Commit | Line | Data |
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5e647d08 | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006, 2007, 2008, 2009 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" | |
a0599745 MD |
63 | |
64 | #include "libguile/validate.h" | |
65 | #include "libguile/numbers.h" | |
1be6b49c | 66 | #include "libguile/deprecation.h" |
f4c627b3 | 67 | |
f92e85f7 MV |
68 | #include "libguile/eq.h" |
69 | ||
55f26379 MV |
70 | #include "libguile/discouraged.h" |
71 | ||
8ab3d8a0 KR |
72 | /* values per glibc, if not already defined */ |
73 | #ifndef M_LOG10E | |
74 | #define M_LOG10E 0.43429448190325182765 | |
75 | #endif | |
76 | #ifndef M_PI | |
77 | #define M_PI 3.14159265358979323846 | |
78 | #endif | |
79 | ||
0f2d19dd | 80 | \f |
f4c627b3 | 81 | |
ca46fb90 RB |
82 | /* |
83 | Wonder if this might be faster for some of our code? A switch on | |
84 | the numtag would jump directly to the right case, and the | |
85 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
86 | ||
87 | #define SCM_I_NUMTAG_NOTNUM 0 | |
88 | #define SCM_I_NUMTAG_INUM 1 | |
89 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
90 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
91 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
92 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 93 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 94 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 95 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
96 | : SCM_I_NUMTAG_NOTNUM))) |
97 | */ | |
f92e85f7 | 98 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
99 | |
100 | ||
34d19ef6 | 101 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 102 | |
56e55ac7 | 103 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
104 | * printed or scm_string representation of an inexact number. |
105 | */ | |
0b799eea | 106 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 107 | |
7351e207 MV |
108 | #if defined (SCO) |
109 | #if ! defined (HAVE_ISNAN) | |
110 | #define HAVE_ISNAN | |
111 | static int | |
112 | isnan (double x) | |
113 | { | |
114 | return (IsNANorINF (x) && NaN (x) && ! IsINF (x)) ? 1 : 0; | |
115 | } | |
0f2d19dd | 116 | #endif |
7351e207 MV |
117 | #if ! defined (HAVE_ISINF) |
118 | #define HAVE_ISINF | |
119 | static int | |
120 | isinf (double x) | |
121 | { | |
122 | return (IsNANorINF (x) && IsINF (x)) ? 1 : 0; | |
123 | } | |
0f2d19dd | 124 | |
7351e207 | 125 | #endif |
e6f3ef58 MD |
126 | #endif |
127 | ||
b127c712 | 128 | |
ad79736c AW |
129 | #if !defined (HAVE_ASINH) |
130 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } | |
131 | #endif | |
132 | #if !defined (HAVE_ACOSH) | |
133 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } | |
134 | #endif | |
135 | #if !defined (HAVE_ATANH) | |
136 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } | |
137 | #endif | |
138 | ||
f8a8200b KR |
139 | /* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses |
140 | an explicit check. In some future gmp (don't know what version number), | |
141 | mpz_cmp_d is supposed to do this itself. */ | |
142 | #if 1 | |
b127c712 KR |
143 | #define xmpz_cmp_d(z, d) \ |
144 | (xisinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) | |
145 | #else | |
146 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
147 | #endif | |
148 | ||
a98ce907 KR |
149 | /* For reference, sparc solaris 7 has infinities (IEEE) but doesn't have |
150 | isinf. It does have finite and isnan though, hence the use of those. | |
151 | fpclass would be a possibility on that system too. */ | |
f92e85f7 MV |
152 | static int |
153 | xisinf (double x) | |
154 | { | |
155 | #if defined (HAVE_ISINF) | |
156 | return isinf (x); | |
157 | #elif defined (HAVE_FINITE) && defined (HAVE_ISNAN) | |
158 | return (! (finite (x) || isnan (x))); | |
159 | #else | |
160 | return 0; | |
161 | #endif | |
162 | } | |
163 | ||
164 | static int | |
165 | xisnan (double x) | |
166 | { | |
167 | #if defined (HAVE_ISNAN) | |
168 | return isnan (x); | |
169 | #else | |
170 | return 0; | |
171 | #endif | |
172 | } | |
173 | ||
4b26c03e | 174 | #if defined (GUILE_I) |
bca69a9f | 175 | #if HAVE_COMPLEX_DOUBLE |
8ab3d8a0 KR |
176 | |
177 | /* For an SCM object Z which is a complex number (ie. satisfies | |
178 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
179 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 180 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 181 | |
7a35784c | 182 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
8ab3d8a0 KR |
183 | |
184 | /* Convert a C "complex double" to an SCM value. */ | |
7a35784c | 185 | static inline SCM |
8ab3d8a0 KR |
186 | scm_from_complex_double (complex double z) |
187 | { | |
188 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
189 | } | |
bca69a9f | 190 | |
8ab3d8a0 | 191 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 192 | #endif /* GUILE_I */ |
8ab3d8a0 | 193 | |
0f2d19dd JB |
194 | \f |
195 | ||
713a4259 | 196 | static mpz_t z_negative_one; |
ac0c002c DH |
197 | |
198 | \f | |
199 | ||
189171c5 | 200 | SCM |
ca46fb90 RB |
201 | scm_i_mkbig () |
202 | { | |
203 | /* Return a newly created bignum. */ | |
204 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
205 | mpz_init (SCM_I_BIG_MPZ (z)); | |
206 | return z; | |
207 | } | |
208 | ||
189171c5 | 209 | SCM |
c71b0706 MV |
210 | scm_i_long2big (long x) |
211 | { | |
212 | /* Return a newly created bignum initialized to X. */ | |
213 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
214 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
215 | return z; | |
216 | } | |
217 | ||
189171c5 | 218 | SCM |
c71b0706 MV |
219 | scm_i_ulong2big (unsigned long x) |
220 | { | |
221 | /* Return a newly created bignum initialized to X. */ | |
222 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
223 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); | |
224 | return z; | |
225 | } | |
226 | ||
189171c5 | 227 | SCM |
ca46fb90 RB |
228 | scm_i_clonebig (SCM src_big, int same_sign_p) |
229 | { | |
230 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
231 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
232 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); | |
0aacf84e MD |
233 | if (!same_sign_p) |
234 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
235 | return z; |
236 | } | |
237 | ||
189171c5 | 238 | int |
ca46fb90 RB |
239 | scm_i_bigcmp (SCM x, SCM y) |
240 | { | |
241 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
242 | /* presume we already know x and y are bignums */ | |
243 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
244 | scm_remember_upto_here_2 (x, y); | |
245 | return result; | |
246 | } | |
247 | ||
189171c5 | 248 | SCM |
ca46fb90 RB |
249 | scm_i_dbl2big (double d) |
250 | { | |
251 | /* results are only defined if d is an integer */ | |
252 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
253 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); | |
254 | return z; | |
255 | } | |
256 | ||
f92e85f7 MV |
257 | /* Convert a integer in double representation to a SCM number. */ |
258 | ||
189171c5 | 259 | SCM |
f92e85f7 MV |
260 | scm_i_dbl2num (double u) |
261 | { | |
262 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
263 | powers of 2, so there's no rounding when making "double" values | |
264 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
265 | get rounded on a 64-bit machine, hence the "+1". | |
266 | ||
267 | The use of floor() to force to an integer value ensures we get a | |
268 | "numerically closest" value without depending on how a | |
269 | double->long cast or how mpz_set_d will round. For reference, | |
270 | double->long probably follows the hardware rounding mode, | |
271 | mpz_set_d truncates towards zero. */ | |
272 | ||
273 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
274 | representable as a double? */ | |
275 | ||
276 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
277 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
d956fa6f | 278 | return SCM_I_MAKINUM ((long) u); |
f92e85f7 MV |
279 | else |
280 | return scm_i_dbl2big (u); | |
281 | } | |
282 | ||
089c9a59 KR |
283 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
284 | with R5RS exact->inexact. | |
285 | ||
286 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
287 | (ie. truncate towards zero), then adjust to get the closest double by |
288 | examining the next lower bit and adding 1 (to the absolute value) if | |
289 | necessary. | |
290 | ||
291 | Bignums exactly half way between representable doubles are rounded to the | |
292 | next higher absolute value (ie. away from zero). This seems like an | |
293 | adequate interpretation of R5RS "numerically closest", and it's easier | |
294 | and faster than a full "nearest-even" style. | |
295 | ||
296 | The bit test must be done on the absolute value of the mpz_t, which means | |
297 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
298 | negatives as twos complement. | |
299 | ||
300 | In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up | |
301 | following the hardware rounding mode, but applied to the absolute value | |
302 | of the mpz_t operand. This is not what we want so we put the high | |
303 | DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when, | |
304 | mpz_get_d is supposed to always truncate towards zero. | |
305 | ||
306 | ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3 | |
307 | is a slowdown. It'd be faster to pick out the relevant high bits with | |
308 | mpz_getlimbn if we could be bothered coding that, and if the new | |
309 | truncating gmp doesn't come out. */ | |
089c9a59 KR |
310 | |
311 | double | |
ca46fb90 RB |
312 | scm_i_big2dbl (SCM b) |
313 | { | |
089c9a59 KR |
314 | double result; |
315 | size_t bits; | |
316 | ||
317 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
318 | ||
f8a8200b | 319 | #if 1 |
089c9a59 | 320 | { |
f8a8200b | 321 | /* Current GMP, eg. 4.1.3, force truncation towards zero */ |
089c9a59 KR |
322 | mpz_t tmp; |
323 | if (bits > DBL_MANT_DIG) | |
324 | { | |
325 | size_t shift = bits - DBL_MANT_DIG; | |
326 | mpz_init2 (tmp, DBL_MANT_DIG); | |
327 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
328 | result = ldexp (mpz_get_d (tmp), shift); | |
329 | mpz_clear (tmp); | |
330 | } | |
331 | else | |
332 | { | |
333 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
334 | } | |
335 | } | |
336 | #else | |
f8a8200b | 337 | /* Future GMP */ |
089c9a59 KR |
338 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
339 | #endif | |
340 | ||
341 | if (bits > DBL_MANT_DIG) | |
342 | { | |
343 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
344 | /* test bit number "pos" in absolute value */ | |
345 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
346 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
347 | { | |
348 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
349 | } | |
350 | } | |
351 | ||
ca46fb90 RB |
352 | scm_remember_upto_here_1 (b); |
353 | return result; | |
354 | } | |
355 | ||
189171c5 | 356 | SCM |
ca46fb90 RB |
357 | scm_i_normbig (SCM b) |
358 | { | |
359 | /* convert a big back to a fixnum if it'll fit */ | |
360 | /* presume b is a bignum */ | |
361 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
362 | { | |
363 | long val = mpz_get_si (SCM_I_BIG_MPZ (b)); | |
364 | if (SCM_FIXABLE (val)) | |
d956fa6f | 365 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
366 | } |
367 | return b; | |
368 | } | |
f872b822 | 369 | |
f92e85f7 MV |
370 | static SCM_C_INLINE_KEYWORD SCM |
371 | scm_i_mpz2num (mpz_t b) | |
372 | { | |
373 | /* convert a mpz number to a SCM number. */ | |
374 | if (mpz_fits_slong_p (b)) | |
375 | { | |
376 | long val = mpz_get_si (b); | |
377 | if (SCM_FIXABLE (val)) | |
d956fa6f | 378 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
379 | } |
380 | ||
381 | { | |
382 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
383 | mpz_init_set (SCM_I_BIG_MPZ (z), b); | |
384 | return z; | |
385 | } | |
386 | } | |
387 | ||
388 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
389 | static SCM scm_divide2real (SCM x, SCM y); | |
390 | ||
cba42c93 MV |
391 | static SCM |
392 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 393 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 394 | { |
c60e130c MV |
395 | /* First make sure the arguments are proper. |
396 | */ | |
e11e83f3 | 397 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 398 | { |
bc36d050 | 399 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 400 | scm_num_overflow ("make-ratio"); |
bc36d050 | 401 | if (scm_is_eq (denominator, SCM_I_MAKINUM(1))) |
f92e85f7 MV |
402 | return numerator; |
403 | } | |
404 | else | |
405 | { | |
406 | if (!(SCM_BIGP(denominator))) | |
407 | SCM_WRONG_TYPE_ARG (2, denominator); | |
408 | } | |
e11e83f3 | 409 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
410 | SCM_WRONG_TYPE_ARG (1, numerator); |
411 | ||
412 | /* Then flip signs so that the denominator is positive. | |
413 | */ | |
73e4de09 | 414 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
415 | { |
416 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
417 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
418 | } | |
419 | ||
420 | /* Now consider for each of the four fixnum/bignum combinations | |
421 | whether the rational number is really an integer. | |
422 | */ | |
e11e83f3 | 423 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 424 | { |
e11e83f3 | 425 | long x = SCM_I_INUM (numerator); |
bc36d050 | 426 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 427 | return SCM_INUM0; |
e11e83f3 | 428 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 429 | { |
dd5130ca | 430 | long y; |
e11e83f3 | 431 | y = SCM_I_INUM (denominator); |
f92e85f7 | 432 | if (x == y) |
d956fa6f | 433 | return SCM_I_MAKINUM(1); |
f92e85f7 | 434 | if ((x % y) == 0) |
d956fa6f | 435 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 436 | } |
dd5130ca KR |
437 | else |
438 | { | |
439 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
440 | of that value for the denominator, as a bignum. Apart from |
441 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
442 | integer. */ | |
443 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
444 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
445 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 446 | return SCM_I_MAKINUM(-1); |
dd5130ca | 447 | } |
f92e85f7 | 448 | } |
c60e130c | 449 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 450 | { |
e11e83f3 | 451 | if (SCM_I_INUMP (denominator)) |
c60e130c | 452 | { |
e11e83f3 | 453 | long yy = SCM_I_INUM (denominator); |
c60e130c MV |
454 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
455 | return scm_divide (numerator, denominator); | |
456 | } | |
457 | else | |
f92e85f7 | 458 | { |
bc36d050 | 459 | if (scm_is_eq (numerator, denominator)) |
d956fa6f | 460 | return SCM_I_MAKINUM(1); |
c60e130c MV |
461 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
462 | SCM_I_BIG_MPZ (denominator))) | |
463 | return scm_divide(numerator, denominator); | |
f92e85f7 | 464 | } |
f92e85f7 | 465 | } |
c60e130c MV |
466 | |
467 | /* No, it's a proper fraction. | |
468 | */ | |
e2bf3b19 HWN |
469 | { |
470 | SCM divisor = scm_gcd (numerator, denominator); | |
471 | if (!(scm_is_eq (divisor, SCM_I_MAKINUM(1)))) | |
472 | { | |
473 | numerator = scm_divide (numerator, divisor); | |
474 | denominator = scm_divide (denominator, divisor); | |
475 | } | |
476 | ||
477 | return scm_double_cell (scm_tc16_fraction, | |
478 | SCM_UNPACK (numerator), | |
479 | SCM_UNPACK (denominator), 0); | |
480 | } | |
f92e85f7 | 481 | } |
c60e130c | 482 | #undef FUNC_NAME |
f92e85f7 | 483 | |
f92e85f7 MV |
484 | double |
485 | scm_i_fraction2double (SCM z) | |
486 | { | |
55f26379 MV |
487 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
488 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
489 | } |
490 | ||
a1ec6916 | 491 | SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0, |
1bbd0b84 | 492 | (SCM x), |
942e5b91 MG |
493 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
494 | "otherwise.") | |
1bbd0b84 | 495 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 496 | { |
e11e83f3 | 497 | if (SCM_I_INUMP (x)) |
0aacf84e MD |
498 | return SCM_BOOL_T; |
499 | if (SCM_BIGP (x)) | |
500 | return SCM_BOOL_T; | |
f92e85f7 MV |
501 | if (SCM_FRACTIONP (x)) |
502 | return SCM_BOOL_T; | |
eb927cb9 MV |
503 | if (SCM_NUMBERP (x)) |
504 | return SCM_BOOL_F; | |
505 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 506 | } |
1bbd0b84 | 507 | #undef FUNC_NAME |
0f2d19dd | 508 | |
4219f20d | 509 | |
a1ec6916 | 510 | SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 511 | (SCM n), |
942e5b91 MG |
512 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
513 | "otherwise.") | |
1bbd0b84 | 514 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 515 | { |
e11e83f3 | 516 | if (SCM_I_INUMP (n)) |
0aacf84e | 517 | { |
e11e83f3 | 518 | long val = SCM_I_INUM (n); |
73e4de09 | 519 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
520 | } |
521 | else if (SCM_BIGP (n)) | |
522 | { | |
523 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
524 | scm_remember_upto_here_1 (n); | |
73e4de09 | 525 | return scm_from_bool (odd_p); |
0aacf84e | 526 | } |
73e4de09 | 527 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 528 | return SCM_BOOL_T; |
f92e85f7 MV |
529 | else if (SCM_REALP (n)) |
530 | { | |
531 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
532 | if (rem == 1.0) | |
533 | return SCM_BOOL_T; | |
534 | else if (rem == 0.0) | |
535 | return SCM_BOOL_F; | |
536 | else | |
537 | SCM_WRONG_TYPE_ARG (1, n); | |
538 | } | |
0aacf84e | 539 | else |
a1a33b0f | 540 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 541 | } |
1bbd0b84 | 542 | #undef FUNC_NAME |
0f2d19dd | 543 | |
4219f20d | 544 | |
a1ec6916 | 545 | SCM_DEFINE (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 546 | (SCM n), |
942e5b91 MG |
547 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
548 | "otherwise.") | |
1bbd0b84 | 549 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 550 | { |
e11e83f3 | 551 | if (SCM_I_INUMP (n)) |
0aacf84e | 552 | { |
e11e83f3 | 553 | long val = SCM_I_INUM (n); |
73e4de09 | 554 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
555 | } |
556 | else if (SCM_BIGP (n)) | |
557 | { | |
558 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
559 | scm_remember_upto_here_1 (n); | |
73e4de09 | 560 | return scm_from_bool (even_p); |
0aacf84e | 561 | } |
73e4de09 | 562 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 563 | return SCM_BOOL_T; |
f92e85f7 MV |
564 | else if (SCM_REALP (n)) |
565 | { | |
566 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
567 | if (rem == 1.0) | |
568 | return SCM_BOOL_F; | |
569 | else if (rem == 0.0) | |
570 | return SCM_BOOL_T; | |
571 | else | |
572 | SCM_WRONG_TYPE_ARG (1, n); | |
573 | } | |
0aacf84e | 574 | else |
a1a33b0f | 575 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 576 | } |
1bbd0b84 | 577 | #undef FUNC_NAME |
0f2d19dd | 578 | |
7351e207 | 579 | SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0, |
b1092b3a MV |
580 | (SCM x), |
581 | "Return @code{#t} if @var{x} is either @samp{+inf.0}\n" | |
582 | "or @samp{-inf.0}, @code{#f} otherwise.") | |
7351e207 MV |
583 | #define FUNC_NAME s_scm_inf_p |
584 | { | |
b1092b3a MV |
585 | if (SCM_REALP (x)) |
586 | return scm_from_bool (xisinf (SCM_REAL_VALUE (x))); | |
587 | else if (SCM_COMPLEXP (x)) | |
588 | return scm_from_bool (xisinf (SCM_COMPLEX_REAL (x)) | |
589 | || xisinf (SCM_COMPLEX_IMAG (x))); | |
0aacf84e | 590 | else |
7351e207 | 591 | return SCM_BOOL_F; |
7351e207 MV |
592 | } |
593 | #undef FUNC_NAME | |
594 | ||
595 | SCM_DEFINE (scm_nan_p, "nan?", 1, 0, 0, | |
596 | (SCM n), | |
597 | "Return @code{#t} if @var{n} is a NaN, @code{#f}\n" | |
598 | "otherwise.") | |
599 | #define FUNC_NAME s_scm_nan_p | |
600 | { | |
0aacf84e | 601 | if (SCM_REALP (n)) |
73e4de09 | 602 | return scm_from_bool (xisnan (SCM_REAL_VALUE (n))); |
0aacf84e | 603 | else if (SCM_COMPLEXP (n)) |
73e4de09 | 604 | return scm_from_bool (xisnan (SCM_COMPLEX_REAL (n)) |
7351e207 | 605 | || xisnan (SCM_COMPLEX_IMAG (n))); |
0aacf84e | 606 | else |
7351e207 | 607 | return SCM_BOOL_F; |
7351e207 MV |
608 | } |
609 | #undef FUNC_NAME | |
610 | ||
611 | /* Guile's idea of infinity. */ | |
612 | static double guile_Inf; | |
613 | ||
614 | /* Guile's idea of not a number. */ | |
615 | static double guile_NaN; | |
616 | ||
617 | static void | |
618 | guile_ieee_init (void) | |
619 | { | |
620 | #if defined (HAVE_ISINF) || defined (HAVE_FINITE) | |
621 | ||
622 | /* Some version of gcc on some old version of Linux used to crash when | |
623 | trying to make Inf and NaN. */ | |
624 | ||
240a27d2 KR |
625 | #ifdef INFINITY |
626 | /* C99 INFINITY, when available. | |
627 | FIXME: The standard allows for INFINITY to be something that overflows | |
628 | at compile time. We ought to have a configure test to check for that | |
629 | before trying to use it. (But in practice we believe this is not a | |
630 | problem on any system guile is likely to target.) */ | |
631 | guile_Inf = INFINITY; | |
56a3dcd4 | 632 | #elif defined HAVE_DINFINITY |
240a27d2 | 633 | /* OSF */ |
7351e207 | 634 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 635 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
636 | #else |
637 | double tmp = 1e+10; | |
638 | guile_Inf = tmp; | |
639 | for (;;) | |
640 | { | |
641 | guile_Inf *= 1e+10; | |
642 | if (guile_Inf == tmp) | |
643 | break; | |
644 | tmp = guile_Inf; | |
645 | } | |
646 | #endif | |
647 | ||
648 | #endif | |
649 | ||
650 | #if defined (HAVE_ISNAN) | |
651 | ||
240a27d2 KR |
652 | #ifdef NAN |
653 | /* C99 NAN, when available */ | |
654 | guile_NaN = NAN; | |
56a3dcd4 | 655 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
656 | { |
657 | /* OSF */ | |
658 | extern unsigned int DQNAN[2]; | |
659 | guile_NaN = (*((double *)(DQNAN))); | |
660 | } | |
7351e207 MV |
661 | #else |
662 | guile_NaN = guile_Inf / guile_Inf; | |
663 | #endif | |
664 | ||
665 | #endif | |
666 | } | |
667 | ||
668 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
669 | (void), | |
670 | "Return Inf.") | |
671 | #define FUNC_NAME s_scm_inf | |
672 | { | |
673 | static int initialized = 0; | |
674 | if (! initialized) | |
675 | { | |
676 | guile_ieee_init (); | |
677 | initialized = 1; | |
678 | } | |
55f26379 | 679 | return scm_from_double (guile_Inf); |
7351e207 MV |
680 | } |
681 | #undef FUNC_NAME | |
682 | ||
683 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
684 | (void), | |
685 | "Return NaN.") | |
686 | #define FUNC_NAME s_scm_nan | |
687 | { | |
688 | static int initialized = 0; | |
0aacf84e | 689 | if (!initialized) |
7351e207 MV |
690 | { |
691 | guile_ieee_init (); | |
692 | initialized = 1; | |
693 | } | |
55f26379 | 694 | return scm_from_double (guile_NaN); |
7351e207 MV |
695 | } |
696 | #undef FUNC_NAME | |
697 | ||
4219f20d | 698 | |
a48d60b1 MD |
699 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
700 | (SCM x), | |
701 | "Return the absolute value of @var{x}.") | |
702 | #define FUNC_NAME | |
0f2d19dd | 703 | { |
e11e83f3 | 704 | if (SCM_I_INUMP (x)) |
0aacf84e | 705 | { |
e11e83f3 | 706 | long int xx = SCM_I_INUM (x); |
0aacf84e MD |
707 | if (xx >= 0) |
708 | return x; | |
709 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 710 | return SCM_I_MAKINUM (-xx); |
0aacf84e MD |
711 | else |
712 | return scm_i_long2big (-xx); | |
4219f20d | 713 | } |
0aacf84e MD |
714 | else if (SCM_BIGP (x)) |
715 | { | |
716 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
717 | if (sgn < 0) | |
718 | return scm_i_clonebig (x, 0); | |
719 | else | |
720 | return x; | |
4219f20d | 721 | } |
0aacf84e | 722 | else if (SCM_REALP (x)) |
ae38324d KR |
723 | { |
724 | /* note that if x is a NaN then xx<0 is false so we return x unchanged */ | |
725 | double xx = SCM_REAL_VALUE (x); | |
726 | if (xx < 0.0) | |
55f26379 | 727 | return scm_from_double (-xx); |
ae38324d KR |
728 | else |
729 | return x; | |
730 | } | |
f92e85f7 MV |
731 | else if (SCM_FRACTIONP (x)) |
732 | { | |
73e4de09 | 733 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 734 | return x; |
cba42c93 | 735 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
736 | SCM_FRACTION_DENOMINATOR (x)); |
737 | } | |
0aacf84e | 738 | else |
a48d60b1 | 739 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 740 | } |
a48d60b1 | 741 | #undef FUNC_NAME |
0f2d19dd | 742 | |
4219f20d | 743 | |
9de33deb | 744 | SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); |
942e5b91 MG |
745 | /* "Return the quotient of the numbers @var{x} and @var{y}." |
746 | */ | |
0f2d19dd | 747 | SCM |
6e8d25a6 | 748 | scm_quotient (SCM x, SCM y) |
0f2d19dd | 749 | { |
e11e83f3 | 750 | if (SCM_I_INUMP (x)) |
0aacf84e | 751 | { |
e11e83f3 MV |
752 | long xx = SCM_I_INUM (x); |
753 | if (SCM_I_INUMP (y)) | |
0aacf84e | 754 | { |
e11e83f3 | 755 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
756 | if (yy == 0) |
757 | scm_num_overflow (s_quotient); | |
758 | else | |
759 | { | |
760 | long z = xx / yy; | |
761 | if (SCM_FIXABLE (z)) | |
d956fa6f | 762 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
763 | else |
764 | return scm_i_long2big (z); | |
765 | } | |
828865c3 | 766 | } |
0aacf84e | 767 | else if (SCM_BIGP (y)) |
ac0c002c | 768 | { |
e11e83f3 | 769 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
770 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
771 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
772 | { | |
773 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
774 | scm_remember_upto_here_1 (y); | |
d956fa6f | 775 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 776 | } |
0aacf84e | 777 | else |
d956fa6f | 778 | return SCM_I_MAKINUM (0); |
ac0c002c DH |
779 | } |
780 | else | |
0aacf84e | 781 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); |
828865c3 | 782 | } |
0aacf84e MD |
783 | else if (SCM_BIGP (x)) |
784 | { | |
e11e83f3 | 785 | if (SCM_I_INUMP (y)) |
0aacf84e | 786 | { |
e11e83f3 | 787 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
788 | if (yy == 0) |
789 | scm_num_overflow (s_quotient); | |
790 | else if (yy == 1) | |
791 | return x; | |
792 | else | |
793 | { | |
794 | SCM result = scm_i_mkbig (); | |
795 | if (yy < 0) | |
796 | { | |
797 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
798 | SCM_I_BIG_MPZ (x), | |
799 | - yy); | |
800 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
801 | } | |
802 | else | |
803 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
804 | scm_remember_upto_here_1 (x); | |
805 | return scm_i_normbig (result); | |
806 | } | |
807 | } | |
808 | else if (SCM_BIGP (y)) | |
809 | { | |
810 | SCM result = scm_i_mkbig (); | |
811 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
812 | SCM_I_BIG_MPZ (x), | |
813 | SCM_I_BIG_MPZ (y)); | |
814 | scm_remember_upto_here_2 (x, y); | |
815 | return scm_i_normbig (result); | |
816 | } | |
817 | else | |
818 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); | |
f872b822 | 819 | } |
0aacf84e | 820 | else |
89a7e495 | 821 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient); |
0f2d19dd JB |
822 | } |
823 | ||
9de33deb | 824 | SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); |
942e5b91 MG |
825 | /* "Return the remainder of the numbers @var{x} and @var{y}.\n" |
826 | * "@lisp\n" | |
827 | * "(remainder 13 4) @result{} 1\n" | |
828 | * "(remainder -13 4) @result{} -1\n" | |
829 | * "@end lisp" | |
830 | */ | |
0f2d19dd | 831 | SCM |
6e8d25a6 | 832 | scm_remainder (SCM x, SCM y) |
0f2d19dd | 833 | { |
e11e83f3 | 834 | if (SCM_I_INUMP (x)) |
0aacf84e | 835 | { |
e11e83f3 | 836 | if (SCM_I_INUMP (y)) |
0aacf84e | 837 | { |
e11e83f3 | 838 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
839 | if (yy == 0) |
840 | scm_num_overflow (s_remainder); | |
841 | else | |
842 | { | |
e11e83f3 | 843 | long z = SCM_I_INUM (x) % yy; |
d956fa6f | 844 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
845 | } |
846 | } | |
847 | else if (SCM_BIGP (y)) | |
ac0c002c | 848 | { |
e11e83f3 | 849 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
850 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
851 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
852 | { | |
853 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
854 | scm_remember_upto_here_1 (y); | |
d956fa6f | 855 | return SCM_I_MAKINUM (0); |
4dc09ee4 | 856 | } |
0aacf84e MD |
857 | else |
858 | return x; | |
ac0c002c DH |
859 | } |
860 | else | |
0aacf84e | 861 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); |
89a7e495 | 862 | } |
0aacf84e MD |
863 | else if (SCM_BIGP (x)) |
864 | { | |
e11e83f3 | 865 | if (SCM_I_INUMP (y)) |
0aacf84e | 866 | { |
e11e83f3 | 867 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
868 | if (yy == 0) |
869 | scm_num_overflow (s_remainder); | |
870 | else | |
871 | { | |
872 | SCM result = scm_i_mkbig (); | |
873 | if (yy < 0) | |
874 | yy = - yy; | |
875 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
876 | scm_remember_upto_here_1 (x); | |
877 | return scm_i_normbig (result); | |
878 | } | |
879 | } | |
880 | else if (SCM_BIGP (y)) | |
881 | { | |
882 | SCM result = scm_i_mkbig (); | |
883 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
884 | SCM_I_BIG_MPZ (x), | |
885 | SCM_I_BIG_MPZ (y)); | |
886 | scm_remember_upto_here_2 (x, y); | |
887 | return scm_i_normbig (result); | |
888 | } | |
889 | else | |
890 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); | |
f872b822 | 891 | } |
0aacf84e | 892 | else |
89a7e495 | 893 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder); |
0f2d19dd JB |
894 | } |
895 | ||
89a7e495 | 896 | |
9de33deb | 897 | SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); |
942e5b91 MG |
898 | /* "Return the modulo of the numbers @var{x} and @var{y}.\n" |
899 | * "@lisp\n" | |
900 | * "(modulo 13 4) @result{} 1\n" | |
901 | * "(modulo -13 4) @result{} 3\n" | |
902 | * "@end lisp" | |
903 | */ | |
0f2d19dd | 904 | SCM |
6e8d25a6 | 905 | scm_modulo (SCM x, SCM y) |
0f2d19dd | 906 | { |
e11e83f3 | 907 | if (SCM_I_INUMP (x)) |
0aacf84e | 908 | { |
e11e83f3 MV |
909 | long xx = SCM_I_INUM (x); |
910 | if (SCM_I_INUMP (y)) | |
0aacf84e | 911 | { |
e11e83f3 | 912 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
913 | if (yy == 0) |
914 | scm_num_overflow (s_modulo); | |
915 | else | |
916 | { | |
66b1c775 KR |
917 | /* C99 specifies that "%" is the remainder corresponding to a |
918 | quotient rounded towards zero, and that's also traditional | |
919 | for machine division, so z here should be well defined. */ | |
0aacf84e MD |
920 | long z = xx % yy; |
921 | long result; | |
922 | ||
923 | if (yy < 0) | |
924 | { | |
925 | if (z > 0) | |
926 | result = z + yy; | |
927 | else | |
928 | result = z; | |
929 | } | |
930 | else | |
931 | { | |
932 | if (z < 0) | |
933 | result = z + yy; | |
934 | else | |
935 | result = z; | |
936 | } | |
d956fa6f | 937 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
938 | } |
939 | } | |
940 | else if (SCM_BIGP (y)) | |
941 | { | |
942 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
943 | { |
944 | mpz_t z_x; | |
945 | SCM result; | |
946 | ||
947 | if (sgn_y < 0) | |
948 | { | |
949 | SCM pos_y = scm_i_clonebig (y, 0); | |
950 | /* do this after the last scm_op */ | |
951 | mpz_init_set_si (z_x, xx); | |
952 | result = pos_y; /* re-use this bignum */ | |
953 | mpz_mod (SCM_I_BIG_MPZ (result), | |
954 | z_x, | |
955 | SCM_I_BIG_MPZ (pos_y)); | |
956 | scm_remember_upto_here_1 (pos_y); | |
957 | } | |
958 | else | |
959 | { | |
960 | result = scm_i_mkbig (); | |
961 | /* do this after the last scm_op */ | |
962 | mpz_init_set_si (z_x, xx); | |
963 | mpz_mod (SCM_I_BIG_MPZ (result), | |
964 | z_x, | |
965 | SCM_I_BIG_MPZ (y)); | |
966 | scm_remember_upto_here_1 (y); | |
967 | } | |
ca46fb90 | 968 | |
0aacf84e MD |
969 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
970 | mpz_add (SCM_I_BIG_MPZ (result), | |
971 | SCM_I_BIG_MPZ (y), | |
972 | SCM_I_BIG_MPZ (result)); | |
973 | scm_remember_upto_here_1 (y); | |
974 | /* and do this before the next one */ | |
975 | mpz_clear (z_x); | |
976 | return scm_i_normbig (result); | |
977 | } | |
978 | } | |
979 | else | |
980 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
f872b822 | 981 | } |
0aacf84e MD |
982 | else if (SCM_BIGP (x)) |
983 | { | |
e11e83f3 | 984 | if (SCM_I_INUMP (y)) |
0aacf84e | 985 | { |
e11e83f3 | 986 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
987 | if (yy == 0) |
988 | scm_num_overflow (s_modulo); | |
989 | else | |
990 | { | |
991 | SCM result = scm_i_mkbig (); | |
992 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
993 | SCM_I_BIG_MPZ (x), | |
994 | (yy < 0) ? - yy : yy); | |
995 | scm_remember_upto_here_1 (x); | |
996 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
997 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
998 | SCM_I_BIG_MPZ (result), | |
999 | - yy); | |
1000 | return scm_i_normbig (result); | |
1001 | } | |
1002 | } | |
1003 | else if (SCM_BIGP (y)) | |
1004 | { | |
0aacf84e MD |
1005 | { |
1006 | SCM result = scm_i_mkbig (); | |
1007 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1008 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
1009 | mpz_mod (SCM_I_BIG_MPZ (result), | |
1010 | SCM_I_BIG_MPZ (x), | |
1011 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 1012 | |
0aacf84e MD |
1013 | scm_remember_upto_here_1 (x); |
1014 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1015 | mpz_add (SCM_I_BIG_MPZ (result), | |
1016 | SCM_I_BIG_MPZ (y), | |
1017 | SCM_I_BIG_MPZ (result)); | |
1018 | scm_remember_upto_here_2 (y, pos_y); | |
1019 | return scm_i_normbig (result); | |
1020 | } | |
1021 | } | |
1022 | else | |
1023 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
828865c3 | 1024 | } |
0aacf84e | 1025 | else |
09fb7599 | 1026 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); |
0f2d19dd JB |
1027 | } |
1028 | ||
78d3deb1 AW |
1029 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
1030 | (SCM x, SCM y, SCM rest), | |
1031 | "Return the greatest common divisor of all parameter values.\n" | |
1032 | "If called without arguments, 0 is returned.") | |
1033 | #define FUNC_NAME s_scm_i_gcd | |
1034 | { | |
1035 | while (!scm_is_null (rest)) | |
1036 | { x = scm_gcd (x, y); | |
1037 | y = scm_car (rest); | |
1038 | rest = scm_cdr (rest); | |
1039 | } | |
1040 | return scm_gcd (x, y); | |
1041 | } | |
1042 | #undef FUNC_NAME | |
1043 | ||
1044 | #define s_gcd s_scm_i_gcd | |
1045 | #define g_gcd g_scm_i_gcd | |
1046 | ||
0f2d19dd | 1047 | SCM |
6e8d25a6 | 1048 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 1049 | { |
ca46fb90 | 1050 | if (SCM_UNBNDP (y)) |
1dd79792 | 1051 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 1052 | |
e11e83f3 | 1053 | if (SCM_I_INUMP (x)) |
ca46fb90 | 1054 | { |
e11e83f3 | 1055 | if (SCM_I_INUMP (y)) |
ca46fb90 | 1056 | { |
e11e83f3 MV |
1057 | long xx = SCM_I_INUM (x); |
1058 | long yy = SCM_I_INUM (y); | |
ca46fb90 RB |
1059 | long u = xx < 0 ? -xx : xx; |
1060 | long v = yy < 0 ? -yy : yy; | |
1061 | long result; | |
0aacf84e MD |
1062 | if (xx == 0) |
1063 | result = v; | |
1064 | else if (yy == 0) | |
1065 | result = u; | |
1066 | else | |
1067 | { | |
1068 | long k = 1; | |
1069 | long t; | |
1070 | /* Determine a common factor 2^k */ | |
1071 | while (!(1 & (u | v))) | |
1072 | { | |
1073 | k <<= 1; | |
1074 | u >>= 1; | |
1075 | v >>= 1; | |
1076 | } | |
1077 | /* Now, any factor 2^n can be eliminated */ | |
1078 | if (u & 1) | |
1079 | t = -v; | |
1080 | else | |
1081 | { | |
1082 | t = u; | |
1083 | b3: | |
1084 | t = SCM_SRS (t, 1); | |
1085 | } | |
1086 | if (!(1 & t)) | |
1087 | goto b3; | |
1088 | if (t > 0) | |
1089 | u = t; | |
1090 | else | |
1091 | v = -t; | |
1092 | t = u - v; | |
1093 | if (t != 0) | |
1094 | goto b3; | |
1095 | result = u * k; | |
1096 | } | |
1097 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 1098 | ? SCM_I_MAKINUM (result) |
0aacf84e | 1099 | : scm_i_long2big (result)); |
ca46fb90 RB |
1100 | } |
1101 | else if (SCM_BIGP (y)) | |
1102 | { | |
0bff4dce KR |
1103 | SCM_SWAP (x, y); |
1104 | goto big_inum; | |
ca46fb90 RB |
1105 | } |
1106 | else | |
1107 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 1108 | } |
ca46fb90 RB |
1109 | else if (SCM_BIGP (x)) |
1110 | { | |
e11e83f3 | 1111 | if (SCM_I_INUMP (y)) |
ca46fb90 RB |
1112 | { |
1113 | unsigned long result; | |
0bff4dce KR |
1114 | long yy; |
1115 | big_inum: | |
e11e83f3 | 1116 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
1117 | if (yy == 0) |
1118 | return scm_abs (x); | |
0aacf84e MD |
1119 | if (yy < 0) |
1120 | yy = -yy; | |
ca46fb90 RB |
1121 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
1122 | scm_remember_upto_here_1 (x); | |
0aacf84e | 1123 | return (SCM_POSFIXABLE (result) |
d956fa6f | 1124 | ? SCM_I_MAKINUM (result) |
c71b0706 | 1125 | : scm_from_ulong (result)); |
ca46fb90 RB |
1126 | } |
1127 | else if (SCM_BIGP (y)) | |
1128 | { | |
1129 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
1130 | mpz_gcd (SCM_I_BIG_MPZ (result), |
1131 | SCM_I_BIG_MPZ (x), | |
1132 | SCM_I_BIG_MPZ (y)); | |
1133 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
1134 | return scm_i_normbig (result); |
1135 | } | |
1136 | else | |
1137 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 1138 | } |
ca46fb90 | 1139 | else |
09fb7599 | 1140 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
1141 | } |
1142 | ||
78d3deb1 AW |
1143 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
1144 | (SCM x, SCM y, SCM rest), | |
1145 | "Return the least common multiple of the arguments.\n" | |
1146 | "If called without arguments, 1 is returned.") | |
1147 | #define FUNC_NAME s_scm_i_lcm | |
1148 | { | |
1149 | while (!scm_is_null (rest)) | |
1150 | { x = scm_lcm (x, y); | |
1151 | y = scm_car (rest); | |
1152 | rest = scm_cdr (rest); | |
1153 | } | |
1154 | return scm_lcm (x, y); | |
1155 | } | |
1156 | #undef FUNC_NAME | |
1157 | ||
1158 | #define s_lcm s_scm_i_lcm | |
1159 | #define g_lcm g_scm_i_lcm | |
1160 | ||
0f2d19dd | 1161 | SCM |
6e8d25a6 | 1162 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 1163 | { |
ca46fb90 RB |
1164 | if (SCM_UNBNDP (n2)) |
1165 | { | |
1166 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
1167 | return SCM_I_MAKINUM (1L); |
1168 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 1169 | } |
09fb7599 | 1170 | |
e11e83f3 | 1171 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 1172 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 1173 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 1174 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 1175 | |
e11e83f3 | 1176 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 1177 | { |
e11e83f3 | 1178 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1179 | { |
1180 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 1181 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
1182 | return d; |
1183 | else | |
1184 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
1185 | } | |
1186 | else | |
1187 | { | |
1188 | /* inum n1, big n2 */ | |
1189 | inumbig: | |
1190 | { | |
1191 | SCM result = scm_i_mkbig (); | |
e11e83f3 | 1192 | long nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
1193 | if (nn1 == 0) return SCM_INUM0; |
1194 | if (nn1 < 0) nn1 = - nn1; | |
1195 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
1196 | scm_remember_upto_here_1 (n2); | |
1197 | return result; | |
1198 | } | |
1199 | } | |
1200 | } | |
1201 | else | |
1202 | { | |
1203 | /* big n1 */ | |
e11e83f3 | 1204 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1205 | { |
1206 | SCM_SWAP (n1, n2); | |
1207 | goto inumbig; | |
1208 | } | |
1209 | else | |
1210 | { | |
1211 | SCM result = scm_i_mkbig (); | |
1212 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
1213 | SCM_I_BIG_MPZ (n1), | |
1214 | SCM_I_BIG_MPZ (n2)); | |
1215 | scm_remember_upto_here_2(n1, n2); | |
1216 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
1217 | return result; | |
1218 | } | |
f872b822 | 1219 | } |
0f2d19dd JB |
1220 | } |
1221 | ||
8a525303 GB |
1222 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
1223 | ||
1224 | Logand: | |
1225 | X Y Result Method: | |
1226 | (len) | |
1227 | + + + x (map digit:logand X Y) | |
1228 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
1229 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
1230 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
1231 | ||
1232 | Logior: | |
1233 | X Y Result Method: | |
1234 | ||
1235 | + + + (map digit:logior X Y) | |
1236 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
1237 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
1238 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
1239 | ||
1240 | Logxor: | |
1241 | X Y Result Method: | |
1242 | ||
1243 | + + + (map digit:logxor X Y) | |
1244 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
1245 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
1246 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
1247 | ||
1248 | Logtest: | |
1249 | X Y Result | |
1250 | ||
1251 | + + (any digit:logand X Y) | |
1252 | + - (any digit:logand X (lognot (+ -1 Y))) | |
1253 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
1254 | - - #t | |
1255 | ||
1256 | */ | |
1257 | ||
78d3deb1 AW |
1258 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
1259 | (SCM x, SCM y, SCM rest), | |
1260 | "Return the bitwise AND of the integer arguments.\n\n" | |
1261 | "@lisp\n" | |
1262 | "(logand) @result{} -1\n" | |
1263 | "(logand 7) @result{} 7\n" | |
1264 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
1265 | "@end lisp") | |
1266 | #define FUNC_NAME s_scm_i_logand | |
1267 | { | |
1268 | while (!scm_is_null (rest)) | |
1269 | { x = scm_logand (x, y); | |
1270 | y = scm_car (rest); | |
1271 | rest = scm_cdr (rest); | |
1272 | } | |
1273 | return scm_logand (x, y); | |
1274 | } | |
1275 | #undef FUNC_NAME | |
1276 | ||
1277 | #define s_scm_logand s_scm_i_logand | |
1278 | ||
1279 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 1280 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 1281 | { |
9a00c9fc DH |
1282 | long int nn1; |
1283 | ||
0aacf84e MD |
1284 | if (SCM_UNBNDP (n2)) |
1285 | { | |
1286 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 1287 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
1288 | else if (!SCM_NUMBERP (n1)) |
1289 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1290 | else if (SCM_NUMBERP (n1)) | |
1291 | return n1; | |
1292 | else | |
1293 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1294 | } |
09fb7599 | 1295 | |
e11e83f3 | 1296 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1297 | { |
e11e83f3 MV |
1298 | nn1 = SCM_I_INUM (n1); |
1299 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1300 | { |
e11e83f3 | 1301 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1302 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
1303 | } |
1304 | else if SCM_BIGP (n2) | |
1305 | { | |
1306 | intbig: | |
1307 | if (n1 == 0) | |
1308 | return SCM_INUM0; | |
1309 | { | |
1310 | SCM result_z = scm_i_mkbig (); | |
1311 | mpz_t nn1_z; | |
1312 | mpz_init_set_si (nn1_z, nn1); | |
1313 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1314 | scm_remember_upto_here_1 (n2); | |
1315 | mpz_clear (nn1_z); | |
1316 | return scm_i_normbig (result_z); | |
1317 | } | |
1318 | } | |
1319 | else | |
1320 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1321 | } | |
1322 | else if (SCM_BIGP (n1)) | |
1323 | { | |
e11e83f3 | 1324 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1325 | { |
1326 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1327 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1328 | goto intbig; |
1329 | } | |
1330 | else if (SCM_BIGP (n2)) | |
1331 | { | |
1332 | SCM result_z = scm_i_mkbig (); | |
1333 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
1334 | SCM_I_BIG_MPZ (n1), | |
1335 | SCM_I_BIG_MPZ (n2)); | |
1336 | scm_remember_upto_here_2 (n1, n2); | |
1337 | return scm_i_normbig (result_z); | |
1338 | } | |
1339 | else | |
1340 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1341 | } |
0aacf84e | 1342 | else |
09fb7599 | 1343 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1344 | } |
1bbd0b84 | 1345 | #undef FUNC_NAME |
0f2d19dd | 1346 | |
09fb7599 | 1347 | |
78d3deb1 AW |
1348 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
1349 | (SCM x, SCM y, SCM rest), | |
1350 | "Return the bitwise OR of the integer arguments.\n\n" | |
1351 | "@lisp\n" | |
1352 | "(logior) @result{} 0\n" | |
1353 | "(logior 7) @result{} 7\n" | |
1354 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1355 | "@end lisp") | |
1356 | #define FUNC_NAME s_scm_i_logior | |
1357 | { | |
1358 | while (!scm_is_null (rest)) | |
1359 | { x = scm_logior (x, y); | |
1360 | y = scm_car (rest); | |
1361 | rest = scm_cdr (rest); | |
1362 | } | |
1363 | return scm_logior (x, y); | |
1364 | } | |
1365 | #undef FUNC_NAME | |
1366 | ||
1367 | #define s_scm_logior s_scm_i_logior | |
1368 | ||
1369 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 1370 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 1371 | { |
9a00c9fc DH |
1372 | long int nn1; |
1373 | ||
0aacf84e MD |
1374 | if (SCM_UNBNDP (n2)) |
1375 | { | |
1376 | if (SCM_UNBNDP (n1)) | |
1377 | return SCM_INUM0; | |
1378 | else if (SCM_NUMBERP (n1)) | |
1379 | return n1; | |
1380 | else | |
1381 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1382 | } |
09fb7599 | 1383 | |
e11e83f3 | 1384 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1385 | { |
e11e83f3 MV |
1386 | nn1 = SCM_I_INUM (n1); |
1387 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1388 | { |
e11e83f3 | 1389 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1390 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
1391 | } |
1392 | else if (SCM_BIGP (n2)) | |
1393 | { | |
1394 | intbig: | |
1395 | if (nn1 == 0) | |
1396 | return n2; | |
1397 | { | |
1398 | SCM result_z = scm_i_mkbig (); | |
1399 | mpz_t nn1_z; | |
1400 | mpz_init_set_si (nn1_z, nn1); | |
1401 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1402 | scm_remember_upto_here_1 (n2); | |
1403 | mpz_clear (nn1_z); | |
9806de0d | 1404 | return scm_i_normbig (result_z); |
0aacf84e MD |
1405 | } |
1406 | } | |
1407 | else | |
1408 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1409 | } | |
1410 | else if (SCM_BIGP (n1)) | |
1411 | { | |
e11e83f3 | 1412 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1413 | { |
1414 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1415 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1416 | goto intbig; |
1417 | } | |
1418 | else if (SCM_BIGP (n2)) | |
1419 | { | |
1420 | SCM result_z = scm_i_mkbig (); | |
1421 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
1422 | SCM_I_BIG_MPZ (n1), | |
1423 | SCM_I_BIG_MPZ (n2)); | |
1424 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 1425 | return scm_i_normbig (result_z); |
0aacf84e MD |
1426 | } |
1427 | else | |
1428 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1429 | } |
0aacf84e | 1430 | else |
09fb7599 | 1431 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1432 | } |
1bbd0b84 | 1433 | #undef FUNC_NAME |
0f2d19dd | 1434 | |
09fb7599 | 1435 | |
78d3deb1 AW |
1436 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
1437 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
1438 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1439 | "set in the result if it is set in an odd number of arguments.\n" | |
1440 | "@lisp\n" | |
1441 | "(logxor) @result{} 0\n" | |
1442 | "(logxor 7) @result{} 7\n" | |
1443 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1444 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1445 | "@end lisp") |
78d3deb1 AW |
1446 | #define FUNC_NAME s_scm_i_logxor |
1447 | { | |
1448 | while (!scm_is_null (rest)) | |
1449 | { x = scm_logxor (x, y); | |
1450 | y = scm_car (rest); | |
1451 | rest = scm_cdr (rest); | |
1452 | } | |
1453 | return scm_logxor (x, y); | |
1454 | } | |
1455 | #undef FUNC_NAME | |
1456 | ||
1457 | #define s_scm_logxor s_scm_i_logxor | |
1458 | ||
1459 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 1460 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1461 | { |
9a00c9fc DH |
1462 | long int nn1; |
1463 | ||
0aacf84e MD |
1464 | if (SCM_UNBNDP (n2)) |
1465 | { | |
1466 | if (SCM_UNBNDP (n1)) | |
1467 | return SCM_INUM0; | |
1468 | else if (SCM_NUMBERP (n1)) | |
1469 | return n1; | |
1470 | else | |
1471 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1472 | } |
09fb7599 | 1473 | |
e11e83f3 | 1474 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1475 | { |
e11e83f3 MV |
1476 | nn1 = SCM_I_INUM (n1); |
1477 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1478 | { |
e11e83f3 | 1479 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1480 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
1481 | } |
1482 | else if (SCM_BIGP (n2)) | |
1483 | { | |
1484 | intbig: | |
1485 | { | |
1486 | SCM result_z = scm_i_mkbig (); | |
1487 | mpz_t nn1_z; | |
1488 | mpz_init_set_si (nn1_z, nn1); | |
1489 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1490 | scm_remember_upto_here_1 (n2); | |
1491 | mpz_clear (nn1_z); | |
1492 | return scm_i_normbig (result_z); | |
1493 | } | |
1494 | } | |
1495 | else | |
1496 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1497 | } | |
1498 | else if (SCM_BIGP (n1)) | |
1499 | { | |
e11e83f3 | 1500 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1501 | { |
1502 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1503 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1504 | goto intbig; |
1505 | } | |
1506 | else if (SCM_BIGP (n2)) | |
1507 | { | |
1508 | SCM result_z = scm_i_mkbig (); | |
1509 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
1510 | SCM_I_BIG_MPZ (n1), | |
1511 | SCM_I_BIG_MPZ (n2)); | |
1512 | scm_remember_upto_here_2 (n1, n2); | |
1513 | return scm_i_normbig (result_z); | |
1514 | } | |
1515 | else | |
1516 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1517 | } |
0aacf84e | 1518 | else |
09fb7599 | 1519 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1520 | } |
1bbd0b84 | 1521 | #undef FUNC_NAME |
0f2d19dd | 1522 | |
09fb7599 | 1523 | |
a1ec6916 | 1524 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 1525 | (SCM j, SCM k), |
ba6e7231 KR |
1526 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
1527 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
1528 | "without actually calculating the @code{logand}, just testing\n" | |
1529 | "for non-zero.\n" | |
1530 | "\n" | |
1e6808ea | 1531 | "@lisp\n" |
b380b885 MD |
1532 | "(logtest #b0100 #b1011) @result{} #f\n" |
1533 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1534 | "@end lisp") |
1bbd0b84 | 1535 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1536 | { |
1e6808ea | 1537 | long int nj; |
9a00c9fc | 1538 | |
e11e83f3 | 1539 | if (SCM_I_INUMP (j)) |
0aacf84e | 1540 | { |
e11e83f3 MV |
1541 | nj = SCM_I_INUM (j); |
1542 | if (SCM_I_INUMP (k)) | |
0aacf84e | 1543 | { |
e11e83f3 | 1544 | long nk = SCM_I_INUM (k); |
73e4de09 | 1545 | return scm_from_bool (nj & nk); |
0aacf84e MD |
1546 | } |
1547 | else if (SCM_BIGP (k)) | |
1548 | { | |
1549 | intbig: | |
1550 | if (nj == 0) | |
1551 | return SCM_BOOL_F; | |
1552 | { | |
1553 | SCM result; | |
1554 | mpz_t nj_z; | |
1555 | mpz_init_set_si (nj_z, nj); | |
1556 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
1557 | scm_remember_upto_here_1 (k); | |
73e4de09 | 1558 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
1559 | mpz_clear (nj_z); |
1560 | return result; | |
1561 | } | |
1562 | } | |
1563 | else | |
1564 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1565 | } | |
1566 | else if (SCM_BIGP (j)) | |
1567 | { | |
e11e83f3 | 1568 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
1569 | { |
1570 | SCM_SWAP (j, k); | |
e11e83f3 | 1571 | nj = SCM_I_INUM (j); |
0aacf84e MD |
1572 | goto intbig; |
1573 | } | |
1574 | else if (SCM_BIGP (k)) | |
1575 | { | |
1576 | SCM result; | |
1577 | mpz_t result_z; | |
1578 | mpz_init (result_z); | |
1579 | mpz_and (result_z, | |
1580 | SCM_I_BIG_MPZ (j), | |
1581 | SCM_I_BIG_MPZ (k)); | |
1582 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 1583 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
1584 | mpz_clear (result_z); |
1585 | return result; | |
1586 | } | |
1587 | else | |
1588 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1589 | } | |
1590 | else | |
1591 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 1592 | } |
1bbd0b84 | 1593 | #undef FUNC_NAME |
0f2d19dd | 1594 | |
c1bfcf60 | 1595 | |
a1ec6916 | 1596 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1597 | (SCM index, SCM j), |
ba6e7231 KR |
1598 | "Test whether bit number @var{index} in @var{j} is set.\n" |
1599 | "@var{index} starts from 0 for the least significant bit.\n" | |
1600 | "\n" | |
1e6808ea | 1601 | "@lisp\n" |
b380b885 MD |
1602 | "(logbit? 0 #b1101) @result{} #t\n" |
1603 | "(logbit? 1 #b1101) @result{} #f\n" | |
1604 | "(logbit? 2 #b1101) @result{} #t\n" | |
1605 | "(logbit? 3 #b1101) @result{} #t\n" | |
1606 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1607 | "@end lisp") |
1bbd0b84 | 1608 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1609 | { |
78166ad5 | 1610 | unsigned long int iindex; |
5efd3c7d | 1611 | iindex = scm_to_ulong (index); |
78166ad5 | 1612 | |
e11e83f3 | 1613 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
1614 | { |
1615 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 1616 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 1617 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 1618 | } |
0aacf84e MD |
1619 | else if (SCM_BIGP (j)) |
1620 | { | |
1621 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
1622 | scm_remember_upto_here_1 (j); | |
73e4de09 | 1623 | return scm_from_bool (val); |
0aacf84e MD |
1624 | } |
1625 | else | |
78166ad5 | 1626 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 1627 | } |
1bbd0b84 | 1628 | #undef FUNC_NAME |
0f2d19dd | 1629 | |
78166ad5 | 1630 | |
a1ec6916 | 1631 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1632 | (SCM n), |
4d814788 | 1633 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
1634 | "argument.\n" |
1635 | "\n" | |
b380b885 MD |
1636 | "@lisp\n" |
1637 | "(number->string (lognot #b10000000) 2)\n" | |
1638 | " @result{} \"-10000001\"\n" | |
1639 | "(number->string (lognot #b0) 2)\n" | |
1640 | " @result{} \"-1\"\n" | |
1e6808ea | 1641 | "@end lisp") |
1bbd0b84 | 1642 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1643 | { |
e11e83f3 | 1644 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
1645 | /* No overflow here, just need to toggle all the bits making up the inum. |
1646 | Enhancement: No need to strip the tag and add it back, could just xor | |
1647 | a block of 1 bits, if that worked with the various debug versions of | |
1648 | the SCM typedef. */ | |
e11e83f3 | 1649 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
1650 | |
1651 | } else if (SCM_BIGP (n)) { | |
1652 | SCM result = scm_i_mkbig (); | |
1653 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
1654 | scm_remember_upto_here_1 (n); | |
1655 | return result; | |
1656 | ||
1657 | } else { | |
1658 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1659 | } | |
0f2d19dd | 1660 | } |
1bbd0b84 | 1661 | #undef FUNC_NAME |
0f2d19dd | 1662 | |
518b7508 KR |
1663 | /* returns 0 if IN is not an integer. OUT must already be |
1664 | initialized. */ | |
1665 | static int | |
1666 | coerce_to_big (SCM in, mpz_t out) | |
1667 | { | |
1668 | if (SCM_BIGP (in)) | |
1669 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
1670 | else if (SCM_I_INUMP (in)) |
1671 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
1672 | else |
1673 | return 0; | |
1674 | ||
1675 | return 1; | |
1676 | } | |
1677 | ||
d885e204 | 1678 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
1679 | (SCM n, SCM k, SCM m), |
1680 | "Return @var{n} raised to the integer exponent\n" | |
1681 | "@var{k}, modulo @var{m}.\n" | |
1682 | "\n" | |
1683 | "@lisp\n" | |
1684 | "(modulo-expt 2 3 5)\n" | |
1685 | " @result{} 3\n" | |
1686 | "@end lisp") | |
d885e204 | 1687 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
1688 | { |
1689 | mpz_t n_tmp; | |
1690 | mpz_t k_tmp; | |
1691 | mpz_t m_tmp; | |
1692 | ||
1693 | /* There are two classes of error we might encounter -- | |
1694 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
1695 | and | |
1696 | 2) wrong-type errors, which of course we'll report by calling | |
1697 | SCM_WRONG_TYPE_ARG. | |
1698 | We don't report those errors immediately, however; instead we do | |
1699 | some cleanup first. These variables tell us which error (if | |
1700 | any) we should report after cleaning up. | |
1701 | */ | |
1702 | int report_overflow = 0; | |
1703 | ||
1704 | int position_of_wrong_type = 0; | |
1705 | SCM value_of_wrong_type = SCM_INUM0; | |
1706 | ||
1707 | SCM result = SCM_UNDEFINED; | |
1708 | ||
1709 | mpz_init (n_tmp); | |
1710 | mpz_init (k_tmp); | |
1711 | mpz_init (m_tmp); | |
1712 | ||
bc36d050 | 1713 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
1714 | { |
1715 | report_overflow = 1; | |
1716 | goto cleanup; | |
1717 | } | |
1718 | ||
1719 | if (!coerce_to_big (n, n_tmp)) | |
1720 | { | |
1721 | value_of_wrong_type = n; | |
1722 | position_of_wrong_type = 1; | |
1723 | goto cleanup; | |
1724 | } | |
1725 | ||
1726 | if (!coerce_to_big (k, k_tmp)) | |
1727 | { | |
1728 | value_of_wrong_type = k; | |
1729 | position_of_wrong_type = 2; | |
1730 | goto cleanup; | |
1731 | } | |
1732 | ||
1733 | if (!coerce_to_big (m, m_tmp)) | |
1734 | { | |
1735 | value_of_wrong_type = m; | |
1736 | position_of_wrong_type = 3; | |
1737 | goto cleanup; | |
1738 | } | |
1739 | ||
1740 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
1741 | will get a divide-by-zero exception when an inverse 1/n mod m | |
1742 | doesn't exist (or is not unique). Since exceptions are hard to | |
1743 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
1744 | a simple failure code, which is easy to handle. */ | |
1745 | ||
1746 | if (-1 == mpz_sgn (k_tmp)) | |
1747 | { | |
1748 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
1749 | { | |
1750 | report_overflow = 1; | |
1751 | goto cleanup; | |
1752 | } | |
1753 | mpz_neg (k_tmp, k_tmp); | |
1754 | } | |
1755 | ||
1756 | result = scm_i_mkbig (); | |
1757 | mpz_powm (SCM_I_BIG_MPZ (result), | |
1758 | n_tmp, | |
1759 | k_tmp, | |
1760 | m_tmp); | |
b7b8c575 KR |
1761 | |
1762 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
1763 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
1764 | ||
518b7508 KR |
1765 | cleanup: |
1766 | mpz_clear (m_tmp); | |
1767 | mpz_clear (k_tmp); | |
1768 | mpz_clear (n_tmp); | |
1769 | ||
1770 | if (report_overflow) | |
1771 | scm_num_overflow (FUNC_NAME); | |
1772 | ||
1773 | if (position_of_wrong_type) | |
1774 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
1775 | value_of_wrong_type); | |
1776 | ||
1777 | return scm_i_normbig (result); | |
1778 | } | |
1779 | #undef FUNC_NAME | |
1780 | ||
a1ec6916 | 1781 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1782 | (SCM n, SCM k), |
ba6e7231 KR |
1783 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
1784 | "exact integer, @var{n} can be any number.\n" | |
1785 | "\n" | |
1786 | "Negative @var{k} is supported, and results in @math{1/n^abs(k)}\n" | |
1787 | "in the usual way. @math{@var{n}^0} is 1, as usual, and that\n" | |
1788 | "includes @math{0^0} is 1.\n" | |
1e6808ea | 1789 | "\n" |
b380b885 | 1790 | "@lisp\n" |
ba6e7231 KR |
1791 | "(integer-expt 2 5) @result{} 32\n" |
1792 | "(integer-expt -3 3) @result{} -27\n" | |
1793 | "(integer-expt 5 -3) @result{} 1/125\n" | |
1794 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 1795 | "@end lisp") |
1bbd0b84 | 1796 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1797 | { |
1c35cb19 RB |
1798 | long i2 = 0; |
1799 | SCM z_i2 = SCM_BOOL_F; | |
1800 | int i2_is_big = 0; | |
d956fa6f | 1801 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 1802 | |
d57ed702 | 1803 | /* 0^0 == 1 according to R5RS */ |
bc36d050 | 1804 | if (scm_is_eq (n, SCM_INUM0) || scm_is_eq (n, acc)) |
73e4de09 | 1805 | return scm_is_false (scm_zero_p(k)) ? n : acc; |
bc36d050 | 1806 | else if (scm_is_eq (n, SCM_I_MAKINUM (-1L))) |
73e4de09 | 1807 | return scm_is_false (scm_even_p (k)) ? n : acc; |
ca46fb90 | 1808 | |
e11e83f3 MV |
1809 | if (SCM_I_INUMP (k)) |
1810 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
1811 | else if (SCM_BIGP (k)) |
1812 | { | |
1813 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
1814 | scm_remember_upto_here_1 (k); |
1815 | i2_is_big = 1; | |
1816 | } | |
2830fd91 | 1817 | else |
ca46fb90 RB |
1818 | SCM_WRONG_TYPE_ARG (2, k); |
1819 | ||
1820 | if (i2_is_big) | |
f872b822 | 1821 | { |
ca46fb90 RB |
1822 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
1823 | { | |
1824 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
1825 | n = scm_divide (n, SCM_UNDEFINED); | |
1826 | } | |
1827 | while (1) | |
1828 | { | |
1829 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
1830 | { | |
ca46fb90 RB |
1831 | return acc; |
1832 | } | |
1833 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
1834 | { | |
ca46fb90 RB |
1835 | return scm_product (acc, n); |
1836 | } | |
1837 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
1838 | acc = scm_product (acc, n); | |
1839 | n = scm_product (n, n); | |
1840 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
1841 | } | |
f872b822 | 1842 | } |
ca46fb90 | 1843 | else |
f872b822 | 1844 | { |
ca46fb90 RB |
1845 | if (i2 < 0) |
1846 | { | |
1847 | i2 = -i2; | |
1848 | n = scm_divide (n, SCM_UNDEFINED); | |
1849 | } | |
1850 | while (1) | |
1851 | { | |
1852 | if (0 == i2) | |
1853 | return acc; | |
1854 | if (1 == i2) | |
1855 | return scm_product (acc, n); | |
1856 | if (i2 & 1) | |
1857 | acc = scm_product (acc, n); | |
1858 | n = scm_product (n, n); | |
1859 | i2 >>= 1; | |
1860 | } | |
f872b822 | 1861 | } |
0f2d19dd | 1862 | } |
1bbd0b84 | 1863 | #undef FUNC_NAME |
0f2d19dd | 1864 | |
a1ec6916 | 1865 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1866 | (SCM n, SCM cnt), |
32f19569 KR |
1867 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
1868 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 1869 | "\n" |
e7644cb2 | 1870 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
1871 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
1872 | "infinity. (Note that this is not the same rounding as\n" | |
1873 | "@code{quotient} does.)\n" | |
1874 | "\n" | |
1875 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
1876 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
1877 | "shift dropping bits.\n" | |
1e6808ea | 1878 | "\n" |
b380b885 | 1879 | "@lisp\n" |
1e6808ea MG |
1880 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1881 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
1882 | "\n" |
1883 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
1884 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 1885 | "@end lisp") |
1bbd0b84 | 1886 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1887 | { |
3ab9f56e | 1888 | long bits_to_shift; |
5efd3c7d | 1889 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 1890 | |
788aca27 KR |
1891 | if (SCM_I_INUMP (n)) |
1892 | { | |
1893 | long nn = SCM_I_INUM (n); | |
1894 | ||
1895 | if (bits_to_shift > 0) | |
1896 | { | |
1897 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
1898 | overflow a non-zero fixnum. For smaller shifts we check the | |
1899 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
1900 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
1901 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
1902 | bits_to_shift)". */ | |
1903 | ||
1904 | if (nn == 0) | |
1905 | return n; | |
1906 | ||
1907 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
1908 | && ((unsigned long) | |
1909 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) | |
1910 | <= 1)) | |
1911 | { | |
1912 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
1913 | } | |
1914 | else | |
1915 | { | |
1916 | SCM result = scm_i_long2big (nn); | |
1917 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1918 | bits_to_shift); | |
1919 | return result; | |
1920 | } | |
1921 | } | |
1922 | else | |
1923 | { | |
1924 | bits_to_shift = -bits_to_shift; | |
1925 | if (bits_to_shift >= SCM_LONG_BIT) | |
1926 | return (nn >= 0 ? SCM_I_MAKINUM (0) : SCM_I_MAKINUM(-1)); | |
1927 | else | |
1928 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
1929 | } | |
1930 | ||
1931 | } | |
1932 | else if (SCM_BIGP (n)) | |
ca46fb90 | 1933 | { |
788aca27 KR |
1934 | SCM result; |
1935 | ||
1936 | if (bits_to_shift == 0) | |
1937 | return n; | |
1938 | ||
1939 | result = scm_i_mkbig (); | |
1940 | if (bits_to_shift >= 0) | |
1941 | { | |
1942 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1943 | bits_to_shift); | |
1944 | return result; | |
1945 | } | |
ca46fb90 | 1946 | else |
788aca27 KR |
1947 | { |
1948 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
1949 | we have to allocate a bignum even if the result is going to be a | |
1950 | fixnum. */ | |
1951 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1952 | -bits_to_shift); | |
1953 | return scm_i_normbig (result); | |
1954 | } | |
1955 | ||
ca46fb90 RB |
1956 | } |
1957 | else | |
788aca27 KR |
1958 | { |
1959 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1960 | } | |
0f2d19dd | 1961 | } |
1bbd0b84 | 1962 | #undef FUNC_NAME |
0f2d19dd | 1963 | |
3c9f20f8 | 1964 | |
a1ec6916 | 1965 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 1966 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
1967 | "Return the integer composed of the @var{start} (inclusive)\n" |
1968 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
1969 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
1970 | "\n" | |
b380b885 MD |
1971 | "@lisp\n" |
1972 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
1973 | " @result{} \"1010\"\n" | |
1974 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
1975 | " @result{} \"10110\"\n" | |
1976 | "@end lisp") | |
1bbd0b84 | 1977 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 1978 | { |
7f848242 | 1979 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
1980 | istart = scm_to_ulong (start); |
1981 | iend = scm_to_ulong (end); | |
c1bfcf60 | 1982 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 1983 | |
7f848242 KR |
1984 | /* how many bits to keep */ |
1985 | bits = iend - istart; | |
1986 | ||
e11e83f3 | 1987 | if (SCM_I_INUMP (n)) |
0aacf84e | 1988 | { |
e11e83f3 | 1989 | long int in = SCM_I_INUM (n); |
7f848242 KR |
1990 | |
1991 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 1992 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 1993 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 1994 | |
0aacf84e MD |
1995 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
1996 | { | |
1997 | /* Since we emulate two's complement encoded numbers, this | |
1998 | * special case requires us to produce a result that has | |
7f848242 | 1999 | * more bits than can be stored in a fixnum. |
0aacf84e | 2000 | */ |
7f848242 KR |
2001 | SCM result = scm_i_long2big (in); |
2002 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
2003 | bits); | |
2004 | return result; | |
0aacf84e | 2005 | } |
ac0c002c | 2006 | |
7f848242 | 2007 | /* mask down to requisite bits */ |
857ae6af | 2008 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 2009 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
2010 | } |
2011 | else if (SCM_BIGP (n)) | |
ac0c002c | 2012 | { |
7f848242 KR |
2013 | SCM result; |
2014 | if (bits == 1) | |
2015 | { | |
d956fa6f | 2016 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
2017 | } |
2018 | else | |
2019 | { | |
2020 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
2021 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
2022 | such bits into a ulong. */ | |
2023 | result = scm_i_mkbig (); | |
2024 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
2025 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
2026 | result = scm_i_normbig (result); | |
2027 | } | |
2028 | scm_remember_upto_here_1 (n); | |
2029 | return result; | |
ac0c002c | 2030 | } |
0aacf84e | 2031 | else |
78166ad5 | 2032 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 2033 | } |
1bbd0b84 | 2034 | #undef FUNC_NAME |
0f2d19dd | 2035 | |
7f848242 | 2036 | |
e4755e5c JB |
2037 | static const char scm_logtab[] = { |
2038 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
2039 | }; | |
1cc91f1b | 2040 | |
a1ec6916 | 2041 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 2042 | (SCM n), |
1e6808ea MG |
2043 | "Return the number of bits in integer @var{n}. If integer is\n" |
2044 | "positive, the 1-bits in its binary representation are counted.\n" | |
2045 | "If negative, the 0-bits in its two's-complement binary\n" | |
2046 | "representation are counted. If 0, 0 is returned.\n" | |
2047 | "\n" | |
b380b885 MD |
2048 | "@lisp\n" |
2049 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
2050 | " @result{} 4\n" |
2051 | "(logcount 0)\n" | |
2052 | " @result{} 0\n" | |
2053 | "(logcount -2)\n" | |
2054 | " @result{} 1\n" | |
2055 | "@end lisp") | |
2056 | #define FUNC_NAME s_scm_logcount | |
2057 | { | |
e11e83f3 | 2058 | if (SCM_I_INUMP (n)) |
f872b822 | 2059 | { |
ca46fb90 | 2060 | unsigned long int c = 0; |
e11e83f3 | 2061 | long int nn = SCM_I_INUM (n); |
ca46fb90 RB |
2062 | if (nn < 0) |
2063 | nn = -1 - nn; | |
2064 | while (nn) | |
2065 | { | |
2066 | c += scm_logtab[15 & nn]; | |
2067 | nn >>= 4; | |
2068 | } | |
d956fa6f | 2069 | return SCM_I_MAKINUM (c); |
f872b822 | 2070 | } |
ca46fb90 | 2071 | else if (SCM_BIGP (n)) |
f872b822 | 2072 | { |
ca46fb90 | 2073 | unsigned long count; |
713a4259 KR |
2074 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
2075 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 2076 | else |
713a4259 KR |
2077 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
2078 | scm_remember_upto_here_1 (n); | |
d956fa6f | 2079 | return SCM_I_MAKINUM (count); |
f872b822 | 2080 | } |
ca46fb90 RB |
2081 | else |
2082 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 2083 | } |
ca46fb90 | 2084 | #undef FUNC_NAME |
0f2d19dd JB |
2085 | |
2086 | ||
ca46fb90 RB |
2087 | static const char scm_ilentab[] = { |
2088 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
2089 | }; | |
2090 | ||
0f2d19dd | 2091 | |
ca46fb90 RB |
2092 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
2093 | (SCM n), | |
2094 | "Return the number of bits necessary to represent @var{n}.\n" | |
2095 | "\n" | |
2096 | "@lisp\n" | |
2097 | "(integer-length #b10101010)\n" | |
2098 | " @result{} 8\n" | |
2099 | "(integer-length 0)\n" | |
2100 | " @result{} 0\n" | |
2101 | "(integer-length #b1111)\n" | |
2102 | " @result{} 4\n" | |
2103 | "@end lisp") | |
2104 | #define FUNC_NAME s_scm_integer_length | |
2105 | { | |
e11e83f3 | 2106 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2107 | { |
2108 | unsigned long int c = 0; | |
2109 | unsigned int l = 4; | |
e11e83f3 | 2110 | long int nn = SCM_I_INUM (n); |
0aacf84e MD |
2111 | if (nn < 0) |
2112 | nn = -1 - nn; | |
2113 | while (nn) | |
2114 | { | |
2115 | c += 4; | |
2116 | l = scm_ilentab [15 & nn]; | |
2117 | nn >>= 4; | |
2118 | } | |
d956fa6f | 2119 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
2120 | } |
2121 | else if (SCM_BIGP (n)) | |
2122 | { | |
2123 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
2124 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
2125 | 1 too big, so check for that and adjust. */ | |
2126 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
2127 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
2128 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
2129 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
2130 | size--; | |
2131 | scm_remember_upto_here_1 (n); | |
d956fa6f | 2132 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
2133 | } |
2134 | else | |
ca46fb90 | 2135 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
2136 | } |
2137 | #undef FUNC_NAME | |
0f2d19dd JB |
2138 | |
2139 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
2140 | #define SCM_MAX_DBL_PREC 60 |
2141 | #define SCM_MAX_DBL_RADIX 36 | |
2142 | ||
2143 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
2144 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
2145 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
2146 | ||
2147 | static | |
2148 | void init_dblprec(int *prec, int radix) { | |
2149 | /* determine floating point precision by adding successively | |
2150 | smaller increments to 1.0 until it is considered == 1.0 */ | |
2151 | double f = ((double)1.0)/radix; | |
2152 | double fsum = 1.0 + f; | |
2153 | ||
2154 | *prec = 0; | |
2155 | while (fsum != 1.0) | |
2156 | { | |
2157 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
2158 | fsum = 1.0; | |
2159 | else | |
2160 | { | |
2161 | f /= radix; | |
2162 | fsum = f + 1.0; | |
2163 | } | |
2164 | } | |
2165 | (*prec) -= 1; | |
2166 | } | |
2167 | ||
2168 | static | |
2169 | void init_fx_radix(double *fx_list, int radix) | |
2170 | { | |
2171 | /* initialize a per-radix list of tolerances. When added | |
2172 | to a number < 1.0, we can determine if we should raund | |
2173 | up and quit converting a number to a string. */ | |
2174 | int i; | |
2175 | fx_list[0] = 0.0; | |
2176 | fx_list[1] = 0.5; | |
2177 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
2178 | fx_list[i] = (fx_list[i-1] / radix); | |
2179 | } | |
2180 | ||
2181 | /* use this array as a way to generate a single digit */ | |
2182 | static const char*number_chars="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; | |
0f2d19dd | 2183 | |
1be6b49c | 2184 | static size_t |
0b799eea | 2185 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 2186 | { |
0b799eea MV |
2187 | int efmt, dpt, d, i, wp; |
2188 | double *fx; | |
2189 | #ifdef DBL_MIN_10_EXP | |
2190 | double f_cpy; | |
2191 | int exp_cpy; | |
2192 | #endif /* DBL_MIN_10_EXP */ | |
2193 | size_t ch = 0; | |
2194 | int exp = 0; | |
2195 | ||
2196 | if(radix < 2 || | |
2197 | radix > SCM_MAX_DBL_RADIX) | |
2198 | { | |
2199 | /* revert to existing behavior */ | |
2200 | radix = 10; | |
2201 | } | |
2202 | ||
2203 | wp = scm_dblprec[radix-2]; | |
2204 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 2205 | |
f872b822 | 2206 | if (f == 0.0) |
abb7e44d MV |
2207 | { |
2208 | #ifdef HAVE_COPYSIGN | |
2209 | double sgn = copysign (1.0, f); | |
2210 | ||
2211 | if (sgn < 0.0) | |
2212 | a[ch++] = '-'; | |
2213 | #endif | |
abb7e44d MV |
2214 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
2215 | } | |
7351e207 MV |
2216 | |
2217 | if (xisinf (f)) | |
2218 | { | |
2219 | if (f < 0) | |
2220 | strcpy (a, "-inf.0"); | |
2221 | else | |
2222 | strcpy (a, "+inf.0"); | |
2223 | return ch+6; | |
2224 | } | |
2225 | else if (xisnan (f)) | |
2226 | { | |
2227 | strcpy (a, "+nan.0"); | |
2228 | return ch+6; | |
2229 | } | |
2230 | ||
f872b822 MD |
2231 | if (f < 0.0) |
2232 | { | |
2233 | f = -f; | |
2234 | a[ch++] = '-'; | |
2235 | } | |
7351e207 | 2236 | |
f872b822 MD |
2237 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
2238 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
2239 | /* just do the checking...if it passes, we do the conversion for our |
2240 | radix again below */ | |
2241 | f_cpy = f; | |
2242 | exp_cpy = exp; | |
2243 | ||
2244 | while (f_cpy < 1.0) | |
f872b822 | 2245 | { |
0b799eea MV |
2246 | f_cpy *= 10.0; |
2247 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
2248 | { |
2249 | a[ch++] = '#'; | |
2250 | a[ch++] = '.'; | |
2251 | a[ch++] = '#'; | |
2252 | return ch; | |
2253 | } | |
f872b822 | 2254 | } |
0b799eea | 2255 | while (f_cpy > 10.0) |
f872b822 | 2256 | { |
0b799eea MV |
2257 | f_cpy *= 0.10; |
2258 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
2259 | { |
2260 | a[ch++] = '#'; | |
2261 | a[ch++] = '.'; | |
2262 | a[ch++] = '#'; | |
2263 | return ch; | |
2264 | } | |
f872b822 | 2265 | } |
0b799eea MV |
2266 | #endif |
2267 | ||
f872b822 MD |
2268 | while (f < 1.0) |
2269 | { | |
0b799eea | 2270 | f *= radix; |
f872b822 MD |
2271 | exp--; |
2272 | } | |
0b799eea | 2273 | while (f > radix) |
f872b822 | 2274 | { |
0b799eea | 2275 | f /= radix; |
f872b822 MD |
2276 | exp++; |
2277 | } | |
0b799eea MV |
2278 | |
2279 | if (f + fx[wp] >= radix) | |
f872b822 MD |
2280 | { |
2281 | f = 1.0; | |
2282 | exp++; | |
2283 | } | |
0f2d19dd | 2284 | zero: |
0b799eea MV |
2285 | #ifdef ENGNOT |
2286 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 2287 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
2288 | exp -= dpt++; |
2289 | efmt = 1; | |
f872b822 MD |
2290 | #else |
2291 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 2292 | if (!efmt) |
cda139a7 MD |
2293 | { |
2294 | if (exp < 0) | |
2295 | { | |
2296 | a[ch++] = '0'; | |
2297 | a[ch++] = '.'; | |
2298 | dpt = exp; | |
f872b822 MD |
2299 | while (++dpt) |
2300 | a[ch++] = '0'; | |
cda139a7 MD |
2301 | } |
2302 | else | |
f872b822 | 2303 | dpt = exp + 1; |
cda139a7 | 2304 | } |
0f2d19dd JB |
2305 | else |
2306 | dpt = 1; | |
f872b822 MD |
2307 | #endif |
2308 | ||
2309 | do | |
2310 | { | |
2311 | d = f; | |
2312 | f -= d; | |
0b799eea | 2313 | a[ch++] = number_chars[d]; |
f872b822 MD |
2314 | if (f < fx[wp]) |
2315 | break; | |
2316 | if (f + fx[wp] >= 1.0) | |
2317 | { | |
0b799eea | 2318 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
2319 | break; |
2320 | } | |
0b799eea | 2321 | f *= radix; |
f872b822 MD |
2322 | if (!(--dpt)) |
2323 | a[ch++] = '.'; | |
0f2d19dd | 2324 | } |
f872b822 | 2325 | while (wp--); |
0f2d19dd JB |
2326 | |
2327 | if (dpt > 0) | |
cda139a7 | 2328 | { |
f872b822 | 2329 | #ifndef ENGNOT |
cda139a7 MD |
2330 | if ((dpt > 4) && (exp > 6)) |
2331 | { | |
f872b822 | 2332 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 2333 | for (i = ch++; i > d; i--) |
f872b822 | 2334 | a[i] = a[i - 1]; |
cda139a7 MD |
2335 | a[d] = '.'; |
2336 | efmt = 1; | |
2337 | } | |
2338 | else | |
f872b822 | 2339 | #endif |
cda139a7 | 2340 | { |
f872b822 MD |
2341 | while (--dpt) |
2342 | a[ch++] = '0'; | |
cda139a7 MD |
2343 | a[ch++] = '.'; |
2344 | } | |
2345 | } | |
f872b822 MD |
2346 | if (a[ch - 1] == '.') |
2347 | a[ch++] = '0'; /* trailing zero */ | |
2348 | if (efmt && exp) | |
2349 | { | |
2350 | a[ch++] = 'e'; | |
2351 | if (exp < 0) | |
2352 | { | |
2353 | exp = -exp; | |
2354 | a[ch++] = '-'; | |
2355 | } | |
0b799eea MV |
2356 | for (i = radix; i <= exp; i *= radix); |
2357 | for (i /= radix; i; i /= radix) | |
f872b822 | 2358 | { |
0b799eea | 2359 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
2360 | exp %= i; |
2361 | } | |
0f2d19dd | 2362 | } |
0f2d19dd JB |
2363 | return ch; |
2364 | } | |
2365 | ||
7a1aba42 MV |
2366 | |
2367 | static size_t | |
2368 | icmplx2str (double real, double imag, char *str, int radix) | |
2369 | { | |
2370 | size_t i; | |
2371 | ||
2372 | i = idbl2str (real, str, radix); | |
2373 | if (imag != 0.0) | |
2374 | { | |
2375 | /* Don't output a '+' for negative numbers or for Inf and | |
2376 | NaN. They will provide their own sign. */ | |
2377 | if (0 <= imag && !xisinf (imag) && !xisnan (imag)) | |
2378 | str[i++] = '+'; | |
2379 | i += idbl2str (imag, &str[i], radix); | |
2380 | str[i++] = 'i'; | |
2381 | } | |
2382 | return i; | |
2383 | } | |
2384 | ||
1be6b49c | 2385 | static size_t |
0b799eea | 2386 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 2387 | { |
1be6b49c | 2388 | size_t i; |
3c9a524f | 2389 | if (SCM_REALP (flt)) |
0b799eea | 2390 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 2391 | else |
7a1aba42 MV |
2392 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
2393 | str, radix); | |
0f2d19dd JB |
2394 | return i; |
2395 | } | |
0f2d19dd | 2396 | |
2881e77b | 2397 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
2398 | characters in the result. |
2399 | rad is output base | |
2400 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2401 | size_t |
2881e77b MV |
2402 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
2403 | { | |
2404 | if (num < 0) | |
2405 | { | |
2406 | *p++ = '-'; | |
2407 | return scm_iuint2str (-num, rad, p) + 1; | |
2408 | } | |
2409 | else | |
2410 | return scm_iuint2str (num, rad, p); | |
2411 | } | |
2412 | ||
2413 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
2414 | characters in the result. | |
2415 | rad is output base | |
2416 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
2417 | size_t | |
2418 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 2419 | { |
1be6b49c ML |
2420 | size_t j = 1; |
2421 | size_t i; | |
2881e77b | 2422 | scm_t_uintmax n = num; |
5c11cc9d | 2423 | |
f872b822 | 2424 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2425 | j++; |
2426 | ||
2427 | i = j; | |
2881e77b | 2428 | n = num; |
f872b822 MD |
2429 | while (i--) |
2430 | { | |
5c11cc9d GH |
2431 | int d = n % rad; |
2432 | ||
f872b822 MD |
2433 | n /= rad; |
2434 | p[i] = d + ((d < 10) ? '0' : 'a' - 10); | |
2435 | } | |
0f2d19dd JB |
2436 | return j; |
2437 | } | |
2438 | ||
a1ec6916 | 2439 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2440 | (SCM n, SCM radix), |
2441 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2442 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2443 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2444 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2445 | { |
1bbd0b84 | 2446 | int base; |
98cb6e75 | 2447 | |
0aacf84e | 2448 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 2449 | base = 10; |
0aacf84e | 2450 | else |
5efd3c7d | 2451 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 2452 | |
e11e83f3 | 2453 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2454 | { |
2455 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 2456 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 2457 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
2458 | } |
2459 | else if (SCM_BIGP (n)) | |
2460 | { | |
2461 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
2462 | scm_remember_upto_here_1 (n); | |
cc95e00a | 2463 | return scm_take_locale_string (str); |
0aacf84e | 2464 | } |
f92e85f7 MV |
2465 | else if (SCM_FRACTIONP (n)) |
2466 | { | |
f92e85f7 | 2467 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 2468 | scm_from_locale_string ("/"), |
f92e85f7 MV |
2469 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
2470 | } | |
0aacf84e MD |
2471 | else if (SCM_INEXACTP (n)) |
2472 | { | |
2473 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 2474 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
2475 | } |
2476 | else | |
bb628794 | 2477 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 2478 | } |
1bbd0b84 | 2479 | #undef FUNC_NAME |
0f2d19dd JB |
2480 | |
2481 | ||
ca46fb90 RB |
2482 | /* These print routines used to be stubbed here so that scm_repl.c |
2483 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 2484 | |
0f2d19dd | 2485 | int |
e81d98ec | 2486 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2487 | { |
56e55ac7 | 2488 | char num_buf[FLOBUFLEN]; |
0b799eea | 2489 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
2490 | return !0; |
2491 | } | |
2492 | ||
b479fe9a MV |
2493 | void |
2494 | scm_i_print_double (double val, SCM port) | |
2495 | { | |
2496 | char num_buf[FLOBUFLEN]; | |
2497 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
2498 | } | |
2499 | ||
f3ae5d60 | 2500 | int |
e81d98ec | 2501 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 2502 | |
f3ae5d60 | 2503 | { |
56e55ac7 | 2504 | char num_buf[FLOBUFLEN]; |
0b799eea | 2505 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
2506 | return !0; |
2507 | } | |
1cc91f1b | 2508 | |
7a1aba42 MV |
2509 | void |
2510 | scm_i_print_complex (double real, double imag, SCM port) | |
2511 | { | |
2512 | char num_buf[FLOBUFLEN]; | |
2513 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
2514 | } | |
2515 | ||
f92e85f7 MV |
2516 | int |
2517 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
2518 | { | |
2519 | SCM str; | |
f92e85f7 | 2520 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
3f47e526 | 2521 | scm_lfwrite_str (str, port); |
f92e85f7 MV |
2522 | scm_remember_upto_here_1 (str); |
2523 | return !0; | |
2524 | } | |
2525 | ||
0f2d19dd | 2526 | int |
e81d98ec | 2527 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2528 | { |
ca46fb90 RB |
2529 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
2530 | scm_remember_upto_here_1 (exp); | |
2531 | scm_lfwrite (str, (size_t) strlen (str), port); | |
2532 | free (str); | |
0f2d19dd JB |
2533 | return !0; |
2534 | } | |
2535 | /*** END nums->strs ***/ | |
2536 | ||
3c9a524f | 2537 | |
0f2d19dd | 2538 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2539 | |
3c9a524f DH |
2540 | /* The following functions implement the conversion from strings to numbers. |
2541 | * The implementation somehow follows the grammar for numbers as it is given | |
2542 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2543 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2544 | * points should be noted about the implementation: | |
2545 | * * Each function keeps a local index variable 'idx' that points at the | |
2546 | * current position within the parsed string. The global index is only | |
2547 | * updated if the function could parse the corresponding syntactic unit | |
2548 | * successfully. | |
2549 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2550 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2551 | * global exactness information is only updated after each part has been | |
2552 | * successfully parsed. | |
2553 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2554 | * Only if these fixnums would overflow, the result variables are updated | |
2555 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2556 | * the temporary variables holding the fixnums are cleared, and the process | |
2557 | * starts over again. If for example fixnums were able to store five decimal | |
2558 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2559 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2560 | * only every five digits two bignum operations were performed. | |
2561 | */ | |
2562 | ||
2563 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2564 | ||
2565 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2566 | ||
2567 | /* In non ASCII-style encodings the following macro might not work. */ | |
3f47e526 MG |
2568 | #define XDIGIT2UINT(d) \ |
2569 | (uc_is_property_decimal_digit ((int) (unsigned char) d) \ | |
2570 | ? (d) - '0' \ | |
cdf8f9e6 | 2571 | : uc_tolower ((int) (unsigned char) d) - 'a' + 10) |
3c9a524f | 2572 | |
2a8fecee | 2573 | static SCM |
3f47e526 | 2574 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 2575 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 2576 | { |
3c9a524f DH |
2577 | unsigned int idx = *p_idx; |
2578 | unsigned int hash_seen = 0; | |
2579 | scm_t_bits shift = 1; | |
2580 | scm_t_bits add = 0; | |
2581 | unsigned int digit_value; | |
2582 | SCM result; | |
2583 | char c; | |
3f47e526 | 2584 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
2585 | |
2586 | if (idx == len) | |
2587 | return SCM_BOOL_F; | |
2a8fecee | 2588 | |
3f47e526 MG |
2589 | c = scm_i_string_ref (mem, idx); |
2590 | if (!uc_is_property_ascii_hex_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
2591 | return SCM_BOOL_F; |
2592 | digit_value = XDIGIT2UINT (c); | |
2593 | if (digit_value >= radix) | |
2594 | return SCM_BOOL_F; | |
2595 | ||
2596 | idx++; | |
d956fa6f | 2597 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 2598 | while (idx != len) |
f872b822 | 2599 | { |
3f47e526 MG |
2600 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
2601 | if (uc_is_property_ascii_hex_digit ((scm_t_uint32) c)) | |
f872b822 | 2602 | { |
3c9a524f | 2603 | if (hash_seen) |
1fe5e088 | 2604 | break; |
3c9a524f DH |
2605 | digit_value = XDIGIT2UINT (c); |
2606 | if (digit_value >= radix) | |
1fe5e088 | 2607 | break; |
f872b822 | 2608 | } |
3c9a524f DH |
2609 | else if (c == '#') |
2610 | { | |
2611 | hash_seen = 1; | |
2612 | digit_value = 0; | |
2613 | } | |
2614 | else | |
2615 | break; | |
2616 | ||
2617 | idx++; | |
2618 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2619 | { | |
d956fa6f | 2620 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2621 | if (add > 0) |
d956fa6f | 2622 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2623 | |
2624 | shift = radix; | |
2625 | add = digit_value; | |
2626 | } | |
2627 | else | |
2628 | { | |
2629 | shift = shift * radix; | |
2630 | add = add * radix + digit_value; | |
2631 | } | |
2632 | }; | |
2633 | ||
2634 | if (shift > 1) | |
d956fa6f | 2635 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2636 | if (add > 0) |
d956fa6f | 2637 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2638 | |
2639 | *p_idx = idx; | |
2640 | if (hash_seen) | |
2641 | *p_exactness = INEXACT; | |
2642 | ||
2643 | return result; | |
2a8fecee JB |
2644 | } |
2645 | ||
2646 | ||
3c9a524f DH |
2647 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2648 | * covers the parts of the rules that start at a potential point. The value | |
2649 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2650 | * in variable result. The content of *p_exactness indicates, whether a hash |
2651 | * has already been seen in the digits before the point. | |
3c9a524f | 2652 | */ |
1cc91f1b | 2653 | |
3f47e526 | 2654 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
2655 | |
2656 | static SCM | |
3f47e526 | 2657 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 2658 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2659 | { |
3c9a524f DH |
2660 | unsigned int idx = *p_idx; |
2661 | enum t_exactness x = *p_exactness; | |
3f47e526 | 2662 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
2663 | |
2664 | if (idx == len) | |
79d34f68 | 2665 | return result; |
3c9a524f | 2666 | |
3f47e526 | 2667 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
2668 | { |
2669 | scm_t_bits shift = 1; | |
2670 | scm_t_bits add = 0; | |
2671 | unsigned int digit_value; | |
d956fa6f | 2672 | SCM big_shift = SCM_I_MAKINUM (1); |
3c9a524f DH |
2673 | |
2674 | idx++; | |
2675 | while (idx != len) | |
2676 | { | |
3f47e526 MG |
2677 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
2678 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
2679 | { |
2680 | if (x == INEXACT) | |
2681 | return SCM_BOOL_F; | |
2682 | else | |
2683 | digit_value = DIGIT2UINT (c); | |
2684 | } | |
2685 | else if (c == '#') | |
2686 | { | |
2687 | x = INEXACT; | |
2688 | digit_value = 0; | |
2689 | } | |
2690 | else | |
2691 | break; | |
2692 | ||
2693 | idx++; | |
2694 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2695 | { | |
d956fa6f MV |
2696 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2697 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 2698 | if (add > 0) |
d956fa6f | 2699 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2700 | |
2701 | shift = 10; | |
2702 | add = digit_value; | |
2703 | } | |
2704 | else | |
2705 | { | |
2706 | shift = shift * 10; | |
2707 | add = add * 10 + digit_value; | |
2708 | } | |
2709 | }; | |
2710 | ||
2711 | if (add > 0) | |
2712 | { | |
d956fa6f MV |
2713 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2714 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
2715 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
2716 | } |
2717 | ||
d8592269 | 2718 | result = scm_divide (result, big_shift); |
79d34f68 | 2719 | |
3c9a524f DH |
2720 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2721 | x = INEXACT; | |
f872b822 | 2722 | } |
3c9a524f | 2723 | |
3c9a524f | 2724 | if (idx != len) |
f872b822 | 2725 | { |
3c9a524f DH |
2726 | int sign = 1; |
2727 | unsigned int start; | |
3f47e526 | 2728 | scm_t_wchar c; |
3c9a524f DH |
2729 | int exponent; |
2730 | SCM e; | |
2731 | ||
2732 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2733 | ||
3f47e526 | 2734 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 2735 | { |
3c9a524f DH |
2736 | case 'd': case 'D': |
2737 | case 'e': case 'E': | |
2738 | case 'f': case 'F': | |
2739 | case 'l': case 'L': | |
2740 | case 's': case 'S': | |
2741 | idx++; | |
ee0ddd21 AW |
2742 | if (idx == len) |
2743 | return SCM_BOOL_F; | |
2744 | ||
3c9a524f | 2745 | start = idx; |
3f47e526 | 2746 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2747 | if (c == '-') |
2748 | { | |
2749 | idx++; | |
ee0ddd21 AW |
2750 | if (idx == len) |
2751 | return SCM_BOOL_F; | |
2752 | ||
3c9a524f | 2753 | sign = -1; |
3f47e526 | 2754 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2755 | } |
2756 | else if (c == '+') | |
2757 | { | |
2758 | idx++; | |
ee0ddd21 AW |
2759 | if (idx == len) |
2760 | return SCM_BOOL_F; | |
2761 | ||
3c9a524f | 2762 | sign = 1; |
3f47e526 | 2763 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2764 | } |
2765 | else | |
2766 | sign = 1; | |
2767 | ||
3f47e526 | 2768 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
2769 | return SCM_BOOL_F; |
2770 | ||
2771 | idx++; | |
2772 | exponent = DIGIT2UINT (c); | |
2773 | while (idx != len) | |
f872b822 | 2774 | { |
3f47e526 MG |
2775 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
2776 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
2777 | { |
2778 | idx++; | |
2779 | if (exponent <= SCM_MAXEXP) | |
2780 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2781 | } | |
2782 | else | |
2783 | break; | |
f872b822 | 2784 | } |
3c9a524f DH |
2785 | |
2786 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2787 | { |
3c9a524f | 2788 | size_t exp_len = idx - start; |
3f47e526 | 2789 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
2790 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
2791 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2792 | } |
3c9a524f | 2793 | |
d956fa6f | 2794 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
2795 | if (sign == 1) |
2796 | result = scm_product (result, e); | |
2797 | else | |
f92e85f7 | 2798 | result = scm_divide2real (result, e); |
3c9a524f DH |
2799 | |
2800 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2801 | x = INEXACT; | |
2802 | ||
f872b822 | 2803 | break; |
3c9a524f | 2804 | |
f872b822 | 2805 | default: |
3c9a524f | 2806 | break; |
f872b822 | 2807 | } |
0f2d19dd | 2808 | } |
3c9a524f DH |
2809 | |
2810 | *p_idx = idx; | |
2811 | if (x == INEXACT) | |
2812 | *p_exactness = x; | |
2813 | ||
2814 | return result; | |
0f2d19dd | 2815 | } |
0f2d19dd | 2816 | |
3c9a524f DH |
2817 | |
2818 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2819 | ||
2820 | static SCM | |
3f47e526 | 2821 | mem2ureal (SCM mem, unsigned int *p_idx, |
3c9a524f | 2822 | unsigned int radix, enum t_exactness *p_exactness) |
0f2d19dd | 2823 | { |
3c9a524f | 2824 | unsigned int idx = *p_idx; |
164d2481 | 2825 | SCM result; |
3f47e526 | 2826 | size_t len = scm_i_string_length (mem); |
3c9a524f | 2827 | |
40f89215 NJ |
2828 | /* Start off believing that the number will be exact. This changes |
2829 | to INEXACT if we see a decimal point or a hash. */ | |
2830 | enum t_exactness x = EXACT; | |
2831 | ||
3c9a524f DH |
2832 | if (idx == len) |
2833 | return SCM_BOOL_F; | |
2834 | ||
3f47e526 | 2835 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
2836 | { |
2837 | *p_idx = idx+5; | |
2838 | return scm_inf (); | |
2839 | } | |
2840 | ||
3f47e526 | 2841 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 2842 | { |
d8592269 MV |
2843 | /* Cobble up the fractional part. We might want to set the |
2844 | NaN's mantissa from it. */ | |
7351e207 | 2845 | idx += 4; |
3f47e526 | 2846 | mem2uinteger (mem, &idx, 10, &x); |
7351e207 MV |
2847 | *p_idx = idx; |
2848 | return scm_nan (); | |
2849 | } | |
2850 | ||
3f47e526 | 2851 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
2852 | { |
2853 | if (radix != 10) | |
2854 | return SCM_BOOL_F; | |
2855 | else if (idx + 1 == len) | |
2856 | return SCM_BOOL_F; | |
3f47e526 | 2857 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
2858 | return SCM_BOOL_F; |
2859 | else | |
3f47e526 | 2860 | result = mem2decimal_from_point (SCM_I_MAKINUM (0), mem, |
40f89215 | 2861 | p_idx, &x); |
f872b822 | 2862 | } |
3c9a524f DH |
2863 | else |
2864 | { | |
3c9a524f | 2865 | SCM uinteger; |
3c9a524f | 2866 | |
3f47e526 | 2867 | uinteger = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 2868 | if (scm_is_false (uinteger)) |
3c9a524f DH |
2869 | return SCM_BOOL_F; |
2870 | ||
2871 | if (idx == len) | |
2872 | result = uinteger; | |
3f47e526 | 2873 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 2874 | { |
3c9a524f DH |
2875 | SCM divisor; |
2876 | ||
2877 | idx++; | |
ee0ddd21 AW |
2878 | if (idx == len) |
2879 | return SCM_BOOL_F; | |
3c9a524f | 2880 | |
3f47e526 | 2881 | divisor = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 2882 | if (scm_is_false (divisor)) |
3c9a524f DH |
2883 | return SCM_BOOL_F; |
2884 | ||
f92e85f7 | 2885 | /* both are int/big here, I assume */ |
cba42c93 | 2886 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 2887 | } |
3c9a524f DH |
2888 | else if (radix == 10) |
2889 | { | |
3f47e526 | 2890 | result = mem2decimal_from_point (uinteger, mem, &idx, &x); |
73e4de09 | 2891 | if (scm_is_false (result)) |
3c9a524f DH |
2892 | return SCM_BOOL_F; |
2893 | } | |
2894 | else | |
2895 | result = uinteger; | |
2896 | ||
2897 | *p_idx = idx; | |
f872b822 | 2898 | } |
164d2481 | 2899 | |
40f89215 NJ |
2900 | /* Update *p_exactness if the number just read was inexact. This is |
2901 | important for complex numbers, so that a complex number is | |
2902 | treated as inexact overall if either its real or imaginary part | |
2903 | is inexact. | |
2904 | */ | |
2905 | if (x == INEXACT) | |
2906 | *p_exactness = x; | |
2907 | ||
164d2481 MV |
2908 | /* When returning an inexact zero, make sure it is represented as a |
2909 | floating point value so that we can change its sign. | |
2910 | */ | |
bc36d050 | 2911 | if (scm_is_eq (result, SCM_I_MAKINUM(0)) && *p_exactness == INEXACT) |
55f26379 | 2912 | result = scm_from_double (0.0); |
164d2481 MV |
2913 | |
2914 | return result; | |
3c9a524f | 2915 | } |
0f2d19dd | 2916 | |
0f2d19dd | 2917 | |
3c9a524f | 2918 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2919 | |
3c9a524f | 2920 | static SCM |
3f47e526 | 2921 | mem2complex (SCM mem, unsigned int idx, |
3c9a524f DH |
2922 | unsigned int radix, enum t_exactness *p_exactness) |
2923 | { | |
3f47e526 | 2924 | scm_t_wchar c; |
3c9a524f DH |
2925 | int sign = 0; |
2926 | SCM ureal; | |
3f47e526 | 2927 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
2928 | |
2929 | if (idx == len) | |
2930 | return SCM_BOOL_F; | |
2931 | ||
3f47e526 | 2932 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2933 | if (c == '+') |
2934 | { | |
2935 | idx++; | |
2936 | sign = 1; | |
2937 | } | |
2938 | else if (c == '-') | |
2939 | { | |
2940 | idx++; | |
2941 | sign = -1; | |
0f2d19dd | 2942 | } |
0f2d19dd | 2943 | |
3c9a524f DH |
2944 | if (idx == len) |
2945 | return SCM_BOOL_F; | |
2946 | ||
3f47e526 | 2947 | ureal = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 2948 | if (scm_is_false (ureal)) |
f872b822 | 2949 | { |
3c9a524f DH |
2950 | /* input must be either +i or -i */ |
2951 | ||
2952 | if (sign == 0) | |
2953 | return SCM_BOOL_F; | |
2954 | ||
3f47e526 MG |
2955 | if (scm_i_string_ref (mem, idx) == 'i' |
2956 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 2957 | { |
3c9a524f DH |
2958 | idx++; |
2959 | if (idx != len) | |
2960 | return SCM_BOOL_F; | |
2961 | ||
d956fa6f | 2962 | return scm_make_rectangular (SCM_I_MAKINUM (0), SCM_I_MAKINUM (sign)); |
f872b822 | 2963 | } |
3c9a524f DH |
2964 | else |
2965 | return SCM_BOOL_F; | |
0f2d19dd | 2966 | } |
3c9a524f DH |
2967 | else |
2968 | { | |
73e4de09 | 2969 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 2970 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 2971 | |
3c9a524f DH |
2972 | if (idx == len) |
2973 | return ureal; | |
2974 | ||
3f47e526 | 2975 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 2976 | switch (c) |
f872b822 | 2977 | { |
3c9a524f DH |
2978 | case 'i': case 'I': |
2979 | /* either +<ureal>i or -<ureal>i */ | |
2980 | ||
2981 | idx++; | |
2982 | if (sign == 0) | |
2983 | return SCM_BOOL_F; | |
2984 | if (idx != len) | |
2985 | return SCM_BOOL_F; | |
d956fa6f | 2986 | return scm_make_rectangular (SCM_I_MAKINUM (0), ureal); |
3c9a524f DH |
2987 | |
2988 | case '@': | |
2989 | /* polar input: <real>@<real>. */ | |
2990 | ||
2991 | idx++; | |
2992 | if (idx == len) | |
2993 | return SCM_BOOL_F; | |
2994 | else | |
f872b822 | 2995 | { |
3c9a524f DH |
2996 | int sign; |
2997 | SCM angle; | |
2998 | SCM result; | |
2999 | ||
3f47e526 | 3000 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
3001 | if (c == '+') |
3002 | { | |
3003 | idx++; | |
ee0ddd21 AW |
3004 | if (idx == len) |
3005 | return SCM_BOOL_F; | |
3c9a524f DH |
3006 | sign = 1; |
3007 | } | |
3008 | else if (c == '-') | |
3009 | { | |
3010 | idx++; | |
ee0ddd21 AW |
3011 | if (idx == len) |
3012 | return SCM_BOOL_F; | |
3c9a524f DH |
3013 | sign = -1; |
3014 | } | |
3015 | else | |
3016 | sign = 1; | |
3017 | ||
3f47e526 | 3018 | angle = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 3019 | if (scm_is_false (angle)) |
3c9a524f DH |
3020 | return SCM_BOOL_F; |
3021 | if (idx != len) | |
3022 | return SCM_BOOL_F; | |
3023 | ||
73e4de09 | 3024 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
3025 | angle = scm_difference (angle, SCM_UNDEFINED); |
3026 | ||
3027 | result = scm_make_polar (ureal, angle); | |
3028 | return result; | |
f872b822 | 3029 | } |
3c9a524f DH |
3030 | case '+': |
3031 | case '-': | |
3032 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 3033 | |
3c9a524f DH |
3034 | idx++; |
3035 | if (idx == len) | |
3036 | return SCM_BOOL_F; | |
3037 | else | |
3038 | { | |
3039 | int sign = (c == '+') ? 1 : -1; | |
3f47e526 | 3040 | SCM imag = mem2ureal (mem, &idx, radix, p_exactness); |
0f2d19dd | 3041 | |
73e4de09 | 3042 | if (scm_is_false (imag)) |
d956fa6f | 3043 | imag = SCM_I_MAKINUM (sign); |
73e4de09 | 3044 | else if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
1fe5e088 | 3045 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 3046 | |
3c9a524f DH |
3047 | if (idx == len) |
3048 | return SCM_BOOL_F; | |
3f47e526 MG |
3049 | if (scm_i_string_ref (mem, idx) != 'i' |
3050 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 3051 | return SCM_BOOL_F; |
0f2d19dd | 3052 | |
3c9a524f DH |
3053 | idx++; |
3054 | if (idx != len) | |
3055 | return SCM_BOOL_F; | |
0f2d19dd | 3056 | |
1fe5e088 | 3057 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
3058 | } |
3059 | default: | |
3060 | return SCM_BOOL_F; | |
3061 | } | |
3062 | } | |
0f2d19dd | 3063 | } |
0f2d19dd JB |
3064 | |
3065 | ||
3c9a524f DH |
3066 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
3067 | ||
3068 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 3069 | |
0f2d19dd | 3070 | SCM |
3f47e526 | 3071 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 3072 | { |
3c9a524f DH |
3073 | unsigned int idx = 0; |
3074 | unsigned int radix = NO_RADIX; | |
3075 | enum t_exactness forced_x = NO_EXACTNESS; | |
3076 | enum t_exactness implicit_x = EXACT; | |
3077 | SCM result; | |
3f47e526 | 3078 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
3079 | |
3080 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 3081 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 3082 | { |
3f47e526 | 3083 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
3084 | { |
3085 | case 'b': case 'B': | |
3086 | if (radix != NO_RADIX) | |
3087 | return SCM_BOOL_F; | |
3088 | radix = DUAL; | |
3089 | break; | |
3090 | case 'd': case 'D': | |
3091 | if (radix != NO_RADIX) | |
3092 | return SCM_BOOL_F; | |
3093 | radix = DEC; | |
3094 | break; | |
3095 | case 'i': case 'I': | |
3096 | if (forced_x != NO_EXACTNESS) | |
3097 | return SCM_BOOL_F; | |
3098 | forced_x = INEXACT; | |
3099 | break; | |
3100 | case 'e': case 'E': | |
3101 | if (forced_x != NO_EXACTNESS) | |
3102 | return SCM_BOOL_F; | |
3103 | forced_x = EXACT; | |
3104 | break; | |
3105 | case 'o': case 'O': | |
3106 | if (radix != NO_RADIX) | |
3107 | return SCM_BOOL_F; | |
3108 | radix = OCT; | |
3109 | break; | |
3110 | case 'x': case 'X': | |
3111 | if (radix != NO_RADIX) | |
3112 | return SCM_BOOL_F; | |
3113 | radix = HEX; | |
3114 | break; | |
3115 | default: | |
f872b822 | 3116 | return SCM_BOOL_F; |
3c9a524f DH |
3117 | } |
3118 | idx += 2; | |
3119 | } | |
3120 | ||
3121 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
3122 | if (radix == NO_RADIX) | |
3f47e526 | 3123 | result = mem2complex (mem, idx, default_radix, &implicit_x); |
3c9a524f | 3124 | else |
3f47e526 | 3125 | result = mem2complex (mem, idx, (unsigned int) radix, &implicit_x); |
3c9a524f | 3126 | |
73e4de09 | 3127 | if (scm_is_false (result)) |
3c9a524f | 3128 | return SCM_BOOL_F; |
f872b822 | 3129 | |
3c9a524f | 3130 | switch (forced_x) |
f872b822 | 3131 | { |
3c9a524f DH |
3132 | case EXACT: |
3133 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
3134 | return scm_inexact_to_exact (result); |
3135 | else | |
3136 | return result; | |
3137 | case INEXACT: | |
3138 | if (SCM_INEXACTP (result)) | |
3139 | return result; | |
3140 | else | |
3141 | return scm_exact_to_inexact (result); | |
3142 | case NO_EXACTNESS: | |
3143 | default: | |
3144 | if (implicit_x == INEXACT) | |
3145 | { | |
3146 | if (SCM_INEXACTP (result)) | |
3147 | return result; | |
3148 | else | |
3149 | return scm_exact_to_inexact (result); | |
3150 | } | |
3151 | else | |
3152 | return result; | |
f872b822 | 3153 | } |
0f2d19dd JB |
3154 | } |
3155 | ||
3f47e526 MG |
3156 | SCM |
3157 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
3158 | unsigned int default_radix) | |
3159 | { | |
3160 | SCM str = scm_from_locale_stringn (mem, len); | |
3161 | ||
3162 | return scm_i_string_to_number (str, default_radix); | |
3163 | } | |
3164 | ||
0f2d19dd | 3165 | |
a1ec6916 | 3166 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 3167 | (SCM string, SCM radix), |
1e6808ea | 3168 | "Return a number of the maximally precise representation\n" |
942e5b91 | 3169 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
3170 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
3171 | "is a default radix that may be overridden by an explicit radix\n" | |
3172 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
3173 | "supplied, then the default radix is 10. If string is not a\n" | |
3174 | "syntactically valid notation for a number, then\n" | |
3175 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 3176 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
3177 | { |
3178 | SCM answer; | |
5efd3c7d | 3179 | unsigned int base; |
a6d9e5ab | 3180 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
3181 | |
3182 | if (SCM_UNBNDP (radix)) | |
3183 | base = 10; | |
3184 | else | |
3185 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
3186 | ||
3f47e526 | 3187 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
3188 | scm_remember_upto_here_1 (string); |
3189 | return answer; | |
0f2d19dd | 3190 | } |
1bbd0b84 | 3191 | #undef FUNC_NAME |
3c9a524f DH |
3192 | |
3193 | ||
0f2d19dd JB |
3194 | /*** END strs->nums ***/ |
3195 | ||
5986c47d | 3196 | |
0f2d19dd | 3197 | SCM |
1bbd0b84 | 3198 | scm_bigequal (SCM x, SCM y) |
0f2d19dd | 3199 | { |
47ae1f0e | 3200 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
ca46fb90 | 3201 | scm_remember_upto_here_2 (x, y); |
73e4de09 | 3202 | return scm_from_bool (0 == result); |
0f2d19dd JB |
3203 | } |
3204 | ||
0f2d19dd | 3205 | SCM |
f3ae5d60 | 3206 | scm_real_equalp (SCM x, SCM y) |
0f2d19dd | 3207 | { |
73e4de09 | 3208 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0f2d19dd JB |
3209 | } |
3210 | ||
f3ae5d60 MD |
3211 | SCM |
3212 | scm_complex_equalp (SCM x, SCM y) | |
3213 | { | |
73e4de09 | 3214 | return scm_from_bool (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) |
f3ae5d60 MD |
3215 | && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); |
3216 | } | |
0f2d19dd | 3217 | |
f92e85f7 MV |
3218 | SCM |
3219 | scm_i_fraction_equalp (SCM x, SCM y) | |
3220 | { | |
73e4de09 | 3221 | if (scm_is_false (scm_equal_p (SCM_FRACTION_NUMERATOR (x), |
02164269 | 3222 | SCM_FRACTION_NUMERATOR (y))) |
73e4de09 | 3223 | || scm_is_false (scm_equal_p (SCM_FRACTION_DENOMINATOR (x), |
02164269 MV |
3224 | SCM_FRACTION_DENOMINATOR (y)))) |
3225 | return SCM_BOOL_F; | |
3226 | else | |
3227 | return SCM_BOOL_T; | |
f92e85f7 | 3228 | } |
0f2d19dd JB |
3229 | |
3230 | ||
8507ec80 MV |
3231 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
3232 | (SCM x), | |
3233 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
3234 | "otherwise.") | |
3235 | #define FUNC_NAME s_scm_number_p | |
3236 | { | |
3237 | return scm_from_bool (SCM_NUMBERP (x)); | |
3238 | } | |
3239 | #undef FUNC_NAME | |
3240 | ||
3241 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 3242 | (SCM x), |
942e5b91 | 3243 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 3244 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
3245 | "values form subsets of the set of complex numbers, i. e. the\n" |
3246 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
3247 | "rational or integer number.") | |
8507ec80 | 3248 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 3249 | { |
8507ec80 MV |
3250 | /* all numbers are complex. */ |
3251 | return scm_number_p (x); | |
0f2d19dd | 3252 | } |
1bbd0b84 | 3253 | #undef FUNC_NAME |
0f2d19dd | 3254 | |
f92e85f7 MV |
3255 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
3256 | (SCM x), | |
3257 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
3258 | "otherwise. Note that the set of integer values forms a subset of\n" | |
3259 | "the set of real numbers, i. e. the predicate will also be\n" | |
3260 | "fulfilled if @var{x} is an integer number.") | |
3261 | #define FUNC_NAME s_scm_real_p | |
3262 | { | |
3263 | /* we can't represent irrational numbers. */ | |
3264 | return scm_rational_p (x); | |
3265 | } | |
3266 | #undef FUNC_NAME | |
3267 | ||
3268 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 3269 | (SCM x), |
942e5b91 | 3270 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 3271 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 3272 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
3273 | "fulfilled if @var{x} is an integer number.") |
3274 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 3275 | { |
e11e83f3 | 3276 | if (SCM_I_INUMP (x)) |
0f2d19dd | 3277 | return SCM_BOOL_T; |
0aacf84e | 3278 | else if (SCM_IMP (x)) |
0f2d19dd | 3279 | return SCM_BOOL_F; |
0aacf84e | 3280 | else if (SCM_BIGP (x)) |
0f2d19dd | 3281 | return SCM_BOOL_T; |
f92e85f7 MV |
3282 | else if (SCM_FRACTIONP (x)) |
3283 | return SCM_BOOL_T; | |
3284 | else if (SCM_REALP (x)) | |
3285 | /* due to their limited precision, all floating point numbers are | |
3286 | rational as well. */ | |
3287 | return SCM_BOOL_T; | |
0aacf84e | 3288 | else |
bb628794 | 3289 | return SCM_BOOL_F; |
0f2d19dd | 3290 | } |
1bbd0b84 | 3291 | #undef FUNC_NAME |
0f2d19dd | 3292 | |
a1ec6916 | 3293 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 3294 | (SCM x), |
942e5b91 MG |
3295 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
3296 | "else.") | |
1bbd0b84 | 3297 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd JB |
3298 | { |
3299 | double r; | |
e11e83f3 | 3300 | if (SCM_I_INUMP (x)) |
f872b822 MD |
3301 | return SCM_BOOL_T; |
3302 | if (SCM_IMP (x)) | |
3303 | return SCM_BOOL_F; | |
f872b822 MD |
3304 | if (SCM_BIGP (x)) |
3305 | return SCM_BOOL_T; | |
3c9a524f | 3306 | if (!SCM_INEXACTP (x)) |
f872b822 | 3307 | return SCM_BOOL_F; |
3c9a524f | 3308 | if (SCM_COMPLEXP (x)) |
f872b822 | 3309 | return SCM_BOOL_F; |
5986c47d | 3310 | r = SCM_REAL_VALUE (x); |
1e35a229 | 3311 | /* +/-inf passes r==floor(r), making those #t */ |
f872b822 MD |
3312 | if (r == floor (r)) |
3313 | return SCM_BOOL_T; | |
0f2d19dd JB |
3314 | return SCM_BOOL_F; |
3315 | } | |
1bbd0b84 | 3316 | #undef FUNC_NAME |
0f2d19dd JB |
3317 | |
3318 | ||
a1ec6916 | 3319 | SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, |
1bbd0b84 | 3320 | (SCM x), |
942e5b91 MG |
3321 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" |
3322 | "else.") | |
1bbd0b84 | 3323 | #define FUNC_NAME s_scm_inexact_p |
0f2d19dd | 3324 | { |
eb927cb9 MV |
3325 | if (SCM_INEXACTP (x)) |
3326 | return SCM_BOOL_T; | |
3327 | if (SCM_NUMBERP (x)) | |
3328 | return SCM_BOOL_F; | |
3329 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 3330 | } |
1bbd0b84 | 3331 | #undef FUNC_NAME |
0f2d19dd JB |
3332 | |
3333 | ||
152f82bf | 3334 | SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p); |
942e5b91 | 3335 | /* "Return @code{#t} if all parameters are numerically equal." */ |
0f2d19dd | 3336 | SCM |
6e8d25a6 | 3337 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 3338 | { |
d8b95e27 | 3339 | again: |
e11e83f3 | 3340 | if (SCM_I_INUMP (x)) |
0aacf84e | 3341 | { |
e11e83f3 MV |
3342 | long xx = SCM_I_INUM (x); |
3343 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3344 | { |
e11e83f3 | 3345 | long yy = SCM_I_INUM (y); |
73e4de09 | 3346 | return scm_from_bool (xx == yy); |
0aacf84e MD |
3347 | } |
3348 | else if (SCM_BIGP (y)) | |
3349 | return SCM_BOOL_F; | |
3350 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
3351 | { |
3352 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
3353 | to a double and compare. | |
3354 | ||
3355 | But on a 64-bit system an inum is bigger than a double and | |
3356 | casting it to a double (call that dxx) will round. dxx is at | |
3357 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
3358 | an integer and fits a long. So we cast yy to a long and | |
3359 | compare with plain xx. | |
3360 | ||
3361 | An alternative (for any size system actually) would be to check | |
3362 | yy is an integer (with floor) and is in range of an inum | |
3363 | (compare against appropriate powers of 2) then test | |
3364 | xx==(long)yy. It's just a matter of which casts/comparisons | |
3365 | might be fastest or easiest for the cpu. */ | |
3366 | ||
3367 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
3368 | return scm_from_bool ((double) xx == yy |
3369 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
3370 | || xx == (long) yy)); | |
e8c5b1f2 | 3371 | } |
0aacf84e | 3372 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3373 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3374 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
3375 | else if (SCM_FRACTIONP (y)) |
3376 | return SCM_BOOL_F; | |
0aacf84e MD |
3377 | else |
3378 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3379 | } |
0aacf84e MD |
3380 | else if (SCM_BIGP (x)) |
3381 | { | |
e11e83f3 | 3382 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3383 | return SCM_BOOL_F; |
3384 | else if (SCM_BIGP (y)) | |
3385 | { | |
3386 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3387 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3388 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3389 | } |
3390 | else if (SCM_REALP (y)) | |
3391 | { | |
3392 | int cmp; | |
3393 | if (xisnan (SCM_REAL_VALUE (y))) | |
3394 | return SCM_BOOL_F; | |
3395 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3396 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3397 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3398 | } |
3399 | else if (SCM_COMPLEXP (y)) | |
3400 | { | |
3401 | int cmp; | |
3402 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
3403 | return SCM_BOOL_F; | |
3404 | if (xisnan (SCM_COMPLEX_REAL (y))) | |
3405 | return SCM_BOOL_F; | |
3406 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
3407 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3408 | return scm_from_bool (0 == cmp); |
0aacf84e | 3409 | } |
f92e85f7 MV |
3410 | else if (SCM_FRACTIONP (y)) |
3411 | return SCM_BOOL_F; | |
0aacf84e MD |
3412 | else |
3413 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3414 | } |
0aacf84e MD |
3415 | else if (SCM_REALP (x)) |
3416 | { | |
e8c5b1f2 | 3417 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 3418 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
3419 | { |
3420 | /* see comments with inum/real above */ | |
3421 | long yy = SCM_I_INUM (y); | |
3a1b45fd MV |
3422 | return scm_from_bool (xx == (double) yy |
3423 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
3424 | || (long) xx == yy)); | |
e8c5b1f2 | 3425 | } |
0aacf84e MD |
3426 | else if (SCM_BIGP (y)) |
3427 | { | |
3428 | int cmp; | |
3429 | if (xisnan (SCM_REAL_VALUE (x))) | |
3430 | return SCM_BOOL_F; | |
3431 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3432 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3433 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3434 | } |
3435 | else if (SCM_REALP (y)) | |
73e4de09 | 3436 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 3437 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3438 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3439 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3440 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3441 | { |
3442 | double xx = SCM_REAL_VALUE (x); | |
3443 | if (xisnan (xx)) | |
3444 | return SCM_BOOL_F; | |
3445 | if (xisinf (xx)) | |
73e4de09 | 3446 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3447 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3448 | goto again; | |
3449 | } | |
0aacf84e MD |
3450 | else |
3451 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3452 | } |
0aacf84e MD |
3453 | else if (SCM_COMPLEXP (x)) |
3454 | { | |
e11e83f3 MV |
3455 | if (SCM_I_INUMP (y)) |
3456 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
3457 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3458 | else if (SCM_BIGP (y)) | |
3459 | { | |
3460 | int cmp; | |
3461 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
3462 | return SCM_BOOL_F; | |
3463 | if (xisnan (SCM_COMPLEX_REAL (x))) | |
3464 | return SCM_BOOL_F; | |
3465 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
3466 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3467 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3468 | } |
3469 | else if (SCM_REALP (y)) | |
73e4de09 | 3470 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
3471 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3472 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 3473 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3474 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3475 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3476 | { |
3477 | double xx; | |
3478 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
3479 | return SCM_BOOL_F; | |
3480 | xx = SCM_COMPLEX_REAL (x); | |
3481 | if (xisnan (xx)) | |
3482 | return SCM_BOOL_F; | |
3483 | if (xisinf (xx)) | |
73e4de09 | 3484 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3485 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3486 | goto again; | |
3487 | } | |
f92e85f7 MV |
3488 | else |
3489 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
3490 | } | |
3491 | else if (SCM_FRACTIONP (x)) | |
3492 | { | |
e11e83f3 | 3493 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
3494 | return SCM_BOOL_F; |
3495 | else if (SCM_BIGP (y)) | |
3496 | return SCM_BOOL_F; | |
3497 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
3498 | { |
3499 | double yy = SCM_REAL_VALUE (y); | |
3500 | if (xisnan (yy)) | |
3501 | return SCM_BOOL_F; | |
3502 | if (xisinf (yy)) | |
73e4de09 | 3503 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3504 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3505 | goto again; | |
3506 | } | |
f92e85f7 | 3507 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
3508 | { |
3509 | double yy; | |
3510 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
3511 | return SCM_BOOL_F; | |
3512 | yy = SCM_COMPLEX_REAL (y); | |
3513 | if (xisnan (yy)) | |
3514 | return SCM_BOOL_F; | |
3515 | if (xisinf (yy)) | |
73e4de09 | 3516 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3517 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3518 | goto again; | |
3519 | } | |
f92e85f7 MV |
3520 | else if (SCM_FRACTIONP (y)) |
3521 | return scm_i_fraction_equalp (x, y); | |
0aacf84e MD |
3522 | else |
3523 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3524 | } |
0aacf84e | 3525 | else |
f4c627b3 | 3526 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p); |
0f2d19dd JB |
3527 | } |
3528 | ||
3529 | ||
a5f0b599 KR |
3530 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
3531 | done are good for inums, but for bignums an answer can almost always be | |
3532 | had by just examining a few high bits of the operands, as done by GMP in | |
3533 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
3534 | of the float exponent to take into account. */ | |
3535 | ||
152f82bf | 3536 | SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p); |
942e5b91 MG |
3537 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3538 | * "increasing." | |
3539 | */ | |
0f2d19dd | 3540 | SCM |
6e8d25a6 | 3541 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3542 | { |
a5f0b599 | 3543 | again: |
e11e83f3 | 3544 | if (SCM_I_INUMP (x)) |
0aacf84e | 3545 | { |
e11e83f3 MV |
3546 | long xx = SCM_I_INUM (x); |
3547 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3548 | { |
e11e83f3 | 3549 | long yy = SCM_I_INUM (y); |
73e4de09 | 3550 | return scm_from_bool (xx < yy); |
0aacf84e MD |
3551 | } |
3552 | else if (SCM_BIGP (y)) | |
3553 | { | |
3554 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3555 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3556 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3557 | } |
3558 | else if (SCM_REALP (y)) | |
73e4de09 | 3559 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 3560 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3561 | { |
3562 | /* "x < a/b" becomes "x*b < a" */ | |
3563 | int_frac: | |
3564 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
3565 | y = SCM_FRACTION_NUMERATOR (y); | |
3566 | goto again; | |
3567 | } | |
0aacf84e MD |
3568 | else |
3569 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3570 | } |
0aacf84e MD |
3571 | else if (SCM_BIGP (x)) |
3572 | { | |
e11e83f3 | 3573 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3574 | { |
3575 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3576 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3577 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3578 | } |
3579 | else if (SCM_BIGP (y)) | |
3580 | { | |
3581 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3582 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3583 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
3584 | } |
3585 | else if (SCM_REALP (y)) | |
3586 | { | |
3587 | int cmp; | |
3588 | if (xisnan (SCM_REAL_VALUE (y))) | |
3589 | return SCM_BOOL_F; | |
3590 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3591 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3592 | return scm_from_bool (cmp < 0); |
0aacf84e | 3593 | } |
f92e85f7 | 3594 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 3595 | goto int_frac; |
0aacf84e MD |
3596 | else |
3597 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f4c627b3 | 3598 | } |
0aacf84e MD |
3599 | else if (SCM_REALP (x)) |
3600 | { | |
e11e83f3 MV |
3601 | if (SCM_I_INUMP (y)) |
3602 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3603 | else if (SCM_BIGP (y)) |
3604 | { | |
3605 | int cmp; | |
3606 | if (xisnan (SCM_REAL_VALUE (x))) | |
3607 | return SCM_BOOL_F; | |
3608 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3609 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3610 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
3611 | } |
3612 | else if (SCM_REALP (y)) | |
73e4de09 | 3613 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 3614 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3615 | { |
3616 | double xx = SCM_REAL_VALUE (x); | |
3617 | if (xisnan (xx)) | |
3618 | return SCM_BOOL_F; | |
3619 | if (xisinf (xx)) | |
73e4de09 | 3620 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
3621 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3622 | goto again; | |
3623 | } | |
f92e85f7 MV |
3624 | else |
3625 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
3626 | } | |
3627 | else if (SCM_FRACTIONP (x)) | |
3628 | { | |
e11e83f3 | 3629 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
3630 | { |
3631 | /* "a/b < y" becomes "a < y*b" */ | |
3632 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
3633 | x = SCM_FRACTION_NUMERATOR (x); | |
3634 | goto again; | |
3635 | } | |
f92e85f7 | 3636 | else if (SCM_REALP (y)) |
a5f0b599 KR |
3637 | { |
3638 | double yy = SCM_REAL_VALUE (y); | |
3639 | if (xisnan (yy)) | |
3640 | return SCM_BOOL_F; | |
3641 | if (xisinf (yy)) | |
73e4de09 | 3642 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
3643 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3644 | goto again; | |
3645 | } | |
f92e85f7 | 3646 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3647 | { |
3648 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
3649 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
3650 | SCM_FRACTION_DENOMINATOR (y)); | |
3651 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
3652 | SCM_FRACTION_DENOMINATOR (x)); | |
3653 | x = new_x; | |
3654 | y = new_y; | |
3655 | goto again; | |
3656 | } | |
0aacf84e MD |
3657 | else |
3658 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3659 | } |
0aacf84e | 3660 | else |
f4c627b3 | 3661 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p); |
0f2d19dd JB |
3662 | } |
3663 | ||
3664 | ||
c76b1eaf | 3665 | SCM_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p); |
942e5b91 MG |
3666 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3667 | * "decreasing." | |
c76b1eaf | 3668 | */ |
1bbd0b84 | 3669 | #define FUNC_NAME s_scm_gr_p |
c76b1eaf MD |
3670 | SCM |
3671 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3672 | { |
c76b1eaf MD |
3673 | if (!SCM_NUMBERP (x)) |
3674 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME); | |
3675 | else if (!SCM_NUMBERP (y)) | |
3676 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME); | |
3677 | else | |
3678 | return scm_less_p (y, x); | |
0f2d19dd | 3679 | } |
1bbd0b84 | 3680 | #undef FUNC_NAME |
0f2d19dd JB |
3681 | |
3682 | ||
c76b1eaf | 3683 | SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p); |
942e5b91 | 3684 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3685 | * "non-decreasing." |
3686 | */ | |
1bbd0b84 | 3687 | #define FUNC_NAME s_scm_leq_p |
c76b1eaf MD |
3688 | SCM |
3689 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3690 | { |
c76b1eaf MD |
3691 | if (!SCM_NUMBERP (x)) |
3692 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3693 | else if (!SCM_NUMBERP (y)) | |
3694 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3695 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3696 | return SCM_BOOL_F; |
c76b1eaf | 3697 | else |
73e4de09 | 3698 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 3699 | } |
1bbd0b84 | 3700 | #undef FUNC_NAME |
0f2d19dd JB |
3701 | |
3702 | ||
c76b1eaf | 3703 | SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p); |
942e5b91 | 3704 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3705 | * "non-increasing." |
3706 | */ | |
1bbd0b84 | 3707 | #define FUNC_NAME s_scm_geq_p |
c76b1eaf MD |
3708 | SCM |
3709 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3710 | { |
c76b1eaf MD |
3711 | if (!SCM_NUMBERP (x)) |
3712 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3713 | else if (!SCM_NUMBERP (y)) | |
3714 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3715 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3716 | return SCM_BOOL_F; |
c76b1eaf | 3717 | else |
73e4de09 | 3718 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 3719 | } |
1bbd0b84 | 3720 | #undef FUNC_NAME |
0f2d19dd JB |
3721 | |
3722 | ||
152f82bf | 3723 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3724 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3725 | * "zero." | |
3726 | */ | |
0f2d19dd | 3727 | SCM |
6e8d25a6 | 3728 | scm_zero_p (SCM z) |
0f2d19dd | 3729 | { |
e11e83f3 | 3730 | if (SCM_I_INUMP (z)) |
bc36d050 | 3731 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 3732 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 3733 | return SCM_BOOL_F; |
0aacf84e | 3734 | else if (SCM_REALP (z)) |
73e4de09 | 3735 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 3736 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 3737 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 3738 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
3739 | else if (SCM_FRACTIONP (z)) |
3740 | return SCM_BOOL_F; | |
0aacf84e | 3741 | else |
c2ff8ab0 | 3742 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); |
0f2d19dd JB |
3743 | } |
3744 | ||
3745 | ||
152f82bf | 3746 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3747 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3748 | * "zero." | |
3749 | */ | |
0f2d19dd | 3750 | SCM |
6e8d25a6 | 3751 | scm_positive_p (SCM x) |
0f2d19dd | 3752 | { |
e11e83f3 MV |
3753 | if (SCM_I_INUMP (x)) |
3754 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
3755 | else if (SCM_BIGP (x)) |
3756 | { | |
3757 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3758 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3759 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3760 | } |
3761 | else if (SCM_REALP (x)) | |
73e4de09 | 3762 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
3763 | else if (SCM_FRACTIONP (x)) |
3764 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3765 | else |
c2ff8ab0 | 3766 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); |
0f2d19dd JB |
3767 | } |
3768 | ||
3769 | ||
152f82bf | 3770 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3771 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3772 | * "zero." | |
3773 | */ | |
0f2d19dd | 3774 | SCM |
6e8d25a6 | 3775 | scm_negative_p (SCM x) |
0f2d19dd | 3776 | { |
e11e83f3 MV |
3777 | if (SCM_I_INUMP (x)) |
3778 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
3779 | else if (SCM_BIGP (x)) |
3780 | { | |
3781 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3782 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3783 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3784 | } |
3785 | else if (SCM_REALP (x)) | |
73e4de09 | 3786 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
3787 | else if (SCM_FRACTIONP (x)) |
3788 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3789 | else |
c2ff8ab0 | 3790 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); |
0f2d19dd JB |
3791 | } |
3792 | ||
3793 | ||
2a06f791 KR |
3794 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
3795 | required by r5rs. On that basis, for exact/inexact combinations the | |
3796 | exact is converted to inexact to compare and possibly return. This is | |
3797 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
3798 | its test, such trouble is not required for min and max. */ | |
3799 | ||
78d3deb1 AW |
3800 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
3801 | (SCM x, SCM y, SCM rest), | |
3802 | "Return the maximum of all parameter values.") | |
3803 | #define FUNC_NAME s_scm_i_max | |
3804 | { | |
3805 | while (!scm_is_null (rest)) | |
3806 | { x = scm_max (x, y); | |
3807 | y = scm_car (rest); | |
3808 | rest = scm_cdr (rest); | |
3809 | } | |
3810 | return scm_max (x, y); | |
3811 | } | |
3812 | #undef FUNC_NAME | |
3813 | ||
3814 | #define s_max s_scm_i_max | |
3815 | #define g_max g_scm_i_max | |
3816 | ||
0f2d19dd | 3817 | SCM |
6e8d25a6 | 3818 | scm_max (SCM x, SCM y) |
0f2d19dd | 3819 | { |
0aacf84e MD |
3820 | if (SCM_UNBNDP (y)) |
3821 | { | |
3822 | if (SCM_UNBNDP (x)) | |
3823 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 3824 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3825 | return x; |
3826 | else | |
3827 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3828 | } |
f4c627b3 | 3829 | |
e11e83f3 | 3830 | if (SCM_I_INUMP (x)) |
0aacf84e | 3831 | { |
e11e83f3 MV |
3832 | long xx = SCM_I_INUM (x); |
3833 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3834 | { |
e11e83f3 | 3835 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3836 | return (xx < yy) ? y : x; |
3837 | } | |
3838 | else if (SCM_BIGP (y)) | |
3839 | { | |
3840 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3841 | scm_remember_upto_here_1 (y); | |
3842 | return (sgn < 0) ? x : y; | |
3843 | } | |
3844 | else if (SCM_REALP (y)) | |
3845 | { | |
3846 | double z = xx; | |
3847 | /* if y==NaN then ">" is false and we return NaN */ | |
55f26379 | 3848 | return (z > SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3849 | } |
f92e85f7 MV |
3850 | else if (SCM_FRACTIONP (y)) |
3851 | { | |
e4bc5d6c | 3852 | use_less: |
73e4de09 | 3853 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 3854 | } |
0aacf84e MD |
3855 | else |
3856 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3857 | } |
0aacf84e MD |
3858 | else if (SCM_BIGP (x)) |
3859 | { | |
e11e83f3 | 3860 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3861 | { |
3862 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3863 | scm_remember_upto_here_1 (x); | |
3864 | return (sgn < 0) ? y : x; | |
3865 | } | |
3866 | else if (SCM_BIGP (y)) | |
3867 | { | |
3868 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3869 | scm_remember_upto_here_2 (x, y); | |
3870 | return (cmp > 0) ? x : y; | |
3871 | } | |
3872 | else if (SCM_REALP (y)) | |
3873 | { | |
2a06f791 KR |
3874 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
3875 | double xx, yy; | |
3876 | big_real: | |
3877 | xx = scm_i_big2dbl (x); | |
3878 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3879 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 3880 | } |
f92e85f7 MV |
3881 | else if (SCM_FRACTIONP (y)) |
3882 | { | |
e4bc5d6c | 3883 | goto use_less; |
f92e85f7 | 3884 | } |
0aacf84e MD |
3885 | else |
3886 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 3887 | } |
0aacf84e MD |
3888 | else if (SCM_REALP (x)) |
3889 | { | |
e11e83f3 | 3890 | if (SCM_I_INUMP (y)) |
0aacf84e | 3891 | { |
e11e83f3 | 3892 | double z = SCM_I_INUM (y); |
0aacf84e | 3893 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3894 | return (SCM_REAL_VALUE (x) < z) ? scm_from_double (z) : x; |
0aacf84e MD |
3895 | } |
3896 | else if (SCM_BIGP (y)) | |
3897 | { | |
b6f8f763 | 3898 | SCM_SWAP (x, y); |
2a06f791 | 3899 | goto big_real; |
0aacf84e MD |
3900 | } |
3901 | else if (SCM_REALP (y)) | |
3902 | { | |
3903 | /* if x==NaN then our explicit check means we return NaN | |
3904 | if y==NaN then ">" is false and we return NaN | |
3905 | calling isnan is unavoidable, since it's the only way to know | |
3906 | which of x or y causes any compares to be false */ | |
3907 | double xx = SCM_REAL_VALUE (x); | |
3908 | return (xisnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y; | |
3909 | } | |
f92e85f7 MV |
3910 | else if (SCM_FRACTIONP (y)) |
3911 | { | |
3912 | double yy = scm_i_fraction2double (y); | |
3913 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3914 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
3915 | } |
3916 | else | |
3917 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3918 | } | |
3919 | else if (SCM_FRACTIONP (x)) | |
3920 | { | |
e11e83f3 | 3921 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3922 | { |
e4bc5d6c | 3923 | goto use_less; |
f92e85f7 MV |
3924 | } |
3925 | else if (SCM_BIGP (y)) | |
3926 | { | |
e4bc5d6c | 3927 | goto use_less; |
f92e85f7 MV |
3928 | } |
3929 | else if (SCM_REALP (y)) | |
3930 | { | |
3931 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3932 | return (xx < SCM_REAL_VALUE (y)) ? y : scm_from_double (xx); |
f92e85f7 MV |
3933 | } |
3934 | else if (SCM_FRACTIONP (y)) | |
3935 | { | |
e4bc5d6c | 3936 | goto use_less; |
f92e85f7 | 3937 | } |
0aacf84e MD |
3938 | else |
3939 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3940 | } |
0aacf84e | 3941 | else |
f4c627b3 | 3942 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
3943 | } |
3944 | ||
3945 | ||
78d3deb1 AW |
3946 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
3947 | (SCM x, SCM y, SCM rest), | |
3948 | "Return the minimum of all parameter values.") | |
3949 | #define FUNC_NAME s_scm_i_min | |
3950 | { | |
3951 | while (!scm_is_null (rest)) | |
3952 | { x = scm_min (x, y); | |
3953 | y = scm_car (rest); | |
3954 | rest = scm_cdr (rest); | |
3955 | } | |
3956 | return scm_min (x, y); | |
3957 | } | |
3958 | #undef FUNC_NAME | |
3959 | ||
3960 | #define s_min s_scm_i_min | |
3961 | #define g_min g_scm_i_min | |
3962 | ||
0f2d19dd | 3963 | SCM |
6e8d25a6 | 3964 | scm_min (SCM x, SCM y) |
0f2d19dd | 3965 | { |
0aacf84e MD |
3966 | if (SCM_UNBNDP (y)) |
3967 | { | |
3968 | if (SCM_UNBNDP (x)) | |
3969 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 3970 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3971 | return x; |
3972 | else | |
3973 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 3974 | } |
f4c627b3 | 3975 | |
e11e83f3 | 3976 | if (SCM_I_INUMP (x)) |
0aacf84e | 3977 | { |
e11e83f3 MV |
3978 | long xx = SCM_I_INUM (x); |
3979 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3980 | { |
e11e83f3 | 3981 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3982 | return (xx < yy) ? x : y; |
3983 | } | |
3984 | else if (SCM_BIGP (y)) | |
3985 | { | |
3986 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3987 | scm_remember_upto_here_1 (y); | |
3988 | return (sgn < 0) ? y : x; | |
3989 | } | |
3990 | else if (SCM_REALP (y)) | |
3991 | { | |
3992 | double z = xx; | |
3993 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 3994 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3995 | } |
f92e85f7 MV |
3996 | else if (SCM_FRACTIONP (y)) |
3997 | { | |
e4bc5d6c | 3998 | use_less: |
73e4de09 | 3999 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 4000 | } |
0aacf84e MD |
4001 | else |
4002 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 4003 | } |
0aacf84e MD |
4004 | else if (SCM_BIGP (x)) |
4005 | { | |
e11e83f3 | 4006 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4007 | { |
4008 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4009 | scm_remember_upto_here_1 (x); | |
4010 | return (sgn < 0) ? x : y; | |
4011 | } | |
4012 | else if (SCM_BIGP (y)) | |
4013 | { | |
4014 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4015 | scm_remember_upto_here_2 (x, y); | |
4016 | return (cmp > 0) ? y : x; | |
4017 | } | |
4018 | else if (SCM_REALP (y)) | |
4019 | { | |
2a06f791 KR |
4020 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
4021 | double xx, yy; | |
4022 | big_real: | |
4023 | xx = scm_i_big2dbl (x); | |
4024 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 4025 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 4026 | } |
f92e85f7 MV |
4027 | else if (SCM_FRACTIONP (y)) |
4028 | { | |
e4bc5d6c | 4029 | goto use_less; |
f92e85f7 | 4030 | } |
0aacf84e MD |
4031 | else |
4032 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 4033 | } |
0aacf84e MD |
4034 | else if (SCM_REALP (x)) |
4035 | { | |
e11e83f3 | 4036 | if (SCM_I_INUMP (y)) |
0aacf84e | 4037 | { |
e11e83f3 | 4038 | double z = SCM_I_INUM (y); |
0aacf84e | 4039 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 4040 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
4041 | } |
4042 | else if (SCM_BIGP (y)) | |
4043 | { | |
b6f8f763 | 4044 | SCM_SWAP (x, y); |
2a06f791 | 4045 | goto big_real; |
0aacf84e MD |
4046 | } |
4047 | else if (SCM_REALP (y)) | |
4048 | { | |
4049 | /* if x==NaN then our explicit check means we return NaN | |
4050 | if y==NaN then "<" is false and we return NaN | |
4051 | calling isnan is unavoidable, since it's the only way to know | |
4052 | which of x or y causes any compares to be false */ | |
4053 | double xx = SCM_REAL_VALUE (x); | |
4054 | return (xisnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y; | |
4055 | } | |
f92e85f7 MV |
4056 | else if (SCM_FRACTIONP (y)) |
4057 | { | |
4058 | double yy = scm_i_fraction2double (y); | |
4059 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 4060 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 4061 | } |
0aacf84e MD |
4062 | else |
4063 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 4064 | } |
f92e85f7 MV |
4065 | else if (SCM_FRACTIONP (x)) |
4066 | { | |
e11e83f3 | 4067 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4068 | { |
e4bc5d6c | 4069 | goto use_less; |
f92e85f7 MV |
4070 | } |
4071 | else if (SCM_BIGP (y)) | |
4072 | { | |
e4bc5d6c | 4073 | goto use_less; |
f92e85f7 MV |
4074 | } |
4075 | else if (SCM_REALP (y)) | |
4076 | { | |
4077 | double xx = scm_i_fraction2double (x); | |
55f26379 | 4078 | return (SCM_REAL_VALUE (y) < xx) ? y : scm_from_double (xx); |
f92e85f7 MV |
4079 | } |
4080 | else if (SCM_FRACTIONP (y)) | |
4081 | { | |
e4bc5d6c | 4082 | goto use_less; |
f92e85f7 MV |
4083 | } |
4084 | else | |
78d3deb1 | 4085 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 4086 | } |
0aacf84e | 4087 | else |
f4c627b3 | 4088 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
4089 | } |
4090 | ||
4091 | ||
8ccd24f7 AW |
4092 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
4093 | (SCM x, SCM y, SCM rest), | |
4094 | "Return the sum of all parameter values. Return 0 if called without\n" | |
4095 | "any parameters." ) | |
4096 | #define FUNC_NAME s_scm_i_sum | |
4097 | { | |
4098 | while (!scm_is_null (rest)) | |
4099 | { x = scm_sum (x, y); | |
4100 | y = scm_car (rest); | |
4101 | rest = scm_cdr (rest); | |
4102 | } | |
4103 | return scm_sum (x, y); | |
4104 | } | |
4105 | #undef FUNC_NAME | |
4106 | ||
4107 | #define s_sum s_scm_i_sum | |
4108 | #define g_sum g_scm_i_sum | |
4109 | ||
0f2d19dd | 4110 | SCM |
6e8d25a6 | 4111 | scm_sum (SCM x, SCM y) |
0f2d19dd | 4112 | { |
9cc37597 | 4113 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
4114 | { |
4115 | if (SCM_NUMBERP (x)) return x; | |
4116 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 4117 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 4118 | } |
c209c88e | 4119 | |
9cc37597 | 4120 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 4121 | { |
9cc37597 | 4122 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 4123 | { |
e11e83f3 MV |
4124 | long xx = SCM_I_INUM (x); |
4125 | long yy = SCM_I_INUM (y); | |
ca46fb90 | 4126 | long int z = xx + yy; |
d956fa6f | 4127 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_long2big (z); |
ca46fb90 RB |
4128 | } |
4129 | else if (SCM_BIGP (y)) | |
4130 | { | |
4131 | SCM_SWAP (x, y); | |
4132 | goto add_big_inum; | |
4133 | } | |
4134 | else if (SCM_REALP (y)) | |
4135 | { | |
e11e83f3 | 4136 | long int xx = SCM_I_INUM (x); |
55f26379 | 4137 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
4138 | } |
4139 | else if (SCM_COMPLEXP (y)) | |
4140 | { | |
e11e83f3 | 4141 | long int xx = SCM_I_INUM (x); |
8507ec80 | 4142 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
4143 | SCM_COMPLEX_IMAG (y)); |
4144 | } | |
f92e85f7 | 4145 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4146 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
4147 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
4148 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
4149 | else |
4150 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
4151 | } else if (SCM_BIGP (x)) |
4152 | { | |
e11e83f3 | 4153 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4154 | { |
4155 | long int inum; | |
4156 | int bigsgn; | |
4157 | add_big_inum: | |
e11e83f3 | 4158 | inum = SCM_I_INUM (y); |
0aacf84e MD |
4159 | if (inum == 0) |
4160 | return x; | |
4161 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4162 | if (inum < 0) | |
4163 | { | |
4164 | SCM result = scm_i_mkbig (); | |
4165 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
4166 | scm_remember_upto_here_1 (x); | |
4167 | /* we know the result will have to be a bignum */ | |
4168 | if (bigsgn == -1) | |
4169 | return result; | |
4170 | return scm_i_normbig (result); | |
4171 | } | |
4172 | else | |
4173 | { | |
4174 | SCM result = scm_i_mkbig (); | |
4175 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
4176 | scm_remember_upto_here_1 (x); | |
4177 | /* we know the result will have to be a bignum */ | |
4178 | if (bigsgn == 1) | |
4179 | return result; | |
4180 | return scm_i_normbig (result); | |
4181 | } | |
4182 | } | |
4183 | else if (SCM_BIGP (y)) | |
4184 | { | |
4185 | SCM result = scm_i_mkbig (); | |
4186 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4187 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4188 | mpz_add (SCM_I_BIG_MPZ (result), | |
4189 | SCM_I_BIG_MPZ (x), | |
4190 | SCM_I_BIG_MPZ (y)); | |
4191 | scm_remember_upto_here_2 (x, y); | |
4192 | /* we know the result will have to be a bignum */ | |
4193 | if (sgn_x == sgn_y) | |
4194 | return result; | |
4195 | return scm_i_normbig (result); | |
4196 | } | |
4197 | else if (SCM_REALP (y)) | |
4198 | { | |
4199 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
4200 | scm_remember_upto_here_1 (x); | |
55f26379 | 4201 | return scm_from_double (result); |
0aacf84e MD |
4202 | } |
4203 | else if (SCM_COMPLEXP (y)) | |
4204 | { | |
4205 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4206 | + SCM_COMPLEX_REAL (y)); | |
4207 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4208 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4209 | } |
f92e85f7 | 4210 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4211 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
4212 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
4213 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4214 | else |
4215 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 4216 | } |
0aacf84e MD |
4217 | else if (SCM_REALP (x)) |
4218 | { | |
e11e83f3 | 4219 | if (SCM_I_INUMP (y)) |
55f26379 | 4220 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
4221 | else if (SCM_BIGP (y)) |
4222 | { | |
4223 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
4224 | scm_remember_upto_here_1 (y); | |
55f26379 | 4225 | return scm_from_double (result); |
0aacf84e MD |
4226 | } |
4227 | else if (SCM_REALP (y)) | |
55f26379 | 4228 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 4229 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4230 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4231 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4232 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4233 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
4234 | else |
4235 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 4236 | } |
0aacf84e MD |
4237 | else if (SCM_COMPLEXP (x)) |
4238 | { | |
e11e83f3 | 4239 | if (SCM_I_INUMP (y)) |
8507ec80 | 4240 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
4241 | SCM_COMPLEX_IMAG (x)); |
4242 | else if (SCM_BIGP (y)) | |
4243 | { | |
4244 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
4245 | + SCM_COMPLEX_REAL (x)); | |
4246 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4247 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4248 | } |
4249 | else if (SCM_REALP (y)) | |
8507ec80 | 4250 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
4251 | SCM_COMPLEX_IMAG (x)); |
4252 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4253 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4254 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4255 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4256 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
4257 | SCM_COMPLEX_IMAG (x)); |
4258 | else | |
4259 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
4260 | } | |
4261 | else if (SCM_FRACTIONP (x)) | |
4262 | { | |
e11e83f3 | 4263 | if (SCM_I_INUMP (y)) |
cba42c93 | 4264 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4265 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4266 | SCM_FRACTION_DENOMINATOR (x)); | |
4267 | else if (SCM_BIGP (y)) | |
cba42c93 | 4268 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4269 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4270 | SCM_FRACTION_DENOMINATOR (x)); | |
4271 | else if (SCM_REALP (y)) | |
55f26379 | 4272 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 4273 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4274 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
4275 | SCM_COMPLEX_IMAG (y)); |
4276 | else if (SCM_FRACTIONP (y)) | |
4277 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 4278 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4279 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4280 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4281 | else |
4282 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 4283 | } |
0aacf84e | 4284 | else |
98cb6e75 | 4285 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
4286 | } |
4287 | ||
4288 | ||
40882e3d KR |
4289 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
4290 | (SCM x), | |
4291 | "Return @math{@var{x}+1}.") | |
4292 | #define FUNC_NAME s_scm_oneplus | |
4293 | { | |
4294 | return scm_sum (x, SCM_I_MAKINUM (1)); | |
4295 | } | |
4296 | #undef FUNC_NAME | |
4297 | ||
4298 | ||
78d3deb1 AW |
4299 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
4300 | (SCM x, SCM y, SCM rest), | |
4301 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
4302 | "the sum of all but the first argument are subtracted from the first\n" | |
4303 | "argument.") | |
4304 | #define FUNC_NAME s_scm_i_difference | |
4305 | { | |
4306 | while (!scm_is_null (rest)) | |
4307 | { x = scm_difference (x, y); | |
4308 | y = scm_car (rest); | |
4309 | rest = scm_cdr (rest); | |
4310 | } | |
4311 | return scm_difference (x, y); | |
4312 | } | |
4313 | #undef FUNC_NAME | |
4314 | ||
4315 | #define s_difference s_scm_i_difference | |
4316 | #define g_difference g_scm_i_difference | |
4317 | ||
0f2d19dd | 4318 | SCM |
6e8d25a6 | 4319 | scm_difference (SCM x, SCM y) |
78d3deb1 | 4320 | #define FUNC_NAME s_difference |
0f2d19dd | 4321 | { |
9cc37597 | 4322 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
4323 | { |
4324 | if (SCM_UNBNDP (x)) | |
4325 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
4326 | else | |
e11e83f3 | 4327 | if (SCM_I_INUMP (x)) |
ca46fb90 | 4328 | { |
e11e83f3 | 4329 | long xx = -SCM_I_INUM (x); |
ca46fb90 | 4330 | if (SCM_FIXABLE (xx)) |
d956fa6f | 4331 | return SCM_I_MAKINUM (xx); |
ca46fb90 RB |
4332 | else |
4333 | return scm_i_long2big (xx); | |
4334 | } | |
4335 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
4336 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
4337 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
4338 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
4339 | else if (SCM_REALP (x)) | |
55f26379 | 4340 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 4341 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 4342 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 4343 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 4344 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4345 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 4346 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
4347 | else |
4348 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 4349 | } |
ca46fb90 | 4350 | |
9cc37597 | 4351 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 4352 | { |
9cc37597 | 4353 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4354 | { |
e11e83f3 MV |
4355 | long int xx = SCM_I_INUM (x); |
4356 | long int yy = SCM_I_INUM (y); | |
0aacf84e MD |
4357 | long int z = xx - yy; |
4358 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4359 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4360 | else |
4361 | return scm_i_long2big (z); | |
4362 | } | |
4363 | else if (SCM_BIGP (y)) | |
4364 | { | |
4365 | /* inum-x - big-y */ | |
e11e83f3 | 4366 | long xx = SCM_I_INUM (x); |
ca46fb90 | 4367 | |
0aacf84e MD |
4368 | if (xx == 0) |
4369 | return scm_i_clonebig (y, 0); | |
4370 | else | |
4371 | { | |
4372 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4373 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4374 | |
0aacf84e MD |
4375 | if (xx >= 0) |
4376 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
4377 | else | |
4378 | { | |
4379 | /* x - y == -(y + -x) */ | |
4380 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
4381 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4382 | } | |
4383 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 4384 | |
0aacf84e MD |
4385 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
4386 | /* we know the result will have to be a bignum */ | |
4387 | return result; | |
4388 | else | |
4389 | return scm_i_normbig (result); | |
4390 | } | |
4391 | } | |
4392 | else if (SCM_REALP (y)) | |
4393 | { | |
e11e83f3 | 4394 | long int xx = SCM_I_INUM (x); |
55f26379 | 4395 | return scm_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
4396 | } |
4397 | else if (SCM_COMPLEXP (y)) | |
4398 | { | |
e11e83f3 | 4399 | long int xx = SCM_I_INUM (x); |
8507ec80 | 4400 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4401 | - SCM_COMPLEX_IMAG (y)); |
4402 | } | |
f92e85f7 MV |
4403 | else if (SCM_FRACTIONP (y)) |
4404 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 4405 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4406 | SCM_FRACTION_NUMERATOR (y)), |
4407 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4408 | else |
4409 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 4410 | } |
0aacf84e MD |
4411 | else if (SCM_BIGP (x)) |
4412 | { | |
e11e83f3 | 4413 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4414 | { |
4415 | /* big-x - inum-y */ | |
e11e83f3 | 4416 | long yy = SCM_I_INUM (y); |
0aacf84e | 4417 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 4418 | |
0aacf84e MD |
4419 | scm_remember_upto_here_1 (x); |
4420 | if (sgn_x == 0) | |
c71b0706 MV |
4421 | return (SCM_FIXABLE (-yy) ? |
4422 | SCM_I_MAKINUM (-yy) : scm_from_long (-yy)); | |
0aacf84e MD |
4423 | else |
4424 | { | |
4425 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4426 | |
708f22c6 KR |
4427 | if (yy >= 0) |
4428 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
4429 | else | |
4430 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 4431 | scm_remember_upto_here_1 (x); |
ca46fb90 | 4432 | |
0aacf84e MD |
4433 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
4434 | /* we know the result will have to be a bignum */ | |
4435 | return result; | |
4436 | else | |
4437 | return scm_i_normbig (result); | |
4438 | } | |
4439 | } | |
4440 | else if (SCM_BIGP (y)) | |
4441 | { | |
4442 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4443 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4444 | SCM result = scm_i_mkbig (); | |
4445 | mpz_sub (SCM_I_BIG_MPZ (result), | |
4446 | SCM_I_BIG_MPZ (x), | |
4447 | SCM_I_BIG_MPZ (y)); | |
4448 | scm_remember_upto_here_2 (x, y); | |
4449 | /* we know the result will have to be a bignum */ | |
4450 | if ((sgn_x == 1) && (sgn_y == -1)) | |
4451 | return result; | |
4452 | if ((sgn_x == -1) && (sgn_y == 1)) | |
4453 | return result; | |
4454 | return scm_i_normbig (result); | |
4455 | } | |
4456 | else if (SCM_REALP (y)) | |
4457 | { | |
4458 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
4459 | scm_remember_upto_here_1 (x); | |
55f26379 | 4460 | return scm_from_double (result); |
0aacf84e MD |
4461 | } |
4462 | else if (SCM_COMPLEXP (y)) | |
4463 | { | |
4464 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4465 | - SCM_COMPLEX_REAL (y)); | |
4466 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4467 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4468 | } |
f92e85f7 | 4469 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4470 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4471 | SCM_FRACTION_NUMERATOR (y)), |
4472 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 4473 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 4474 | } |
0aacf84e MD |
4475 | else if (SCM_REALP (x)) |
4476 | { | |
e11e83f3 | 4477 | if (SCM_I_INUMP (y)) |
55f26379 | 4478 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
4479 | else if (SCM_BIGP (y)) |
4480 | { | |
4481 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4482 | scm_remember_upto_here_1 (x); | |
55f26379 | 4483 | return scm_from_double (result); |
0aacf84e MD |
4484 | } |
4485 | else if (SCM_REALP (y)) | |
55f26379 | 4486 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 4487 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4488 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4489 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4490 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4491 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
4492 | else |
4493 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4494 | } |
0aacf84e MD |
4495 | else if (SCM_COMPLEXP (x)) |
4496 | { | |
e11e83f3 | 4497 | if (SCM_I_INUMP (y)) |
8507ec80 | 4498 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
4499 | SCM_COMPLEX_IMAG (x)); |
4500 | else if (SCM_BIGP (y)) | |
4501 | { | |
4502 | double real_part = (SCM_COMPLEX_REAL (x) | |
4503 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
4504 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4505 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
4506 | } |
4507 | else if (SCM_REALP (y)) | |
8507ec80 | 4508 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
4509 | SCM_COMPLEX_IMAG (x)); |
4510 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4511 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4512 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4513 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4514 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
4515 | SCM_COMPLEX_IMAG (x)); |
4516 | else | |
4517 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
4518 | } | |
4519 | else if (SCM_FRACTIONP (x)) | |
4520 | { | |
e11e83f3 | 4521 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4522 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 4523 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4524 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4525 | SCM_FRACTION_DENOMINATOR (x)); | |
4526 | else if (SCM_BIGP (y)) | |
cba42c93 | 4527 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4528 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4529 | SCM_FRACTION_DENOMINATOR (x)); | |
4530 | else if (SCM_REALP (y)) | |
55f26379 | 4531 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 4532 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4533 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4534 | -SCM_COMPLEX_IMAG (y)); |
4535 | else if (SCM_FRACTIONP (y)) | |
4536 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 4537 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4538 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4539 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4540 | else |
4541 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4542 | } |
0aacf84e | 4543 | else |
98cb6e75 | 4544 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 4545 | } |
c05e97b7 | 4546 | #undef FUNC_NAME |
0f2d19dd | 4547 | |
ca46fb90 | 4548 | |
40882e3d KR |
4549 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
4550 | (SCM x), | |
4551 | "Return @math{@var{x}-1}.") | |
4552 | #define FUNC_NAME s_scm_oneminus | |
4553 | { | |
4554 | return scm_difference (x, SCM_I_MAKINUM (1)); | |
4555 | } | |
4556 | #undef FUNC_NAME | |
4557 | ||
4558 | ||
78d3deb1 AW |
4559 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
4560 | (SCM x, SCM y, SCM rest), | |
4561 | "Return the product of all arguments. If called without arguments,\n" | |
4562 | "1 is returned.") | |
4563 | #define FUNC_NAME s_scm_i_product | |
4564 | { | |
4565 | while (!scm_is_null (rest)) | |
4566 | { x = scm_product (x, y); | |
4567 | y = scm_car (rest); | |
4568 | rest = scm_cdr (rest); | |
4569 | } | |
4570 | return scm_product (x, y); | |
4571 | } | |
4572 | #undef FUNC_NAME | |
4573 | ||
4574 | #define s_product s_scm_i_product | |
4575 | #define g_product g_scm_i_product | |
4576 | ||
0f2d19dd | 4577 | SCM |
6e8d25a6 | 4578 | scm_product (SCM x, SCM y) |
0f2d19dd | 4579 | { |
9cc37597 | 4580 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
4581 | { |
4582 | if (SCM_UNBNDP (x)) | |
d956fa6f | 4583 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
4584 | else if (SCM_NUMBERP (x)) |
4585 | return x; | |
4586 | else | |
4587 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 4588 | } |
ca46fb90 | 4589 | |
9cc37597 | 4590 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e MD |
4591 | { |
4592 | long xx; | |
f4c627b3 | 4593 | |
0aacf84e | 4594 | intbig: |
e11e83f3 | 4595 | xx = SCM_I_INUM (x); |
f4c627b3 | 4596 | |
0aacf84e MD |
4597 | switch (xx) |
4598 | { | |
ca46fb90 RB |
4599 | case 0: return x; break; |
4600 | case 1: return y; break; | |
0aacf84e | 4601 | } |
f4c627b3 | 4602 | |
9cc37597 | 4603 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4604 | { |
e11e83f3 | 4605 | long yy = SCM_I_INUM (y); |
0aacf84e | 4606 | long kk = xx * yy; |
d956fa6f | 4607 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 4608 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
4609 | return k; |
4610 | else | |
4611 | { | |
4612 | SCM result = scm_i_long2big (xx); | |
4613 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); | |
4614 | return scm_i_normbig (result); | |
4615 | } | |
4616 | } | |
4617 | else if (SCM_BIGP (y)) | |
4618 | { | |
4619 | SCM result = scm_i_mkbig (); | |
4620 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
4621 | scm_remember_upto_here_1 (y); | |
4622 | return result; | |
4623 | } | |
4624 | else if (SCM_REALP (y)) | |
55f26379 | 4625 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 4626 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4627 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 4628 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4629 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4630 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4631 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4632 | else |
4633 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4634 | } |
0aacf84e MD |
4635 | else if (SCM_BIGP (x)) |
4636 | { | |
e11e83f3 | 4637 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4638 | { |
4639 | SCM_SWAP (x, y); | |
4640 | goto intbig; | |
4641 | } | |
4642 | else if (SCM_BIGP (y)) | |
4643 | { | |
4644 | SCM result = scm_i_mkbig (); | |
4645 | mpz_mul (SCM_I_BIG_MPZ (result), | |
4646 | SCM_I_BIG_MPZ (x), | |
4647 | SCM_I_BIG_MPZ (y)); | |
4648 | scm_remember_upto_here_2 (x, y); | |
4649 | return result; | |
4650 | } | |
4651 | else if (SCM_REALP (y)) | |
4652 | { | |
4653 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
4654 | scm_remember_upto_here_1 (x); | |
55f26379 | 4655 | return scm_from_double (result); |
0aacf84e MD |
4656 | } |
4657 | else if (SCM_COMPLEXP (y)) | |
4658 | { | |
4659 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4660 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4661 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4662 | z * SCM_COMPLEX_IMAG (y)); |
4663 | } | |
f92e85f7 | 4664 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4665 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4666 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4667 | else |
4668 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4669 | } |
0aacf84e MD |
4670 | else if (SCM_REALP (x)) |
4671 | { | |
e11e83f3 | 4672 | if (SCM_I_INUMP (y)) |
23d72566 KR |
4673 | { |
4674 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
4675 | if (scm_is_eq (y, SCM_INUM0)) | |
4676 | return y; | |
4677 | return scm_from_double (SCM_I_INUM (y) * SCM_REAL_VALUE (x)); | |
4678 | } | |
0aacf84e MD |
4679 | else if (SCM_BIGP (y)) |
4680 | { | |
4681 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
4682 | scm_remember_upto_here_1 (y); | |
55f26379 | 4683 | return scm_from_double (result); |
0aacf84e MD |
4684 | } |
4685 | else if (SCM_REALP (y)) | |
55f26379 | 4686 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 4687 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4688 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 4689 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4690 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4691 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
4692 | else |
4693 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4694 | } |
0aacf84e MD |
4695 | else if (SCM_COMPLEXP (x)) |
4696 | { | |
e11e83f3 | 4697 | if (SCM_I_INUMP (y)) |
23d72566 KR |
4698 | { |
4699 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
4700 | if (scm_is_eq (y, SCM_INUM0)) | |
4701 | return y; | |
4702 | return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x), | |
4703 | SCM_I_INUM (y) * SCM_COMPLEX_IMAG (x)); | |
4704 | } | |
0aacf84e MD |
4705 | else if (SCM_BIGP (y)) |
4706 | { | |
4707 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4708 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4709 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 4710 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4711 | } |
4712 | else if (SCM_REALP (y)) | |
8507ec80 | 4713 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
4714 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
4715 | else if (SCM_COMPLEXP (y)) | |
4716 | { | |
8507ec80 | 4717 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
4718 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
4719 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
4720 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
4721 | } | |
f92e85f7 MV |
4722 | else if (SCM_FRACTIONP (y)) |
4723 | { | |
4724 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4725 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
4726 | yy * SCM_COMPLEX_IMAG (x)); |
4727 | } | |
4728 | else | |
4729 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
4730 | } | |
4731 | else if (SCM_FRACTIONP (x)) | |
4732 | { | |
e11e83f3 | 4733 | if (SCM_I_INUMP (y)) |
cba42c93 | 4734 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4735 | SCM_FRACTION_DENOMINATOR (x)); |
4736 | else if (SCM_BIGP (y)) | |
cba42c93 | 4737 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4738 | SCM_FRACTION_DENOMINATOR (x)); |
4739 | else if (SCM_REALP (y)) | |
55f26379 | 4740 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
4741 | else if (SCM_COMPLEXP (y)) |
4742 | { | |
4743 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 4744 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4745 | xx * SCM_COMPLEX_IMAG (y)); |
4746 | } | |
4747 | else if (SCM_FRACTIONP (y)) | |
4748 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 4749 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4750 | SCM_FRACTION_NUMERATOR (y)), |
4751 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
4752 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4753 | else |
4754 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4755 | } |
0aacf84e | 4756 | else |
f4c627b3 | 4757 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
4758 | } |
4759 | ||
7351e207 MV |
4760 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
4761 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
4762 | #define ALLOW_DIVIDE_BY_ZERO | |
4763 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
4764 | #endif | |
0f2d19dd | 4765 | |
ba74ef4e MV |
4766 | /* The code below for complex division is adapted from the GNU |
4767 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
4768 | this copyright: */ | |
4769 | ||
4770 | /**************************************************************** | |
4771 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
4772 | ||
4773 | Permission to use, copy, modify, and distribute this software | |
4774 | and its documentation for any purpose and without fee is hereby | |
4775 | granted, provided that the above copyright notice appear in all | |
4776 | copies and that both that the copyright notice and this | |
4777 | permission notice and warranty disclaimer appear in supporting | |
4778 | documentation, and that the names of AT&T Bell Laboratories or | |
4779 | Bellcore or any of their entities not be used in advertising or | |
4780 | publicity pertaining to distribution of the software without | |
4781 | specific, written prior permission. | |
4782 | ||
4783 | AT&T and Bellcore disclaim all warranties with regard to this | |
4784 | software, including all implied warranties of merchantability | |
4785 | and fitness. In no event shall AT&T or Bellcore be liable for | |
4786 | any special, indirect or consequential damages or any damages | |
4787 | whatsoever resulting from loss of use, data or profits, whether | |
4788 | in an action of contract, negligence or other tortious action, | |
4789 | arising out of or in connection with the use or performance of | |
4790 | this software. | |
4791 | ****************************************************************/ | |
4792 | ||
78d3deb1 AW |
4793 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
4794 | (SCM x, SCM y, SCM rest), | |
4795 | "Divide the first argument by the product of the remaining\n" | |
4796 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
4797 | "returned.") | |
4798 | #define FUNC_NAME s_scm_i_divide | |
4799 | { | |
4800 | while (!scm_is_null (rest)) | |
4801 | { x = scm_divide (x, y); | |
4802 | y = scm_car (rest); | |
4803 | rest = scm_cdr (rest); | |
4804 | } | |
4805 | return scm_divide (x, y); | |
4806 | } | |
4807 | #undef FUNC_NAME | |
4808 | ||
4809 | #define s_divide s_scm_i_divide | |
4810 | #define g_divide g_scm_i_divide | |
4811 | ||
f92e85f7 | 4812 | static SCM |
78d3deb1 AW |
4813 | do_divide (SCM x, SCM y, int inexact) |
4814 | #define FUNC_NAME s_divide | |
0f2d19dd | 4815 | { |
f8de44c1 DH |
4816 | double a; |
4817 | ||
9cc37597 | 4818 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
4819 | { |
4820 | if (SCM_UNBNDP (x)) | |
4821 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 4822 | else if (SCM_I_INUMP (x)) |
0aacf84e | 4823 | { |
e11e83f3 | 4824 | long xx = SCM_I_INUM (x); |
0aacf84e MD |
4825 | if (xx == 1 || xx == -1) |
4826 | return x; | |
7351e207 | 4827 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4828 | else if (xx == 0) |
4829 | scm_num_overflow (s_divide); | |
7351e207 | 4830 | #endif |
0aacf84e | 4831 | else |
f92e85f7 MV |
4832 | { |
4833 | if (inexact) | |
55f26379 | 4834 | return scm_from_double (1.0 / (double) xx); |
cba42c93 | 4835 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4836 | } |
0aacf84e MD |
4837 | } |
4838 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
4839 | { |
4840 | if (inexact) | |
55f26379 | 4841 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cba42c93 | 4842 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4843 | } |
0aacf84e MD |
4844 | else if (SCM_REALP (x)) |
4845 | { | |
4846 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 4847 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4848 | if (xx == 0.0) |
4849 | scm_num_overflow (s_divide); | |
4850 | else | |
7351e207 | 4851 | #endif |
55f26379 | 4852 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
4853 | } |
4854 | else if (SCM_COMPLEXP (x)) | |
4855 | { | |
4856 | double r = SCM_COMPLEX_REAL (x); | |
4857 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 4858 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
4859 | { |
4860 | double t = r / i; | |
4861 | double d = i * (1.0 + t * t); | |
8507ec80 | 4862 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
4863 | } |
4864 | else | |
4865 | { | |
4866 | double t = i / r; | |
4867 | double d = r * (1.0 + t * t); | |
8507ec80 | 4868 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
4869 | } |
4870 | } | |
f92e85f7 | 4871 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4872 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 4873 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
4874 | else |
4875 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 4876 | } |
f8de44c1 | 4877 | |
9cc37597 | 4878 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 4879 | { |
e11e83f3 | 4880 | long xx = SCM_I_INUM (x); |
9cc37597 | 4881 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4882 | { |
e11e83f3 | 4883 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
4884 | if (yy == 0) |
4885 | { | |
7351e207 | 4886 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4887 | scm_num_overflow (s_divide); |
7351e207 | 4888 | #else |
55f26379 | 4889 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 4890 | #endif |
0aacf84e MD |
4891 | } |
4892 | else if (xx % yy != 0) | |
f92e85f7 MV |
4893 | { |
4894 | if (inexact) | |
55f26379 | 4895 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 4896 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4897 | } |
0aacf84e MD |
4898 | else |
4899 | { | |
4900 | long z = xx / yy; | |
4901 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4902 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4903 | else |
4904 | return scm_i_long2big (z); | |
4905 | } | |
f872b822 | 4906 | } |
0aacf84e | 4907 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
4908 | { |
4909 | if (inexact) | |
55f26379 | 4910 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 4911 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4912 | } |
0aacf84e MD |
4913 | else if (SCM_REALP (y)) |
4914 | { | |
4915 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4916 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4917 | if (yy == 0.0) |
4918 | scm_num_overflow (s_divide); | |
4919 | else | |
7351e207 | 4920 | #endif |
55f26379 | 4921 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 4922 | } |
0aacf84e MD |
4923 | else if (SCM_COMPLEXP (y)) |
4924 | { | |
4925 | a = xx; | |
4926 | complex_div: /* y _must_ be a complex number */ | |
4927 | { | |
4928 | double r = SCM_COMPLEX_REAL (y); | |
4929 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 4930 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
4931 | { |
4932 | double t = r / i; | |
4933 | double d = i * (1.0 + t * t); | |
8507ec80 | 4934 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
4935 | } |
4936 | else | |
4937 | { | |
4938 | double t = i / r; | |
4939 | double d = r * (1.0 + t * t); | |
8507ec80 | 4940 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
4941 | } |
4942 | } | |
4943 | } | |
f92e85f7 MV |
4944 | else if (SCM_FRACTIONP (y)) |
4945 | /* a / b/c = ac / b */ | |
cba42c93 | 4946 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4947 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4948 | else |
4949 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4950 | } |
0aacf84e MD |
4951 | else if (SCM_BIGP (x)) |
4952 | { | |
e11e83f3 | 4953 | if (SCM_I_INUMP (y)) |
0aacf84e | 4954 | { |
e11e83f3 | 4955 | long int yy = SCM_I_INUM (y); |
0aacf84e MD |
4956 | if (yy == 0) |
4957 | { | |
7351e207 | 4958 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4959 | scm_num_overflow (s_divide); |
7351e207 | 4960 | #else |
0aacf84e MD |
4961 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4962 | scm_remember_upto_here_1 (x); | |
4963 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 4964 | #endif |
0aacf84e MD |
4965 | } |
4966 | else if (yy == 1) | |
4967 | return x; | |
4968 | else | |
4969 | { | |
4970 | /* FIXME: HMM, what are the relative performance issues here? | |
4971 | We need to test. Is it faster on average to test | |
4972 | divisible_p, then perform whichever operation, or is it | |
4973 | faster to perform the integer div opportunistically and | |
4974 | switch to real if there's a remainder? For now we take the | |
4975 | middle ground: test, then if divisible, use the faster div | |
4976 | func. */ | |
4977 | ||
4978 | long abs_yy = yy < 0 ? -yy : yy; | |
4979 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); | |
4980 | ||
4981 | if (divisible_p) | |
4982 | { | |
4983 | SCM result = scm_i_mkbig (); | |
4984 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
4985 | scm_remember_upto_here_1 (x); | |
4986 | if (yy < 0) | |
4987 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4988 | return scm_i_normbig (result); | |
4989 | } | |
4990 | else | |
f92e85f7 MV |
4991 | { |
4992 | if (inexact) | |
55f26379 | 4993 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 4994 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4995 | } |
0aacf84e MD |
4996 | } |
4997 | } | |
4998 | else if (SCM_BIGP (y)) | |
4999 | { | |
5000 | int y_is_zero = (mpz_sgn (SCM_I_BIG_MPZ (y)) == 0); | |
5001 | if (y_is_zero) | |
5002 | { | |
ca46fb90 | 5003 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 5004 | scm_num_overflow (s_divide); |
f872b822 | 5005 | #else |
0aacf84e MD |
5006 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
5007 | scm_remember_upto_here_1 (x); | |
5008 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
f872b822 | 5009 | #endif |
0aacf84e MD |
5010 | } |
5011 | else | |
5012 | { | |
5013 | /* big_x / big_y */ | |
23f2b9a3 KR |
5014 | if (inexact) |
5015 | { | |
5016 | /* It's easily possible for the ratio x/y to fit a double | |
5017 | but one or both x and y be too big to fit a double, | |
5018 | hence the use of mpq_get_d rather than converting and | |
5019 | dividing. */ | |
5020 | mpq_t q; | |
5021 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
5022 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
5023 | return scm_from_double (mpq_get_d (q)); | |
5024 | } | |
5025 | else | |
5026 | { | |
5027 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), | |
5028 | SCM_I_BIG_MPZ (y)); | |
5029 | if (divisible_p) | |
5030 | { | |
5031 | SCM result = scm_i_mkbig (); | |
5032 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
5033 | SCM_I_BIG_MPZ (x), | |
5034 | SCM_I_BIG_MPZ (y)); | |
5035 | scm_remember_upto_here_2 (x, y); | |
5036 | return scm_i_normbig (result); | |
5037 | } | |
5038 | else | |
5039 | return scm_i_make_ratio (x, y); | |
5040 | } | |
0aacf84e MD |
5041 | } |
5042 | } | |
5043 | else if (SCM_REALP (y)) | |
5044 | { | |
5045 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5046 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5047 | if (yy == 0.0) |
5048 | scm_num_overflow (s_divide); | |
5049 | else | |
7351e207 | 5050 | #endif |
55f26379 | 5051 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
5052 | } |
5053 | else if (SCM_COMPLEXP (y)) | |
5054 | { | |
5055 | a = scm_i_big2dbl (x); | |
5056 | goto complex_div; | |
5057 | } | |
f92e85f7 | 5058 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5059 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 5060 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
5061 | else |
5062 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 5063 | } |
0aacf84e MD |
5064 | else if (SCM_REALP (x)) |
5065 | { | |
5066 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 5067 | if (SCM_I_INUMP (y)) |
0aacf84e | 5068 | { |
e11e83f3 | 5069 | long int yy = SCM_I_INUM (y); |
7351e207 | 5070 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
5071 | if (yy == 0) |
5072 | scm_num_overflow (s_divide); | |
5073 | else | |
7351e207 | 5074 | #endif |
55f26379 | 5075 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
5076 | } |
5077 | else if (SCM_BIGP (y)) | |
5078 | { | |
5079 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
5080 | scm_remember_upto_here_1 (y); | |
55f26379 | 5081 | return scm_from_double (rx / dby); |
0aacf84e MD |
5082 | } |
5083 | else if (SCM_REALP (y)) | |
5084 | { | |
5085 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5086 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5087 | if (yy == 0.0) |
5088 | scm_num_overflow (s_divide); | |
5089 | else | |
7351e207 | 5090 | #endif |
55f26379 | 5091 | return scm_from_double (rx / yy); |
0aacf84e MD |
5092 | } |
5093 | else if (SCM_COMPLEXP (y)) | |
5094 | { | |
5095 | a = rx; | |
5096 | goto complex_div; | |
5097 | } | |
f92e85f7 | 5098 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5099 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
5100 | else |
5101 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 5102 | } |
0aacf84e MD |
5103 | else if (SCM_COMPLEXP (x)) |
5104 | { | |
5105 | double rx = SCM_COMPLEX_REAL (x); | |
5106 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 5107 | if (SCM_I_INUMP (y)) |
0aacf84e | 5108 | { |
e11e83f3 | 5109 | long int yy = SCM_I_INUM (y); |
7351e207 | 5110 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
5111 | if (yy == 0) |
5112 | scm_num_overflow (s_divide); | |
5113 | else | |
7351e207 | 5114 | #endif |
0aacf84e MD |
5115 | { |
5116 | double d = yy; | |
8507ec80 | 5117 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
5118 | } |
5119 | } | |
5120 | else if (SCM_BIGP (y)) | |
5121 | { | |
5122 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
5123 | scm_remember_upto_here_1 (y); | |
8507ec80 | 5124 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
5125 | } |
5126 | else if (SCM_REALP (y)) | |
5127 | { | |
5128 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5129 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5130 | if (yy == 0.0) |
5131 | scm_num_overflow (s_divide); | |
5132 | else | |
7351e207 | 5133 | #endif |
8507ec80 | 5134 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
5135 | } |
5136 | else if (SCM_COMPLEXP (y)) | |
5137 | { | |
5138 | double ry = SCM_COMPLEX_REAL (y); | |
5139 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 5140 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
5141 | { |
5142 | double t = ry / iy; | |
5143 | double d = iy * (1.0 + t * t); | |
8507ec80 | 5144 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
5145 | } |
5146 | else | |
5147 | { | |
5148 | double t = iy / ry; | |
5149 | double d = ry * (1.0 + t * t); | |
8507ec80 | 5150 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
5151 | } |
5152 | } | |
f92e85f7 MV |
5153 | else if (SCM_FRACTIONP (y)) |
5154 | { | |
5155 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 5156 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 5157 | } |
0aacf84e MD |
5158 | else |
5159 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 5160 | } |
f92e85f7 MV |
5161 | else if (SCM_FRACTIONP (x)) |
5162 | { | |
e11e83f3 | 5163 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5164 | { |
e11e83f3 | 5165 | long int yy = SCM_I_INUM (y); |
f92e85f7 MV |
5166 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
5167 | if (yy == 0) | |
5168 | scm_num_overflow (s_divide); | |
5169 | else | |
5170 | #endif | |
cba42c93 | 5171 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5172 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
5173 | } | |
5174 | else if (SCM_BIGP (y)) | |
5175 | { | |
cba42c93 | 5176 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5177 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
5178 | } | |
5179 | else if (SCM_REALP (y)) | |
5180 | { | |
5181 | double yy = SCM_REAL_VALUE (y); | |
5182 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
5183 | if (yy == 0.0) | |
5184 | scm_num_overflow (s_divide); | |
5185 | else | |
5186 | #endif | |
55f26379 | 5187 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
5188 | } |
5189 | else if (SCM_COMPLEXP (y)) | |
5190 | { | |
5191 | a = scm_i_fraction2double (x); | |
5192 | goto complex_div; | |
5193 | } | |
5194 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 5195 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5196 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
5197 | else | |
5198 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
5199 | } | |
0aacf84e | 5200 | else |
f8de44c1 | 5201 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 5202 | } |
f92e85f7 MV |
5203 | |
5204 | SCM | |
5205 | scm_divide (SCM x, SCM y) | |
5206 | { | |
78d3deb1 | 5207 | return do_divide (x, y, 0); |
f92e85f7 MV |
5208 | } |
5209 | ||
5210 | static SCM scm_divide2real (SCM x, SCM y) | |
5211 | { | |
78d3deb1 | 5212 | return do_divide (x, y, 1); |
f92e85f7 | 5213 | } |
c05e97b7 | 5214 | #undef FUNC_NAME |
0f2d19dd | 5215 | |
fa605590 | 5216 | |
0f2d19dd | 5217 | double |
3101f40f | 5218 | scm_c_truncate (double x) |
0f2d19dd | 5219 | { |
fa605590 KR |
5220 | #if HAVE_TRUNC |
5221 | return trunc (x); | |
5222 | #else | |
f872b822 MD |
5223 | if (x < 0.0) |
5224 | return -floor (-x); | |
5225 | return floor (x); | |
fa605590 | 5226 | #endif |
0f2d19dd | 5227 | } |
0f2d19dd | 5228 | |
3101f40f MV |
5229 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
5230 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
5231 | Then half-way cases are identified and adjusted down if the | |
5232 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
5233 | |
5234 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
5235 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
5236 | ||
5237 | An odd "result" value is identified with result/2 != floor(result/2). | |
5238 | This is done with plus_half, since that value is ready for use sooner in | |
5239 | a pipelined cpu, and we're already requiring plus_half == result. | |
5240 | ||
5241 | Note however that we need to be careful when x is big and already an | |
5242 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
5243 | us to return such a value, incorrectly. For instance if the hardware is | |
5244 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
5245 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
5246 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
5247 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
5248 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
5249 | ||
5250 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
5251 | x is already an integer. If it is then clearly that's the desired result | |
5252 | already. And if it's not then the exponent must be small enough to allow | |
5253 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
5254 | ||
0f2d19dd | 5255 | double |
3101f40f | 5256 | scm_c_round (double x) |
0f2d19dd | 5257 | { |
6187f48b KR |
5258 | double plus_half, result; |
5259 | ||
5260 | if (x == floor (x)) | |
5261 | return x; | |
5262 | ||
5263 | plus_half = x + 0.5; | |
5264 | result = floor (plus_half); | |
3101f40f | 5265 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
5266 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
5267 | ? result - 1 | |
5268 | : result); | |
0f2d19dd JB |
5269 | } |
5270 | ||
f92e85f7 MV |
5271 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
5272 | (SCM x), | |
5273 | "Round the number @var{x} towards zero.") | |
5274 | #define FUNC_NAME s_scm_truncate_number | |
5275 | { | |
73e4de09 | 5276 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5277 | return scm_floor (x); |
5278 | else | |
5279 | return scm_ceiling (x); | |
5280 | } | |
5281 | #undef FUNC_NAME | |
5282 | ||
5283 | static SCM exactly_one_half; | |
5284 | ||
5285 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, | |
5286 | (SCM x), | |
5287 | "Round the number @var{x} towards the nearest integer. " | |
5288 | "When it is exactly halfway between two integers, " | |
5289 | "round towards the even one.") | |
5290 | #define FUNC_NAME s_scm_round_number | |
5291 | { | |
e11e83f3 | 5292 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
5293 | return x; |
5294 | else if (SCM_REALP (x)) | |
3101f40f | 5295 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 5296 | else |
bae30667 KR |
5297 | { |
5298 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
5299 | single quotient+remainder division then examining to see which way | |
5300 | the rounding should go. */ | |
5301 | SCM plus_half = scm_sum (x, exactly_one_half); | |
5302 | SCM result = scm_floor (plus_half); | |
3101f40f | 5303 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
5304 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
5305 | && scm_is_true (scm_odd_p (result))) | |
d956fa6f | 5306 | return scm_difference (result, SCM_I_MAKINUM (1)); |
bae30667 KR |
5307 | else |
5308 | return result; | |
5309 | } | |
f92e85f7 MV |
5310 | } |
5311 | #undef FUNC_NAME | |
5312 | ||
5313 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
5314 | (SCM x), | |
5315 | "Round the number @var{x} towards minus infinity.") | |
5316 | #define FUNC_NAME s_scm_floor | |
5317 | { | |
e11e83f3 | 5318 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5319 | return x; |
5320 | else if (SCM_REALP (x)) | |
55f26379 | 5321 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5322 | else if (SCM_FRACTIONP (x)) |
5323 | { | |
5324 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5325 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5326 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5327 | { |
5328 | /* For positive x, rounding towards zero is correct. */ | |
5329 | return q; | |
5330 | } | |
5331 | else | |
5332 | { | |
5333 | /* For negative x, we need to return q-1 unless x is an | |
5334 | integer. But fractions are never integer, per our | |
5335 | assumptions. */ | |
d956fa6f | 5336 | return scm_difference (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5337 | } |
5338 | } | |
5339 | else | |
5340 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
5341 | } | |
5342 | #undef FUNC_NAME | |
5343 | ||
5344 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
5345 | (SCM x), | |
5346 | "Round the number @var{x} towards infinity.") | |
5347 | #define FUNC_NAME s_scm_ceiling | |
5348 | { | |
e11e83f3 | 5349 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5350 | return x; |
5351 | else if (SCM_REALP (x)) | |
55f26379 | 5352 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5353 | else if (SCM_FRACTIONP (x)) |
5354 | { | |
5355 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5356 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5357 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
5358 | { |
5359 | /* For negative x, rounding towards zero is correct. */ | |
5360 | return q; | |
5361 | } | |
5362 | else | |
5363 | { | |
5364 | /* For positive x, we need to return q+1 unless x is an | |
5365 | integer. But fractions are never integer, per our | |
5366 | assumptions. */ | |
d956fa6f | 5367 | return scm_sum (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5368 | } |
5369 | } | |
5370 | else | |
5371 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
5372 | } | |
5373 | #undef FUNC_NAME | |
0f2d19dd | 5374 | |
ad79736c AW |
5375 | /* sin/cos/tan/asin/acos/atan |
5376 | sinh/cosh/tanh/asinh/acosh/atanh | |
5377 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
5378 | Written by Jerry D. Hedden, (C) FSF. | |
5379 | See the file `COPYING' for terms applying to this program. */ | |
0f2d19dd | 5380 | |
6fc4d012 | 5381 | SCM_DEFINE (scm_expt, "expt", 2, 0, 0, |
27c37006 | 5382 | (SCM x, SCM y), |
6fc4d012 AW |
5383 | "Return @var{x} raised to the power of @var{y}.") |
5384 | #define FUNC_NAME s_scm_expt | |
0f2d19dd | 5385 | { |
6fc4d012 AW |
5386 | if (!SCM_INEXACTP (y) && scm_is_integer (y)) |
5387 | return scm_integer_expt (x, y); | |
5388 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) | |
5389 | { | |
5390 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
5391 | } | |
5392 | else | |
5393 | return scm_exp (scm_product (scm_log (x), y)); | |
0f2d19dd | 5394 | } |
1bbd0b84 | 5395 | #undef FUNC_NAME |
0f2d19dd | 5396 | |
ad79736c AW |
5397 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
5398 | (SCM z), | |
5399 | "Compute the sine of @var{z}.") | |
5400 | #define FUNC_NAME s_scm_sin | |
5401 | { | |
5402 | if (scm_is_real (z)) | |
5403 | return scm_from_double (sin (scm_to_double (z))); | |
5404 | else if (SCM_COMPLEXP (z)) | |
5405 | { double x, y; | |
5406 | x = SCM_COMPLEX_REAL (z); | |
5407 | y = SCM_COMPLEX_IMAG (z); | |
5408 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
5409 | cos (x) * sinh (y)); | |
5410 | } | |
5411 | else | |
5412 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
5413 | } | |
5414 | #undef FUNC_NAME | |
0f2d19dd | 5415 | |
ad79736c AW |
5416 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
5417 | (SCM z), | |
5418 | "Compute the cosine of @var{z}.") | |
5419 | #define FUNC_NAME s_scm_cos | |
5420 | { | |
5421 | if (scm_is_real (z)) | |
5422 | return scm_from_double (cos (scm_to_double (z))); | |
5423 | else if (SCM_COMPLEXP (z)) | |
5424 | { double x, y; | |
5425 | x = SCM_COMPLEX_REAL (z); | |
5426 | y = SCM_COMPLEX_IMAG (z); | |
5427 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
5428 | -sin (x) * sinh (y)); | |
5429 | } | |
5430 | else | |
5431 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
5432 | } | |
5433 | #undef FUNC_NAME | |
5434 | ||
5435 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
5436 | (SCM z), | |
5437 | "Compute the tangent of @var{z}.") | |
5438 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 5439 | { |
ad79736c AW |
5440 | if (scm_is_real (z)) |
5441 | return scm_from_double (tan (scm_to_double (z))); | |
5442 | else if (SCM_COMPLEXP (z)) | |
5443 | { double x, y, w; | |
5444 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
5445 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
5446 | w = cos (x) + cosh (y); | |
5447 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
5448 | if (w == 0.0) | |
5449 | scm_num_overflow (s_scm_tan); | |
5450 | #endif | |
5451 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
5452 | } | |
5453 | else | |
5454 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
5455 | } | |
5456 | #undef FUNC_NAME | |
5457 | ||
5458 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
5459 | (SCM z), | |
5460 | "Compute the hyperbolic sine of @var{z}.") | |
5461 | #define FUNC_NAME s_scm_sinh | |
5462 | { | |
5463 | if (scm_is_real (z)) | |
5464 | return scm_from_double (sinh (scm_to_double (z))); | |
5465 | else if (SCM_COMPLEXP (z)) | |
5466 | { double x, y; | |
5467 | x = SCM_COMPLEX_REAL (z); | |
5468 | y = SCM_COMPLEX_IMAG (z); | |
5469 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
5470 | cosh (x) * sin (y)); | |
5471 | } | |
5472 | else | |
5473 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
5474 | } | |
5475 | #undef FUNC_NAME | |
5476 | ||
5477 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
5478 | (SCM z), | |
5479 | "Compute the hyperbolic cosine of @var{z}.") | |
5480 | #define FUNC_NAME s_scm_cosh | |
5481 | { | |
5482 | if (scm_is_real (z)) | |
5483 | return scm_from_double (cosh (scm_to_double (z))); | |
5484 | else if (SCM_COMPLEXP (z)) | |
5485 | { double x, y; | |
5486 | x = SCM_COMPLEX_REAL (z); | |
5487 | y = SCM_COMPLEX_IMAG (z); | |
5488 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
5489 | sinh (x) * sin (y)); | |
5490 | } | |
5491 | else | |
5492 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
5493 | } | |
5494 | #undef FUNC_NAME | |
5495 | ||
5496 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
5497 | (SCM z), | |
5498 | "Compute the hyperbolic tangent of @var{z}.") | |
5499 | #define FUNC_NAME s_scm_tanh | |
5500 | { | |
5501 | if (scm_is_real (z)) | |
5502 | return scm_from_double (tanh (scm_to_double (z))); | |
5503 | else if (SCM_COMPLEXP (z)) | |
5504 | { double x, y, w; | |
5505 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
5506 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
5507 | w = cosh (x) + cos (y); | |
5508 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
5509 | if (w == 0.0) | |
5510 | scm_num_overflow (s_scm_tanh); | |
5511 | #endif | |
5512 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
5513 | } | |
5514 | else | |
5515 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
5516 | } | |
5517 | #undef FUNC_NAME | |
5518 | ||
5519 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
5520 | (SCM z), | |
5521 | "Compute the arc sine of @var{z}.") | |
5522 | #define FUNC_NAME s_scm_asin | |
5523 | { | |
5524 | if (scm_is_real (z)) | |
5525 | { | |
5526 | double w = scm_to_double (z); | |
5527 | if (w >= -1.0 && w <= 1.0) | |
5528 | return scm_from_double (asin (w)); | |
5529 | else | |
5530 | return scm_product (scm_c_make_rectangular (0, -1), | |
5531 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
5532 | } | |
5533 | else if (SCM_COMPLEXP (z)) | |
5534 | { double x, y; | |
5535 | x = SCM_COMPLEX_REAL (z); | |
5536 | y = SCM_COMPLEX_IMAG (z); | |
5537 | return scm_product (scm_c_make_rectangular (0, -1), | |
5538 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
5539 | } | |
5540 | else | |
5541 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
5542 | } | |
5543 | #undef FUNC_NAME | |
5544 | ||
5545 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
5546 | (SCM z), | |
5547 | "Compute the arc cosine of @var{z}.") | |
5548 | #define FUNC_NAME s_scm_acos | |
5549 | { | |
5550 | if (scm_is_real (z)) | |
5551 | { | |
5552 | double w = scm_to_double (z); | |
5553 | if (w >= -1.0 && w <= 1.0) | |
5554 | return scm_from_double (acos (w)); | |
5555 | else | |
5556 | return scm_sum (scm_from_double (acos (0.0)), | |
5557 | scm_product (scm_c_make_rectangular (0, 1), | |
5558 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
5559 | } | |
5560 | else if (SCM_COMPLEXP (z)) | |
5561 | { double x, y; | |
5562 | x = SCM_COMPLEX_REAL (z); | |
5563 | y = SCM_COMPLEX_IMAG (z); | |
5564 | return scm_sum (scm_from_double (acos (0.0)), | |
5565 | scm_product (scm_c_make_rectangular (0, 1), | |
5566 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
5567 | } | |
5568 | else | |
5569 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
5570 | } | |
5571 | #undef FUNC_NAME | |
5572 | ||
5573 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
5574 | (SCM z, SCM y), | |
5575 | "With one argument, compute the arc tangent of @var{z}.\n" | |
5576 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
5577 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
5578 | #define FUNC_NAME s_scm_atan | |
5579 | { | |
5580 | if (SCM_UNBNDP (y)) | |
5581 | { | |
5582 | if (scm_is_real (z)) | |
5583 | return scm_from_double (atan (scm_to_double (z))); | |
5584 | else if (SCM_COMPLEXP (z)) | |
5585 | { | |
5586 | double v, w; | |
5587 | v = SCM_COMPLEX_REAL (z); | |
5588 | w = SCM_COMPLEX_IMAG (z); | |
5589 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
5590 | scm_c_make_rectangular (v, w + 1.0))), | |
5591 | scm_c_make_rectangular (0, 2)); | |
5592 | } | |
5593 | else | |
5594 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
5595 | } | |
5596 | else if (scm_is_real (z)) | |
5597 | { | |
5598 | if (scm_is_real (y)) | |
5599 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
5600 | else | |
5601 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
5602 | } | |
5603 | else | |
5604 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
5605 | } | |
5606 | #undef FUNC_NAME | |
5607 | ||
5608 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
5609 | (SCM z), | |
5610 | "Compute the inverse hyperbolic sine of @var{z}.") | |
5611 | #define FUNC_NAME s_scm_sys_asinh | |
5612 | { | |
5613 | if (scm_is_real (z)) | |
5614 | return scm_from_double (asinh (scm_to_double (z))); | |
5615 | else if (scm_is_number (z)) | |
5616 | return scm_log (scm_sum (z, | |
5617 | scm_sqrt (scm_sum (scm_product (z, z), | |
5618 | SCM_I_MAKINUM (1))))); | |
5619 | else | |
5620 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
5621 | } | |
5622 | #undef FUNC_NAME | |
5623 | ||
5624 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
5625 | (SCM z), | |
5626 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
5627 | #define FUNC_NAME s_scm_sys_acosh | |
5628 | { | |
5629 | if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
5630 | return scm_from_double (acosh (scm_to_double (z))); | |
5631 | else if (scm_is_number (z)) | |
5632 | return scm_log (scm_sum (z, | |
5633 | scm_sqrt (scm_difference (scm_product (z, z), | |
5634 | SCM_I_MAKINUM (1))))); | |
5635 | else | |
5636 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
5637 | } | |
5638 | #undef FUNC_NAME | |
5639 | ||
5640 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
5641 | (SCM z), | |
5642 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
5643 | #define FUNC_NAME s_scm_sys_atanh | |
5644 | { | |
5645 | if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
5646 | return scm_from_double (atanh (scm_to_double (z))); | |
5647 | else if (scm_is_number (z)) | |
5648 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_I_MAKINUM (1), z), | |
5649 | scm_difference (SCM_I_MAKINUM (1), z))), | |
5650 | SCM_I_MAKINUM (2)); | |
5651 | else | |
5652 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 5653 | } |
1bbd0b84 | 5654 | #undef FUNC_NAME |
0f2d19dd | 5655 | |
8507ec80 MV |
5656 | SCM |
5657 | scm_c_make_rectangular (double re, double im) | |
5658 | { | |
5659 | if (im == 0.0) | |
5660 | return scm_from_double (re); | |
5661 | else | |
5662 | { | |
5663 | SCM z; | |
92d8fd32 LC |
5664 | SCM_NEWSMOB (z, scm_tc16_complex, |
5665 | scm_gc_malloc_pointerless (sizeof (scm_t_complex), | |
5666 | "complex")); | |
8507ec80 MV |
5667 | SCM_COMPLEX_REAL (z) = re; |
5668 | SCM_COMPLEX_IMAG (z) = im; | |
5669 | return z; | |
5670 | } | |
5671 | } | |
0f2d19dd | 5672 | |
a1ec6916 | 5673 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
5674 | (SCM real_part, SCM imaginary_part), |
5675 | "Return a complex number constructed of the given @var{real-part} " | |
5676 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 5677 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 5678 | { |
ad79736c AW |
5679 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
5680 | SCM_ARG1, FUNC_NAME, "real"); | |
5681 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
5682 | SCM_ARG2, FUNC_NAME, "real"); | |
5683 | return scm_c_make_rectangular (scm_to_double (real_part), | |
5684 | scm_to_double (imaginary_part)); | |
0f2d19dd | 5685 | } |
1bbd0b84 | 5686 | #undef FUNC_NAME |
0f2d19dd | 5687 | |
8507ec80 MV |
5688 | SCM |
5689 | scm_c_make_polar (double mag, double ang) | |
5690 | { | |
5691 | double s, c; | |
5e647d08 LC |
5692 | |
5693 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
5694 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
5695 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
5696 | details. */ | |
5697 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
5698 | sincos (ang, &s, &c); |
5699 | #else | |
5700 | s = sin (ang); | |
5701 | c = cos (ang); | |
5702 | #endif | |
5703 | return scm_c_make_rectangular (mag * c, mag * s); | |
5704 | } | |
0f2d19dd | 5705 | |
a1ec6916 | 5706 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 5707 | (SCM x, SCM y), |
942e5b91 | 5708 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 5709 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 5710 | { |
ad79736c AW |
5711 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
5712 | SCM_ASSERT_TYPE (scm_is_real (y), y, SCM_ARG2, FUNC_NAME, "real"); | |
5713 | return scm_c_make_polar (scm_to_double (x), scm_to_double (y)); | |
0f2d19dd | 5714 | } |
1bbd0b84 | 5715 | #undef FUNC_NAME |
0f2d19dd JB |
5716 | |
5717 | ||
152f82bf | 5718 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
5719 | /* "Return the real part of the number @var{z}." |
5720 | */ | |
0f2d19dd | 5721 | SCM |
6e8d25a6 | 5722 | scm_real_part (SCM z) |
0f2d19dd | 5723 | { |
e11e83f3 | 5724 | if (SCM_I_INUMP (z)) |
c2ff8ab0 | 5725 | return z; |
0aacf84e | 5726 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5727 | return z; |
0aacf84e | 5728 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5729 | return z; |
0aacf84e | 5730 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5731 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
f92e85f7 | 5732 | else if (SCM_FRACTIONP (z)) |
2fa2d879 | 5733 | return z; |
0aacf84e | 5734 | else |
c2ff8ab0 | 5735 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); |
0f2d19dd JB |
5736 | } |
5737 | ||
5738 | ||
152f82bf | 5739 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
5740 | /* "Return the imaginary part of the number @var{z}." |
5741 | */ | |
0f2d19dd | 5742 | SCM |
6e8d25a6 | 5743 | scm_imag_part (SCM z) |
0f2d19dd | 5744 | { |
e11e83f3 | 5745 | if (SCM_I_INUMP (z)) |
f872b822 | 5746 | return SCM_INUM0; |
0aacf84e | 5747 | else if (SCM_BIGP (z)) |
f872b822 | 5748 | return SCM_INUM0; |
0aacf84e | 5749 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5750 | return scm_flo0; |
0aacf84e | 5751 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5752 | return scm_from_double (SCM_COMPLEX_IMAG (z)); |
f92e85f7 MV |
5753 | else if (SCM_FRACTIONP (z)) |
5754 | return SCM_INUM0; | |
0aacf84e | 5755 | else |
c2ff8ab0 | 5756 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); |
0f2d19dd JB |
5757 | } |
5758 | ||
f92e85f7 MV |
5759 | SCM_GPROC (s_numerator, "numerator", 1, 0, 0, scm_numerator, g_numerator); |
5760 | /* "Return the numerator of the number @var{z}." | |
5761 | */ | |
5762 | SCM | |
5763 | scm_numerator (SCM z) | |
5764 | { | |
e11e83f3 | 5765 | if (SCM_I_INUMP (z)) |
f92e85f7 MV |
5766 | return z; |
5767 | else if (SCM_BIGP (z)) | |
5768 | return z; | |
5769 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 5770 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
5771 | else if (SCM_REALP (z)) |
5772 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
5773 | else | |
5774 | SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator); | |
5775 | } | |
5776 | ||
5777 | ||
5778 | SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator); | |
5779 | /* "Return the denominator of the number @var{z}." | |
5780 | */ | |
5781 | SCM | |
5782 | scm_denominator (SCM z) | |
5783 | { | |
e11e83f3 | 5784 | if (SCM_I_INUMP (z)) |
d956fa6f | 5785 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5786 | else if (SCM_BIGP (z)) |
d956fa6f | 5787 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5788 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 5789 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
5790 | else if (SCM_REALP (z)) |
5791 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
5792 | else | |
5793 | SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator); | |
5794 | } | |
0f2d19dd | 5795 | |
9de33deb | 5796 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
5797 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
5798 | * "@code{abs} for real arguments, but also allows complex numbers." | |
5799 | */ | |
0f2d19dd | 5800 | SCM |
6e8d25a6 | 5801 | scm_magnitude (SCM z) |
0f2d19dd | 5802 | { |
e11e83f3 | 5803 | if (SCM_I_INUMP (z)) |
0aacf84e | 5804 | { |
e11e83f3 | 5805 | long int zz = SCM_I_INUM (z); |
0aacf84e MD |
5806 | if (zz >= 0) |
5807 | return z; | |
5808 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 5809 | return SCM_I_MAKINUM (-zz); |
0aacf84e MD |
5810 | else |
5811 | return scm_i_long2big (-zz); | |
5986c47d | 5812 | } |
0aacf84e MD |
5813 | else if (SCM_BIGP (z)) |
5814 | { | |
5815 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5816 | scm_remember_upto_here_1 (z); | |
5817 | if (sgn < 0) | |
5818 | return scm_i_clonebig (z, 0); | |
5819 | else | |
5820 | return z; | |
5986c47d | 5821 | } |
0aacf84e | 5822 | else if (SCM_REALP (z)) |
55f26379 | 5823 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 5824 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5825 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
5826 | else if (SCM_FRACTIONP (z)) |
5827 | { | |
73e4de09 | 5828 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5829 | return z; |
cba42c93 | 5830 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
5831 | SCM_FRACTION_DENOMINATOR (z)); |
5832 | } | |
0aacf84e | 5833 | else |
c2ff8ab0 | 5834 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); |
0f2d19dd JB |
5835 | } |
5836 | ||
5837 | ||
9de33deb | 5838 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
5839 | /* "Return the angle of the complex number @var{z}." |
5840 | */ | |
0f2d19dd | 5841 | SCM |
6e8d25a6 | 5842 | scm_angle (SCM z) |
0f2d19dd | 5843 | { |
c8ae173e | 5844 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
55f26379 | 5845 | scm_flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
5846 | But if atan2 follows the floating point rounding mode, then the value |
5847 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 5848 | if (SCM_I_INUMP (z)) |
0aacf84e | 5849 | { |
e11e83f3 | 5850 | if (SCM_I_INUM (z) >= 0) |
c8ae173e | 5851 | return scm_flo0; |
0aacf84e | 5852 | else |
55f26379 | 5853 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 5854 | } |
0aacf84e MD |
5855 | else if (SCM_BIGP (z)) |
5856 | { | |
5857 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5858 | scm_remember_upto_here_1 (z); | |
5859 | if (sgn < 0) | |
55f26379 | 5860 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 5861 | else |
c8ae173e | 5862 | return scm_flo0; |
0f2d19dd | 5863 | } |
0aacf84e | 5864 | else if (SCM_REALP (z)) |
c8ae173e KR |
5865 | { |
5866 | if (SCM_REAL_VALUE (z) >= 0) | |
5867 | return scm_flo0; | |
5868 | else | |
55f26379 | 5869 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 5870 | } |
0aacf84e | 5871 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5872 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
5873 | else if (SCM_FRACTIONP (z)) |
5874 | { | |
73e4de09 | 5875 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5876 | return scm_flo0; |
55f26379 | 5877 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 5878 | } |
0aacf84e | 5879 | else |
f4c627b3 | 5880 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); |
0f2d19dd JB |
5881 | } |
5882 | ||
5883 | ||
3c9a524f DH |
5884 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
5885 | /* Convert the number @var{x} to its inexact representation.\n" | |
5886 | */ | |
5887 | SCM | |
5888 | scm_exact_to_inexact (SCM z) | |
5889 | { | |
e11e83f3 | 5890 | if (SCM_I_INUMP (z)) |
55f26379 | 5891 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 5892 | else if (SCM_BIGP (z)) |
55f26379 | 5893 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 5894 | else if (SCM_FRACTIONP (z)) |
55f26379 | 5895 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
5896 | else if (SCM_INEXACTP (z)) |
5897 | return z; | |
5898 | else | |
5899 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
5900 | } | |
5901 | ||
5902 | ||
a1ec6916 | 5903 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 5904 | (SCM z), |
1e6808ea | 5905 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 5906 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 5907 | { |
e11e83f3 | 5908 | if (SCM_I_INUMP (z)) |
f872b822 | 5909 | return z; |
0aacf84e | 5910 | else if (SCM_BIGP (z)) |
f872b822 | 5911 | return z; |
0aacf84e MD |
5912 | else if (SCM_REALP (z)) |
5913 | { | |
f92e85f7 MV |
5914 | if (xisinf (SCM_REAL_VALUE (z)) || xisnan (SCM_REAL_VALUE (z))) |
5915 | SCM_OUT_OF_RANGE (1, z); | |
2be24db4 | 5916 | else |
f92e85f7 MV |
5917 | { |
5918 | mpq_t frac; | |
5919 | SCM q; | |
5920 | ||
5921 | mpq_init (frac); | |
5922 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 5923 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
5924 | scm_i_mpz2num (mpq_denref (frac))); |
5925 | ||
cba42c93 | 5926 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
5927 | for frac... |
5928 | */ | |
5929 | mpq_clear (frac); | |
5930 | return q; | |
5931 | } | |
c2ff8ab0 | 5932 | } |
f92e85f7 MV |
5933 | else if (SCM_FRACTIONP (z)) |
5934 | return z; | |
0aacf84e | 5935 | else |
c2ff8ab0 | 5936 | SCM_WRONG_TYPE_ARG (1, z); |
0f2d19dd | 5937 | } |
1bbd0b84 | 5938 | #undef FUNC_NAME |
0f2d19dd | 5939 | |
f92e85f7 | 5940 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
5941 | (SCM x, SCM eps), |
5942 | "Returns the @emph{simplest} rational number differing\n" | |
5943 | "from @var{x} by no more than @var{eps}.\n" | |
5944 | "\n" | |
5945 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
5946 | "exact result when both its arguments are exact. Thus, you might need\n" | |
5947 | "to use @code{inexact->exact} on the arguments.\n" | |
5948 | "\n" | |
5949 | "@lisp\n" | |
5950 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
5951 | "@result{} 6/5\n" | |
5952 | "@end lisp") | |
f92e85f7 MV |
5953 | #define FUNC_NAME s_scm_rationalize |
5954 | { | |
e11e83f3 | 5955 | if (SCM_I_INUMP (x)) |
f92e85f7 MV |
5956 | return x; |
5957 | else if (SCM_BIGP (x)) | |
5958 | return x; | |
5959 | else if ((SCM_REALP (x)) || SCM_FRACTIONP (x)) | |
5960 | { | |
5961 | /* Use continued fractions to find closest ratio. All | |
5962 | arithmetic is done with exact numbers. | |
5963 | */ | |
5964 | ||
5965 | SCM ex = scm_inexact_to_exact (x); | |
5966 | SCM int_part = scm_floor (ex); | |
d956fa6f MV |
5967 | SCM tt = SCM_I_MAKINUM (1); |
5968 | SCM a1 = SCM_I_MAKINUM (0), a2 = SCM_I_MAKINUM (1), a = SCM_I_MAKINUM (0); | |
5969 | SCM b1 = SCM_I_MAKINUM (1), b2 = SCM_I_MAKINUM (0), b = SCM_I_MAKINUM (0); | |
f92e85f7 MV |
5970 | SCM rx; |
5971 | int i = 0; | |
5972 | ||
73e4de09 | 5973 | if (scm_is_true (scm_num_eq_p (ex, int_part))) |
f92e85f7 MV |
5974 | return ex; |
5975 | ||
5976 | ex = scm_difference (ex, int_part); /* x = x-int_part */ | |
5977 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
5978 | ||
5979 | /* We stop after a million iterations just to be absolutely sure | |
5980 | that we don't go into an infinite loop. The process normally | |
5981 | converges after less than a dozen iterations. | |
5982 | */ | |
5983 | ||
76dae881 | 5984 | eps = scm_abs (eps); |
f92e85f7 MV |
5985 | while (++i < 1000000) |
5986 | { | |
5987 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
5988 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
5989 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
5990 | scm_is_false | |
f92e85f7 | 5991 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 5992 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
5993 | { |
5994 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
73e4de09 | 5995 | if (scm_is_false (scm_exact_p (x)) |
76dae881 | 5996 | || scm_is_false (scm_exact_p (eps))) |
02164269 MV |
5997 | return scm_exact_to_inexact (res); |
5998 | else | |
5999 | return res; | |
6000 | } | |
f92e85f7 MV |
6001 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
6002 | SCM_UNDEFINED); | |
6003 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
6004 | a2 = a1; | |
6005 | b2 = b1; | |
6006 | a1 = a; | |
6007 | b1 = b; | |
6008 | } | |
6009 | scm_num_overflow (s_scm_rationalize); | |
6010 | } | |
6011 | else | |
6012 | SCM_WRONG_TYPE_ARG (1, x); | |
6013 | } | |
6014 | #undef FUNC_NAME | |
6015 | ||
73e4de09 MV |
6016 | /* conversion functions */ |
6017 | ||
6018 | int | |
6019 | scm_is_integer (SCM val) | |
6020 | { | |
6021 | return scm_is_true (scm_integer_p (val)); | |
6022 | } | |
6023 | ||
6024 | int | |
6025 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
6026 | { | |
e11e83f3 | 6027 | if (SCM_I_INUMP (val)) |
73e4de09 | 6028 | { |
e11e83f3 | 6029 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
6030 | return n >= min && n <= max; |
6031 | } | |
6032 | else if (SCM_BIGP (val)) | |
6033 | { | |
6034 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
6035 | return 0; | |
6036 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
6037 | { |
6038 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
6039 | { | |
6040 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
6041 | return n >= min && n <= max; | |
6042 | } | |
6043 | else | |
6044 | return 0; | |
6045 | } | |
73e4de09 MV |
6046 | else |
6047 | { | |
d956fa6f MV |
6048 | scm_t_intmax n; |
6049 | size_t count; | |
73e4de09 | 6050 | |
d956fa6f MV |
6051 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
6052 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
6053 | return 0; | |
6054 | ||
6055 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
6056 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 6057 | |
d956fa6f | 6058 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 6059 | { |
d956fa6f MV |
6060 | if (n < 0) |
6061 | return 0; | |
73e4de09 | 6062 | } |
73e4de09 MV |
6063 | else |
6064 | { | |
d956fa6f MV |
6065 | n = -n; |
6066 | if (n >= 0) | |
6067 | return 0; | |
73e4de09 | 6068 | } |
d956fa6f MV |
6069 | |
6070 | return n >= min && n <= max; | |
73e4de09 MV |
6071 | } |
6072 | } | |
73e4de09 MV |
6073 | else |
6074 | return 0; | |
6075 | } | |
6076 | ||
6077 | int | |
6078 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
6079 | { | |
e11e83f3 | 6080 | if (SCM_I_INUMP (val)) |
73e4de09 | 6081 | { |
e11e83f3 | 6082 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
6083 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
6084 | } | |
6085 | else if (SCM_BIGP (val)) | |
6086 | { | |
6087 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
6088 | return 0; | |
6089 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
6090 | { |
6091 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
6092 | { | |
6093 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
6094 | return n >= min && n <= max; | |
6095 | } | |
6096 | else | |
6097 | return 0; | |
6098 | } | |
73e4de09 MV |
6099 | else |
6100 | { | |
d956fa6f MV |
6101 | scm_t_uintmax n; |
6102 | size_t count; | |
73e4de09 | 6103 | |
d956fa6f MV |
6104 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
6105 | return 0; | |
73e4de09 | 6106 | |
d956fa6f MV |
6107 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
6108 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 6109 | return 0; |
d956fa6f MV |
6110 | |
6111 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
6112 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 6113 | |
d956fa6f | 6114 | return n >= min && n <= max; |
73e4de09 MV |
6115 | } |
6116 | } | |
73e4de09 MV |
6117 | else |
6118 | return 0; | |
6119 | } | |
6120 | ||
1713d319 MV |
6121 | static void |
6122 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
6123 | { | |
6124 | scm_error (scm_out_of_range_key, | |
6125 | NULL, | |
6126 | "Value out of range ~S to ~S: ~S", | |
6127 | scm_list_3 (min, max, bad_val), | |
6128 | scm_list_1 (bad_val)); | |
6129 | } | |
6130 | ||
bfd7932e MV |
6131 | #define TYPE scm_t_intmax |
6132 | #define TYPE_MIN min | |
6133 | #define TYPE_MAX max | |
6134 | #define SIZEOF_TYPE 0 | |
6135 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
6136 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
6137 | #include "libguile/conv-integer.i.c" | |
6138 | ||
6139 | #define TYPE scm_t_uintmax | |
6140 | #define TYPE_MIN min | |
6141 | #define TYPE_MAX max | |
6142 | #define SIZEOF_TYPE 0 | |
6143 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
6144 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
6145 | #include "libguile/conv-uinteger.i.c" | |
6146 | ||
6147 | #define TYPE scm_t_int8 | |
6148 | #define TYPE_MIN SCM_T_INT8_MIN | |
6149 | #define TYPE_MAX SCM_T_INT8_MAX | |
6150 | #define SIZEOF_TYPE 1 | |
6151 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
6152 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
6153 | #include "libguile/conv-integer.i.c" | |
6154 | ||
6155 | #define TYPE scm_t_uint8 | |
6156 | #define TYPE_MIN 0 | |
6157 | #define TYPE_MAX SCM_T_UINT8_MAX | |
6158 | #define SIZEOF_TYPE 1 | |
6159 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
6160 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
6161 | #include "libguile/conv-uinteger.i.c" | |
6162 | ||
6163 | #define TYPE scm_t_int16 | |
6164 | #define TYPE_MIN SCM_T_INT16_MIN | |
6165 | #define TYPE_MAX SCM_T_INT16_MAX | |
6166 | #define SIZEOF_TYPE 2 | |
6167 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
6168 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
6169 | #include "libguile/conv-integer.i.c" | |
6170 | ||
6171 | #define TYPE scm_t_uint16 | |
6172 | #define TYPE_MIN 0 | |
6173 | #define TYPE_MAX SCM_T_UINT16_MAX | |
6174 | #define SIZEOF_TYPE 2 | |
6175 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
6176 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
6177 | #include "libguile/conv-uinteger.i.c" | |
6178 | ||
6179 | #define TYPE scm_t_int32 | |
6180 | #define TYPE_MIN SCM_T_INT32_MIN | |
6181 | #define TYPE_MAX SCM_T_INT32_MAX | |
6182 | #define SIZEOF_TYPE 4 | |
6183 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
6184 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
6185 | #include "libguile/conv-integer.i.c" | |
6186 | ||
6187 | #define TYPE scm_t_uint32 | |
6188 | #define TYPE_MIN 0 | |
6189 | #define TYPE_MAX SCM_T_UINT32_MAX | |
6190 | #define SIZEOF_TYPE 4 | |
6191 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
6192 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
6193 | #include "libguile/conv-uinteger.i.c" | |
6194 | ||
904a78f1 MG |
6195 | #define TYPE scm_t_wchar |
6196 | #define TYPE_MIN (scm_t_int32)-1 | |
6197 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
6198 | #define SIZEOF_TYPE 4 | |
6199 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
6200 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
6201 | #include "libguile/conv-integer.i.c" | |
6202 | ||
bfd7932e MV |
6203 | #if SCM_HAVE_T_INT64 |
6204 | ||
6205 | #define TYPE scm_t_int64 | |
6206 | #define TYPE_MIN SCM_T_INT64_MIN | |
6207 | #define TYPE_MAX SCM_T_INT64_MAX | |
6208 | #define SIZEOF_TYPE 8 | |
6209 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
6210 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
6211 | #include "libguile/conv-integer.i.c" | |
6212 | ||
6213 | #define TYPE scm_t_uint64 | |
6214 | #define TYPE_MIN 0 | |
6215 | #define TYPE_MAX SCM_T_UINT64_MAX | |
6216 | #define SIZEOF_TYPE 8 | |
6217 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
6218 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
6219 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 6220 | |
bfd7932e | 6221 | #endif |
73e4de09 | 6222 | |
cd036260 MV |
6223 | void |
6224 | scm_to_mpz (SCM val, mpz_t rop) | |
6225 | { | |
6226 | if (SCM_I_INUMP (val)) | |
6227 | mpz_set_si (rop, SCM_I_INUM (val)); | |
6228 | else if (SCM_BIGP (val)) | |
6229 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
6230 | else | |
6231 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
6232 | } | |
6233 | ||
6234 | SCM | |
6235 | scm_from_mpz (mpz_t val) | |
6236 | { | |
6237 | return scm_i_mpz2num (val); | |
6238 | } | |
6239 | ||
73e4de09 MV |
6240 | int |
6241 | scm_is_real (SCM val) | |
6242 | { | |
6243 | return scm_is_true (scm_real_p (val)); | |
6244 | } | |
6245 | ||
55f26379 MV |
6246 | int |
6247 | scm_is_rational (SCM val) | |
6248 | { | |
6249 | return scm_is_true (scm_rational_p (val)); | |
6250 | } | |
6251 | ||
73e4de09 MV |
6252 | double |
6253 | scm_to_double (SCM val) | |
6254 | { | |
55f26379 MV |
6255 | if (SCM_I_INUMP (val)) |
6256 | return SCM_I_INUM (val); | |
6257 | else if (SCM_BIGP (val)) | |
6258 | return scm_i_big2dbl (val); | |
6259 | else if (SCM_FRACTIONP (val)) | |
6260 | return scm_i_fraction2double (val); | |
6261 | else if (SCM_REALP (val)) | |
6262 | return SCM_REAL_VALUE (val); | |
6263 | else | |
7a1aba42 | 6264 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
6265 | } |
6266 | ||
6267 | SCM | |
6268 | scm_from_double (double val) | |
6269 | { | |
55f26379 MV |
6270 | SCM z = scm_double_cell (scm_tc16_real, 0, 0, 0); |
6271 | SCM_REAL_VALUE (z) = val; | |
6272 | return z; | |
73e4de09 MV |
6273 | } |
6274 | ||
55f26379 MV |
6275 | #if SCM_ENABLE_DISCOURAGED == 1 |
6276 | ||
6277 | float | |
6278 | scm_num2float (SCM num, unsigned long int pos, const char *s_caller) | |
6279 | { | |
6280 | if (SCM_BIGP (num)) | |
6281 | { | |
6282 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
6283 | if (!xisinf (res)) | |
6284 | return res; | |
6285 | else | |
6286 | scm_out_of_range (NULL, num); | |
6287 | } | |
6288 | else | |
6289 | return scm_to_double (num); | |
6290 | } | |
6291 | ||
6292 | double | |
6293 | scm_num2double (SCM num, unsigned long int pos, const char *s_caller) | |
6294 | { | |
6295 | if (SCM_BIGP (num)) | |
6296 | { | |
6297 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
6298 | if (!xisinf (res)) | |
6299 | return res; | |
6300 | else | |
6301 | scm_out_of_range (NULL, num); | |
6302 | } | |
6303 | else | |
6304 | return scm_to_double (num); | |
6305 | } | |
6306 | ||
6307 | #endif | |
6308 | ||
8507ec80 MV |
6309 | int |
6310 | scm_is_complex (SCM val) | |
6311 | { | |
6312 | return scm_is_true (scm_complex_p (val)); | |
6313 | } | |
6314 | ||
6315 | double | |
6316 | scm_c_real_part (SCM z) | |
6317 | { | |
6318 | if (SCM_COMPLEXP (z)) | |
6319 | return SCM_COMPLEX_REAL (z); | |
6320 | else | |
6321 | { | |
6322 | /* Use the scm_real_part to get proper error checking and | |
6323 | dispatching. | |
6324 | */ | |
6325 | return scm_to_double (scm_real_part (z)); | |
6326 | } | |
6327 | } | |
6328 | ||
6329 | double | |
6330 | scm_c_imag_part (SCM z) | |
6331 | { | |
6332 | if (SCM_COMPLEXP (z)) | |
6333 | return SCM_COMPLEX_IMAG (z); | |
6334 | else | |
6335 | { | |
6336 | /* Use the scm_imag_part to get proper error checking and | |
6337 | dispatching. The result will almost always be 0.0, but not | |
6338 | always. | |
6339 | */ | |
6340 | return scm_to_double (scm_imag_part (z)); | |
6341 | } | |
6342 | } | |
6343 | ||
6344 | double | |
6345 | scm_c_magnitude (SCM z) | |
6346 | { | |
6347 | return scm_to_double (scm_magnitude (z)); | |
6348 | } | |
6349 | ||
6350 | double | |
6351 | scm_c_angle (SCM z) | |
6352 | { | |
6353 | return scm_to_double (scm_angle (z)); | |
6354 | } | |
6355 | ||
6356 | int | |
6357 | scm_is_number (SCM z) | |
6358 | { | |
6359 | return scm_is_true (scm_number_p (z)); | |
6360 | } | |
6361 | ||
8ab3d8a0 KR |
6362 | |
6363 | /* In the following functions we dispatch to the real-arg funcs like log() | |
6364 | when we know the arg is real, instead of just handing everything to | |
6365 | clog() for instance. This is in case clog() doesn't optimize for a | |
6366 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
6367 | well use it to go straight to the applicable C func. */ | |
6368 | ||
6369 | SCM_DEFINE (scm_log, "log", 1, 0, 0, | |
6370 | (SCM z), | |
6371 | "Return the natural logarithm of @var{z}.") | |
6372 | #define FUNC_NAME s_scm_log | |
6373 | { | |
6374 | if (SCM_COMPLEXP (z)) | |
6375 | { | |
4b26c03e | 6376 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6377 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
6378 | #else | |
6379 | double re = SCM_COMPLEX_REAL (z); | |
6380 | double im = SCM_COMPLEX_IMAG (z); | |
6381 | return scm_c_make_rectangular (log (hypot (re, im)), | |
6382 | atan2 (im, re)); | |
6383 | #endif | |
6384 | } | |
6385 | else | |
6386 | { | |
6387 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6388 | although the value itself overflows. */ | |
6389 | double re = scm_to_double (z); | |
6390 | double l = log (fabs (re)); | |
6391 | if (re >= 0.0) | |
6392 | return scm_from_double (l); | |
6393 | else | |
6394 | return scm_c_make_rectangular (l, M_PI); | |
6395 | } | |
6396 | } | |
6397 | #undef FUNC_NAME | |
6398 | ||
6399 | ||
6400 | SCM_DEFINE (scm_log10, "log10", 1, 0, 0, | |
6401 | (SCM z), | |
6402 | "Return the base 10 logarithm of @var{z}.") | |
6403 | #define FUNC_NAME s_scm_log10 | |
6404 | { | |
6405 | if (SCM_COMPLEXP (z)) | |
6406 | { | |
6407 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
6408 | clog() and a multiply by M_LOG10E, rather than the fallback | |
6409 | log10+hypot+atan2.) */ | |
4b26c03e | 6410 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG10 && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6411 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
6412 | #else | |
6413 | double re = SCM_COMPLEX_REAL (z); | |
6414 | double im = SCM_COMPLEX_IMAG (z); | |
6415 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
6416 | M_LOG10E * atan2 (im, re)); | |
6417 | #endif | |
6418 | } | |
6419 | else | |
6420 | { | |
6421 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6422 | although the value itself overflows. */ | |
6423 | double re = scm_to_double (z); | |
6424 | double l = log10 (fabs (re)); | |
6425 | if (re >= 0.0) | |
6426 | return scm_from_double (l); | |
6427 | else | |
6428 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
6429 | } | |
6430 | } | |
6431 | #undef FUNC_NAME | |
6432 | ||
6433 | ||
6434 | SCM_DEFINE (scm_exp, "exp", 1, 0, 0, | |
6435 | (SCM z), | |
6436 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
6437 | "base of natural logarithms (2.71828@dots{}).") | |
6438 | #define FUNC_NAME s_scm_exp | |
6439 | { | |
6440 | if (SCM_COMPLEXP (z)) | |
6441 | { | |
4b26c03e | 6442 | #if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6443 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
6444 | #else | |
6445 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
6446 | SCM_COMPLEX_IMAG (z)); | |
6447 | #endif | |
6448 | } | |
6449 | else | |
6450 | { | |
6451 | /* When z is a negative bignum the conversion to double overflows, | |
6452 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
6453 | return scm_from_double (exp (scm_to_double (z))); | |
6454 | } | |
6455 | } | |
6456 | #undef FUNC_NAME | |
6457 | ||
6458 | ||
6459 | SCM_DEFINE (scm_sqrt, "sqrt", 1, 0, 0, | |
6460 | (SCM x), | |
6461 | "Return the square root of @var{z}. Of the two possible roots\n" | |
6462 | "(positive and negative), the one with the a positive real part\n" | |
6463 | "is returned, or if that's zero then a positive imaginary part.\n" | |
6464 | "Thus,\n" | |
6465 | "\n" | |
6466 | "@example\n" | |
6467 | "(sqrt 9.0) @result{} 3.0\n" | |
6468 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
6469 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
6470 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
6471 | "@end example") | |
6472 | #define FUNC_NAME s_scm_sqrt | |
6473 | { | |
6474 | if (SCM_COMPLEXP (x)) | |
6475 | { | |
4b26c03e | 6476 | #if HAVE_COMPLEX_DOUBLE && HAVE_USABLE_CSQRT && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6477 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (x))); |
6478 | #else | |
6479 | double re = SCM_COMPLEX_REAL (x); | |
6480 | double im = SCM_COMPLEX_IMAG (x); | |
6481 | return scm_c_make_polar (sqrt (hypot (re, im)), | |
6482 | 0.5 * atan2 (im, re)); | |
6483 | #endif | |
6484 | } | |
6485 | else | |
6486 | { | |
6487 | double xx = scm_to_double (x); | |
6488 | if (xx < 0) | |
6489 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
6490 | else | |
6491 | return scm_from_double (sqrt (xx)); | |
6492 | } | |
6493 | } | |
6494 | #undef FUNC_NAME | |
6495 | ||
6496 | ||
6497 | ||
0f2d19dd JB |
6498 | void |
6499 | scm_init_numbers () | |
0f2d19dd | 6500 | { |
0b799eea MV |
6501 | int i; |
6502 | ||
713a4259 KR |
6503 | mpz_init_set_si (z_negative_one, -1); |
6504 | ||
a261c0e9 DH |
6505 | /* It may be possible to tune the performance of some algorithms by using |
6506 | * the following constants to avoid the creation of bignums. Please, before | |
6507 | * using these values, remember the two rules of program optimization: | |
6508 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 6509 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 6510 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 6511 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 6512 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 6513 | |
f3ae5d60 MD |
6514 | scm_add_feature ("complex"); |
6515 | scm_add_feature ("inexact"); | |
55f26379 | 6516 | scm_flo0 = scm_from_double (0.0); |
0b799eea MV |
6517 | |
6518 | /* determine floating point precision */ | |
55f26379 | 6519 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
6520 | { |
6521 | init_dblprec(&scm_dblprec[i-2],i); | |
6522 | init_fx_radix(fx_per_radix[i-2],i); | |
6523 | } | |
f872b822 | 6524 | #ifdef DBL_DIG |
0b799eea MV |
6525 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
6526 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; | |
6527 | #endif | |
1be6b49c | 6528 | |
d956fa6f MV |
6529 | exactly_one_half = scm_permanent_object (scm_divide (SCM_I_MAKINUM (1), |
6530 | SCM_I_MAKINUM (2))); | |
a0599745 | 6531 | #include "libguile/numbers.x" |
0f2d19dd | 6532 | } |
89e00824 ML |
6533 | |
6534 | /* | |
6535 | Local Variables: | |
6536 | c-file-style: "gnu" | |
6537 | End: | |
6538 | */ |