigned long count; |
713a4259 KR |
2055 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
2056 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 2057 | else |
713a4259 KR |
2058 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
2059 | scm_remember_upto_here_1 (n); | |
d956fa6f | 2060 | return SCM_I_MAKINUM (count); |
f872b822 | 2061 | } |
ca46fb90 RB |
2062 | else |
2063 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 2064 | } |
ca46fb90 | 2065 | #undef FUNC_NAME |
0f2d19dd JB |
2066 | |
2067 | ||
ca46fb90 RB |
2068 | static const char scm_ilentab[] = { |
2069 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
2070 | }; | |
2071 | ||
0f2d19dd | 2072 | |
ca46fb90 RB |
2073 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
2074 | (SCM n), | |
2075 | "Return the number of bits necessary to represent @var{n}.\n" | |
2076 | "\n" | |
2077 | "@lisp\n" | |
2078 | "(integer-length #b10101010)\n" | |
2079 | " @result{} 8\n" | |
2080 | "(integer-length 0)\n" | |
2081 | " @result{} 0\n" | |
2082 | "(integer-length #b1111)\n" | |
2083 | " @result{} 4\n" | |
2084 | "@end lisp") | |
2085 | #define FUNC_NAME s_scm_integer_length | |
2086 | { | |
e11e83f3 | 2087 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2088 | { |
2089 | unsigned long int c = 0; | |
2090 | unsigned int l = 4; | |
e11e83f3 | 2091 | long int nn = SCM_I_INUM (n); |
0aacf84e MD |
2092 | if (nn < 0) |
2093 | nn = -1 - nn; | |
2094 | while (nn) | |
2095 | { | |
2096 | c += 4; | |
2097 | l = scm_ilentab [15 & nn]; | |
2098 | nn >>= 4; | |
2099 | } | |
d956fa6f | 2100 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
2101 | } |
2102 | else if (SCM_BIGP (n)) | |
2103 | { | |
2104 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
2105 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
2106 | 1 too big, so check for that and adjust. */ | |
2107 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
2108 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
2109 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
2110 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
2111 | size--; | |
2112 | scm_remember_upto_here_1 (n); | |
d956fa6f | 2113 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
2114 | } |
2115 | else | |
ca46fb90 | 2116 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
2117 | } |
2118 | #undef FUNC_NAME | |
0f2d19dd JB |
2119 | |
2120 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
2121 | #define SCM_MAX_DBL_PREC 60 |
2122 | #define SCM_MAX_DBL_RADIX 36 | |
2123 | ||
2124 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
2125 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
2126 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
2127 | ||
2128 | static | |
2129 | void init_dblprec(int *prec, int radix) { | |
2130 | /* determine floating point precision by adding successively | |
2131 | smaller increments to 1.0 until it is considered == 1.0 */ | |
2132 | double f = ((double)1.0)/radix; | |
2133 | double fsum = 1.0 + f; | |
2134 | ||
2135 | *prec = 0; | |
2136 | while (fsum != 1.0) | |
2137 | { | |
2138 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
2139 | fsum = 1.0; | |
2140 | else | |
2141 | { | |
2142 | f /= radix; | |
2143 | fsum = f + 1.0; | |
2144 | } | |
2145 | } | |
2146 | (*prec) -= 1; | |
2147 | } | |
2148 | ||
2149 | static | |
2150 | void init_fx_radix(double *fx_list, int radix) | |
2151 | { | |
2152 | /* initialize a per-radix list of tolerances. When added | |
2153 | to a number < 1.0, we can determine if we should raund | |
2154 | up and quit converting a number to a string. */ | |
2155 | int i; | |
2156 | fx_list[0] = 0.0; | |
2157 | fx_list[1] = 0.5; | |
2158 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
2159 | fx_list[i] = (fx_list[i-1] / radix); | |
2160 | } | |
2161 | ||
2162 | /* use this array as a way to generate a single digit */ | |
2163 | static const char*number_chars="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; | |
0f2d19dd | 2164 | |
1be6b49c | 2165 | static size_t |
0b799eea | 2166 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 2167 | { |
0b799eea MV |
2168 | int efmt, dpt, d, i, wp; |
2169 | double *fx; | |
2170 | #ifdef DBL_MIN_10_EXP | |
2171 | double f_cpy; | |
2172 | int exp_cpy; | |
2173 | #endif /* DBL_MIN_10_EXP */ | |
2174 | size_t ch = 0; | |
2175 | int exp = 0; | |
2176 | ||
2177 | if(radix < 2 || | |
2178 | radix > SCM_MAX_DBL_RADIX) | |
2179 | { | |
2180 | /* revert to existing behavior */ | |
2181 | radix = 10; | |
2182 | } | |
2183 | ||
2184 | wp = scm_dblprec[radix-2]; | |
2185 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 2186 | |
f872b822 | 2187 | if (f == 0.0) |
abb7e44d MV |
2188 | { |
2189 | #ifdef HAVE_COPYSIGN | |
2190 | double sgn = copysign (1.0, f); | |
2191 | ||
2192 | if (sgn < 0.0) | |
2193 | a[ch++] = '-'; | |
2194 | #endif | |
abb7e44d MV |
2195 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
2196 | } | |
7351e207 | 2197 | |
2e65b52f | 2198 | if (isinf (f)) |
7351e207 MV |
2199 | { |
2200 | if (f < 0) | |
2201 | strcpy (a, "-inf.0"); | |
2202 | else | |
2203 | strcpy (a, "+inf.0"); | |
2204 | return ch+6; | |
2205 | } | |
2e65b52f | 2206 | else if (isnan (f)) |
7351e207 MV |
2207 | { |
2208 | strcpy (a, "+nan.0"); | |
2209 | return ch+6; | |
2210 | } | |
2211 | ||
f872b822 MD |
2212 | if (f < 0.0) |
2213 | { | |
2214 | f = -f; | |
2215 | a[ch++] = '-'; | |
2216 | } | |
7351e207 | 2217 | |
f872b822 MD |
2218 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
2219 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
2220 | /* just do the checking...if it passes, we do the conversion for our |
2221 | radix again below */ | |
2222 | f_cpy = f; | |
2223 | exp_cpy = exp; | |
2224 | ||
2225 | while (f_cpy < 1.0) | |
f872b822 | 2226 | { |
0b799eea MV |
2227 | f_cpy *= 10.0; |
2228 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
2229 | { |
2230 | a[ch++] = '#'; | |
2231 | a[ch++] = '.'; | |
2232 | a[ch++] = '#'; | |
2233 | return ch; | |
2234 | } | |
f872b822 | 2235 | } |
0b799eea | 2236 | while (f_cpy > 10.0) |
f872b822 | 2237 | { |
0b799eea MV |
2238 | f_cpy *= 0.10; |
2239 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
2240 | { |
2241 | a[ch++] = '#'; | |
2242 | a[ch++] = '.'; | |
2243 | a[ch++] = '#'; | |
2244 | return ch; | |
2245 | } | |
f872b822 | 2246 | } |
0b799eea MV |
2247 | #endif |
2248 | ||
f872b822 MD |
2249 | while (f < 1.0) |
2250 | { | |
0b799eea | 2251 | f *= radix; |
f872b822 MD |
2252 | exp--; |
2253 | } | |
0b799eea | 2254 | while (f > radix) |
f872b822 | 2255 | { |
0b799eea | 2256 | f /= radix; |
f872b822 MD |
2257 | exp++; |
2258 | } | |
0b799eea MV |
2259 | |
2260 | if (f + fx[wp] >= radix) | |
f872b822 MD |
2261 | { |
2262 | f = 1.0; | |
2263 | exp++; | |
2264 | } | |
0f2d19dd | 2265 | zero: |
0b799eea MV |
2266 | #ifdef ENGNOT |
2267 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 2268 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
2269 | exp -= dpt++; |
2270 | efmt = 1; | |
f872b822 MD |
2271 | #else |
2272 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 2273 | if (!efmt) |
cda139a7 MD |
2274 | { |
2275 | if (exp < 0) | |
2276 | { | |
2277 | a[ch++] = '0'; | |
2278 | a[ch++] = '.'; | |
2279 | dpt = exp; | |
f872b822 MD |
2280 | while (++dpt) |
2281 | a[ch++] = '0'; | |
cda139a7 MD |
2282 | } |
2283 | else | |
f872b822 | 2284 | dpt = exp + 1; |
cda139a7 | 2285 | } |
0f2d19dd JB |
2286 | else |
2287 | dpt = 1; | |
f872b822 MD |
2288 | #endif |
2289 | ||
2290 | do | |
2291 | { | |
2292 | d = f; | |
2293 | f -= d; | |
0b799eea | 2294 | a[ch++] = number_chars[d]; |
f872b822 MD |
2295 | if (f < fx[wp]) |
2296 | break; | |
2297 | if (f + fx[wp] >= 1.0) | |
2298 | { | |
0b799eea | 2299 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
2300 | break; |
2301 | } | |
0b799eea | 2302 | f *= radix; |
f872b822 MD |
2303 | if (!(--dpt)) |
2304 | a[ch++] = '.'; | |
0f2d19dd | 2305 | } |
f872b822 | 2306 | while (wp--); |
0f2d19dd JB |
2307 | |
2308 | if (dpt > 0) | |
cda139a7 | 2309 | { |
f872b822 | 2310 | #ifndef ENGNOT |
cda139a7 MD |
2311 | if ((dpt > 4) && (exp > 6)) |
2312 | { | |
f872b822 | 2313 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 2314 | for (i = ch++; i > d; i--) |
f872b822 | 2315 | a[i] = a[i - 1]; |
cda139a7 MD |
2316 | a[d] = '.'; |
2317 | efmt = 1; | |
2318 | } | |
2319 | else | |
f872b822 | 2320 | #endif |
cda139a7 | 2321 | { |
f872b822 MD |
2322 | while (--dpt) |
2323 | a[ch++] = '0'; | |
cda139a7 MD |
2324 | a[ch++] = '.'; |
2325 | } | |
2326 | } | |
f872b822 MD |
2327 | if (a[ch - 1] == '.') |
2328 | a[ch++] = '0'; /* trailing zero */ | |
2329 | if (efmt && exp) | |
2330 | { | |
2331 | a[ch++] = 'e'; | |
2332 | if (exp < 0) | |
2333 | { | |
2334 | exp = -exp; | |
2335 | a[ch++] = '-'; | |
2336 | } | |
0b799eea MV |
2337 | for (i = radix; i <= exp; i *= radix); |
2338 | for (i /= radix; i; i /= radix) | |
f872b822 | 2339 | { |
0b799eea | 2340 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
2341 | exp %= i; |
2342 | } | |
0f2d19dd | 2343 | } |
0f2d19dd JB |
2344 | return ch; |
2345 | } | |
2346 | ||
7a1aba42 MV |
2347 | |
2348 | static size_t | |
2349 | icmplx2str (double real, double imag, char *str, int radix) | |
2350 | { | |
2351 | size_t i; | |
2352 | ||
2353 | i = idbl2str (real, str, radix); | |
2354 | if (imag != 0.0) | |
2355 | { | |
2356 | /* Don't output a '+' for negative numbers or for Inf and | |
2357 | NaN. They will provide their own sign. */ | |
2e65b52f | 2358 | if (0 <= imag && !isinf (imag) && !isnan (imag)) |
7a1aba42 MV |
2359 | str[i++] = '+'; |
2360 | i += idbl2str (imag, &str[i], radix); | |
2361 | str[i++] = 'i'; | |
2362 | } | |
2363 | return i; | |
2364 | } | |
2365 | ||
1be6b49c | 2366 | static size_t |
0b799eea | 2367 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 2368 | { |
1be6b49c | 2369 | size_t i; |
3c9a524f | 2370 | if (SCM_REALP (flt)) |
0b799eea | 2371 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 2372 | else |
7a1aba42 MV |
2373 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
2374 | str, radix); | |
0f2d19dd JB |
2375 | return i; |
2376 | } | |
0f2d19dd | 2377 | |
2881e77b | 2378 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
2379 | characters in the result. |
2380 | rad is output base | |
2381 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2382 | size_t |
2881e77b MV |
2383 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
2384 | { | |
2385 | if (num < 0) | |
2386 | { | |
2387 | *p++ = '-'; | |
2388 | return scm_iuint2str (-num, rad, p) + 1; | |
2389 | } | |
2390 | else | |
2391 | return scm_iuint2str (num, rad, p); | |
2392 | } | |
2393 | ||
2394 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
2395 | characters in the result. | |
2396 | rad is output base | |
2397 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
2398 | size_t | |
2399 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 2400 | { |
1be6b49c ML |
2401 | size_t j = 1; |
2402 | size_t i; | |
2881e77b | 2403 | scm_t_uintmax n = num; |
5c11cc9d | 2404 | |
a6f3af16 AW |
2405 | if (rad < 2 || rad > 36) |
2406 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
2407 | ||
f872b822 | 2408 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2409 | j++; |
2410 | ||
2411 | i = j; | |
2881e77b | 2412 | n = num; |
f872b822 MD |
2413 | while (i--) |
2414 | { | |
5c11cc9d GH |
2415 | int d = n % rad; |
2416 | ||
f872b822 | 2417 | n /= rad; |
a6f3af16 | 2418 | p[i] = number_chars[d]; |
f872b822 | 2419 | } |
0f2d19dd JB |
2420 | return j; |
2421 | } | |
2422 | ||
a1ec6916 | 2423 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2424 | (SCM n, SCM radix), |
2425 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2426 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2427 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2428 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2429 | { |
1bbd0b84 | 2430 | int base; |
98cb6e75 | 2431 | |
0aacf84e | 2432 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 2433 | base = 10; |
0aacf84e | 2434 | else |
5efd3c7d | 2435 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 2436 | |
e11e83f3 | 2437 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2438 | { |
2439 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 2440 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 2441 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
2442 | } |
2443 | else if (SCM_BIGP (n)) | |
2444 | { | |
2445 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
2446 | scm_remember_upto_here_1 (n); | |
cc95e00a | 2447 | return scm_take_locale_string (str); |
0aacf84e | 2448 | } |
f92e85f7 MV |
2449 | else if (SCM_FRACTIONP (n)) |
2450 | { | |
f92e85f7 | 2451 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 2452 | scm_from_locale_string ("/"), |
f92e85f7 MV |
2453 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
2454 | } | |
0aacf84e MD |
2455 | else if (SCM_INEXACTP (n)) |
2456 | { | |
2457 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 2458 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
2459 | } |
2460 | else | |
bb628794 | 2461 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 2462 | } |
1bbd0b84 | 2463 | #undef FUNC_NAME |
0f2d19dd JB |
2464 | |
2465 | ||
ca46fb90 RB |
2466 | /* These print routines used to be stubbed here so that scm_repl.c |
2467 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 2468 | |
0f2d19dd | 2469 | int |
e81d98ec | 2470 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2471 | { |
56e55ac7 | 2472 | char num_buf[FLOBUFLEN]; |
0b799eea | 2473 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
2474 | return !0; |
2475 | } | |
2476 | ||
b479fe9a MV |
2477 | void |
2478 | scm_i_print_double (double val, SCM port) | |
2479 | { | |
2480 | char num_buf[FLOBUFLEN]; | |
2481 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
2482 | } | |
2483 | ||
f3ae5d60 | 2484 | int |
e81d98ec | 2485 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 2486 | |
f3ae5d60 | 2487 | { |
56e55ac7 | 2488 | char num_buf[FLOBUFLEN]; |
0b799eea | 2489 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
2490 | return !0; |
2491 | } | |
1cc91f1b | 2492 | |
7a1aba42 MV |
2493 | void |
2494 | scm_i_print_complex (double real, double imag, SCM port) | |
2495 | { | |
2496 | char num_buf[FLOBUFLEN]; | |
2497 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
2498 | } | |
2499 | ||
f92e85f7 MV |
2500 | int |
2501 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
2502 | { | |
2503 | SCM str; | |
f92e85f7 | 2504 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
3f47e526 | 2505 | scm_lfwrite_str (str, port); |
f92e85f7 MV |
2506 | scm_remember_upto_here_1 (str); |
2507 | return !0; | |
2508 | } | |
2509 | ||
0f2d19dd | 2510 | int |
e81d98ec | 2511 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2512 | { |
ca46fb90 RB |
2513 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
2514 | scm_remember_upto_here_1 (exp); | |
2515 | scm_lfwrite (str, (size_t) strlen (str), port); | |
2516 | free (str); | |
0f2d19dd JB |
2517 | return !0; |
2518 | } | |
2519 | /*** END nums->strs ***/ | |
2520 | ||
3c9a524f | 2521 | |
0f2d19dd | 2522 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2523 | |
3c9a524f DH |
2524 | /* The following functions implement the conversion from strings to numbers. |
2525 | * The implementation somehow follows the grammar for numbers as it is given | |
2526 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2527 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2528 | * points should be noted about the implementation: | |
2529 | * * Each function keeps a local index variable 'idx' that points at the | |
2530 | * current position within the parsed string. The global index is only | |
2531 | * updated if the function could parse the corresponding syntactic unit | |
2532 | * successfully. | |
2533 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2534 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2535 | * global exactness information is only updated after each part has been | |
2536 | * successfully parsed. | |
2537 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2538 | * Only if these fixnums would overflow, the result variables are updated | |
2539 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2540 | * the temporary variables holding the fixnums are cleared, and the process | |
2541 | * starts over again. If for example fixnums were able to store five decimal | |
2542 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2543 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2544 | * only every five digits two bignum operations were performed. | |
2545 | */ | |
2546 | ||
2547 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2548 | ||
2549 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2550 | ||
a6f3af16 AW |
2551 | /* Caller is responsible for checking that the return value is in range |
2552 | for the given radix, which should be <= 36. */ | |
2553 | static unsigned int | |
2554 | char_decimal_value (scm_t_uint32 c) | |
2555 | { | |
2556 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
2557 | that's certainly above any valid decimal, so we take advantage of | |
2558 | that to elide some tests. */ | |
2559 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
2560 | ||
2561 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
2562 | hexadecimals. */ | |
2563 | if (d >= 10U) | |
2564 | { | |
2565 | c = uc_tolower (c); | |
2566 | if (c >= (scm_t_uint32) 'a') | |
2567 | d = c - (scm_t_uint32)'a' + 10U; | |
2568 | } | |
2569 | return d; | |
2570 | } | |
3c9a524f | 2571 | |
2a8fecee | 2572 | static SCM |
3f47e526 | 2573 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 2574 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 2575 | { |
3c9a524f DH |
2576 | unsigned int idx = *p_idx; |
2577 | unsigned int hash_seen = 0; | |
2578 | scm_t_bits shift = 1; | |
2579 | scm_t_bits add = 0; | |
2580 | unsigned int digit_value; | |
2581 | SCM result; | |
2582 | char c; | |
3f47e526 | 2583 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
2584 | |
2585 | if (idx == len) | |
2586 | return SCM_BOOL_F; | |
2a8fecee | 2587 | |
3f47e526 | 2588 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 2589 | digit_value = char_decimal_value (c); |
3c9a524f DH |
2590 | if (digit_value >= radix) |
2591 | return SCM_BOOL_F; | |
2592 | ||
2593 | idx++; | |
d956fa6f | 2594 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 2595 | while (idx != len) |
f872b822 | 2596 | { |
3f47e526 | 2597 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 2598 | if (c == '#') |
3c9a524f DH |
2599 | { |
2600 | hash_seen = 1; | |
2601 | digit_value = 0; | |
2602 | } | |
a6f3af16 AW |
2603 | else if (hash_seen) |
2604 | break; | |
3c9a524f | 2605 | else |
a6f3af16 AW |
2606 | { |
2607 | digit_value = char_decimal_value (c); | |
2608 | /* This check catches non-decimals in addition to out-of-range | |
2609 | decimals. */ | |
2610 | if (digit_value >= radix) | |
2611 | break; | |
2612 | } | |
3c9a524f DH |
2613 | |
2614 | idx++; | |
2615 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2616 | { | |
d956fa6f | 2617 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2618 | if (add > 0) |
d956fa6f | 2619 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2620 | |
2621 | shift = radix; | |
2622 | add = digit_value; | |
2623 | } | |
2624 | else | |
2625 | { | |
2626 | shift = shift * radix; | |
2627 | add = add * radix + digit_value; | |
2628 | } | |
2629 | }; | |
2630 | ||
2631 | if (shift > 1) | |
d956fa6f | 2632 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2633 | if (add > 0) |
d956fa6f | 2634 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2635 | |
2636 | *p_idx = idx; | |
2637 | if (hash_seen) | |
2638 | *p_exactness = INEXACT; | |
2639 | ||
2640 | return result; | |
2a8fecee JB |
2641 | } |
2642 | ||
2643 | ||
3c9a524f DH |
2644 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2645 | * covers the parts of the rules that start at a potential point. The value | |
2646 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2647 | * in variable result. The content of *p_exactness indicates, whether a hash |
2648 | * has already been seen in the digits before the point. | |
3c9a524f | 2649 | */ |
1cc91f1b | 2650 | |
3f47e526 | 2651 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
2652 | |
2653 | static SCM | |
3f47e526 | 2654 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 2655 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2656 | { |
3c9a524f DH |
2657 | unsigned int idx = *p_idx; |
2658 | enum t_exactness x = *p_exactness; | |
3f47e526 | 2659 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
2660 | |
2661 | if (idx == len) | |
79d34f68 | 2662 | return result; |
3c9a524f | 2663 | |
3f47e526 | 2664 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
2665 | { |
2666 | scm_t_bits shift = 1; | |
2667 | scm_t_bits add = 0; | |
2668 | unsigned int digit_value; | |
d956fa6f | 2669 | SCM big_shift = SCM_I_MAKINUM (1); |
3c9a524f DH |
2670 | |
2671 | idx++; | |
2672 | while (idx != len) | |
2673 | { | |
3f47e526 MG |
2674 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
2675 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
2676 | { |
2677 | if (x == INEXACT) | |
2678 | return SCM_BOOL_F; | |
2679 | else | |
2680 | digit_value = DIGIT2UINT (c); | |
2681 | } | |
2682 | else if (c == '#') | |
2683 | { | |
2684 | x = INEXACT; | |
2685 | digit_value = 0; | |
2686 | } | |
2687 | else | |
2688 | break; | |
2689 | ||
2690 | idx++; | |
2691 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2692 | { | |
d956fa6f MV |
2693 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2694 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 2695 | if (add > 0) |
d956fa6f | 2696 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2697 | |
2698 | shift = 10; | |
2699 | add = digit_value; | |
2700 | } | |
2701 | else | |
2702 | { | |
2703 | shift = shift * 10; | |
2704 | add = add * 10 + digit_value; | |
2705 | } | |
2706 | }; | |
2707 | ||
2708 | if (add > 0) | |
2709 | { | |
d956fa6f MV |
2710 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2711 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
2712 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
2713 | } |
2714 | ||
d8592269 | 2715 | result = scm_divide (result, big_shift); |
79d34f68 | 2716 | |
3c9a524f DH |
2717 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2718 | x = INEXACT; | |
f872b822 | 2719 | } |
3c9a524f | 2720 | |
3c9a524f | 2721 | if (idx != len) |
f872b822 | 2722 | { |
3c9a524f DH |
2723 | int sign = 1; |
2724 | unsigned int start; | |
3f47e526 | 2725 | scm_t_wchar c; |
3c9a524f DH |
2726 | int exponent; |
2727 | SCM e; | |
2728 | ||
2729 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2730 | ||
3f47e526 | 2731 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 2732 | { |
3c9a524f DH |
2733 | case 'd': case 'D': |
2734 | case 'e': case 'E': | |
2735 | case 'f': case 'F': | |
2736 | case 'l': case 'L': | |
2737 | case 's': case 'S': | |
2738 | idx++; | |
ee0ddd21 AW |
2739 | if (idx == len) |
2740 | return SCM_BOOL_F; | |
2741 | ||
3c9a524f | 2742 | start = idx; |
3f47e526 | 2743 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2744 | if (c == '-') |
2745 | { | |
2746 | idx++; | |
ee0ddd21 AW |
2747 | if (idx == len) |
2748 | return SCM_BOOL_F; | |
2749 | ||
3c9a524f | 2750 | sign = -1; |
3f47e526 | 2751 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2752 | } |
2753 | else if (c == '+') | |
2754 | { | |
2755 | idx++; | |
ee0ddd21 AW |
2756 | if (idx == len) |
2757 | return SCM_BOOL_F; | |
2758 | ||
3c9a524f | 2759 | sign = 1; |
3f47e526 | 2760 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2761 | } |
2762 | else | |
2763 | sign = 1; | |
2764 | ||
3f47e526 | 2765 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
2766 | return SCM_BOOL_F; |
2767 | ||
2768 | idx++; | |
2769 | exponent = DIGIT2UINT (c); | |
2770 | while (idx != len) | |
f872b822 | 2771 | { |
3f47e526 MG |
2772 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
2773 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
2774 | { |
2775 | idx++; | |
2776 | if (exponent <= SCM_MAXEXP) | |
2777 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2778 | } | |
2779 | else | |
2780 | break; | |
f872b822 | 2781 | } |
3c9a524f DH |
2782 | |
2783 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2784 | { |
3c9a524f | 2785 | size_t exp_len = idx - start; |
3f47e526 | 2786 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
2787 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
2788 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2789 | } |
3c9a524f | 2790 | |
d956fa6f | 2791 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
2792 | if (sign == 1) |
2793 | result = scm_product (result, e); | |
2794 | else | |
f92e85f7 | 2795 | result = scm_divide2real (result, e); |
3c9a524f DH |
2796 | |
2797 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2798 | x = INEXACT; | |
2799 | ||
f872b822 | 2800 | break; |
3c9a524f | 2801 | |
f872b822 | 2802 | default: |
3c9a524f | 2803 | break; |
f872b822 | 2804 | } |
0f2d19dd | 2805 | } |
3c9a524f DH |
2806 | |
2807 | *p_idx = idx; | |
2808 | if (x == INEXACT) | |
2809 | *p_exactness = x; | |
2810 | ||
2811 | return result; | |
0f2d19dd | 2812 | } |
0f2d19dd | 2813 | |
3c9a524f DH |
2814 | |
2815 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2816 | ||
2817 | static SCM | |
3f47e526 | 2818 | mem2ureal (SCM mem, unsigned int *p_idx, |
3c9a524f | 2819 | unsigned int radix, enum t_exactness *p_exactness) |
0f2d19dd | 2820 | { |
3c9a524f | 2821 | unsigned int idx = *p_idx; |
164d2481 | 2822 | SCM result; |
3f47e526 | 2823 | size_t len = scm_i_string_length (mem); |
3c9a524f | 2824 | |
40f89215 NJ |
2825 | /* Start off believing that the number will be exact. This changes |
2826 | to INEXACT if we see a decimal point or a hash. */ | |
2827 | enum t_exactness x = EXACT; | |
2828 | ||
3c9a524f DH |
2829 | if (idx == len) |
2830 | return SCM_BOOL_F; | |
2831 | ||
3f47e526 | 2832 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
2833 | { |
2834 | *p_idx = idx+5; | |
2835 | return scm_inf (); | |
2836 | } | |
2837 | ||
3f47e526 | 2838 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 2839 | { |
d8592269 MV |
2840 | /* Cobble up the fractional part. We might want to set the |
2841 | NaN's mantissa from it. */ | |
7351e207 | 2842 | idx += 4; |
3f47e526 | 2843 | mem2uinteger (mem, &idx, 10, &x); |
7351e207 MV |
2844 | *p_idx = idx; |
2845 | return scm_nan (); | |
2846 | } | |
2847 | ||
3f47e526 | 2848 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
2849 | { |
2850 | if (radix != 10) | |
2851 | return SCM_BOOL_F; | |
2852 | else if (idx + 1 == len) | |
2853 | return SCM_BOOL_F; | |
3f47e526 | 2854 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
2855 | return SCM_BOOL_F; |
2856 | else | |
3f47e526 | 2857 | result = mem2decimal_from_point (SCM_I_MAKINUM (0), mem, |
40f89215 | 2858 | p_idx, &x); |
f872b822 | 2859 | } |
3c9a524f DH |
2860 | else |
2861 | { | |
3c9a524f | 2862 | SCM uinteger; |
3c9a524f | 2863 | |
3f47e526 | 2864 | uinteger = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 2865 | if (scm_is_false (uinteger)) |
3c9a524f DH |
2866 | return SCM_BOOL_F; |
2867 | ||
2868 | if (idx == len) | |
2869 | result = uinteger; | |
3f47e526 | 2870 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 2871 | { |
3c9a524f DH |
2872 | SCM divisor; |
2873 | ||
2874 | idx++; | |
ee0ddd21 AW |
2875 | if (idx == len) |
2876 | return SCM_BOOL_F; | |
3c9a524f | 2877 | |
3f47e526 | 2878 | divisor = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 2879 | if (scm_is_false (divisor)) |
3c9a524f DH |
2880 | return SCM_BOOL_F; |
2881 | ||
f92e85f7 | 2882 | /* both are int/big here, I assume */ |
cba42c93 | 2883 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 2884 | } |
3c9a524f DH |
2885 | else if (radix == 10) |
2886 | { | |
3f47e526 | 2887 | result = mem2decimal_from_point (uinteger, mem, &idx, &x); |
73e4de09 | 2888 | if (scm_is_false (result)) |
3c9a524f DH |
2889 | return SCM_BOOL_F; |
2890 | } | |
2891 | else | |
2892 | result = uinteger; | |
2893 | ||
2894 | *p_idx = idx; | |
f872b822 | 2895 | } |
164d2481 | 2896 | |
40f89215 NJ |
2897 | /* Update *p_exactness if the number just read was inexact. This is |
2898 | important for complex numbers, so that a complex number is | |
2899 | treated as inexact overall if either its real or imaginary part | |
2900 | is inexact. | |
2901 | */ | |
2902 | if (x == INEXACT) | |
2903 | *p_exactness = x; | |
2904 | ||
164d2481 MV |
2905 | /* When returning an inexact zero, make sure it is represented as a |
2906 | floating point value so that we can change its sign. | |
2907 | */ | |
bc36d050 | 2908 | if (scm_is_eq (result, SCM_I_MAKINUM(0)) && *p_exactness == INEXACT) |
55f26379 | 2909 | result = scm_from_double (0.0); |
164d2481 MV |
2910 | |
2911 | return result; | |
3c9a524f | 2912 | } |
0f2d19dd | 2913 | |
0f2d19dd | 2914 | |
3c9a524f | 2915 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2916 | |
3c9a524f | 2917 | static SCM |
3f47e526 | 2918 | mem2complex (SCM mem, unsigned int idx, |
3c9a524f DH |
2919 | unsigned int radix, enum t_exactness *p_exactness) |
2920 | { | |
3f47e526 | 2921 | scm_t_wchar c; |
3c9a524f DH |
2922 | int sign = 0; |
2923 | SCM ureal; | |
3f47e526 | 2924 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
2925 | |
2926 | if (idx == len) | |
2927 | return SCM_BOOL_F; | |
2928 | ||
3f47e526 | 2929 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2930 | if (c == '+') |
2931 | { | |
2932 | idx++; | |
2933 | sign = 1; | |
2934 | } | |
2935 | else if (c == '-') | |
2936 | { | |
2937 | idx++; | |
2938 | sign = -1; | |
0f2d19dd | 2939 | } |
0f2d19dd | 2940 | |
3c9a524f DH |
2941 | if (idx == len) |
2942 | return SCM_BOOL_F; | |
2943 | ||
3f47e526 | 2944 | ureal = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 2945 | if (scm_is_false (ureal)) |
f872b822 | 2946 | { |
3c9a524f DH |
2947 | /* input must be either +i or -i */ |
2948 | ||
2949 | if (sign == 0) | |
2950 | return SCM_BOOL_F; | |
2951 | ||
3f47e526 MG |
2952 | if (scm_i_string_ref (mem, idx) == 'i' |
2953 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 2954 | { |
3c9a524f DH |
2955 | idx++; |
2956 | if (idx != len) | |
2957 | return SCM_BOOL_F; | |
2958 | ||
d956fa6f | 2959 | return scm_make_rectangular (SCM_I_MAKINUM (0), SCM_I_MAKINUM (sign)); |
f872b822 | 2960 | } |
3c9a524f DH |
2961 | else |
2962 | return SCM_BOOL_F; | |
0f2d19dd | 2963 | } |
3c9a524f DH |
2964 | else |
2965 | { | |
73e4de09 | 2966 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 2967 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 2968 | |
3c9a524f DH |
2969 | if (idx == len) |
2970 | return ureal; | |
2971 | ||
3f47e526 | 2972 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 2973 | switch (c) |
f872b822 | 2974 | { |
3c9a524f DH |
2975 | case 'i': case 'I': |
2976 | /* either +<ureal>i or -<ureal>i */ | |
2977 | ||
2978 | idx++; | |
2979 | if (sign == 0) | |
2980 | return SCM_BOOL_F; | |
2981 | if (idx != len) | |
2982 | return SCM_BOOL_F; | |
d956fa6f | 2983 | return scm_make_rectangular (SCM_I_MAKINUM (0), ureal); |
3c9a524f DH |
2984 | |
2985 | case '@': | |
2986 | /* polar input: <real>@<real>. */ | |
2987 | ||
2988 | idx++; | |
2989 | if (idx == len) | |
2990 | return SCM_BOOL_F; | |
2991 | else | |
f872b822 | 2992 | { |
3c9a524f DH |
2993 | int sign; |
2994 | SCM angle; | |
2995 | SCM result; | |
2996 | ||
3f47e526 | 2997 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2998 | if (c == '+') |
2999 | { | |
3000 | idx++; | |
ee0ddd21 AW |
3001 | if (idx == len) |
3002 | return SCM_BOOL_F; | |
3c9a524f DH |
3003 | sign = 1; |
3004 | } | |
3005 | else if (c == '-') | |
3006 | { | |
3007 | idx++; | |
ee0ddd21 AW |
3008 | if (idx == len) |
3009 | return SCM_BOOL_F; | |
3c9a524f DH |
3010 | sign = -1; |
3011 | } | |
3012 | else | |
3013 | sign = 1; | |
3014 | ||
3f47e526 | 3015 | angle = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 3016 | if (scm_is_false (angle)) |
3c9a524f DH |
3017 | return SCM_BOOL_F; |
3018 | if (idx != len) | |
3019 | return SCM_BOOL_F; | |
3020 | ||
73e4de09 | 3021 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
3022 | angle = scm_difference (angle, SCM_UNDEFINED); |
3023 | ||
3024 | result = scm_make_polar (ureal, angle); | |
3025 | return result; | |
f872b822 | 3026 | } |
3c9a524f DH |
3027 | case '+': |
3028 | case '-': | |
3029 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 3030 | |
3c9a524f DH |
3031 | idx++; |
3032 | if (idx == len) | |
3033 | return SCM_BOOL_F; | |
3034 | else | |
3035 | { | |
3036 | int sign = (c == '+') ? 1 : -1; | |
3f47e526 | 3037 | SCM imag = mem2ureal (mem, &idx, radix, p_exactness); |
0f2d19dd | 3038 | |
73e4de09 | 3039 | if (scm_is_false (imag)) |
d956fa6f | 3040 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 3041 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 3042 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 3043 | |
3c9a524f DH |
3044 | if (idx == len) |
3045 | return SCM_BOOL_F; | |
3f47e526 MG |
3046 | if (scm_i_string_ref (mem, idx) != 'i' |
3047 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 3048 | return SCM_BOOL_F; |
0f2d19dd | 3049 | |
3c9a524f DH |
3050 | idx++; |
3051 | if (idx != len) | |
3052 | return SCM_BOOL_F; | |
0f2d19dd | 3053 | |
1fe5e088 | 3054 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
3055 | } |
3056 | default: | |
3057 | return SCM_BOOL_F; | |
3058 | } | |
3059 | } | |
0f2d19dd | 3060 | } |
0f2d19dd JB |
3061 | |
3062 | ||
3c9a524f DH |
3063 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
3064 | ||
3065 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 3066 | |
0f2d19dd | 3067 | SCM |
3f47e526 | 3068 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 3069 | { |
3c9a524f DH |
3070 | unsigned int idx = 0; |
3071 | unsigned int radix = NO_RADIX; | |
3072 | enum t_exactness forced_x = NO_EXACTNESS; | |
3073 | enum t_exactness implicit_x = EXACT; | |
3074 | SCM result; | |
3f47e526 | 3075 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
3076 | |
3077 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 3078 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 3079 | { |
3f47e526 | 3080 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
3081 | { |
3082 | case 'b': case 'B': | |
3083 | if (radix != NO_RADIX) | |
3084 | return SCM_BOOL_F; | |
3085 | radix = DUAL; | |
3086 | break; | |
3087 | case 'd': case 'D': | |
3088 | if (radix != NO_RADIX) | |
3089 | return SCM_BOOL_F; | |
3090 | radix = DEC; | |
3091 | break; | |
3092 | case 'i': case 'I': | |
3093 | if (forced_x != NO_EXACTNESS) | |
3094 | return SCM_BOOL_F; | |
3095 | forced_x = INEXACT; | |
3096 | break; | |
3097 | case 'e': case 'E': | |
3098 | if (forced_x != NO_EXACTNESS) | |
3099 | return SCM_BOOL_F; | |
3100 | forced_x = EXACT; | |
3101 | break; | |
3102 | case 'o': case 'O': | |
3103 | if (radix != NO_RADIX) | |
3104 | return SCM_BOOL_F; | |
3105 | radix = OCT; | |
3106 | break; | |
3107 | case 'x': case 'X': | |
3108 | if (radix != NO_RADIX) | |
3109 | return SCM_BOOL_F; | |
3110 | radix = HEX; | |
3111 | break; | |
3112 | default: | |
f872b822 | 3113 | return SCM_BOOL_F; |
3c9a524f DH |
3114 | } |
3115 | idx += 2; | |
3116 | } | |
3117 | ||
3118 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
3119 | if (radix == NO_RADIX) | |
3f47e526 | 3120 | result = mem2complex (mem, idx, default_radix, &implicit_x); |
3c9a524f | 3121 | else |
3f47e526 | 3122 | result = mem2complex (mem, idx, (unsigned int) radix, &implicit_x); |
3c9a524f | 3123 | |
73e4de09 | 3124 | if (scm_is_false (result)) |
3c9a524f | 3125 | return SCM_BOOL_F; |
f872b822 | 3126 | |
3c9a524f | 3127 | switch (forced_x) |
f872b822 | 3128 | { |
3c9a524f DH |
3129 | case EXACT: |
3130 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
3131 | return scm_inexact_to_exact (result); |
3132 | else | |
3133 | return result; | |
3134 | case INEXACT: | |
3135 | if (SCM_INEXACTP (result)) | |
3136 | return result; | |
3137 | else | |
3138 | return scm_exact_to_inexact (result); | |
3139 | case NO_EXACTNESS: | |
3140 | default: | |
3141 | if (implicit_x == INEXACT) | |
3142 | { | |
3143 | if (SCM_INEXACTP (result)) | |
3144 | return result; | |
3145 | else | |
3146 | return scm_exact_to_inexact (result); | |
3147 | } | |
3148 | else | |
3149 | return result; | |
f872b822 | 3150 | } |
0f2d19dd JB |
3151 | } |
3152 | ||
3f47e526 MG |
3153 | SCM |
3154 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
3155 | unsigned int default_radix) | |
3156 | { | |
3157 | SCM str = scm_from_locale_stringn (mem, len); | |
3158 | ||
3159 | return scm_i_string_to_number (str, default_radix); | |
3160 | } | |
3161 | ||
0f2d19dd | 3162 | |
a1ec6916 | 3163 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 3164 | (SCM string, SCM radix), |
1e6808ea | 3165 | "Return a number of the maximally precise representation\n" |
942e5b91 | 3166 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
3167 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
3168 | "is a default radix that may be overridden by an explicit radix\n" | |
3169 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
3170 | "supplied, then the default radix is 10. If string is not a\n" | |
3171 | "syntactically valid notation for a number, then\n" | |
3172 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 3173 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
3174 | { |
3175 | SCM answer; | |
5efd3c7d | 3176 | unsigned int base; |
a6d9e5ab | 3177 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
3178 | |
3179 | if (SCM_UNBNDP (radix)) | |
3180 | base = 10; | |
3181 | else | |
3182 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
3183 | ||
3f47e526 | 3184 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
3185 | scm_remember_upto_here_1 (string); |
3186 | return answer; | |
0f2d19dd | 3187 | } |
1bbd0b84 | 3188 | #undef FUNC_NAME |
3c9a524f DH |
3189 | |
3190 | ||
0f2d19dd JB |
3191 | /*** END strs->nums ***/ |
3192 | ||
5986c47d | 3193 | |
0f2d19dd | 3194 | SCM |
1bbd0b84 | 3195 | scm_bigequal (SCM x, SCM y) |
0f2d19dd | 3196 | { |
47ae1f0e | 3197 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
ca46fb90 | 3198 | scm_remember_upto_here_2 (x, y); |
73e4de09 | 3199 | return scm_from_bool (0 == result); |
0f2d19dd JB |
3200 | } |
3201 | ||
0f2d19dd | 3202 | SCM |
f3ae5d60 | 3203 | scm_real_equalp (SCM x, SCM y) |
0f2d19dd | 3204 | { |
73e4de09 | 3205 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0f2d19dd JB |
3206 | } |
3207 | ||
f3ae5d60 MD |
3208 | SCM |
3209 | scm_complex_equalp (SCM x, SCM y) | |
3210 | { | |
73e4de09 | 3211 | return scm_from_bool (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) |
f3ae5d60 MD |
3212 | && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); |
3213 | } | |
0f2d19dd | 3214 | |
f92e85f7 MV |
3215 | SCM |
3216 | scm_i_fraction_equalp (SCM x, SCM y) | |
3217 | { | |
73e4de09 | 3218 | if (scm_is_false (scm_equal_p (SCM_FRACTION_NUMERATOR (x), |
02164269 | 3219 | SCM_FRACTION_NUMERATOR (y))) |
73e4de09 | 3220 | || scm_is_false (scm_equal_p (SCM_FRACTION_DENOMINATOR (x), |
02164269 MV |
3221 | SCM_FRACTION_DENOMINATOR (y)))) |
3222 | return SCM_BOOL_F; | |
3223 | else | |
3224 | return SCM_BOOL_T; | |
f92e85f7 | 3225 | } |
0f2d19dd JB |
3226 | |
3227 | ||
8507ec80 MV |
3228 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
3229 | (SCM x), | |
3230 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
3231 | "otherwise.") | |
3232 | #define FUNC_NAME s_scm_number_p | |
3233 | { | |
3234 | return scm_from_bool (SCM_NUMBERP (x)); | |
3235 | } | |
3236 | #undef FUNC_NAME | |
3237 | ||
3238 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 3239 | (SCM x), |
942e5b91 | 3240 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 3241 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
3242 | "values form subsets of the set of complex numbers, i. e. the\n" |
3243 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
3244 | "rational or integer number.") | |
8507ec80 | 3245 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 3246 | { |
8507ec80 MV |
3247 | /* all numbers are complex. */ |
3248 | return scm_number_p (x); | |
0f2d19dd | 3249 | } |
1bbd0b84 | 3250 | #undef FUNC_NAME |
0f2d19dd | 3251 | |
f92e85f7 MV |
3252 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
3253 | (SCM x), | |
3254 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
3255 | "otherwise. Note that the set of integer values forms a subset of\n" | |
3256 | "the set of real numbers, i. e. the predicate will also be\n" | |
3257 | "fulfilled if @var{x} is an integer number.") | |
3258 | #define FUNC_NAME s_scm_real_p | |
3259 | { | |
3260 | /* we can't represent irrational numbers. */ | |
3261 | return scm_rational_p (x); | |
3262 | } | |
3263 | #undef FUNC_NAME | |
3264 | ||
3265 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 3266 | (SCM x), |
942e5b91 | 3267 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 3268 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 3269 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
3270 | "fulfilled if @var{x} is an integer number.") |
3271 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 3272 | { |
e11e83f3 | 3273 | if (SCM_I_INUMP (x)) |
0f2d19dd | 3274 | return SCM_BOOL_T; |
0aacf84e | 3275 | else if (SCM_IMP (x)) |
0f2d19dd | 3276 | return SCM_BOOL_F; |
0aacf84e | 3277 | else if (SCM_BIGP (x)) |
0f2d19dd | 3278 | return SCM_BOOL_T; |
f92e85f7 MV |
3279 | else if (SCM_FRACTIONP (x)) |
3280 | return SCM_BOOL_T; | |
3281 | else if (SCM_REALP (x)) | |
3282 | /* due to their limited precision, all floating point numbers are | |
3283 | rational as well. */ | |
3284 | return SCM_BOOL_T; | |
0aacf84e | 3285 | else |
bb628794 | 3286 | return SCM_BOOL_F; |
0f2d19dd | 3287 | } |
1bbd0b84 | 3288 | #undef FUNC_NAME |
0f2d19dd | 3289 | |
a1ec6916 | 3290 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 3291 | (SCM x), |
942e5b91 MG |
3292 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
3293 | "else.") | |
1bbd0b84 | 3294 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd JB |
3295 | { |
3296 | double r; | |
e11e83f3 | 3297 | if (SCM_I_INUMP (x)) |
f872b822 MD |
3298 | return SCM_BOOL_T; |
3299 | if (SCM_IMP (x)) | |
3300 | return SCM_BOOL_F; | |
f872b822 MD |
3301 | if (SCM_BIGP (x)) |
3302 | return SCM_BOOL_T; | |
3c9a524f | 3303 | if (!SCM_INEXACTP (x)) |
f872b822 | 3304 | return SCM_BOOL_F; |
3c9a524f | 3305 | if (SCM_COMPLEXP (x)) |
f872b822 | 3306 | return SCM_BOOL_F; |
5986c47d | 3307 | r = SCM_REAL_VALUE (x); |
1e35a229 | 3308 | /* +/-inf passes r==floor(r), making those #t */ |
f872b822 MD |
3309 | if (r == floor (r)) |
3310 | return SCM_BOOL_T; | |
0f2d19dd JB |
3311 | return SCM_BOOL_F; |
3312 | } | |
1bbd0b84 | 3313 | #undef FUNC_NAME |
0f2d19dd JB |
3314 | |
3315 | ||
a1ec6916 | 3316 | SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, |
1bbd0b84 | 3317 | (SCM x), |
942e5b91 MG |
3318 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" |
3319 | "else.") | |
1bbd0b84 | 3320 | #define FUNC_NAME s_scm_inexact_p |
0f2d19dd | 3321 | { |
eb927cb9 MV |
3322 | if (SCM_INEXACTP (x)) |
3323 | return SCM_BOOL_T; | |
3324 | if (SCM_NUMBERP (x)) | |
3325 | return SCM_BOOL_F; | |
3326 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 3327 | } |
1bbd0b84 | 3328 | #undef FUNC_NAME |
0f2d19dd JB |
3329 | |
3330 | ||
8a1f4f98 AW |
3331 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
3332 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
3333 | (SCM x, SCM y, SCM rest), | |
3334 | "Return @code{#t} if all parameters are numerically equal.") | |
3335 | #define FUNC_NAME s_scm_i_num_eq_p | |
3336 | { | |
3337 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3338 | return SCM_BOOL_T; | |
3339 | while (!scm_is_null (rest)) | |
3340 | { | |
3341 | if (scm_is_false (scm_num_eq_p (x, y))) | |
3342 | return SCM_BOOL_F; | |
3343 | x = y; | |
3344 | y = scm_car (rest); | |
3345 | rest = scm_cdr (rest); | |
3346 | } | |
3347 | return scm_num_eq_p (x, y); | |
3348 | } | |
3349 | #undef FUNC_NAME | |
0f2d19dd | 3350 | SCM |
6e8d25a6 | 3351 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 3352 | { |
d8b95e27 | 3353 | again: |
e11e83f3 | 3354 | if (SCM_I_INUMP (x)) |
0aacf84e | 3355 | { |
e11e83f3 MV |
3356 | long xx = SCM_I_INUM (x); |
3357 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3358 | { |
e11e83f3 | 3359 | long yy = SCM_I_INUM (y); |
73e4de09 | 3360 | return scm_from_bool (xx == yy); |
0aacf84e MD |
3361 | } |
3362 | else if (SCM_BIGP (y)) | |
3363 | return SCM_BOOL_F; | |
3364 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
3365 | { |
3366 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
3367 | to a double and compare. | |
3368 | ||
3369 | But on a 64-bit system an inum is bigger than a double and | |
3370 | casting it to a double (call that dxx) will round. dxx is at | |
3371 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
3372 | an integer and fits a long. So we cast yy to a long and | |
3373 | compare with plain xx. | |
3374 | ||
3375 | An alternative (for any size system actually) would be to check | |
3376 | yy is an integer (with floor) and is in range of an inum | |
3377 | (compare against appropriate powers of 2) then test | |
3378 | xx==(long)yy. It's just a matter of which casts/comparisons | |
3379 | might be fastest or easiest for the cpu. */ | |
3380 | ||
3381 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
3382 | return scm_from_bool ((double) xx == yy |
3383 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
3384 | || xx == (long) yy)); | |
e8c5b1f2 | 3385 | } |
0aacf84e | 3386 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3387 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3388 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
3389 | else if (SCM_FRACTIONP (y)) |
3390 | return SCM_BOOL_F; | |
0aacf84e | 3391 | else |
8a1f4f98 | 3392 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 3393 | } |
0aacf84e MD |
3394 | else if (SCM_BIGP (x)) |
3395 | { | |
e11e83f3 | 3396 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3397 | return SCM_BOOL_F; |
3398 | else if (SCM_BIGP (y)) | |
3399 | { | |
3400 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3401 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3402 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3403 | } |
3404 | else if (SCM_REALP (y)) | |
3405 | { | |
3406 | int cmp; | |
2e65b52f | 3407 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
3408 | return SCM_BOOL_F; |
3409 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3410 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3411 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3412 | } |
3413 | else if (SCM_COMPLEXP (y)) | |
3414 | { | |
3415 | int cmp; | |
3416 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
3417 | return SCM_BOOL_F; | |
2e65b52f | 3418 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
3419 | return SCM_BOOL_F; |
3420 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
3421 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3422 | return scm_from_bool (0 == cmp); |
0aacf84e | 3423 | } |
f92e85f7 MV |
3424 | else if (SCM_FRACTIONP (y)) |
3425 | return SCM_BOOL_F; | |
0aacf84e | 3426 | else |
8a1f4f98 | 3427 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 3428 | } |
0aacf84e MD |
3429 | else if (SCM_REALP (x)) |
3430 | { | |
e8c5b1f2 | 3431 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 3432 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
3433 | { |
3434 | /* see comments with inum/real above */ | |
3435 | long yy = SCM_I_INUM (y); | |
3a1b45fd MV |
3436 | return scm_from_bool (xx == (double) yy |
3437 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
3438 | || (long) xx == yy)); | |
e8c5b1f2 | 3439 | } |
0aacf84e MD |
3440 | else if (SCM_BIGP (y)) |
3441 | { | |
3442 | int cmp; | |
2e65b52f | 3443 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
3444 | return SCM_BOOL_F; |
3445 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3446 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3447 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3448 | } |
3449 | else if (SCM_REALP (y)) | |
73e4de09 | 3450 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 3451 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3452 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3453 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3454 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3455 | { |
3456 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 3457 | if (isnan (xx)) |
d8b95e27 | 3458 | return SCM_BOOL_F; |
2e65b52f | 3459 | if (isinf (xx)) |
73e4de09 | 3460 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3461 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3462 | goto again; | |
3463 | } | |
0aacf84e | 3464 | else |
8a1f4f98 | 3465 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 3466 | } |
0aacf84e MD |
3467 | else if (SCM_COMPLEXP (x)) |
3468 | { | |
e11e83f3 MV |
3469 | if (SCM_I_INUMP (y)) |
3470 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
3471 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3472 | else if (SCM_BIGP (y)) | |
3473 | { | |
3474 | int cmp; | |
3475 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
3476 | return SCM_BOOL_F; | |
2e65b52f | 3477 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
3478 | return SCM_BOOL_F; |
3479 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
3480 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3481 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3482 | } |
3483 | else if (SCM_REALP (y)) | |
73e4de09 | 3484 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
3485 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3486 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 3487 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3488 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3489 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3490 | { |
3491 | double xx; | |
3492 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
3493 | return SCM_BOOL_F; | |
3494 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 3495 | if (isnan (xx)) |
d8b95e27 | 3496 | return SCM_BOOL_F; |
2e65b52f | 3497 | if (isinf (xx)) |
73e4de09 | 3498 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3499 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3500 | goto again; | |
3501 | } | |
f92e85f7 | 3502 | else |
8a1f4f98 | 3503 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
3504 | } |
3505 | else if (SCM_FRACTIONP (x)) | |
3506 | { | |
e11e83f3 | 3507 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
3508 | return SCM_BOOL_F; |
3509 | else if (SCM_BIGP (y)) | |
3510 | return SCM_BOOL_F; | |
3511 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
3512 | { |
3513 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 3514 | if (isnan (yy)) |
d8b95e27 | 3515 | return SCM_BOOL_F; |
2e65b52f | 3516 | if (isinf (yy)) |
73e4de09 | 3517 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3518 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3519 | goto again; | |
3520 | } | |
f92e85f7 | 3521 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
3522 | { |
3523 | double yy; | |
3524 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
3525 | return SCM_BOOL_F; | |
3526 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 3527 | if (isnan (yy)) |
d8b95e27 | 3528 | return SCM_BOOL_F; |
2e65b52f | 3529 | if (isinf (yy)) |
73e4de09 | 3530 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3531 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3532 | goto again; | |
3533 | } | |
f92e85f7 MV |
3534 | else if (SCM_FRACTIONP (y)) |
3535 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 3536 | else |
8a1f4f98 | 3537 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 3538 | } |
0aacf84e | 3539 | else |
8a1f4f98 | 3540 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
3541 | } |
3542 | ||
3543 | ||
a5f0b599 KR |
3544 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
3545 | done are good for inums, but for bignums an answer can almost always be | |
3546 | had by just examining a few high bits of the operands, as done by GMP in | |
3547 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
3548 | of the float exponent to take into account. */ | |
3549 | ||
8c93b597 | 3550 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
3551 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
3552 | (SCM x, SCM y, SCM rest), | |
3553 | "Return @code{#t} if the list of parameters is monotonically\n" | |
3554 | "increasing.") | |
3555 | #define FUNC_NAME s_scm_i_num_less_p | |
3556 | { | |
3557 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3558 | return SCM_BOOL_T; | |
3559 | while (!scm_is_null (rest)) | |
3560 | { | |
3561 | if (scm_is_false (scm_less_p (x, y))) | |
3562 | return SCM_BOOL_F; | |
3563 | x = y; | |
3564 | y = scm_car (rest); | |
3565 | rest = scm_cdr (rest); | |
3566 | } | |
3567 | return scm_less_p (x, y); | |
3568 | } | |
3569 | #undef FUNC_NAME | |
0f2d19dd | 3570 | SCM |
6e8d25a6 | 3571 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3572 | { |
a5f0b599 | 3573 | again: |
e11e83f3 | 3574 | if (SCM_I_INUMP (x)) |
0aacf84e | 3575 | { |
e11e83f3 MV |
3576 | long xx = SCM_I_INUM (x); |
3577 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3578 | { |
e11e83f3 | 3579 | long yy = SCM_I_INUM (y); |
73e4de09 | 3580 | return scm_from_bool (xx < yy); |
0aacf84e MD |
3581 | } |
3582 | else if (SCM_BIGP (y)) | |
3583 | { | |
3584 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3585 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3586 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3587 | } |
3588 | else if (SCM_REALP (y)) | |
73e4de09 | 3589 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 3590 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3591 | { |
3592 | /* "x < a/b" becomes "x*b < a" */ | |
3593 | int_frac: | |
3594 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
3595 | y = SCM_FRACTION_NUMERATOR (y); | |
3596 | goto again; | |
3597 | } | |
0aacf84e | 3598 | else |
8a1f4f98 | 3599 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 3600 | } |
0aacf84e MD |
3601 | else if (SCM_BIGP (x)) |
3602 | { | |
e11e83f3 | 3603 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3604 | { |
3605 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3606 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3607 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3608 | } |
3609 | else if (SCM_BIGP (y)) | |
3610 | { | |
3611 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3612 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3613 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
3614 | } |
3615 | else if (SCM_REALP (y)) | |
3616 | { | |
3617 | int cmp; | |
2e65b52f | 3618 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
3619 | return SCM_BOOL_F; |
3620 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3621 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3622 | return scm_from_bool (cmp < 0); |
0aacf84e | 3623 | } |
f92e85f7 | 3624 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 3625 | goto int_frac; |
0aacf84e | 3626 | else |
8a1f4f98 | 3627 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 3628 | } |
0aacf84e MD |
3629 | else if (SCM_REALP (x)) |
3630 | { | |
e11e83f3 MV |
3631 | if (SCM_I_INUMP (y)) |
3632 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3633 | else if (SCM_BIGP (y)) |
3634 | { | |
3635 | int cmp; | |
2e65b52f | 3636 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
3637 | return SCM_BOOL_F; |
3638 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3639 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3640 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
3641 | } |
3642 | else if (SCM_REALP (y)) | |
73e4de09 | 3643 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 3644 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3645 | { |
3646 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 3647 | if (isnan (xx)) |
a5f0b599 | 3648 | return SCM_BOOL_F; |
2e65b52f | 3649 | if (isinf (xx)) |
73e4de09 | 3650 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
3651 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3652 | goto again; | |
3653 | } | |
f92e85f7 | 3654 | else |
8a1f4f98 | 3655 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
3656 | } |
3657 | else if (SCM_FRACTIONP (x)) | |
3658 | { | |
e11e83f3 | 3659 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
3660 | { |
3661 | /* "a/b < y" becomes "a < y*b" */ | |
3662 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
3663 | x = SCM_FRACTION_NUMERATOR (x); | |
3664 | goto again; | |
3665 | } | |
f92e85f7 | 3666 | else if (SCM_REALP (y)) |
a5f0b599 KR |
3667 | { |
3668 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 3669 | if (isnan (yy)) |
a5f0b599 | 3670 | return SCM_BOOL_F; |
2e65b52f | 3671 | if (isinf (yy)) |
73e4de09 | 3672 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
3673 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3674 | goto again; | |
3675 | } | |
f92e85f7 | 3676 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3677 | { |
3678 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
3679 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
3680 | SCM_FRACTION_DENOMINATOR (y)); | |
3681 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
3682 | SCM_FRACTION_DENOMINATOR (x)); | |
3683 | x = new_x; | |
3684 | y = new_y; | |
3685 | goto again; | |
3686 | } | |
0aacf84e | 3687 | else |
8a1f4f98 | 3688 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 3689 | } |
0aacf84e | 3690 | else |
8a1f4f98 | 3691 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
3692 | } |
3693 | ||
3694 | ||
8a1f4f98 AW |
3695 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
3696 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
3697 | (SCM x, SCM y, SCM rest), | |
3698 | "Return @code{#t} if the list of parameters is monotonically\n" | |
3699 | "decreasing.") | |
3700 | #define FUNC_NAME s_scm_i_num_gr_p | |
3701 | { | |
3702 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3703 | return SCM_BOOL_T; | |
3704 | while (!scm_is_null (rest)) | |
3705 | { | |
3706 | if (scm_is_false (scm_gr_p (x, y))) | |
3707 | return SCM_BOOL_F; | |
3708 | x = y; | |
3709 | y = scm_car (rest); | |
3710 | rest = scm_cdr (rest); | |
3711 | } | |
3712 | return scm_gr_p (x, y); | |
3713 | } | |
3714 | #undef FUNC_NAME | |
3715 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
3716 | SCM |
3717 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3718 | { |
c76b1eaf | 3719 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 3720 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 3721 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 3722 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
3723 | else |
3724 | return scm_less_p (y, x); | |
0f2d19dd | 3725 | } |
1bbd0b84 | 3726 | #undef FUNC_NAME |
0f2d19dd JB |
3727 | |
3728 | ||
8a1f4f98 AW |
3729 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
3730 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
3731 | (SCM x, SCM y, SCM rest), | |
3732 | "Return @code{#t} if the list of parameters is monotonically\n" | |
3733 | "non-decreasing.") | |
3734 | #define FUNC_NAME s_scm_i_num_leq_p | |
3735 | { | |
3736 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3737 | return SCM_BOOL_T; | |
3738 | while (!scm_is_null (rest)) | |
3739 | { | |
3740 | if (scm_is_false (scm_leq_p (x, y))) | |
3741 | return SCM_BOOL_F; | |
3742 | x = y; | |
3743 | y = scm_car (rest); | |
3744 | rest = scm_cdr (rest); | |
3745 | } | |
3746 | return scm_leq_p (x, y); | |
3747 | } | |
3748 | #undef FUNC_NAME | |
3749 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
3750 | SCM |
3751 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3752 | { |
c76b1eaf | 3753 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 3754 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 3755 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 3756 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 3757 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3758 | return SCM_BOOL_F; |
c76b1eaf | 3759 | else |
73e4de09 | 3760 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 3761 | } |
1bbd0b84 | 3762 | #undef FUNC_NAME |
0f2d19dd JB |
3763 | |
3764 | ||
8a1f4f98 AW |
3765 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
3766 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
3767 | (SCM x, SCM y, SCM rest), | |
3768 | "Return @code{#t} if the list of parameters is monotonically\n" | |
3769 | "non-increasing.") | |
3770 | #define FUNC_NAME s_scm_i_num_geq_p | |
3771 | { | |
3772 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3773 | return SCM_BOOL_T; | |
3774 | while (!scm_is_null (rest)) | |
3775 | { | |
3776 | if (scm_is_false (scm_geq_p (x, y))) | |
3777 | return SCM_BOOL_F; | |
3778 | x = y; | |
3779 | y = scm_car (rest); | |
3780 | rest = scm_cdr (rest); | |
3781 | } | |
3782 | return scm_geq_p (x, y); | |
3783 | } | |
3784 | #undef FUNC_NAME | |
3785 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
3786 | SCM |
3787 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3788 | { |
c76b1eaf | 3789 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 3790 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 3791 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 3792 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 3793 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3794 | return SCM_BOOL_F; |
c76b1eaf | 3795 | else |
73e4de09 | 3796 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 3797 | } |
1bbd0b84 | 3798 | #undef FUNC_NAME |
0f2d19dd JB |
3799 | |
3800 | ||
152f82bf | 3801 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3802 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3803 | * "zero." | |
3804 | */ | |
0f2d19dd | 3805 | SCM |
6e8d25a6 | 3806 | scm_zero_p (SCM z) |
0f2d19dd | 3807 | { |
e11e83f3 | 3808 | if (SCM_I_INUMP (z)) |
bc36d050 | 3809 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 3810 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 3811 | return SCM_BOOL_F; |
0aacf84e | 3812 | else if (SCM_REALP (z)) |
73e4de09 | 3813 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 3814 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 3815 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 3816 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
3817 | else if (SCM_FRACTIONP (z)) |
3818 | return SCM_BOOL_F; | |
0aacf84e | 3819 | else |
c2ff8ab0 | 3820 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); |
0f2d19dd JB |
3821 | } |
3822 | ||
3823 | ||
152f82bf | 3824 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3825 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3826 | * "zero." | |
3827 | */ | |
0f2d19dd | 3828 | SCM |
6e8d25a6 | 3829 | scm_positive_p (SCM x) |
0f2d19dd | 3830 | { |
e11e83f3 MV |
3831 | if (SCM_I_INUMP (x)) |
3832 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
3833 | else if (SCM_BIGP (x)) |
3834 | { | |
3835 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3836 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3837 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3838 | } |
3839 | else if (SCM_REALP (x)) | |
73e4de09 | 3840 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
3841 | else if (SCM_FRACTIONP (x)) |
3842 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3843 | else |
c2ff8ab0 | 3844 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); |
0f2d19dd JB |
3845 | } |
3846 | ||
3847 | ||
152f82bf | 3848 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3849 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3850 | * "zero." | |
3851 | */ | |
0f2d19dd | 3852 | SCM |
6e8d25a6 | 3853 | scm_negative_p (SCM x) |
0f2d19dd | 3854 | { |
e11e83f3 MV |
3855 | if (SCM_I_INUMP (x)) |
3856 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
3857 | else if (SCM_BIGP (x)) |
3858 | { | |
3859 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3860 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3861 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3862 | } |
3863 | else if (SCM_REALP (x)) | |
73e4de09 | 3864 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
3865 | else if (SCM_FRACTIONP (x)) |
3866 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3867 | else |
c2ff8ab0 | 3868 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); |
0f2d19dd JB |
3869 | } |
3870 | ||
3871 | ||
2a06f791 KR |
3872 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
3873 | required by r5rs. On that basis, for exact/inexact combinations the | |
3874 | exact is converted to inexact to compare and possibly return. This is | |
3875 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
3876 | its test, such trouble is not required for min and max. */ | |
3877 | ||
78d3deb1 AW |
3878 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
3879 | (SCM x, SCM y, SCM rest), | |
3880 | "Return the maximum of all parameter values.") | |
3881 | #define FUNC_NAME s_scm_i_max | |
3882 | { | |
3883 | while (!scm_is_null (rest)) | |
3884 | { x = scm_max (x, y); | |
3885 | y = scm_car (rest); | |
3886 | rest = scm_cdr (rest); | |
3887 | } | |
3888 | return scm_max (x, y); | |
3889 | } | |
3890 | #undef FUNC_NAME | |
3891 | ||
3892 | #define s_max s_scm_i_max | |
3893 | #define g_max g_scm_i_max | |
3894 | ||
0f2d19dd | 3895 | SCM |
6e8d25a6 | 3896 | scm_max (SCM x, SCM y) |
0f2d19dd | 3897 | { |
0aacf84e MD |
3898 | if (SCM_UNBNDP (y)) |
3899 | { | |
3900 | if (SCM_UNBNDP (x)) | |
3901 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 3902 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3903 | return x; |
3904 | else | |
3905 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3906 | } |
f4c627b3 | 3907 | |
e11e83f3 | 3908 | if (SCM_I_INUMP (x)) |
0aacf84e | 3909 | { |
e11e83f3 MV |
3910 | long xx = SCM_I_INUM (x); |
3911 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3912 | { |
e11e83f3 | 3913 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3914 | return (xx < yy) ? y : x; |
3915 | } | |
3916 | else if (SCM_BIGP (y)) | |
3917 | { | |
3918 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3919 | scm_remember_upto_here_1 (y); | |
3920 | return (sgn < 0) ? x : y; | |
3921 | } | |
3922 | else if (SCM_REALP (y)) | |
3923 | { | |
3924 | double z = xx; | |
3925 | /* if y==NaN then ">" is false and we return NaN */ | |
55f26379 | 3926 | return (z > SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3927 | } |
f92e85f7 MV |
3928 | else if (SCM_FRACTIONP (y)) |
3929 | { | |
e4bc5d6c | 3930 | use_less: |
73e4de09 | 3931 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 3932 | } |
0aacf84e MD |
3933 | else |
3934 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3935 | } |
0aacf84e MD |
3936 | else if (SCM_BIGP (x)) |
3937 | { | |
e11e83f3 | 3938 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3939 | { |
3940 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3941 | scm_remember_upto_here_1 (x); | |
3942 | return (sgn < 0) ? y : x; | |
3943 | } | |
3944 | else if (SCM_BIGP (y)) | |
3945 | { | |
3946 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3947 | scm_remember_upto_here_2 (x, y); | |
3948 | return (cmp > 0) ? x : y; | |
3949 | } | |
3950 | else if (SCM_REALP (y)) | |
3951 | { | |
2a06f791 KR |
3952 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
3953 | double xx, yy; | |
3954 | big_real: | |
3955 | xx = scm_i_big2dbl (x); | |
3956 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3957 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 3958 | } |
f92e85f7 MV |
3959 | else if (SCM_FRACTIONP (y)) |
3960 | { | |
e4bc5d6c | 3961 | goto use_less; |
f92e85f7 | 3962 | } |
0aacf84e MD |
3963 | else |
3964 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 3965 | } |
0aacf84e MD |
3966 | else if (SCM_REALP (x)) |
3967 | { | |
e11e83f3 | 3968 | if (SCM_I_INUMP (y)) |
0aacf84e | 3969 | { |
e11e83f3 | 3970 | double z = SCM_I_INUM (y); |
0aacf84e | 3971 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3972 | return (SCM_REAL_VALUE (x) < z) ? scm_from_double (z) : x; |
0aacf84e MD |
3973 | } |
3974 | else if (SCM_BIGP (y)) | |
3975 | { | |
b6f8f763 | 3976 | SCM_SWAP (x, y); |
2a06f791 | 3977 | goto big_real; |
0aacf84e MD |
3978 | } |
3979 | else if (SCM_REALP (y)) | |
3980 | { | |
3981 | /* if x==NaN then our explicit check means we return NaN | |
3982 | if y==NaN then ">" is false and we return NaN | |
3983 | calling isnan is unavoidable, since it's the only way to know | |
3984 | which of x or y causes any compares to be false */ | |
3985 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 3986 | return (isnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y; |
0aacf84e | 3987 | } |
f92e85f7 MV |
3988 | else if (SCM_FRACTIONP (y)) |
3989 | { | |
3990 | double yy = scm_i_fraction2double (y); | |
3991 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3992 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
3993 | } |
3994 | else | |
3995 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3996 | } | |
3997 | else if (SCM_FRACTIONP (x)) | |
3998 | { | |
e11e83f3 | 3999 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4000 | { |
e4bc5d6c | 4001 | goto use_less; |
f92e85f7 MV |
4002 | } |
4003 | else if (SCM_BIGP (y)) | |
4004 | { | |
e4bc5d6c | 4005 | goto use_less; |
f92e85f7 MV |
4006 | } |
4007 | else if (SCM_REALP (y)) | |
4008 | { | |
4009 | double xx = scm_i_fraction2double (x); | |
55f26379 | 4010 | return (xx < SCM_REAL_VALUE (y)) ? y : scm_from_double (xx); |
f92e85f7 MV |
4011 | } |
4012 | else if (SCM_FRACTIONP (y)) | |
4013 | { | |
e4bc5d6c | 4014 | goto use_less; |
f92e85f7 | 4015 | } |
0aacf84e MD |
4016 | else |
4017 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 4018 | } |
0aacf84e | 4019 | else |
f4c627b3 | 4020 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
4021 | } |
4022 | ||
4023 | ||
78d3deb1 AW |
4024 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
4025 | (SCM x, SCM y, SCM rest), | |
4026 | "Return the minimum of all parameter values.") | |
4027 | #define FUNC_NAME s_scm_i_min | |
4028 | { | |
4029 | while (!scm_is_null (rest)) | |
4030 | { x = scm_min (x, y); | |
4031 | y = scm_car (rest); | |
4032 | rest = scm_cdr (rest); | |
4033 | } | |
4034 | return scm_min (x, y); | |
4035 | } | |
4036 | #undef FUNC_NAME | |
4037 | ||
4038 | #define s_min s_scm_i_min | |
4039 | #define g_min g_scm_i_min | |
4040 | ||
0f2d19dd | 4041 | SCM |
6e8d25a6 | 4042 | scm_min (SCM x, SCM y) |
0f2d19dd | 4043 | { |
0aacf84e MD |
4044 | if (SCM_UNBNDP (y)) |
4045 | { | |
4046 | if (SCM_UNBNDP (x)) | |
4047 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 4048 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
4049 | return x; |
4050 | else | |
4051 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 4052 | } |
f4c627b3 | 4053 | |
e11e83f3 | 4054 | if (SCM_I_INUMP (x)) |
0aacf84e | 4055 | { |
e11e83f3 MV |
4056 | long xx = SCM_I_INUM (x); |
4057 | if (SCM_I_INUMP (y)) | |
0aacf84e | 4058 | { |
e11e83f3 | 4059 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
4060 | return (xx < yy) ? x : y; |
4061 | } | |
4062 | else if (SCM_BIGP (y)) | |
4063 | { | |
4064 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4065 | scm_remember_upto_here_1 (y); | |
4066 | return (sgn < 0) ? y : x; | |
4067 | } | |
4068 | else if (SCM_REALP (y)) | |
4069 | { | |
4070 | double z = xx; | |
4071 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 4072 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 4073 | } |
f92e85f7 MV |
4074 | else if (SCM_FRACTIONP (y)) |
4075 | { | |
e4bc5d6c | 4076 | use_less: |
73e4de09 | 4077 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 4078 | } |
0aacf84e MD |
4079 | else |
4080 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 4081 | } |
0aacf84e MD |
4082 | else if (SCM_BIGP (x)) |
4083 | { | |
e11e83f3 | 4084 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4085 | { |
4086 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4087 | scm_remember_upto_here_1 (x); | |
4088 | return (sgn < 0) ? x : y; | |
4089 | } | |
4090 | else if (SCM_BIGP (y)) | |
4091 | { | |
4092 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4093 | scm_remember_upto_here_2 (x, y); | |
4094 | return (cmp > 0) ? y : x; | |
4095 | } | |
4096 | else if (SCM_REALP (y)) | |
4097 | { | |
2a06f791 KR |
4098 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
4099 | double xx, yy; | |
4100 | big_real: | |
4101 | xx = scm_i_big2dbl (x); | |
4102 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 4103 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 4104 | } |
f92e85f7 MV |
4105 | else if (SCM_FRACTIONP (y)) |
4106 | { | |
e4bc5d6c | 4107 | goto use_less; |
f92e85f7 | 4108 | } |
0aacf84e MD |
4109 | else |
4110 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 4111 | } |
0aacf84e MD |
4112 | else if (SCM_REALP (x)) |
4113 | { | |
e11e83f3 | 4114 | if (SCM_I_INUMP (y)) |
0aacf84e | 4115 | { |
e11e83f3 | 4116 | double z = SCM_I_INUM (y); |
0aacf84e | 4117 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 4118 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
4119 | } |
4120 | else if (SCM_BIGP (y)) | |
4121 | { | |
b6f8f763 | 4122 | SCM_SWAP (x, y); |
2a06f791 | 4123 | goto big_real; |
0aacf84e MD |
4124 | } |
4125 | else if (SCM_REALP (y)) | |
4126 | { | |
4127 | /* if x==NaN then our explicit check means we return NaN | |
4128 | if y==NaN then "<" is false and we return NaN | |
4129 | calling isnan is unavoidable, since it's the only way to know | |
4130 | which of x or y causes any compares to be false */ | |
4131 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4132 | return (isnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y; |
0aacf84e | 4133 | } |
f92e85f7 MV |
4134 | else if (SCM_FRACTIONP (y)) |
4135 | { | |
4136 | double yy = scm_i_fraction2double (y); | |
4137 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 4138 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 4139 | } |
0aacf84e MD |
4140 | else |
4141 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 4142 | } |
f92e85f7 MV |
4143 | else if (SCM_FRACTIONP (x)) |
4144 | { | |
e11e83f3 | 4145 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4146 | { |
e4bc5d6c | 4147 | goto use_less; |
f92e85f7 MV |
4148 | } |
4149 | else if (SCM_BIGP (y)) | |
4150 | { | |
e4bc5d6c | 4151 | goto use_less; |
f92e85f7 MV |
4152 | } |
4153 | else if (SCM_REALP (y)) | |
4154 | { | |
4155 | double xx = scm_i_fraction2double (x); | |
55f26379 | 4156 | return (SCM_REAL_VALUE (y) < xx) ? y : scm_from_double (xx); |
f92e85f7 MV |
4157 | } |
4158 | else if (SCM_FRACTIONP (y)) | |
4159 | { | |
e4bc5d6c | 4160 | goto use_less; |
f92e85f7 MV |
4161 | } |
4162 | else | |
78d3deb1 | 4163 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 4164 | } |
0aacf84e | 4165 | else |
f4c627b3 | 4166 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
4167 | } |
4168 | ||
4169 | ||
8ccd24f7 AW |
4170 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
4171 | (SCM x, SCM y, SCM rest), | |
4172 | "Return the sum of all parameter values. Return 0 if called without\n" | |
4173 | "any parameters." ) | |
4174 | #define FUNC_NAME s_scm_i_sum | |
4175 | { | |
4176 | while (!scm_is_null (rest)) | |
4177 | { x = scm_sum (x, y); | |
4178 | y = scm_car (rest); | |
4179 | rest = scm_cdr (rest); | |
4180 | } | |
4181 | return scm_sum (x, y); | |
4182 | } | |
4183 | #undef FUNC_NAME | |
4184 | ||
4185 | #define s_sum s_scm_i_sum | |
4186 | #define g_sum g_scm_i_sum | |
4187 | ||
0f2d19dd | 4188 | SCM |
6e8d25a6 | 4189 | scm_sum (SCM x, SCM y) |
0f2d19dd | 4190 | { |
9cc37597 | 4191 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
4192 | { |
4193 | if (SCM_NUMBERP (x)) return x; | |
4194 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 4195 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 4196 | } |
c209c88e | 4197 | |
9cc37597 | 4198 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 4199 | { |
9cc37597 | 4200 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 4201 | { |
e11e83f3 MV |
4202 | long xx = SCM_I_INUM (x); |
4203 | long yy = SCM_I_INUM (y); | |
ca46fb90 | 4204 | long int z = xx + yy; |
d956fa6f | 4205 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_long2big (z); |
ca46fb90 RB |
4206 | } |
4207 | else if (SCM_BIGP (y)) | |
4208 | { | |
4209 | SCM_SWAP (x, y); | |
4210 | goto add_big_inum; | |
4211 | } | |
4212 | else if (SCM_REALP (y)) | |
4213 | { | |
e11e83f3 | 4214 | long int xx = SCM_I_INUM (x); |
55f26379 | 4215 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
4216 | } |
4217 | else if (SCM_COMPLEXP (y)) | |
4218 | { | |
e11e83f3 | 4219 | long int xx = SCM_I_INUM (x); |
8507ec80 | 4220 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
4221 | SCM_COMPLEX_IMAG (y)); |
4222 | } | |
f92e85f7 | 4223 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4224 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
4225 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
4226 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
4227 | else |
4228 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
4229 | } else if (SCM_BIGP (x)) |
4230 | { | |
e11e83f3 | 4231 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4232 | { |
4233 | long int inum; | |
4234 | int bigsgn; | |
4235 | add_big_inum: | |
e11e83f3 | 4236 | inum = SCM_I_INUM (y); |
0aacf84e MD |
4237 | if (inum == 0) |
4238 | return x; | |
4239 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4240 | if (inum < 0) | |
4241 | { | |
4242 | SCM result = scm_i_mkbig (); | |
4243 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
4244 | scm_remember_upto_here_1 (x); | |
4245 | /* we know the result will have to be a bignum */ | |
4246 | if (bigsgn == -1) | |
4247 | return result; | |
4248 | return scm_i_normbig (result); | |
4249 | } | |
4250 | else | |
4251 | { | |
4252 | SCM result = scm_i_mkbig (); | |
4253 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
4254 | scm_remember_upto_here_1 (x); | |
4255 | /* we know the result will have to be a bignum */ | |
4256 | if (bigsgn == 1) | |
4257 | return result; | |
4258 | return scm_i_normbig (result); | |
4259 | } | |
4260 | } | |
4261 | else if (SCM_BIGP (y)) | |
4262 | { | |
4263 | SCM result = scm_i_mkbig (); | |
4264 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4265 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4266 | mpz_add (SCM_I_BIG_MPZ (result), | |
4267 | SCM_I_BIG_MPZ (x), | |
4268 | SCM_I_BIG_MPZ (y)); | |
4269 | scm_remember_upto_here_2 (x, y); | |
4270 | /* we know the result will have to be a bignum */ | |
4271 | if (sgn_x == sgn_y) | |
4272 | return result; | |
4273 | return scm_i_normbig (result); | |
4274 | } | |
4275 | else if (SCM_REALP (y)) | |
4276 | { | |
4277 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
4278 | scm_remember_upto_here_1 (x); | |
55f26379 | 4279 | return scm_from_double (result); |
0aacf84e MD |
4280 | } |
4281 | else if (SCM_COMPLEXP (y)) | |
4282 | { | |
4283 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4284 | + SCM_COMPLEX_REAL (y)); | |
4285 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4286 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4287 | } |
f92e85f7 | 4288 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4289 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
4290 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
4291 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4292 | else |
4293 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 4294 | } |
0aacf84e MD |
4295 | else if (SCM_REALP (x)) |
4296 | { | |
e11e83f3 | 4297 | if (SCM_I_INUMP (y)) |
55f26379 | 4298 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
4299 | else if (SCM_BIGP (y)) |
4300 | { | |
4301 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
4302 | scm_remember_upto_here_1 (y); | |
55f26379 | 4303 | return scm_from_double (result); |
0aacf84e MD |
4304 | } |
4305 | else if (SCM_REALP (y)) | |
55f26379 | 4306 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 4307 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4308 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4309 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4310 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4311 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
4312 | else |
4313 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 4314 | } |
0aacf84e MD |
4315 | else if (SCM_COMPLEXP (x)) |
4316 | { | |
e11e83f3 | 4317 | if (SCM_I_INUMP (y)) |
8507ec80 | 4318 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
4319 | SCM_COMPLEX_IMAG (x)); |
4320 | else if (SCM_BIGP (y)) | |
4321 | { | |
4322 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
4323 | + SCM_COMPLEX_REAL (x)); | |
4324 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4325 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4326 | } |
4327 | else if (SCM_REALP (y)) | |
8507ec80 | 4328 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
4329 | SCM_COMPLEX_IMAG (x)); |
4330 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4331 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4332 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4333 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4334 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
4335 | SCM_COMPLEX_IMAG (x)); |
4336 | else | |
4337 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
4338 | } | |
4339 | else if (SCM_FRACTIONP (x)) | |
4340 | { | |
e11e83f3 | 4341 | if (SCM_I_INUMP (y)) |
cba42c93 | 4342 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4343 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4344 | SCM_FRACTION_DENOMINATOR (x)); | |
4345 | else if (SCM_BIGP (y)) | |
cba42c93 | 4346 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4347 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4348 | SCM_FRACTION_DENOMINATOR (x)); | |
4349 | else if (SCM_REALP (y)) | |
55f26379 | 4350 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 4351 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4352 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
4353 | SCM_COMPLEX_IMAG (y)); |
4354 | else if (SCM_FRACTIONP (y)) | |
4355 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 4356 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4357 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4358 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4359 | else |
4360 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 4361 | } |
0aacf84e | 4362 | else |
98cb6e75 | 4363 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
4364 | } |
4365 | ||
4366 | ||
40882e3d KR |
4367 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
4368 | (SCM x), | |
4369 | "Return @math{@var{x}+1}.") | |
4370 | #define FUNC_NAME s_scm_oneplus | |
4371 | { | |
4372 | return scm_sum (x, SCM_I_MAKINUM (1)); | |
4373 | } | |
4374 | #undef FUNC_NAME | |
4375 | ||
4376 | ||
78d3deb1 AW |
4377 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
4378 | (SCM x, SCM y, SCM rest), | |
4379 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
4380 | "the sum of all but the first argument are subtracted from the first\n" | |
4381 | "argument.") | |
4382 | #define FUNC_NAME s_scm_i_difference | |
4383 | { | |
4384 | while (!scm_is_null (rest)) | |
4385 | { x = scm_difference (x, y); | |
4386 | y = scm_car (rest); | |
4387 | rest = scm_cdr (rest); | |
4388 | } | |
4389 | return scm_difference (x, y); | |
4390 | } | |
4391 | #undef FUNC_NAME | |
4392 | ||
4393 | #define s_difference s_scm_i_difference | |
4394 | #define g_difference g_scm_i_difference | |
4395 | ||
0f2d19dd | 4396 | SCM |
6e8d25a6 | 4397 | scm_difference (SCM x, SCM y) |
78d3deb1 | 4398 | #define FUNC_NAME s_difference |
0f2d19dd | 4399 | { |
9cc37597 | 4400 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
4401 | { |
4402 | if (SCM_UNBNDP (x)) | |
4403 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
4404 | else | |
e11e83f3 | 4405 | if (SCM_I_INUMP (x)) |
ca46fb90 | 4406 | { |
e11e83f3 | 4407 | long xx = -SCM_I_INUM (x); |
ca46fb90 | 4408 | if (SCM_FIXABLE (xx)) |
d956fa6f | 4409 | return SCM_I_MAKINUM (xx); |
ca46fb90 RB |
4410 | else |
4411 | return scm_i_long2big (xx); | |
4412 | } | |
4413 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
4414 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
4415 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
4416 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
4417 | else if (SCM_REALP (x)) | |
55f26379 | 4418 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 4419 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 4420 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 4421 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 4422 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4423 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 4424 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
4425 | else |
4426 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 4427 | } |
ca46fb90 | 4428 | |
9cc37597 | 4429 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 4430 | { |
9cc37597 | 4431 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4432 | { |
e11e83f3 MV |
4433 | long int xx = SCM_I_INUM (x); |
4434 | long int yy = SCM_I_INUM (y); | |
0aacf84e MD |
4435 | long int z = xx - yy; |
4436 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4437 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4438 | else |
4439 | return scm_i_long2big (z); | |
4440 | } | |
4441 | else if (SCM_BIGP (y)) | |
4442 | { | |
4443 | /* inum-x - big-y */ | |
e11e83f3 | 4444 | long xx = SCM_I_INUM (x); |
ca46fb90 | 4445 | |
0aacf84e MD |
4446 | if (xx == 0) |
4447 | return scm_i_clonebig (y, 0); | |
4448 | else | |
4449 | { | |
4450 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4451 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4452 | |
0aacf84e MD |
4453 | if (xx >= 0) |
4454 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
4455 | else | |
4456 | { | |
4457 | /* x - y == -(y + -x) */ | |
4458 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
4459 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4460 | } | |
4461 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 4462 | |
0aacf84e MD |
4463 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
4464 | /* we know the result will have to be a bignum */ | |
4465 | return result; | |
4466 | else | |
4467 | return scm_i_normbig (result); | |
4468 | } | |
4469 | } | |
4470 | else if (SCM_REALP (y)) | |
4471 | { | |
e11e83f3 | 4472 | long int xx = SCM_I_INUM (x); |
55f26379 | 4473 | return scm_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
4474 | } |
4475 | else if (SCM_COMPLEXP (y)) | |
4476 | { | |
e11e83f3 | 4477 | long int xx = SCM_I_INUM (x); |
8507ec80 | 4478 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4479 | - SCM_COMPLEX_IMAG (y)); |
4480 | } | |
f92e85f7 MV |
4481 | else if (SCM_FRACTIONP (y)) |
4482 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 4483 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4484 | SCM_FRACTION_NUMERATOR (y)), |
4485 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4486 | else |
4487 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 4488 | } |
0aacf84e MD |
4489 | else if (SCM_BIGP (x)) |
4490 | { | |
e11e83f3 | 4491 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4492 | { |
4493 | /* big-x - inum-y */ | |
e11e83f3 | 4494 | long yy = SCM_I_INUM (y); |
0aacf84e | 4495 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 4496 | |
0aacf84e MD |
4497 | scm_remember_upto_here_1 (x); |
4498 | if (sgn_x == 0) | |
c71b0706 MV |
4499 | return (SCM_FIXABLE (-yy) ? |
4500 | SCM_I_MAKINUM (-yy) : scm_from_long (-yy)); | |
0aacf84e MD |
4501 | else |
4502 | { | |
4503 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4504 | |
708f22c6 KR |
4505 | if (yy >= 0) |
4506 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
4507 | else | |
4508 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 4509 | scm_remember_upto_here_1 (x); |
ca46fb90 | 4510 | |
0aacf84e MD |
4511 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
4512 | /* we know the result will have to be a bignum */ | |
4513 | return result; | |
4514 | else | |
4515 | return scm_i_normbig (result); | |
4516 | } | |
4517 | } | |
4518 | else if (SCM_BIGP (y)) | |
4519 | { | |
4520 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4521 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4522 | SCM result = scm_i_mkbig (); | |
4523 | mpz_sub (SCM_I_BIG_MPZ (result), | |
4524 | SCM_I_BIG_MPZ (x), | |
4525 | SCM_I_BIG_MPZ (y)); | |
4526 | scm_remember_upto_here_2 (x, y); | |
4527 | /* we know the result will have to be a bignum */ | |
4528 | if ((sgn_x == 1) && (sgn_y == -1)) | |
4529 | return result; | |
4530 | if ((sgn_x == -1) && (sgn_y == 1)) | |
4531 | return result; | |
4532 | return scm_i_normbig (result); | |
4533 | } | |
4534 | else if (SCM_REALP (y)) | |
4535 | { | |
4536 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
4537 | scm_remember_upto_here_1 (x); | |
55f26379 | 4538 | return scm_from_double (result); |
0aacf84e MD |
4539 | } |
4540 | else if (SCM_COMPLEXP (y)) | |
4541 | { | |
4542 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4543 | - SCM_COMPLEX_REAL (y)); | |
4544 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4545 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4546 | } |
f92e85f7 | 4547 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4548 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4549 | SCM_FRACTION_NUMERATOR (y)), |
4550 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 4551 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 4552 | } |
0aacf84e MD |
4553 | else if (SCM_REALP (x)) |
4554 | { | |
e11e83f3 | 4555 | if (SCM_I_INUMP (y)) |
55f26379 | 4556 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
4557 | else if (SCM_BIGP (y)) |
4558 | { | |
4559 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4560 | scm_remember_upto_here_1 (x); | |
55f26379 | 4561 | return scm_from_double (result); |
0aacf84e MD |
4562 | } |
4563 | else if (SCM_REALP (y)) | |
55f26379 | 4564 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 4565 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4566 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4567 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4568 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4569 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
4570 | else |
4571 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4572 | } |
0aacf84e MD |
4573 | else if (SCM_COMPLEXP (x)) |
4574 | { | |
e11e83f3 | 4575 | if (SCM_I_INUMP (y)) |
8507ec80 | 4576 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
4577 | SCM_COMPLEX_IMAG (x)); |
4578 | else if (SCM_BIGP (y)) | |
4579 | { | |
4580 | double real_part = (SCM_COMPLEX_REAL (x) | |
4581 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
4582 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4583 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
4584 | } |
4585 | else if (SCM_REALP (y)) | |
8507ec80 | 4586 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
4587 | SCM_COMPLEX_IMAG (x)); |
4588 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4589 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4590 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4591 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4592 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
4593 | SCM_COMPLEX_IMAG (x)); |
4594 | else | |
4595 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
4596 | } | |
4597 | else if (SCM_FRACTIONP (x)) | |
4598 | { | |
e11e83f3 | 4599 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4600 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 4601 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4602 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4603 | SCM_FRACTION_DENOMINATOR (x)); | |
4604 | else if (SCM_BIGP (y)) | |
cba42c93 | 4605 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4606 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4607 | SCM_FRACTION_DENOMINATOR (x)); | |
4608 | else if (SCM_REALP (y)) | |
55f26379 | 4609 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 4610 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4611 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4612 | -SCM_COMPLEX_IMAG (y)); |
4613 | else if (SCM_FRACTIONP (y)) | |
4614 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 4615 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4616 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4617 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4618 | else |
4619 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4620 | } |
0aacf84e | 4621 | else |
98cb6e75 | 4622 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 4623 | } |
c05e97b7 | 4624 | #undef FUNC_NAME |
0f2d19dd | 4625 | |
ca46fb90 | 4626 | |
40882e3d KR |
4627 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
4628 | (SCM x), | |
4629 | "Return @math{@var{x}-1}.") | |
4630 | #define FUNC_NAME s_scm_oneminus | |
4631 | { | |
4632 | return scm_difference (x, SCM_I_MAKINUM (1)); | |
4633 | } | |
4634 | #undef FUNC_NAME | |
4635 | ||
4636 | ||
78d3deb1 AW |
4637 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
4638 | (SCM x, SCM y, SCM rest), | |
4639 | "Return the product of all arguments. If called without arguments,\n" | |
4640 | "1 is returned.") | |
4641 | #define FUNC_NAME s_scm_i_product | |
4642 | { | |
4643 | while (!scm_is_null (rest)) | |
4644 | { x = scm_product (x, y); | |
4645 | y = scm_car (rest); | |
4646 | rest = scm_cdr (rest); | |
4647 | } | |
4648 | return scm_product (x, y); | |
4649 | } | |
4650 | #undef FUNC_NAME | |
4651 | ||
4652 | #define s_product s_scm_i_product | |
4653 | #define g_product g_scm_i_product | |
4654 | ||
0f2d19dd | 4655 | SCM |
6e8d25a6 | 4656 | scm_product (SCM x, SCM y) |
0f2d19dd | 4657 | { |
9cc37597 | 4658 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
4659 | { |
4660 | if (SCM_UNBNDP (x)) | |
d956fa6f | 4661 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
4662 | else if (SCM_NUMBERP (x)) |
4663 | return x; | |
4664 | else | |
4665 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 4666 | } |
ca46fb90 | 4667 | |
9cc37597 | 4668 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e MD |
4669 | { |
4670 | long xx; | |
f4c627b3 | 4671 | |
0aacf84e | 4672 | intbig: |
e11e83f3 | 4673 | xx = SCM_I_INUM (x); |
f4c627b3 | 4674 | |
0aacf84e MD |
4675 | switch (xx) |
4676 | { | |
ca46fb90 RB |
4677 | case 0: return x; break; |
4678 | case 1: return y; break; | |
0aacf84e | 4679 | } |
f4c627b3 | 4680 | |
9cc37597 | 4681 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4682 | { |
e11e83f3 | 4683 | long yy = SCM_I_INUM (y); |
0aacf84e | 4684 | long kk = xx * yy; |
d956fa6f | 4685 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 4686 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
4687 | return k; |
4688 | else | |
4689 | { | |
4690 | SCM result = scm_i_long2big (xx); | |
4691 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); | |
4692 | return scm_i_normbig (result); | |
4693 | } | |
4694 | } | |
4695 | else if (SCM_BIGP (y)) | |
4696 | { | |
4697 | SCM result = scm_i_mkbig (); | |
4698 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
4699 | scm_remember_upto_here_1 (y); | |
4700 | return result; | |
4701 | } | |
4702 | else if (SCM_REALP (y)) | |
55f26379 | 4703 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 4704 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4705 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 4706 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4707 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4708 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4709 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4710 | else |
4711 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4712 | } |
0aacf84e MD |
4713 | else if (SCM_BIGP (x)) |
4714 | { | |
e11e83f3 | 4715 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4716 | { |
4717 | SCM_SWAP (x, y); | |
4718 | goto intbig; | |
4719 | } | |
4720 | else if (SCM_BIGP (y)) | |
4721 | { | |
4722 | SCM result = scm_i_mkbig (); | |
4723 | mpz_mul (SCM_I_BIG_MPZ (result), | |
4724 | SCM_I_BIG_MPZ (x), | |
4725 | SCM_I_BIG_MPZ (y)); | |
4726 | scm_remember_upto_here_2 (x, y); | |
4727 | return result; | |
4728 | } | |
4729 | else if (SCM_REALP (y)) | |
4730 | { | |
4731 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
4732 | scm_remember_upto_here_1 (x); | |
55f26379 | 4733 | return scm_from_double (result); |
0aacf84e MD |
4734 | } |
4735 | else if (SCM_COMPLEXP (y)) | |
4736 | { | |
4737 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4738 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4739 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4740 | z * SCM_COMPLEX_IMAG (y)); |
4741 | } | |
f92e85f7 | 4742 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4743 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4744 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4745 | else |
4746 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4747 | } |
0aacf84e MD |
4748 | else if (SCM_REALP (x)) |
4749 | { | |
e11e83f3 | 4750 | if (SCM_I_INUMP (y)) |
23d72566 KR |
4751 | { |
4752 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
4753 | if (scm_is_eq (y, SCM_INUM0)) | |
4754 | return y; | |
4755 | return scm_from_double (SCM_I_INUM (y) * SCM_REAL_VALUE (x)); | |
4756 | } | |
0aacf84e MD |
4757 | else if (SCM_BIGP (y)) |
4758 | { | |
4759 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
4760 | scm_remember_upto_here_1 (y); | |
55f26379 | 4761 | return scm_from_double (result); |
0aacf84e MD |
4762 | } |
4763 | else if (SCM_REALP (y)) | |
55f26379 | 4764 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 4765 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4766 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 4767 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4768 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4769 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
4770 | else |
4771 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4772 | } |
0aacf84e MD |
4773 | else if (SCM_COMPLEXP (x)) |
4774 | { | |
e11e83f3 | 4775 | if (SCM_I_INUMP (y)) |
23d72566 KR |
4776 | { |
4777 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
4778 | if (scm_is_eq (y, SCM_INUM0)) | |
4779 | return y; | |
4780 | return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x), | |
4781 | SCM_I_INUM (y) * SCM_COMPLEX_IMAG (x)); | |
4782 | } | |
0aacf84e MD |
4783 | else if (SCM_BIGP (y)) |
4784 | { | |
4785 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4786 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4787 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 4788 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4789 | } |
4790 | else if (SCM_REALP (y)) | |
8507ec80 | 4791 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
4792 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
4793 | else if (SCM_COMPLEXP (y)) | |
4794 | { | |
8507ec80 | 4795 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
4796 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
4797 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
4798 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
4799 | } | |
f92e85f7 MV |
4800 | else if (SCM_FRACTIONP (y)) |
4801 | { | |
4802 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4803 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
4804 | yy * SCM_COMPLEX_IMAG (x)); |
4805 | } | |
4806 | else | |
4807 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
4808 | } | |
4809 | else if (SCM_FRACTIONP (x)) | |
4810 | { | |
e11e83f3 | 4811 | if (SCM_I_INUMP (y)) |
cba42c93 | 4812 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4813 | SCM_FRACTION_DENOMINATOR (x)); |
4814 | else if (SCM_BIGP (y)) | |
cba42c93 | 4815 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4816 | SCM_FRACTION_DENOMINATOR (x)); |
4817 | else if (SCM_REALP (y)) | |
55f26379 | 4818 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
4819 | else if (SCM_COMPLEXP (y)) |
4820 | { | |
4821 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 4822 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4823 | xx * SCM_COMPLEX_IMAG (y)); |
4824 | } | |
4825 | else if (SCM_FRACTIONP (y)) | |
4826 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 4827 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4828 | SCM_FRACTION_NUMERATOR (y)), |
4829 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
4830 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4831 | else |
4832 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4833 | } |
0aacf84e | 4834 | else |
f4c627b3 | 4835 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
4836 | } |
4837 | ||
7351e207 MV |
4838 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
4839 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
4840 | #define ALLOW_DIVIDE_BY_ZERO | |
4841 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
4842 | #endif | |
0f2d19dd | 4843 | |
ba74ef4e MV |
4844 | /* The code below for complex division is adapted from the GNU |
4845 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
4846 | this copyright: */ | |
4847 | ||
4848 | /**************************************************************** | |
4849 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
4850 | ||
4851 | Permission to use, copy, modify, and distribute this software | |
4852 | and its documentation for any purpose and without fee is hereby | |
4853 | granted, provided that the above copyright notice appear in all | |
4854 | copies and that both that the copyright notice and this | |
4855 | permission notice and warranty disclaimer appear in supporting | |
4856 | documentation, and that the names of AT&T Bell Laboratories or | |
4857 | Bellcore or any of their entities not be used in advertising or | |
4858 | publicity pertaining to distribution of the software without | |
4859 | specific, written prior permission. | |
4860 | ||
4861 | AT&T and Bellcore disclaim all warranties with regard to this | |
4862 | software, including all implied warranties of merchantability | |
4863 | and fitness. In no event shall AT&T or Bellcore be liable for | |
4864 | any special, indirect or consequential damages or any damages | |
4865 | whatsoever resulting from loss of use, data or profits, whether | |
4866 | in an action of contract, negligence or other tortious action, | |
4867 | arising out of or in connection with the use or performance of | |
4868 | this software. | |
4869 | ****************************************************************/ | |
4870 | ||
78d3deb1 AW |
4871 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
4872 | (SCM x, SCM y, SCM rest), | |
4873 | "Divide the first argument by the product of the remaining\n" | |
4874 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
4875 | "returned.") | |
4876 | #define FUNC_NAME s_scm_i_divide | |
4877 | { | |
4878 | while (!scm_is_null (rest)) | |
4879 | { x = scm_divide (x, y); | |
4880 | y = scm_car (rest); | |
4881 | rest = scm_cdr (rest); | |
4882 | } | |
4883 | return scm_divide (x, y); | |
4884 | } | |
4885 | #undef FUNC_NAME | |
4886 | ||
4887 | #define s_divide s_scm_i_divide | |
4888 | #define g_divide g_scm_i_divide | |
4889 | ||
f92e85f7 | 4890 | static SCM |
78d3deb1 AW |
4891 | do_divide (SCM x, SCM y, int inexact) |
4892 | #define FUNC_NAME s_divide | |
0f2d19dd | 4893 | { |
f8de44c1 DH |
4894 | double a; |
4895 | ||
9cc37597 | 4896 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
4897 | { |
4898 | if (SCM_UNBNDP (x)) | |
4899 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 4900 | else if (SCM_I_INUMP (x)) |
0aacf84e | 4901 | { |
e11e83f3 | 4902 | long xx = SCM_I_INUM (x); |
0aacf84e MD |
4903 | if (xx == 1 || xx == -1) |
4904 | return x; | |
7351e207 | 4905 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4906 | else if (xx == 0) |
4907 | scm_num_overflow (s_divide); | |
7351e207 | 4908 | #endif |
0aacf84e | 4909 | else |
f92e85f7 MV |
4910 | { |
4911 | if (inexact) | |
55f26379 | 4912 | return scm_from_double (1.0 / (double) xx); |
cba42c93 | 4913 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4914 | } |
0aacf84e MD |
4915 | } |
4916 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
4917 | { |
4918 | if (inexact) | |
55f26379 | 4919 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cba42c93 | 4920 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4921 | } |
0aacf84e MD |
4922 | else if (SCM_REALP (x)) |
4923 | { | |
4924 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 4925 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4926 | if (xx == 0.0) |
4927 | scm_num_overflow (s_divide); | |
4928 | else | |
7351e207 | 4929 | #endif |
55f26379 | 4930 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
4931 | } |
4932 | else if (SCM_COMPLEXP (x)) | |
4933 | { | |
4934 | double r = SCM_COMPLEX_REAL (x); | |
4935 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 4936 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
4937 | { |
4938 | double t = r / i; | |
4939 | double d = i * (1.0 + t * t); | |
8507ec80 | 4940 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
4941 | } |
4942 | else | |
4943 | { | |
4944 | double t = i / r; | |
4945 | double d = r * (1.0 + t * t); | |
8507ec80 | 4946 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
4947 | } |
4948 | } | |
f92e85f7 | 4949 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4950 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 4951 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
4952 | else |
4953 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 4954 | } |
f8de44c1 | 4955 | |
9cc37597 | 4956 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 4957 | { |
e11e83f3 | 4958 | long xx = SCM_I_INUM (x); |
9cc37597 | 4959 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4960 | { |
e11e83f3 | 4961 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
4962 | if (yy == 0) |
4963 | { | |
7351e207 | 4964 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4965 | scm_num_overflow (s_divide); |
7351e207 | 4966 | #else |
55f26379 | 4967 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 4968 | #endif |
0aacf84e MD |
4969 | } |
4970 | else if (xx % yy != 0) | |
f92e85f7 MV |
4971 | { |
4972 | if (inexact) | |
55f26379 | 4973 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 4974 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4975 | } |
0aacf84e MD |
4976 | else |
4977 | { | |
4978 | long z = xx / yy; | |
4979 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4980 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4981 | else |
4982 | return scm_i_long2big (z); | |
4983 | } | |
f872b822 | 4984 | } |
0aacf84e | 4985 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
4986 | { |
4987 | if (inexact) | |
55f26379 | 4988 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 4989 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4990 | } |
0aacf84e MD |
4991 | else if (SCM_REALP (y)) |
4992 | { | |
4993 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4994 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4995 | if (yy == 0.0) |
4996 | scm_num_overflow (s_divide); | |
4997 | else | |
7351e207 | 4998 | #endif |
55f26379 | 4999 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 5000 | } |
0aacf84e MD |
5001 | else if (SCM_COMPLEXP (y)) |
5002 | { | |
5003 | a = xx; | |
5004 | complex_div: /* y _must_ be a complex number */ | |
5005 | { | |
5006 | double r = SCM_COMPLEX_REAL (y); | |
5007 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 5008 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
5009 | { |
5010 | double t = r / i; | |
5011 | double d = i * (1.0 + t * t); | |
8507ec80 | 5012 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
5013 | } |
5014 | else | |
5015 | { | |
5016 | double t = i / r; | |
5017 | double d = r * (1.0 + t * t); | |
8507ec80 | 5018 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
5019 | } |
5020 | } | |
5021 | } | |
f92e85f7 MV |
5022 | else if (SCM_FRACTIONP (y)) |
5023 | /* a / b/c = ac / b */ | |
cba42c93 | 5024 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 5025 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
5026 | else |
5027 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 5028 | } |
0aacf84e MD |
5029 | else if (SCM_BIGP (x)) |
5030 | { | |
e11e83f3 | 5031 | if (SCM_I_INUMP (y)) |
0aacf84e | 5032 | { |
e11e83f3 | 5033 | long int yy = SCM_I_INUM (y); |
0aacf84e MD |
5034 | if (yy == 0) |
5035 | { | |
7351e207 | 5036 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 5037 | scm_num_overflow (s_divide); |
7351e207 | 5038 | #else |
0aacf84e MD |
5039 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
5040 | scm_remember_upto_here_1 (x); | |
5041 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 5042 | #endif |
0aacf84e MD |
5043 | } |
5044 | else if (yy == 1) | |
5045 | return x; | |
5046 | else | |
5047 | { | |
5048 | /* FIXME: HMM, what are the relative performance issues here? | |
5049 | We need to test. Is it faster on average to test | |
5050 | divisible_p, then perform whichever operation, or is it | |
5051 | faster to perform the integer div opportunistically and | |
5052 | switch to real if there's a remainder? For now we take the | |
5053 | middle ground: test, then if divisible, use the faster div | |
5054 | func. */ | |
5055 | ||
5056 | long abs_yy = yy < 0 ? -yy : yy; | |
5057 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); | |
5058 | ||
5059 | if (divisible_p) | |
5060 | { | |
5061 | SCM result = scm_i_mkbig (); | |
5062 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
5063 | scm_remember_upto_here_1 (x); | |
5064 | if (yy < 0) | |
5065 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
5066 | return scm_i_normbig (result); | |
5067 | } | |
5068 | else | |
f92e85f7 MV |
5069 | { |
5070 | if (inexact) | |
55f26379 | 5071 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 5072 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 5073 | } |
0aacf84e MD |
5074 | } |
5075 | } | |
5076 | else if (SCM_BIGP (y)) | |
5077 | { | |
5078 | int y_is_zero = (mpz_sgn (SCM_I_BIG_MPZ (y)) == 0); | |
5079 | if (y_is_zero) | |
5080 | { | |
ca46fb90 | 5081 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 5082 | scm_num_overflow (s_divide); |
f872b822 | 5083 | #else |
0aacf84e MD |
5084 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
5085 | scm_remember_upto_here_1 (x); | |
5086 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
f872b822 | 5087 | #endif |
0aacf84e MD |
5088 | } |
5089 | else | |
5090 | { | |
5091 | /* big_x / big_y */ | |
23f2b9a3 KR |
5092 | if (inexact) |
5093 | { | |
5094 | /* It's easily possible for the ratio x/y to fit a double | |
5095 | but one or both x and y be too big to fit a double, | |
5096 | hence the use of mpq_get_d rather than converting and | |
5097 | dividing. */ | |
5098 | mpq_t q; | |
5099 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
5100 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
5101 | return scm_from_double (mpq_get_d (q)); | |
5102 | } | |
5103 | else | |
5104 | { | |
5105 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), | |
5106 | SCM_I_BIG_MPZ (y)); | |
5107 | if (divisible_p) | |
5108 | { | |
5109 | SCM result = scm_i_mkbig (); | |
5110 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
5111 | SCM_I_BIG_MPZ (x), | |
5112 | SCM_I_BIG_MPZ (y)); | |
5113 | scm_remember_upto_here_2 (x, y); | |
5114 | return scm_i_normbig (result); | |
5115 | } | |
5116 | else | |
5117 | return scm_i_make_ratio (x, y); | |
5118 | } | |
0aacf84e MD |
5119 | } |
5120 | } | |
5121 | else if (SCM_REALP (y)) | |
5122 | { | |
5123 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5124 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5125 | if (yy == 0.0) |
5126 | scm_num_overflow (s_divide); | |
5127 | else | |
7351e207 | 5128 | #endif |
55f26379 | 5129 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
5130 | } |
5131 | else if (SCM_COMPLEXP (y)) | |
5132 | { | |
5133 | a = scm_i_big2dbl (x); | |
5134 | goto complex_div; | |
5135 | } | |
f92e85f7 | 5136 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5137 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 5138 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
5139 | else |
5140 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 5141 | } |
0aacf84e MD |
5142 | else if (SCM_REALP (x)) |
5143 | { | |
5144 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 5145 | if (SCM_I_INUMP (y)) |
0aacf84e | 5146 | { |
e11e83f3 | 5147 | long int yy = SCM_I_INUM (y); |
7351e207 | 5148 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
5149 | if (yy == 0) |
5150 | scm_num_overflow (s_divide); | |
5151 | else | |
7351e207 | 5152 | #endif |
55f26379 | 5153 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
5154 | } |
5155 | else if (SCM_BIGP (y)) | |
5156 | { | |
5157 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
5158 | scm_remember_upto_here_1 (y); | |
55f26379 | 5159 | return scm_from_double (rx / dby); |
0aacf84e MD |
5160 | } |
5161 | else if (SCM_REALP (y)) | |
5162 | { | |
5163 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5164 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5165 | if (yy == 0.0) |
5166 | scm_num_overflow (s_divide); | |
5167 | else | |
7351e207 | 5168 | #endif |
55f26379 | 5169 | return scm_from_double (rx / yy); |
0aacf84e MD |
5170 | } |
5171 | else if (SCM_COMPLEXP (y)) | |
5172 | { | |
5173 | a = rx; | |
5174 | goto complex_div; | |
5175 | } | |
f92e85f7 | 5176 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5177 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
5178 | else |
5179 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 5180 | } |
0aacf84e MD |
5181 | else if (SCM_COMPLEXP (x)) |
5182 | { | |
5183 | double rx = SCM_COMPLEX_REAL (x); | |
5184 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 5185 | if (SCM_I_INUMP (y)) |
0aacf84e | 5186 | { |
e11e83f3 | 5187 | long int yy = SCM_I_INUM (y); |
7351e207 | 5188 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
5189 | if (yy == 0) |
5190 | scm_num_overflow (s_divide); | |
5191 | else | |
7351e207 | 5192 | #endif |
0aacf84e MD |
5193 | { |
5194 | double d = yy; | |
8507ec80 | 5195 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
5196 | } |
5197 | } | |
5198 | else if (SCM_BIGP (y)) | |
5199 | { | |
5200 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
5201 | scm_remember_upto_here_1 (y); | |
8507ec80 | 5202 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
5203 | } |
5204 | else if (SCM_REALP (y)) | |
5205 | { | |
5206 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5207 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5208 | if (yy == 0.0) |
5209 | scm_num_overflow (s_divide); | |
5210 | else | |
7351e207 | 5211 | #endif |
8507ec80 | 5212 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
5213 | } |
5214 | else if (SCM_COMPLEXP (y)) | |
5215 | { | |
5216 | double ry = SCM_COMPLEX_REAL (y); | |
5217 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 5218 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
5219 | { |
5220 | double t = ry / iy; | |
5221 | double d = iy * (1.0 + t * t); | |
8507ec80 | 5222 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
5223 | } |
5224 | else | |
5225 | { | |
5226 | double t = iy / ry; | |
5227 | double d = ry * (1.0 + t * t); | |
8507ec80 | 5228 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
5229 | } |
5230 | } | |
f92e85f7 MV |
5231 | else if (SCM_FRACTIONP (y)) |
5232 | { | |
5233 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 5234 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 5235 | } |
0aacf84e MD |
5236 | else |
5237 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 5238 | } |
f92e85f7 MV |
5239 | else if (SCM_FRACTIONP (x)) |
5240 | { | |
e11e83f3 | 5241 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5242 | { |
e11e83f3 | 5243 | long int yy = SCM_I_INUM (y); |
f92e85f7 MV |
5244 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
5245 | if (yy == 0) | |
5246 | scm_num_overflow (s_divide); | |
5247 | else | |
5248 | #endif | |
cba42c93 | 5249 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5250 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
5251 | } | |
5252 | else if (SCM_BIGP (y)) | |
5253 | { | |
cba42c93 | 5254 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5255 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
5256 | } | |
5257 | else if (SCM_REALP (y)) | |
5258 | { | |
5259 | double yy = SCM_REAL_VALUE (y); | |
5260 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
5261 | if (yy == 0.0) | |
5262 | scm_num_overflow (s_divide); | |
5263 | else | |
5264 | #endif | |
55f26379 | 5265 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
5266 | } |
5267 | else if (SCM_COMPLEXP (y)) | |
5268 | { | |
5269 | a = scm_i_fraction2double (x); | |
5270 | goto complex_div; | |
5271 | } | |
5272 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 5273 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5274 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
5275 | else | |
5276 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
5277 | } | |
0aacf84e | 5278 | else |
f8de44c1 | 5279 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 5280 | } |
f92e85f7 MV |
5281 | |
5282 | SCM | |
5283 | scm_divide (SCM x, SCM y) | |
5284 | { | |
78d3deb1 | 5285 | return do_divide (x, y, 0); |
f92e85f7 MV |
5286 | } |
5287 | ||
5288 | static SCM scm_divide2real (SCM x, SCM y) | |
5289 | { | |
78d3deb1 | 5290 | return do_divide (x, y, 1); |
f92e85f7 | 5291 | } |
c05e97b7 | 5292 | #undef FUNC_NAME |
0f2d19dd | 5293 | |
fa605590 | 5294 | |
0f2d19dd | 5295 | double |
3101f40f | 5296 | scm_c_truncate (double x) |
0f2d19dd | 5297 | { |
fa605590 KR |
5298 | #if HAVE_TRUNC |
5299 | return trunc (x); | |
5300 | #else | |
f872b822 MD |
5301 | if (x < 0.0) |
5302 | return -floor (-x); | |
5303 | return floor (x); | |
fa605590 | 5304 | #endif |
0f2d19dd | 5305 | } |
0f2d19dd | 5306 | |
3101f40f MV |
5307 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
5308 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
5309 | Then half-way cases are identified and adjusted down if the | |
5310 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
5311 | |
5312 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
5313 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
5314 | ||
5315 | An odd "result" value is identified with result/2 != floor(result/2). | |
5316 | This is done with plus_half, since that value is ready for use sooner in | |
5317 | a pipelined cpu, and we're already requiring plus_half == result. | |
5318 | ||
5319 | Note however that we need to be careful when x is big and already an | |
5320 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
5321 | us to return such a value, incorrectly. For instance if the hardware is | |
5322 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
5323 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
5324 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
5325 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
5326 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
5327 | ||
5328 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
5329 | x is already an integer. If it is then clearly that's the desired result | |
5330 | already. And if it's not then the exponent must be small enough to allow | |
5331 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
5332 | ||
0f2d19dd | 5333 | double |
3101f40f | 5334 | scm_c_round (double x) |
0f2d19dd | 5335 | { |
6187f48b KR |
5336 | double plus_half, result; |
5337 | ||
5338 | if (x == floor (x)) | |
5339 | return x; | |
5340 | ||
5341 | plus_half = x + 0.5; | |
5342 | result = floor (plus_half); | |
3101f40f | 5343 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
5344 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
5345 | ? result - 1 | |
5346 | : result); | |
0f2d19dd JB |
5347 | } |
5348 | ||
f92e85f7 MV |
5349 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
5350 | (SCM x), | |
5351 | "Round the number @var{x} towards zero.") | |
5352 | #define FUNC_NAME s_scm_truncate_number | |
5353 | { | |
73e4de09 | 5354 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5355 | return scm_floor (x); |
5356 | else | |
5357 | return scm_ceiling (x); | |
5358 | } | |
5359 | #undef FUNC_NAME | |
5360 | ||
5361 | static SCM exactly_one_half; | |
5362 | ||
5363 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, | |
5364 | (SCM x), | |
5365 | "Round the number @var{x} towards the nearest integer. " | |
5366 | "When it is exactly halfway between two integers, " | |
5367 | "round towards the even one.") | |
5368 | #define FUNC_NAME s_scm_round_number | |
5369 | { | |
e11e83f3 | 5370 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
5371 | return x; |
5372 | else if (SCM_REALP (x)) | |
3101f40f | 5373 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 5374 | else |
bae30667 KR |
5375 | { |
5376 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
5377 | single quotient+remainder division then examining to see which way | |
5378 | the rounding should go. */ | |
5379 | SCM plus_half = scm_sum (x, exactly_one_half); | |
5380 | SCM result = scm_floor (plus_half); | |
3101f40f | 5381 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
5382 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
5383 | && scm_is_true (scm_odd_p (result))) | |
d956fa6f | 5384 | return scm_difference (result, SCM_I_MAKINUM (1)); |
bae30667 KR |
5385 | else |
5386 | return result; | |
5387 | } | |
f92e85f7 MV |
5388 | } |
5389 | #undef FUNC_NAME | |
5390 | ||
5391 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
5392 | (SCM x), | |
5393 | "Round the number @var{x} towards minus infinity.") | |
5394 | #define FUNC_NAME s_scm_floor | |
5395 | { | |
e11e83f3 | 5396 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5397 | return x; |
5398 | else if (SCM_REALP (x)) | |
55f26379 | 5399 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5400 | else if (SCM_FRACTIONP (x)) |
5401 | { | |
5402 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5403 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5404 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5405 | { |
5406 | /* For positive x, rounding towards zero is correct. */ | |
5407 | return q; | |
5408 | } | |
5409 | else | |
5410 | { | |
5411 | /* For negative x, we need to return q-1 unless x is an | |
5412 | integer. But fractions are never integer, per our | |
5413 | assumptions. */ | |
d956fa6f | 5414 | return scm_difference (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5415 | } |
5416 | } | |
5417 | else | |
5418 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
5419 | } | |
5420 | #undef FUNC_NAME | |
5421 | ||
5422 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
5423 | (SCM x), | |
5424 | "Round the number @var{x} towards infinity.") | |
5425 | #define FUNC_NAME s_scm_ceiling | |
5426 | { | |
e11e83f3 | 5427 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5428 | return x; |
5429 | else if (SCM_REALP (x)) | |
55f26379 | 5430 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5431 | else if (SCM_FRACTIONP (x)) |
5432 | { | |
5433 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5434 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5435 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
5436 | { |
5437 | /* For negative x, rounding towards zero is correct. */ | |
5438 | return q; | |
5439 | } | |
5440 | else | |
5441 | { | |
5442 | /* For positive x, we need to return q+1 unless x is an | |
5443 | integer. But fractions are never integer, per our | |
5444 | assumptions. */ | |
d956fa6f | 5445 | return scm_sum (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5446 | } |
5447 | } | |
5448 | else | |
5449 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
5450 | } | |
5451 | #undef FUNC_NAME | |
0f2d19dd | 5452 | |
ad79736c AW |
5453 | /* sin/cos/tan/asin/acos/atan |
5454 | sinh/cosh/tanh/asinh/acosh/atanh | |
5455 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
5456 | Written by Jerry D. Hedden, (C) FSF. | |
5457 | See the file `COPYING' for terms applying to this program. */ | |
0f2d19dd | 5458 | |
6fc4d012 | 5459 | SCM_DEFINE (scm_expt, "expt", 2, 0, 0, |
27c37006 | 5460 | (SCM x, SCM y), |
6fc4d012 AW |
5461 | "Return @var{x} raised to the power of @var{y}.") |
5462 | #define FUNC_NAME s_scm_expt | |
0f2d19dd | 5463 | { |
5a8fc758 | 5464 | if (scm_is_true (scm_exact_p (x)) && scm_is_integer (y)) |
6fc4d012 AW |
5465 | return scm_integer_expt (x, y); |
5466 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) | |
5467 | { | |
5468 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
5469 | } | |
5470 | else | |
5471 | return scm_exp (scm_product (scm_log (x), y)); | |
0f2d19dd | 5472 | } |
1bbd0b84 | 5473 | #undef FUNC_NAME |
0f2d19dd | 5474 | |
ad79736c AW |
5475 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
5476 | (SCM z), | |
5477 | "Compute the sine of @var{z}.") | |
5478 | #define FUNC_NAME s_scm_sin | |
5479 | { | |
5480 | if (scm_is_real (z)) | |
5481 | return scm_from_double (sin (scm_to_double (z))); | |
5482 | else if (SCM_COMPLEXP (z)) | |
5483 | { double x, y; | |
5484 | x = SCM_COMPLEX_REAL (z); | |
5485 | y = SCM_COMPLEX_IMAG (z); | |
5486 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
5487 | cos (x) * sinh (y)); | |
5488 | } | |
5489 | else | |
5490 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
5491 | } | |
5492 | #undef FUNC_NAME | |
0f2d19dd | 5493 | |
ad79736c AW |
5494 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
5495 | (SCM z), | |
5496 | "Compute the cosine of @var{z}.") | |
5497 | #define FUNC_NAME s_scm_cos | |
5498 | { | |
5499 | if (scm_is_real (z)) | |
5500 | return scm_from_double (cos (scm_to_double (z))); | |
5501 | else if (SCM_COMPLEXP (z)) | |
5502 | { double x, y; | |
5503 | x = SCM_COMPLEX_REAL (z); | |
5504 | y = SCM_COMPLEX_IMAG (z); | |
5505 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
5506 | -sin (x) * sinh (y)); | |
5507 | } | |
5508 | else | |
5509 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
5510 | } | |
5511 | #undef FUNC_NAME | |
5512 | ||
5513 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
5514 | (SCM z), | |
5515 | "Compute the tangent of @var{z}.") | |
5516 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 5517 | { |
ad79736c AW |
5518 | if (scm_is_real (z)) |
5519 | return scm_from_double (tan (scm_to_double (z))); | |
5520 | else if (SCM_COMPLEXP (z)) | |
5521 | { double x, y, w; | |
5522 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
5523 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
5524 | w = cos (x) + cosh (y); | |
5525 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
5526 | if (w == 0.0) | |
5527 | scm_num_overflow (s_scm_tan); | |
5528 | #endif | |
5529 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
5530 | } | |
5531 | else | |
5532 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
5533 | } | |
5534 | #undef FUNC_NAME | |
5535 | ||
5536 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
5537 | (SCM z), | |
5538 | "Compute the hyperbolic sine of @var{z}.") | |
5539 | #define FUNC_NAME s_scm_sinh | |
5540 | { | |
5541 | if (scm_is_real (z)) | |
5542 | return scm_from_double (sinh (scm_to_double (z))); | |
5543 | else if (SCM_COMPLEXP (z)) | |
5544 | { double x, y; | |
5545 | x = SCM_COMPLEX_REAL (z); | |
5546 | y = SCM_COMPLEX_IMAG (z); | |
5547 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
5548 | cosh (x) * sin (y)); | |
5549 | } | |
5550 | else | |
5551 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
5552 | } | |
5553 | #undef FUNC_NAME | |
5554 | ||
5555 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
5556 | (SCM z), | |
5557 | "Compute the hyperbolic cosine of @var{z}.") | |
5558 | #define FUNC_NAME s_scm_cosh | |
5559 | { | |
5560 | if (scm_is_real (z)) | |
5561 | return scm_from_double (cosh (scm_to_double (z))); | |
5562 | else if (SCM_COMPLEXP (z)) | |
5563 | { double x, y; | |
5564 | x = SCM_COMPLEX_REAL (z); | |
5565 | y = SCM_COMPLEX_IMAG (z); | |
5566 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
5567 | sinh (x) * sin (y)); | |
5568 | } | |
5569 | else | |
5570 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
5571 | } | |
5572 | #undef FUNC_NAME | |
5573 | ||
5574 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
5575 | (SCM z), | |
5576 | "Compute the hyperbolic tangent of @var{z}.") | |
5577 | #define FUNC_NAME s_scm_tanh | |
5578 | { | |
5579 | if (scm_is_real (z)) | |
5580 | return scm_from_double (tanh (scm_to_double (z))); | |
5581 | else if (SCM_COMPLEXP (z)) | |
5582 | { double x, y, w; | |
5583 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
5584 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
5585 | w = cosh (x) + cos (y); | |
5586 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
5587 | if (w == 0.0) | |
5588 | scm_num_overflow (s_scm_tanh); | |
5589 | #endif | |
5590 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
5591 | } | |
5592 | else | |
5593 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
5594 | } | |
5595 | #undef FUNC_NAME | |
5596 | ||
5597 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
5598 | (SCM z), | |
5599 | "Compute the arc sine of @var{z}.") | |
5600 | #define FUNC_NAME s_scm_asin | |
5601 | { | |
5602 | if (scm_is_real (z)) | |
5603 | { | |
5604 | double w = scm_to_double (z); | |
5605 | if (w >= -1.0 && w <= 1.0) | |
5606 | return scm_from_double (asin (w)); | |
5607 | else | |
5608 | return scm_product (scm_c_make_rectangular (0, -1), | |
5609 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
5610 | } | |
5611 | else if (SCM_COMPLEXP (z)) | |
5612 | { double x, y; | |
5613 | x = SCM_COMPLEX_REAL (z); | |
5614 | y = SCM_COMPLEX_IMAG (z); | |
5615 | return scm_product (scm_c_make_rectangular (0, -1), | |
5616 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
5617 | } | |
5618 | else | |
5619 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
5620 | } | |
5621 | #undef FUNC_NAME | |
5622 | ||
5623 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
5624 | (SCM z), | |
5625 | "Compute the arc cosine of @var{z}.") | |
5626 | #define FUNC_NAME s_scm_acos | |
5627 | { | |
5628 | if (scm_is_real (z)) | |
5629 | { | |
5630 | double w = scm_to_double (z); | |
5631 | if (w >= -1.0 && w <= 1.0) | |
5632 | return scm_from_double (acos (w)); | |
5633 | else | |
5634 | return scm_sum (scm_from_double (acos (0.0)), | |
5635 | scm_product (scm_c_make_rectangular (0, 1), | |
5636 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
5637 | } | |
5638 | else if (SCM_COMPLEXP (z)) | |
5639 | { double x, y; | |
5640 | x = SCM_COMPLEX_REAL (z); | |
5641 | y = SCM_COMPLEX_IMAG (z); | |
5642 | return scm_sum (scm_from_double (acos (0.0)), | |
5643 | scm_product (scm_c_make_rectangular (0, 1), | |
5644 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
5645 | } | |
5646 | else | |
5647 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
5648 | } | |
5649 | #undef FUNC_NAME | |
5650 | ||
5651 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
5652 | (SCM z, SCM y), | |
5653 | "With one argument, compute the arc tangent of @var{z}.\n" | |
5654 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
5655 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
5656 | #define FUNC_NAME s_scm_atan | |
5657 | { | |
5658 | if (SCM_UNBNDP (y)) | |
5659 | { | |
5660 | if (scm_is_real (z)) | |
5661 | return scm_from_double (atan (scm_to_double (z))); | |
5662 | else if (SCM_COMPLEXP (z)) | |
5663 | { | |
5664 | double v, w; | |
5665 | v = SCM_COMPLEX_REAL (z); | |
5666 | w = SCM_COMPLEX_IMAG (z); | |
5667 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
5668 | scm_c_make_rectangular (v, w + 1.0))), | |
5669 | scm_c_make_rectangular (0, 2)); | |
5670 | } | |
5671 | else | |
5672 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
5673 | } | |
5674 | else if (scm_is_real (z)) | |
5675 | { | |
5676 | if (scm_is_real (y)) | |
5677 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
5678 | else | |
5679 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
5680 | } | |
5681 | else | |
5682 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
5683 | } | |
5684 | #undef FUNC_NAME | |
5685 | ||
5686 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
5687 | (SCM z), | |
5688 | "Compute the inverse hyperbolic sine of @var{z}.") | |
5689 | #define FUNC_NAME s_scm_sys_asinh | |
5690 | { | |
5691 | if (scm_is_real (z)) | |
5692 | return scm_from_double (asinh (scm_to_double (z))); | |
5693 | else if (scm_is_number (z)) | |
5694 | return scm_log (scm_sum (z, | |
5695 | scm_sqrt (scm_sum (scm_product (z, z), | |
5696 | SCM_I_MAKINUM (1))))); | |
5697 | else | |
5698 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
5699 | } | |
5700 | #undef FUNC_NAME | |
5701 | ||
5702 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
5703 | (SCM z), | |
5704 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
5705 | #define FUNC_NAME s_scm_sys_acosh | |
5706 | { | |
5707 | if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
5708 | return scm_from_double (acosh (scm_to_double (z))); | |
5709 | else if (scm_is_number (z)) | |
5710 | return scm_log (scm_sum (z, | |
5711 | scm_sqrt (scm_difference (scm_product (z, z), | |
5712 | SCM_I_MAKINUM (1))))); | |
5713 | else | |
5714 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
5715 | } | |
5716 | #undef FUNC_NAME | |
5717 | ||
5718 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
5719 | (SCM z), | |
5720 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
5721 | #define FUNC_NAME s_scm_sys_atanh | |
5722 | { | |
5723 | if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
5724 | return scm_from_double (atanh (scm_to_double (z))); | |
5725 | else if (scm_is_number (z)) | |
5726 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_I_MAKINUM (1), z), | |
5727 | scm_difference (SCM_I_MAKINUM (1), z))), | |
5728 | SCM_I_MAKINUM (2)); | |
5729 | else | |
5730 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 5731 | } |
1bbd0b84 | 5732 | #undef FUNC_NAME |
0f2d19dd | 5733 | |
8507ec80 MV |
5734 | SCM |
5735 | scm_c_make_rectangular (double re, double im) | |
5736 | { | |
5737 | if (im == 0.0) | |
5738 | return scm_from_double (re); | |
5739 | else | |
5740 | { | |
5741 | SCM z; | |
03604fcf LC |
5742 | |
5743 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), | |
92d8fd32 | 5744 | "complex")); |
03604fcf | 5745 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); |
8507ec80 MV |
5746 | SCM_COMPLEX_REAL (z) = re; |
5747 | SCM_COMPLEX_IMAG (z) = im; | |
5748 | return z; | |
5749 | } | |
5750 | } | |
0f2d19dd | 5751 | |
a1ec6916 | 5752 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
5753 | (SCM real_part, SCM imaginary_part), |
5754 | "Return a complex number constructed of the given @var{real-part} " | |
5755 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 5756 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 5757 | { |
ad79736c AW |
5758 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
5759 | SCM_ARG1, FUNC_NAME, "real"); | |
5760 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
5761 | SCM_ARG2, FUNC_NAME, "real"); | |
5762 | return scm_c_make_rectangular (scm_to_double (real_part), | |
5763 | scm_to_double (imaginary_part)); | |
0f2d19dd | 5764 | } |
1bbd0b84 | 5765 | #undef FUNC_NAME |
0f2d19dd | 5766 | |
8507ec80 MV |
5767 | SCM |
5768 | scm_c_make_polar (double mag, double ang) | |
5769 | { | |
5770 | double s, c; | |
5e647d08 LC |
5771 | |
5772 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
5773 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
5774 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
5775 | details. */ | |
5776 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
5777 | sincos (ang, &s, &c); |
5778 | #else | |
5779 | s = sin (ang); | |
5780 | c = cos (ang); | |
5781 | #endif | |
5782 | return scm_c_make_rectangular (mag * c, mag * s); | |
5783 | } | |
0f2d19dd | 5784 | |
a1ec6916 | 5785 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 5786 | (SCM x, SCM y), |
942e5b91 | 5787 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 5788 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 5789 | { |
ad79736c AW |
5790 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
5791 | SCM_ASSERT_TYPE (scm_is_real (y), y, SCM_ARG2, FUNC_NAME, "real"); | |
5792 | return scm_c_make_polar (scm_to_double (x), scm_to_double (y)); | |
0f2d19dd | 5793 | } |
1bbd0b84 | 5794 | #undef FUNC_NAME |
0f2d19dd JB |
5795 | |
5796 | ||
152f82bf | 5797 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
5798 | /* "Return the real part of the number @var{z}." |
5799 | */ | |
0f2d19dd | 5800 | SCM |
6e8d25a6 | 5801 | scm_real_part (SCM z) |
0f2d19dd | 5802 | { |
e11e83f3 | 5803 | if (SCM_I_INUMP (z)) |
c2ff8ab0 | 5804 | return z; |
0aacf84e | 5805 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5806 | return z; |
0aacf84e | 5807 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5808 | return z; |
0aacf84e | 5809 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5810 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
f92e85f7 | 5811 | else if (SCM_FRACTIONP (z)) |
2fa2d879 | 5812 | return z; |
0aacf84e | 5813 | else |
c2ff8ab0 | 5814 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); |
0f2d19dd JB |
5815 | } |
5816 | ||
5817 | ||
152f82bf | 5818 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
5819 | /* "Return the imaginary part of the number @var{z}." |
5820 | */ | |
0f2d19dd | 5821 | SCM |
6e8d25a6 | 5822 | scm_imag_part (SCM z) |
0f2d19dd | 5823 | { |
e11e83f3 | 5824 | if (SCM_I_INUMP (z)) |
f872b822 | 5825 | return SCM_INUM0; |
0aacf84e | 5826 | else if (SCM_BIGP (z)) |
f872b822 | 5827 | return SCM_INUM0; |
0aacf84e | 5828 | else if (SCM_REALP (z)) |
e7efe8e7 | 5829 | return flo0; |
0aacf84e | 5830 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5831 | return scm_from_double (SCM_COMPLEX_IMAG (z)); |
f92e85f7 MV |
5832 | else if (SCM_FRACTIONP (z)) |
5833 | return SCM_INUM0; | |
0aacf84e | 5834 | else |
c2ff8ab0 | 5835 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); |
0f2d19dd JB |
5836 | } |
5837 | ||
f92e85f7 MV |
5838 | SCM_GPROC (s_numerator, "numerator", 1, 0, 0, scm_numerator, g_numerator); |
5839 | /* "Return the numerator of the number @var{z}." | |
5840 | */ | |
5841 | SCM | |
5842 | scm_numerator (SCM z) | |
5843 | { | |
e11e83f3 | 5844 | if (SCM_I_INUMP (z)) |
f92e85f7 MV |
5845 | return z; |
5846 | else if (SCM_BIGP (z)) | |
5847 | return z; | |
5848 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 5849 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
5850 | else if (SCM_REALP (z)) |
5851 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
5852 | else | |
5853 | SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator); | |
5854 | } | |
5855 | ||
5856 | ||
5857 | SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator); | |
5858 | /* "Return the denominator of the number @var{z}." | |
5859 | */ | |
5860 | SCM | |
5861 | scm_denominator (SCM z) | |
5862 | { | |
e11e83f3 | 5863 | if (SCM_I_INUMP (z)) |
d956fa6f | 5864 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5865 | else if (SCM_BIGP (z)) |
d956fa6f | 5866 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5867 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 5868 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
5869 | else if (SCM_REALP (z)) |
5870 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
5871 | else | |
5872 | SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator); | |
5873 | } | |
0f2d19dd | 5874 | |
9de33deb | 5875 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
5876 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
5877 | * "@code{abs} for real arguments, but also allows complex numbers." | |
5878 | */ | |
0f2d19dd | 5879 | SCM |
6e8d25a6 | 5880 | scm_magnitude (SCM z) |
0f2d19dd | 5881 | { |
e11e83f3 | 5882 | if (SCM_I_INUMP (z)) |
0aacf84e | 5883 | { |
e11e83f3 | 5884 | long int zz = SCM_I_INUM (z); |
0aacf84e MD |
5885 | if (zz >= 0) |
5886 | return z; | |
5887 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 5888 | return SCM_I_MAKINUM (-zz); |
0aacf84e MD |
5889 | else |
5890 | return scm_i_long2big (-zz); | |
5986c47d | 5891 | } |
0aacf84e MD |
5892 | else if (SCM_BIGP (z)) |
5893 | { | |
5894 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5895 | scm_remember_upto_here_1 (z); | |
5896 | if (sgn < 0) | |
5897 | return scm_i_clonebig (z, 0); | |
5898 | else | |
5899 | return z; | |
5986c47d | 5900 | } |
0aacf84e | 5901 | else if (SCM_REALP (z)) |
55f26379 | 5902 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 5903 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5904 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
5905 | else if (SCM_FRACTIONP (z)) |
5906 | { | |
73e4de09 | 5907 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5908 | return z; |
cba42c93 | 5909 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
5910 | SCM_FRACTION_DENOMINATOR (z)); |
5911 | } | |
0aacf84e | 5912 | else |
c2ff8ab0 | 5913 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); |
0f2d19dd JB |
5914 | } |
5915 | ||
5916 | ||
9de33deb | 5917 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
5918 | /* "Return the angle of the complex number @var{z}." |
5919 | */ | |
0f2d19dd | 5920 | SCM |
6e8d25a6 | 5921 | scm_angle (SCM z) |
0f2d19dd | 5922 | { |
c8ae173e | 5923 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 5924 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
5925 | But if atan2 follows the floating point rounding mode, then the value |
5926 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 5927 | if (SCM_I_INUMP (z)) |
0aacf84e | 5928 | { |
e11e83f3 | 5929 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 5930 | return flo0; |
0aacf84e | 5931 | else |
55f26379 | 5932 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 5933 | } |
0aacf84e MD |
5934 | else if (SCM_BIGP (z)) |
5935 | { | |
5936 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5937 | scm_remember_upto_here_1 (z); | |
5938 | if (sgn < 0) | |
55f26379 | 5939 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 5940 | else |
e7efe8e7 | 5941 | return flo0; |
0f2d19dd | 5942 | } |
0aacf84e | 5943 | else if (SCM_REALP (z)) |
c8ae173e KR |
5944 | { |
5945 | if (SCM_REAL_VALUE (z) >= 0) | |
e7efe8e7 | 5946 | return flo0; |
c8ae173e | 5947 | else |
55f26379 | 5948 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 5949 | } |
0aacf84e | 5950 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5951 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
5952 | else if (SCM_FRACTIONP (z)) |
5953 | { | |
73e4de09 | 5954 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 5955 | return flo0; |
55f26379 | 5956 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 5957 | } |
0aacf84e | 5958 | else |
f4c627b3 | 5959 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); |
0f2d19dd JB |
5960 | } |
5961 | ||
5962 | ||
3c9a524f DH |
5963 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
5964 | /* Convert the number @var{x} to its inexact representation.\n" | |
5965 | */ | |
5966 | SCM | |
5967 | scm_exact_to_inexact (SCM z) | |
5968 | { | |
e11e83f3 | 5969 | if (SCM_I_INUMP (z)) |
55f26379 | 5970 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 5971 | else if (SCM_BIGP (z)) |
55f26379 | 5972 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 5973 | else if (SCM_FRACTIONP (z)) |
55f26379 | 5974 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
5975 | else if (SCM_INEXACTP (z)) |
5976 | return z; | |
5977 | else | |
5978 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
5979 | } | |
5980 | ||
5981 | ||
a1ec6916 | 5982 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 5983 | (SCM z), |
1e6808ea | 5984 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 5985 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 5986 | { |
e11e83f3 | 5987 | if (SCM_I_INUMP (z)) |
f872b822 | 5988 | return z; |
0aacf84e | 5989 | else if (SCM_BIGP (z)) |
f872b822 | 5990 | return z; |
0aacf84e MD |
5991 | else if (SCM_REALP (z)) |
5992 | { | |
2e65b52f | 5993 | if (isinf (SCM_REAL_VALUE (z)) || isnan (SCM_REAL_VALUE (z))) |
f92e85f7 | 5994 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 5995 | else |
f92e85f7 MV |
5996 | { |
5997 | mpq_t frac; | |
5998 | SCM q; | |
5999 | ||
6000 | mpq_init (frac); | |
6001 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 6002 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
6003 | scm_i_mpz2num (mpq_denref (frac))); |
6004 | ||
cba42c93 | 6005 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
6006 | for frac... |
6007 | */ | |
6008 | mpq_clear (frac); | |
6009 | return q; | |
6010 | } | |
c2ff8ab0 | 6011 | } |
f92e85f7 MV |
6012 | else if (SCM_FRACTIONP (z)) |
6013 | return z; | |
0aacf84e | 6014 | else |
c2ff8ab0 | 6015 | SCM_WRONG_TYPE_ARG (1, z); |
0f2d19dd | 6016 | } |
1bbd0b84 | 6017 | #undef FUNC_NAME |
0f2d19dd | 6018 | |
f92e85f7 | 6019 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
6020 | (SCM x, SCM eps), |
6021 | "Returns the @emph{simplest} rational number differing\n" | |
6022 | "from @var{x} by no more than @var{eps}.\n" | |
6023 | "\n" | |
6024 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
6025 | "exact result when both its arguments are exact. Thus, you might need\n" | |
6026 | "to use @code{inexact->exact} on the arguments.\n" | |
6027 | "\n" | |
6028 | "@lisp\n" | |
6029 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
6030 | "@result{} 6/5\n" | |
6031 | "@end lisp") | |
f92e85f7 MV |
6032 | #define FUNC_NAME s_scm_rationalize |
6033 | { | |
e11e83f3 | 6034 | if (SCM_I_INUMP (x)) |
f92e85f7 MV |
6035 | return x; |
6036 | else if (SCM_BIGP (x)) | |
6037 | return x; | |
6038 | else if ((SCM_REALP (x)) || SCM_FRACTIONP (x)) | |
6039 | { | |
6040 | /* Use continued fractions to find closest ratio. All | |
6041 | arithmetic is done with exact numbers. | |
6042 | */ | |
6043 | ||
6044 | SCM ex = scm_inexact_to_exact (x); | |
6045 | SCM int_part = scm_floor (ex); | |
d956fa6f MV |
6046 | SCM tt = SCM_I_MAKINUM (1); |
6047 | SCM a1 = SCM_I_MAKINUM (0), a2 = SCM_I_MAKINUM (1), a = SCM_I_MAKINUM (0); | |
6048 | SCM b1 = SCM_I_MAKINUM (1), b2 = SCM_I_MAKINUM (0), b = SCM_I_MAKINUM (0); | |
f92e85f7 MV |
6049 | SCM rx; |
6050 | int i = 0; | |
6051 | ||
73e4de09 | 6052 | if (scm_is_true (scm_num_eq_p (ex, int_part))) |
f92e85f7 MV |
6053 | return ex; |
6054 | ||
6055 | ex = scm_difference (ex, int_part); /* x = x-int_part */ | |
6056 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
6057 | ||
6058 | /* We stop after a million iterations just to be absolutely sure | |
6059 | that we don't go into an infinite loop. The process normally | |
6060 | converges after less than a dozen iterations. | |
6061 | */ | |
6062 | ||
76dae881 | 6063 | eps = scm_abs (eps); |
f92e85f7 MV |
6064 | while (++i < 1000000) |
6065 | { | |
6066 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
6067 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
6068 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
6069 | scm_is_false | |
f92e85f7 | 6070 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 6071 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
6072 | { |
6073 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
73e4de09 | 6074 | if (scm_is_false (scm_exact_p (x)) |
76dae881 | 6075 | || scm_is_false (scm_exact_p (eps))) |
02164269 MV |
6076 | return scm_exact_to_inexact (res); |
6077 | else | |
6078 | return res; | |
6079 | } | |
f92e85f7 MV |
6080 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
6081 | SCM_UNDEFINED); | |
6082 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
6083 | a2 = a1; | |
6084 | b2 = b1; | |
6085 | a1 = a; | |
6086 | b1 = b; | |
6087 | } | |
6088 | scm_num_overflow (s_scm_rationalize); | |
6089 | } | |
6090 | else | |
6091 | SCM_WRONG_TYPE_ARG (1, x); | |
6092 | } | |
6093 | #undef FUNC_NAME | |
6094 | ||
73e4de09 MV |
6095 | /* conversion functions */ |
6096 | ||
6097 | int | |
6098 | scm_is_integer (SCM val) | |
6099 | { | |
6100 | return scm_is_true (scm_integer_p (val)); | |
6101 | } | |
6102 | ||
6103 | int | |
6104 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
6105 | { | |
e11e83f3 | 6106 | if (SCM_I_INUMP (val)) |
73e4de09 | 6107 | { |
e11e83f3 | 6108 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
6109 | return n >= min && n <= max; |
6110 | } | |
6111 | else if (SCM_BIGP (val)) | |
6112 | { | |
6113 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
6114 | return 0; | |
6115 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
6116 | { |
6117 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
6118 | { | |
6119 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
6120 | return n >= min && n <= max; | |
6121 | } | |
6122 | else | |
6123 | return 0; | |
6124 | } | |
73e4de09 MV |
6125 | else |
6126 | { | |
d956fa6f MV |
6127 | scm_t_intmax n; |
6128 | size_t count; | |
73e4de09 | 6129 | |
d956fa6f MV |
6130 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
6131 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
6132 | return 0; | |
6133 | ||
6134 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
6135 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 6136 | |
d956fa6f | 6137 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 6138 | { |
d956fa6f MV |
6139 | if (n < 0) |
6140 | return 0; | |
73e4de09 | 6141 | } |
73e4de09 MV |
6142 | else |
6143 | { | |
d956fa6f MV |
6144 | n = -n; |
6145 | if (n >= 0) | |
6146 | return 0; | |
73e4de09 | 6147 | } |
d956fa6f MV |
6148 | |
6149 | return n >= min && n <= max; | |
73e4de09 MV |
6150 | } |
6151 | } | |
73e4de09 MV |
6152 | else |
6153 | return 0; | |
6154 | } | |
6155 | ||
6156 | int | |
6157 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
6158 | { | |
e11e83f3 | 6159 | if (SCM_I_INUMP (val)) |
73e4de09 | 6160 | { |
e11e83f3 | 6161 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
6162 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
6163 | } | |
6164 | else if (SCM_BIGP (val)) | |
6165 | { | |
6166 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
6167 | return 0; | |
6168 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
6169 | { |
6170 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
6171 | { | |
6172 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
6173 | return n >= min && n <= max; | |
6174 | } | |
6175 | else | |
6176 | return 0; | |
6177 | } | |
73e4de09 MV |
6178 | else |
6179 | { | |
d956fa6f MV |
6180 | scm_t_uintmax n; |
6181 | size_t count; | |
73e4de09 | 6182 | |
d956fa6f MV |
6183 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
6184 | return 0; | |
73e4de09 | 6185 | |
d956fa6f MV |
6186 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
6187 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 6188 | return 0; |
d956fa6f MV |
6189 | |
6190 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
6191 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 6192 | |
d956fa6f | 6193 | return n >= min && n <= max; |
73e4de09 MV |
6194 | } |
6195 | } | |
73e4de09 MV |
6196 | else |
6197 | return 0; | |
6198 | } | |
6199 | ||
1713d319 MV |
6200 | static void |
6201 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
6202 | { | |
6203 | scm_error (scm_out_of_range_key, | |
6204 | NULL, | |
6205 | "Value out of range ~S to ~S: ~S", | |
6206 | scm_list_3 (min, max, bad_val), | |
6207 | scm_list_1 (bad_val)); | |
6208 | } | |
6209 | ||
bfd7932e MV |
6210 | #define TYPE scm_t_intmax |
6211 | #define TYPE_MIN min | |
6212 | #define TYPE_MAX max | |
6213 | #define SIZEOF_TYPE 0 | |
6214 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
6215 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
6216 | #include "libguile/conv-integer.i.c" | |
6217 | ||
6218 | #define TYPE scm_t_uintmax | |
6219 | #define TYPE_MIN min | |
6220 | #define TYPE_MAX max | |
6221 | #define SIZEOF_TYPE 0 | |
6222 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
6223 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
6224 | #include "libguile/conv-uinteger.i.c" | |
6225 | ||
6226 | #define TYPE scm_t_int8 | |
6227 | #define TYPE_MIN SCM_T_INT8_MIN | |
6228 | #define TYPE_MAX SCM_T_INT8_MAX | |
6229 | #define SIZEOF_TYPE 1 | |
6230 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
6231 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
6232 | #include "libguile/conv-integer.i.c" | |
6233 | ||
6234 | #define TYPE scm_t_uint8 | |
6235 | #define TYPE_MIN 0 | |
6236 | #define TYPE_MAX SCM_T_UINT8_MAX | |
6237 | #define SIZEOF_TYPE 1 | |
6238 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
6239 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
6240 | #include "libguile/conv-uinteger.i.c" | |
6241 | ||
6242 | #define TYPE scm_t_int16 | |
6243 | #define TYPE_MIN SCM_T_INT16_MIN | |
6244 | #define TYPE_MAX SCM_T_INT16_MAX | |
6245 | #define SIZEOF_TYPE 2 | |
6246 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
6247 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
6248 | #include "libguile/conv-integer.i.c" | |
6249 | ||
6250 | #define TYPE scm_t_uint16 | |
6251 | #define TYPE_MIN 0 | |
6252 | #define TYPE_MAX SCM_T_UINT16_MAX | |
6253 | #define SIZEOF_TYPE 2 | |
6254 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
6255 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
6256 | #include "libguile/conv-uinteger.i.c" | |
6257 | ||
6258 | #define TYPE scm_t_int32 | |
6259 | #define TYPE_MIN SCM_T_INT32_MIN | |
6260 | #define TYPE_MAX SCM_T_INT32_MAX | |
6261 | #define SIZEOF_TYPE 4 | |
6262 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
6263 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
6264 | #include "libguile/conv-integer.i.c" | |
6265 | ||
6266 | #define TYPE scm_t_uint32 | |
6267 | #define TYPE_MIN 0 | |
6268 | #define TYPE_MAX SCM_T_UINT32_MAX | |
6269 | #define SIZEOF_TYPE 4 | |
6270 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
6271 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
6272 | #include "libguile/conv-uinteger.i.c" | |
6273 | ||
904a78f1 MG |
6274 | #define TYPE scm_t_wchar |
6275 | #define TYPE_MIN (scm_t_int32)-1 | |
6276 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
6277 | #define SIZEOF_TYPE 4 | |
6278 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
6279 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
6280 | #include "libguile/conv-integer.i.c" | |
6281 | ||
bfd7932e MV |
6282 | #define TYPE scm_t_int64 |
6283 | #define TYPE_MIN SCM_T_INT64_MIN | |
6284 | #define TYPE_MAX SCM_T_INT64_MAX | |
6285 | #define SIZEOF_TYPE 8 | |
6286 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
6287 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
6288 | #include "libguile/conv-integer.i.c" | |
6289 | ||
6290 | #define TYPE scm_t_uint64 | |
6291 | #define TYPE_MIN 0 | |
6292 | #define TYPE_MAX SCM_T_UINT64_MAX | |
6293 | #define SIZEOF_TYPE 8 | |
6294 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
6295 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
6296 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 6297 | |
cd036260 MV |
6298 | void |
6299 | scm_to_mpz (SCM val, mpz_t rop) | |
6300 | { | |
6301 | if (SCM_I_INUMP (val)) | |
6302 | mpz_set_si (rop, SCM_I_INUM (val)); | |
6303 | else if (SCM_BIGP (val)) | |
6304 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
6305 | else | |
6306 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
6307 | } | |
6308 | ||
6309 | SCM | |
6310 | scm_from_mpz (mpz_t val) | |
6311 | { | |
6312 | return scm_i_mpz2num (val); | |
6313 | } | |
6314 | ||
73e4de09 MV |
6315 | int |
6316 | scm_is_real (SCM val) | |
6317 | { | |
6318 | return scm_is_true (scm_real_p (val)); | |
6319 | } | |
6320 | ||
55f26379 MV |
6321 | int |
6322 | scm_is_rational (SCM val) | |
6323 | { | |
6324 | return scm_is_true (scm_rational_p (val)); | |
6325 | } | |
6326 | ||
73e4de09 MV |
6327 | double |
6328 | scm_to_double (SCM val) | |
6329 | { | |
55f26379 MV |
6330 | if (SCM_I_INUMP (val)) |
6331 | return SCM_I_INUM (val); | |
6332 | else if (SCM_BIGP (val)) | |
6333 | return scm_i_big2dbl (val); | |
6334 | else if (SCM_FRACTIONP (val)) | |
6335 | return scm_i_fraction2double (val); | |
6336 | else if (SCM_REALP (val)) | |
6337 | return SCM_REAL_VALUE (val); | |
6338 | else | |
7a1aba42 | 6339 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
6340 | } |
6341 | ||
6342 | SCM | |
6343 | scm_from_double (double val) | |
6344 | { | |
978c52d1 LC |
6345 | SCM z; |
6346 | ||
6347 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
6348 | ||
6349 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 6350 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 6351 | |
55f26379 | 6352 | return z; |
73e4de09 MV |
6353 | } |
6354 | ||
220058a8 | 6355 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
6356 | |
6357 | float | |
6358 | scm_num2float (SCM num, unsigned long int pos, const char *s_caller) | |
6359 | { | |
220058a8 AW |
6360 | scm_c_issue_deprecation_warning |
6361 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
6362 | ||
55f26379 MV |
6363 | if (SCM_BIGP (num)) |
6364 | { | |
6365 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 6366 | if (!isinf (res)) |
55f26379 MV |
6367 | return res; |
6368 | else | |
6369 | scm_out_of_range (NULL, num); | |
6370 | } | |
6371 | else | |
6372 | return scm_to_double (num); | |
6373 | } | |
6374 | ||
6375 | double | |
6376 | scm_num2double (SCM num, unsigned long int pos, const char *s_caller) | |
6377 | { | |
220058a8 AW |
6378 | scm_c_issue_deprecation_warning |
6379 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
6380 | ||
55f26379 MV |
6381 | if (SCM_BIGP (num)) |
6382 | { | |
6383 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 6384 | if (!isinf (res)) |
55f26379 MV |
6385 | return res; |
6386 | else | |
6387 | scm_out_of_range (NULL, num); | |
6388 | } | |
6389 | else | |
6390 | return scm_to_double (num); | |
6391 | } | |
6392 | ||
6393 | #endif | |
6394 | ||
8507ec80 MV |
6395 | int |
6396 | scm_is_complex (SCM val) | |
6397 | { | |
6398 | return scm_is_true (scm_complex_p (val)); | |
6399 | } | |
6400 | ||
6401 | double | |
6402 | scm_c_real_part (SCM z) | |
6403 | { | |
6404 | if (SCM_COMPLEXP (z)) | |
6405 | return SCM_COMPLEX_REAL (z); | |
6406 | else | |
6407 | { | |
6408 | /* Use the scm_real_part to get proper error checking and | |
6409 | dispatching. | |
6410 | */ | |
6411 | return scm_to_double (scm_real_part (z)); | |
6412 | } | |
6413 | } | |
6414 | ||
6415 | double | |
6416 | scm_c_imag_part (SCM z) | |
6417 | { | |
6418 | if (SCM_COMPLEXP (z)) | |
6419 | return SCM_COMPLEX_IMAG (z); | |
6420 | else | |
6421 | { | |
6422 | /* Use the scm_imag_part to get proper error checking and | |
6423 | dispatching. The result will almost always be 0.0, but not | |
6424 | always. | |
6425 | */ | |
6426 | return scm_to_double (scm_imag_part (z)); | |
6427 | } | |
6428 | } | |
6429 | ||
6430 | double | |
6431 | scm_c_magnitude (SCM z) | |
6432 | { | |
6433 | return scm_to_double (scm_magnitude (z)); | |
6434 | } | |
6435 | ||
6436 | double | |
6437 | scm_c_angle (SCM z) | |
6438 | { | |
6439 | return scm_to_double (scm_angle (z)); | |
6440 | } | |
6441 | ||
6442 | int | |
6443 | scm_is_number (SCM z) | |
6444 | { | |
6445 | return scm_is_true (scm_number_p (z)); | |
6446 | } | |
6447 | ||
8ab3d8a0 KR |
6448 | |
6449 | /* In the following functions we dispatch to the real-arg funcs like log() | |
6450 | when we know the arg is real, instead of just handing everything to | |
6451 | clog() for instance. This is in case clog() doesn't optimize for a | |
6452 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
6453 | well use it to go straight to the applicable C func. */ | |
6454 | ||
6455 | SCM_DEFINE (scm_log, "log", 1, 0, 0, | |
6456 | (SCM z), | |
6457 | "Return the natural logarithm of @var{z}.") | |
6458 | #define FUNC_NAME s_scm_log | |
6459 | { | |
6460 | if (SCM_COMPLEXP (z)) | |
6461 | { | |
4b26c03e | 6462 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6463 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
6464 | #else | |
6465 | double re = SCM_COMPLEX_REAL (z); | |
6466 | double im = SCM_COMPLEX_IMAG (z); | |
6467 | return scm_c_make_rectangular (log (hypot (re, im)), | |
6468 | atan2 (im, re)); | |
6469 | #endif | |
6470 | } | |
6471 | else | |
6472 | { | |
6473 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6474 | although the value itself overflows. */ | |
6475 | double re = scm_to_double (z); | |
6476 | double l = log (fabs (re)); | |
6477 | if (re >= 0.0) | |
6478 | return scm_from_double (l); | |
6479 | else | |
6480 | return scm_c_make_rectangular (l, M_PI); | |
6481 | } | |
6482 | } | |
6483 | #undef FUNC_NAME | |
6484 | ||
6485 | ||
6486 | SCM_DEFINE (scm_log10, "log10", 1, 0, 0, | |
6487 | (SCM z), | |
6488 | "Return the base 10 logarithm of @var{z}.") | |
6489 | #define FUNC_NAME s_scm_log10 | |
6490 | { | |
6491 | if (SCM_COMPLEXP (z)) | |
6492 | { | |
6493 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
6494 | clog() and a multiply by M_LOG10E, rather than the fallback | |
6495 | log10+hypot+atan2.) */ | |
f328f862 LC |
6496 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
6497 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
6498 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
6499 | #else | |
6500 | double re = SCM_COMPLEX_REAL (z); | |
6501 | double im = SCM_COMPLEX_IMAG (z); | |
6502 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
6503 | M_LOG10E * atan2 (im, re)); | |
6504 | #endif | |
6505 | } | |
6506 | else | |
6507 | { | |
6508 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6509 | although the value itself overflows. */ | |
6510 | double re = scm_to_double (z); | |
6511 | double l = log10 (fabs (re)); | |
6512 | if (re >= 0.0) | |
6513 | return scm_from_double (l); | |
6514 | else | |
6515 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
6516 | } | |
6517 | } | |
6518 | #undef FUNC_NAME | |
6519 | ||
6520 | ||
6521 | SCM_DEFINE (scm_exp, "exp", 1, 0, 0, | |
6522 | (SCM z), | |
6523 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
6524 | "base of natural logarithms (2.71828@dots{}).") | |
6525 | #define FUNC_NAME s_scm_exp | |
6526 | { | |
6527 | if (SCM_COMPLEXP (z)) | |
6528 | { | |
4b26c03e | 6529 | #if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6530 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
6531 | #else | |
6532 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
6533 | SCM_COMPLEX_IMAG (z)); | |
6534 | #endif | |
6535 | } | |
6536 | else | |
6537 | { | |
6538 | /* When z is a negative bignum the conversion to double overflows, | |
6539 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
6540 | return scm_from_double (exp (scm_to_double (z))); | |
6541 | } | |
6542 | } | |
6543 | #undef FUNC_NAME | |
6544 | ||
6545 | ||
6546 | SCM_DEFINE (scm_sqrt, "sqrt", 1, 0, 0, | |
6547 | (SCM x), | |
6548 | "Return the square root of @var{z}. Of the two possible roots\n" | |
6549 | "(positive and negative), the one with the a positive real part\n" | |
6550 | "is returned, or if that's zero then a positive imaginary part.\n" | |
6551 | "Thus,\n" | |
6552 | "\n" | |
6553 | "@example\n" | |
6554 | "(sqrt 9.0) @result{} 3.0\n" | |
6555 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
6556 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
6557 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
6558 | "@end example") | |
6559 | #define FUNC_NAME s_scm_sqrt | |
6560 | { | |
6561 | if (SCM_COMPLEXP (x)) | |
6562 | { | |
f328f862 LC |
6563 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
6564 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
6565 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (x))); |
6566 | #else | |
6567 | double re = SCM_COMPLEX_REAL (x); | |
6568 | double im = SCM_COMPLEX_IMAG (x); | |
6569 | return scm_c_make_polar (sqrt (hypot (re, im)), | |
6570 | 0.5 * atan2 (im, re)); | |
6571 | #endif | |
6572 | } | |
6573 | else | |
6574 | { | |
6575 | double xx = scm_to_double (x); | |
6576 | if (xx < 0) | |
6577 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
6578 | else | |
6579 | return scm_from_double (sqrt (xx)); | |
6580 | } | |
6581 | } | |
6582 | #undef FUNC_NAME | |
6583 | ||
6584 | ||
6585 | ||
0f2d19dd JB |
6586 | void |
6587 | scm_init_numbers () | |
0f2d19dd | 6588 | { |
0b799eea MV |
6589 | int i; |
6590 | ||
713a4259 KR |
6591 | mpz_init_set_si (z_negative_one, -1); |
6592 | ||
a261c0e9 DH |
6593 | /* It may be possible to tune the performance of some algorithms by using |
6594 | * the following constants to avoid the creation of bignums. Please, before | |
6595 | * using these values, remember the two rules of program optimization: | |
6596 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 6597 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 6598 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 6599 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 6600 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 6601 | |
f3ae5d60 MD |
6602 | scm_add_feature ("complex"); |
6603 | scm_add_feature ("inexact"); | |
e7efe8e7 | 6604 | flo0 = scm_from_double (0.0); |
0b799eea MV |
6605 | |
6606 | /* determine floating point precision */ | |
55f26379 | 6607 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
6608 | { |
6609 | init_dblprec(&scm_dblprec[i-2],i); | |
6610 | init_fx_radix(fx_per_radix[i-2],i); | |
6611 | } | |
f872b822 | 6612 | #ifdef DBL_DIG |
0b799eea | 6613 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 6614 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 6615 | #endif |
1be6b49c | 6616 | |
f39448c5 | 6617 | exactly_one_half = scm_divide (SCM_I_MAKINUM (1), SCM_I_MAKINUM (2)); |
a0599745 | 6618 | #include "libguile/numbers.x" |
0f2d19dd | 6619 | } |
89e00824 ML |
6620 | |
6621 | /* | |
6622 | Local Variables: | |
6623 | c-file-style: "gnu" | |
6624 | End: | |
6625 | */ |