Commit | Line | Data |
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8e43ed5d | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc. |
ba74ef4e MV |
2 | * |
3 | * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories | |
4 | * and Bellcore. See scm_divide. | |
5 | * | |
f81e080b | 6 | * |
73be1d9e | 7 | * This library is free software; you can redistribute it and/or |
53befeb7 NJ |
8 | * modify it under the terms of the GNU Lesser General Public License |
9 | * as published by the Free Software Foundation; either version 3 of | |
10 | * the License, or (at your option) any later version. | |
0f2d19dd | 11 | * |
53befeb7 NJ |
12 | * This library is distributed in the hope that it will be useful, but |
13 | * WITHOUT ANY WARRANTY; without even the implied warranty of | |
73be1d9e MV |
14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
15 | * Lesser General Public License for more details. | |
0f2d19dd | 16 | * |
73be1d9e MV |
17 | * You should have received a copy of the GNU Lesser General Public |
18 | * License along with this library; if not, write to the Free Software | |
53befeb7 NJ |
19 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
20 | * 02110-1301 USA | |
73be1d9e | 21 | */ |
1bbd0b84 | 22 | |
0f2d19dd | 23 | \f |
ca46fb90 RB |
24 | /* General assumptions: |
25 | * All objects satisfying SCM_COMPLEXP() have a non-zero complex component. | |
26 | * All objects satisfying SCM_BIGP() are too large to fit in a fixnum. | |
27 | * If an object satisfies integer?, it's either an inum, a bignum, or a real. | |
28 | * If floor (r) == r, r is an int, and mpz_set_d will DTRT. | |
f92e85f7 | 29 | * All objects satisfying SCM_FRACTIONP are never an integer. |
ca46fb90 RB |
30 | */ |
31 | ||
32 | /* TODO: | |
33 | ||
34 | - see if special casing bignums and reals in integer-exponent when | |
35 | possible (to use mpz_pow and mpf_pow_ui) is faster. | |
36 | ||
37 | - look in to better short-circuiting of common cases in | |
38 | integer-expt and elsewhere. | |
39 | ||
40 | - see if direct mpz operations can help in ash and elsewhere. | |
41 | ||
42 | */ | |
0f2d19dd | 43 | |
dbb605f5 | 44 | #ifdef HAVE_CONFIG_H |
ee33d62a RB |
45 | # include <config.h> |
46 | #endif | |
47 | ||
0f2d19dd | 48 | #include <math.h> |
fc194577 | 49 | #include <string.h> |
3f47e526 MG |
50 | #include <unicase.h> |
51 | #include <unictype.h> | |
f92e85f7 | 52 | |
8ab3d8a0 KR |
53 | #if HAVE_COMPLEX_H |
54 | #include <complex.h> | |
55 | #endif | |
56 | ||
a0599745 | 57 | #include "libguile/_scm.h" |
a0599745 MD |
58 | #include "libguile/feature.h" |
59 | #include "libguile/ports.h" | |
60 | #include "libguile/root.h" | |
61 | #include "libguile/smob.h" | |
62 | #include "libguile/strings.h" | |
864e7d42 | 63 | #include "libguile/bdw-gc.h" |
a0599745 MD |
64 | |
65 | #include "libguile/validate.h" | |
66 | #include "libguile/numbers.h" | |
1be6b49c | 67 | #include "libguile/deprecation.h" |
f4c627b3 | 68 | |
f92e85f7 MV |
69 | #include "libguile/eq.h" |
70 | ||
8ab3d8a0 KR |
71 | /* values per glibc, if not already defined */ |
72 | #ifndef M_LOG10E | |
73 | #define M_LOG10E 0.43429448190325182765 | |
74 | #endif | |
75 | #ifndef M_PI | |
76 | #define M_PI 3.14159265358979323846 | |
77 | #endif | |
78 | ||
e25f3727 AW |
79 | typedef scm_t_signed_bits scm_t_inum; |
80 | #define scm_from_inum(x) (scm_from_signed_integer (x)) | |
81 | ||
7112615f MW |
82 | /* Tests to see if a C double is neither infinite nor a NaN. |
83 | TODO: if it's available, use C99's isfinite(x) instead */ | |
84 | #define DOUBLE_IS_FINITE(x) (!isinf(x) && !isnan(x)) | |
85 | ||
0f2d19dd | 86 | \f |
f4c627b3 | 87 | |
ca46fb90 RB |
88 | /* |
89 | Wonder if this might be faster for some of our code? A switch on | |
90 | the numtag would jump directly to the right case, and the | |
91 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
92 | ||
93 | #define SCM_I_NUMTAG_NOTNUM 0 | |
94 | #define SCM_I_NUMTAG_INUM 1 | |
95 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
96 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
97 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
98 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 99 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 100 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 101 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
102 | : SCM_I_NUMTAG_NOTNUM))) |
103 | */ | |
f92e85f7 | 104 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
105 | |
106 | ||
e7efe8e7 AW |
107 | static SCM flo0; |
108 | ||
34d19ef6 | 109 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 110 | |
56e55ac7 | 111 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
112 | * printed or scm_string representation of an inexact number. |
113 | */ | |
0b799eea | 114 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 115 | |
b127c712 | 116 | |
ad79736c AW |
117 | #if !defined (HAVE_ASINH) |
118 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } | |
119 | #endif | |
120 | #if !defined (HAVE_ACOSH) | |
121 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } | |
122 | #endif | |
123 | #if !defined (HAVE_ATANH) | |
124 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } | |
125 | #endif | |
126 | ||
f8a8200b KR |
127 | /* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses |
128 | an explicit check. In some future gmp (don't know what version number), | |
129 | mpz_cmp_d is supposed to do this itself. */ | |
130 | #if 1 | |
b127c712 | 131 | #define xmpz_cmp_d(z, d) \ |
2e65b52f | 132 | (isinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) |
b127c712 KR |
133 | #else |
134 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
135 | #endif | |
136 | ||
f92e85f7 | 137 | |
4b26c03e | 138 | #if defined (GUILE_I) |
bca69a9f | 139 | #if HAVE_COMPLEX_DOUBLE |
8ab3d8a0 KR |
140 | |
141 | /* For an SCM object Z which is a complex number (ie. satisfies | |
142 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
143 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 144 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 145 | |
7a35784c | 146 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
8ab3d8a0 KR |
147 | |
148 | /* Convert a C "complex double" to an SCM value. */ | |
7a35784c | 149 | static inline SCM |
8ab3d8a0 KR |
150 | scm_from_complex_double (complex double z) |
151 | { | |
152 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
153 | } | |
bca69a9f | 154 | |
8ab3d8a0 | 155 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 156 | #endif /* GUILE_I */ |
8ab3d8a0 | 157 | |
0f2d19dd JB |
158 | \f |
159 | ||
713a4259 | 160 | static mpz_t z_negative_one; |
ac0c002c DH |
161 | |
162 | \f | |
864e7d42 LC |
163 | /* Clear the `mpz_t' embedded in bignum PTR. */ |
164 | static void | |
165 | finalize_bignum (GC_PTR ptr, GC_PTR data) | |
166 | { | |
167 | SCM bignum; | |
168 | ||
169 | bignum = PTR2SCM (ptr); | |
170 | mpz_clear (SCM_I_BIG_MPZ (bignum)); | |
171 | } | |
172 | ||
d017fcdf LC |
173 | /* Return a new uninitialized bignum. */ |
174 | static inline SCM | |
175 | make_bignum (void) | |
176 | { | |
177 | scm_t_bits *p; | |
864e7d42 LC |
178 | GC_finalization_proc prev_finalizer; |
179 | GC_PTR prev_finalizer_data; | |
d017fcdf LC |
180 | |
181 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ | |
182 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), | |
183 | "bignum"); | |
184 | p[0] = scm_tc16_big; | |
185 | ||
864e7d42 LC |
186 | GC_REGISTER_FINALIZER_NO_ORDER (p, finalize_bignum, NULL, |
187 | &prev_finalizer, | |
188 | &prev_finalizer_data); | |
189 | ||
d017fcdf LC |
190 | return SCM_PACK (p); |
191 | } | |
ac0c002c | 192 | |
864e7d42 | 193 | |
189171c5 | 194 | SCM |
ca46fb90 RB |
195 | scm_i_mkbig () |
196 | { | |
197 | /* Return a newly created bignum. */ | |
d017fcdf | 198 | SCM z = make_bignum (); |
ca46fb90 RB |
199 | mpz_init (SCM_I_BIG_MPZ (z)); |
200 | return z; | |
201 | } | |
202 | ||
e25f3727 AW |
203 | static SCM |
204 | scm_i_inum2big (scm_t_inum x) | |
205 | { | |
206 | /* Return a newly created bignum initialized to X. */ | |
207 | SCM z = make_bignum (); | |
208 | #if SIZEOF_VOID_P == SIZEOF_LONG | |
209 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
210 | #else | |
211 | /* Note that in this case, you'll also have to check all mpz_*_ui and | |
212 | mpz_*_si invocations in Guile. */ | |
213 | #error creation of mpz not implemented for this inum size | |
214 | #endif | |
215 | return z; | |
216 | } | |
217 | ||
189171c5 | 218 | SCM |
c71b0706 MV |
219 | scm_i_long2big (long x) |
220 | { | |
221 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 222 | SCM z = make_bignum (); |
c71b0706 MV |
223 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
224 | return z; | |
225 | } | |
226 | ||
189171c5 | 227 | SCM |
c71b0706 MV |
228 | scm_i_ulong2big (unsigned long x) |
229 | { | |
230 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 231 | SCM z = make_bignum (); |
c71b0706 MV |
232 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
233 | return z; | |
234 | } | |
235 | ||
189171c5 | 236 | SCM |
ca46fb90 RB |
237 | scm_i_clonebig (SCM src_big, int same_sign_p) |
238 | { | |
239 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
d017fcdf | 240 | SCM z = make_bignum (); |
ca46fb90 | 241 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
0aacf84e MD |
242 | if (!same_sign_p) |
243 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
244 | return z; |
245 | } | |
246 | ||
189171c5 | 247 | int |
ca46fb90 RB |
248 | scm_i_bigcmp (SCM x, SCM y) |
249 | { | |
250 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
251 | /* presume we already know x and y are bignums */ | |
252 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
253 | scm_remember_upto_here_2 (x, y); | |
254 | return result; | |
255 | } | |
256 | ||
189171c5 | 257 | SCM |
ca46fb90 RB |
258 | scm_i_dbl2big (double d) |
259 | { | |
260 | /* results are only defined if d is an integer */ | |
d017fcdf | 261 | SCM z = make_bignum (); |
ca46fb90 RB |
262 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
263 | return z; | |
264 | } | |
265 | ||
f92e85f7 MV |
266 | /* Convert a integer in double representation to a SCM number. */ |
267 | ||
189171c5 | 268 | SCM |
f92e85f7 MV |
269 | scm_i_dbl2num (double u) |
270 | { | |
271 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
272 | powers of 2, so there's no rounding when making "double" values | |
273 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
274 | get rounded on a 64-bit machine, hence the "+1". | |
275 | ||
276 | The use of floor() to force to an integer value ensures we get a | |
277 | "numerically closest" value without depending on how a | |
278 | double->long cast or how mpz_set_d will round. For reference, | |
279 | double->long probably follows the hardware rounding mode, | |
280 | mpz_set_d truncates towards zero. */ | |
281 | ||
282 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
283 | representable as a double? */ | |
284 | ||
285 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
286 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
e25f3727 | 287 | return SCM_I_MAKINUM ((scm_t_inum) u); |
f92e85f7 MV |
288 | else |
289 | return scm_i_dbl2big (u); | |
290 | } | |
291 | ||
089c9a59 KR |
292 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
293 | with R5RS exact->inexact. | |
294 | ||
295 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
296 | (ie. truncate towards zero), then adjust to get the closest double by |
297 | examining the next lower bit and adding 1 (to the absolute value) if | |
298 | necessary. | |
299 | ||
300 | Bignums exactly half way between representable doubles are rounded to the | |
301 | next higher absolute value (ie. away from zero). This seems like an | |
302 | adequate interpretation of R5RS "numerically closest", and it's easier | |
303 | and faster than a full "nearest-even" style. | |
304 | ||
305 | The bit test must be done on the absolute value of the mpz_t, which means | |
306 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
307 | negatives as twos complement. | |
308 | ||
309 | In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up | |
310 | following the hardware rounding mode, but applied to the absolute value | |
311 | of the mpz_t operand. This is not what we want so we put the high | |
312 | DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when, | |
313 | mpz_get_d is supposed to always truncate towards zero. | |
314 | ||
315 | ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3 | |
316 | is a slowdown. It'd be faster to pick out the relevant high bits with | |
317 | mpz_getlimbn if we could be bothered coding that, and if the new | |
318 | truncating gmp doesn't come out. */ | |
089c9a59 KR |
319 | |
320 | double | |
ca46fb90 RB |
321 | scm_i_big2dbl (SCM b) |
322 | { | |
089c9a59 KR |
323 | double result; |
324 | size_t bits; | |
325 | ||
326 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
327 | ||
f8a8200b | 328 | #if 1 |
089c9a59 | 329 | { |
f8a8200b | 330 | /* Current GMP, eg. 4.1.3, force truncation towards zero */ |
089c9a59 KR |
331 | mpz_t tmp; |
332 | if (bits > DBL_MANT_DIG) | |
333 | { | |
334 | size_t shift = bits - DBL_MANT_DIG; | |
335 | mpz_init2 (tmp, DBL_MANT_DIG); | |
336 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
337 | result = ldexp (mpz_get_d (tmp), shift); | |
338 | mpz_clear (tmp); | |
339 | } | |
340 | else | |
341 | { | |
342 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
343 | } | |
344 | } | |
345 | #else | |
f8a8200b | 346 | /* Future GMP */ |
089c9a59 KR |
347 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
348 | #endif | |
349 | ||
350 | if (bits > DBL_MANT_DIG) | |
351 | { | |
352 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
353 | /* test bit number "pos" in absolute value */ | |
354 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
355 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
356 | { | |
357 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
358 | } | |
359 | } | |
360 | ||
ca46fb90 RB |
361 | scm_remember_upto_here_1 (b); |
362 | return result; | |
363 | } | |
364 | ||
189171c5 | 365 | SCM |
ca46fb90 RB |
366 | scm_i_normbig (SCM b) |
367 | { | |
368 | /* convert a big back to a fixnum if it'll fit */ | |
369 | /* presume b is a bignum */ | |
370 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
371 | { | |
e25f3727 | 372 | scm_t_inum val = mpz_get_si (SCM_I_BIG_MPZ (b)); |
ca46fb90 | 373 | if (SCM_FIXABLE (val)) |
d956fa6f | 374 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
375 | } |
376 | return b; | |
377 | } | |
f872b822 | 378 | |
f92e85f7 MV |
379 | static SCM_C_INLINE_KEYWORD SCM |
380 | scm_i_mpz2num (mpz_t b) | |
381 | { | |
382 | /* convert a mpz number to a SCM number. */ | |
383 | if (mpz_fits_slong_p (b)) | |
384 | { | |
e25f3727 | 385 | scm_t_inum val = mpz_get_si (b); |
f92e85f7 | 386 | if (SCM_FIXABLE (val)) |
d956fa6f | 387 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
388 | } |
389 | ||
390 | { | |
d017fcdf | 391 | SCM z = make_bignum (); |
f92e85f7 MV |
392 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
393 | return z; | |
394 | } | |
395 | } | |
396 | ||
397 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
398 | static SCM scm_divide2real (SCM x, SCM y); | |
399 | ||
cba42c93 MV |
400 | static SCM |
401 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 402 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 403 | { |
c60e130c MV |
404 | /* First make sure the arguments are proper. |
405 | */ | |
e11e83f3 | 406 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 407 | { |
bc36d050 | 408 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 409 | scm_num_overflow ("make-ratio"); |
cff5fa33 | 410 | if (scm_is_eq (denominator, SCM_INUM1)) |
f92e85f7 MV |
411 | return numerator; |
412 | } | |
413 | else | |
414 | { | |
415 | if (!(SCM_BIGP(denominator))) | |
416 | SCM_WRONG_TYPE_ARG (2, denominator); | |
417 | } | |
e11e83f3 | 418 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
419 | SCM_WRONG_TYPE_ARG (1, numerator); |
420 | ||
421 | /* Then flip signs so that the denominator is positive. | |
422 | */ | |
73e4de09 | 423 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
424 | { |
425 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
426 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
427 | } | |
428 | ||
429 | /* Now consider for each of the four fixnum/bignum combinations | |
430 | whether the rational number is really an integer. | |
431 | */ | |
e11e83f3 | 432 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 433 | { |
e25f3727 | 434 | scm_t_inum x = SCM_I_INUM (numerator); |
bc36d050 | 435 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 436 | return SCM_INUM0; |
e11e83f3 | 437 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 438 | { |
e25f3727 | 439 | scm_t_inum y; |
e11e83f3 | 440 | y = SCM_I_INUM (denominator); |
f92e85f7 | 441 | if (x == y) |
cff5fa33 | 442 | return SCM_INUM1; |
f92e85f7 | 443 | if ((x % y) == 0) |
d956fa6f | 444 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 445 | } |
dd5130ca KR |
446 | else |
447 | { | |
448 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
449 | of that value for the denominator, as a bignum. Apart from |
450 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
451 | integer. */ | |
452 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
453 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
454 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 455 | return SCM_I_MAKINUM(-1); |
dd5130ca | 456 | } |
f92e85f7 | 457 | } |
c60e130c | 458 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 459 | { |
e11e83f3 | 460 | if (SCM_I_INUMP (denominator)) |
c60e130c | 461 | { |
e25f3727 | 462 | scm_t_inum yy = SCM_I_INUM (denominator); |
c60e130c MV |
463 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
464 | return scm_divide (numerator, denominator); | |
465 | } | |
466 | else | |
f92e85f7 | 467 | { |
bc36d050 | 468 | if (scm_is_eq (numerator, denominator)) |
cff5fa33 | 469 | return SCM_INUM1; |
c60e130c MV |
470 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
471 | SCM_I_BIG_MPZ (denominator))) | |
472 | return scm_divide(numerator, denominator); | |
f92e85f7 | 473 | } |
f92e85f7 | 474 | } |
c60e130c MV |
475 | |
476 | /* No, it's a proper fraction. | |
477 | */ | |
e2bf3b19 HWN |
478 | { |
479 | SCM divisor = scm_gcd (numerator, denominator); | |
cff5fa33 | 480 | if (!(scm_is_eq (divisor, SCM_INUM1))) |
e2bf3b19 HWN |
481 | { |
482 | numerator = scm_divide (numerator, divisor); | |
483 | denominator = scm_divide (denominator, divisor); | |
484 | } | |
485 | ||
486 | return scm_double_cell (scm_tc16_fraction, | |
487 | SCM_UNPACK (numerator), | |
488 | SCM_UNPACK (denominator), 0); | |
489 | } | |
f92e85f7 | 490 | } |
c60e130c | 491 | #undef FUNC_NAME |
f92e85f7 | 492 | |
f92e85f7 MV |
493 | double |
494 | scm_i_fraction2double (SCM z) | |
495 | { | |
55f26379 MV |
496 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
497 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
498 | } |
499 | ||
a1ec6916 | 500 | SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0, |
1bbd0b84 | 501 | (SCM x), |
942e5b91 MG |
502 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
503 | "otherwise.") | |
1bbd0b84 | 504 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 505 | { |
41df63cf MW |
506 | if (SCM_INEXACTP (x)) |
507 | return SCM_BOOL_F; | |
508 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 509 | return SCM_BOOL_T; |
41df63cf MW |
510 | else |
511 | SCM_WRONG_TYPE_ARG (1, x); | |
512 | } | |
513 | #undef FUNC_NAME | |
514 | ||
515 | ||
516 | SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, | |
517 | (SCM x), | |
518 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
519 | "else.") | |
520 | #define FUNC_NAME s_scm_inexact_p | |
521 | { | |
522 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 523 | return SCM_BOOL_T; |
41df63cf | 524 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 525 | return SCM_BOOL_F; |
41df63cf MW |
526 | else |
527 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 528 | } |
1bbd0b84 | 529 | #undef FUNC_NAME |
0f2d19dd | 530 | |
4219f20d | 531 | |
a1ec6916 | 532 | SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 533 | (SCM n), |
942e5b91 MG |
534 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
535 | "otherwise.") | |
1bbd0b84 | 536 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 537 | { |
e11e83f3 | 538 | if (SCM_I_INUMP (n)) |
0aacf84e | 539 | { |
e25f3727 | 540 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 541 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
542 | } |
543 | else if (SCM_BIGP (n)) | |
544 | { | |
545 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
546 | scm_remember_upto_here_1 (n); | |
73e4de09 | 547 | return scm_from_bool (odd_p); |
0aacf84e | 548 | } |
73e4de09 | 549 | else if (scm_is_true (scm_inf_p (n))) |
8e43ed5d | 550 | SCM_WRONG_TYPE_ARG (1, n); |
f92e85f7 MV |
551 | else if (SCM_REALP (n)) |
552 | { | |
553 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
554 | if (rem == 1.0) | |
555 | return SCM_BOOL_T; | |
556 | else if (rem == 0.0) | |
557 | return SCM_BOOL_F; | |
558 | else | |
559 | SCM_WRONG_TYPE_ARG (1, n); | |
560 | } | |
0aacf84e | 561 | else |
a1a33b0f | 562 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 563 | } |
1bbd0b84 | 564 | #undef FUNC_NAME |
0f2d19dd | 565 | |
4219f20d | 566 | |
a1ec6916 | 567 | SCM_DEFINE (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 568 | (SCM n), |
942e5b91 MG |
569 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
570 | "otherwise.") | |
1bbd0b84 | 571 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 572 | { |
e11e83f3 | 573 | if (SCM_I_INUMP (n)) |
0aacf84e | 574 | { |
e25f3727 | 575 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 576 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
577 | } |
578 | else if (SCM_BIGP (n)) | |
579 | { | |
580 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
581 | scm_remember_upto_here_1 (n); | |
73e4de09 | 582 | return scm_from_bool (even_p); |
0aacf84e | 583 | } |
73e4de09 | 584 | else if (scm_is_true (scm_inf_p (n))) |
8e43ed5d | 585 | SCM_WRONG_TYPE_ARG (1, n); |
f92e85f7 MV |
586 | else if (SCM_REALP (n)) |
587 | { | |
588 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
589 | if (rem == 1.0) | |
590 | return SCM_BOOL_F; | |
591 | else if (rem == 0.0) | |
592 | return SCM_BOOL_T; | |
593 | else | |
594 | SCM_WRONG_TYPE_ARG (1, n); | |
595 | } | |
0aacf84e | 596 | else |
a1a33b0f | 597 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 598 | } |
1bbd0b84 | 599 | #undef FUNC_NAME |
0f2d19dd | 600 | |
7112615f MW |
601 | SCM_DEFINE (scm_finite_p, "finite?", 1, 0, 0, |
602 | (SCM x), | |
10391e06 AW |
603 | "Return @code{#t} if the real number @var{x} is neither\n" |
604 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
605 | #define FUNC_NAME s_scm_finite_p |
606 | { | |
607 | if (SCM_REALP (x)) | |
608 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 609 | else if (scm_is_real (x)) |
7112615f MW |
610 | return SCM_BOOL_T; |
611 | else | |
612 | SCM_WRONG_TYPE_ARG (1, x); | |
613 | } | |
614 | #undef FUNC_NAME | |
615 | ||
7351e207 | 616 | SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0, |
b1092b3a | 617 | (SCM x), |
10391e06 AW |
618 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" |
619 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
620 | #define FUNC_NAME s_scm_inf_p |
621 | { | |
b1092b3a | 622 | if (SCM_REALP (x)) |
2e65b52f | 623 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 624 | else if (scm_is_real (x)) |
7351e207 | 625 | return SCM_BOOL_F; |
10391e06 AW |
626 | else |
627 | SCM_WRONG_TYPE_ARG (1, x); | |
7351e207 MV |
628 | } |
629 | #undef FUNC_NAME | |
630 | ||
631 | SCM_DEFINE (scm_nan_p, "nan?", 1, 0, 0, | |
10391e06 AW |
632 | (SCM x), |
633 | "Return @code{#t} if the real number @var{x} is a NaN,\n" | |
634 | "or @code{#f} otherwise.") | |
7351e207 MV |
635 | #define FUNC_NAME s_scm_nan_p |
636 | { | |
10391e06 AW |
637 | if (SCM_REALP (x)) |
638 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
639 | else if (scm_is_real (x)) | |
7351e207 | 640 | return SCM_BOOL_F; |
10391e06 AW |
641 | else |
642 | SCM_WRONG_TYPE_ARG (1, x); | |
7351e207 MV |
643 | } |
644 | #undef FUNC_NAME | |
645 | ||
646 | /* Guile's idea of infinity. */ | |
647 | static double guile_Inf; | |
648 | ||
649 | /* Guile's idea of not a number. */ | |
650 | static double guile_NaN; | |
651 | ||
652 | static void | |
653 | guile_ieee_init (void) | |
654 | { | |
7351e207 MV |
655 | /* Some version of gcc on some old version of Linux used to crash when |
656 | trying to make Inf and NaN. */ | |
657 | ||
240a27d2 KR |
658 | #ifdef INFINITY |
659 | /* C99 INFINITY, when available. | |
660 | FIXME: The standard allows for INFINITY to be something that overflows | |
661 | at compile time. We ought to have a configure test to check for that | |
662 | before trying to use it. (But in practice we believe this is not a | |
663 | problem on any system guile is likely to target.) */ | |
664 | guile_Inf = INFINITY; | |
56a3dcd4 | 665 | #elif defined HAVE_DINFINITY |
240a27d2 | 666 | /* OSF */ |
7351e207 | 667 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 668 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
669 | #else |
670 | double tmp = 1e+10; | |
671 | guile_Inf = tmp; | |
672 | for (;;) | |
673 | { | |
674 | guile_Inf *= 1e+10; | |
675 | if (guile_Inf == tmp) | |
676 | break; | |
677 | tmp = guile_Inf; | |
678 | } | |
679 | #endif | |
680 | ||
240a27d2 KR |
681 | #ifdef NAN |
682 | /* C99 NAN, when available */ | |
683 | guile_NaN = NAN; | |
56a3dcd4 | 684 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
685 | { |
686 | /* OSF */ | |
687 | extern unsigned int DQNAN[2]; | |
688 | guile_NaN = (*((double *)(DQNAN))); | |
689 | } | |
7351e207 MV |
690 | #else |
691 | guile_NaN = guile_Inf / guile_Inf; | |
692 | #endif | |
7351e207 MV |
693 | } |
694 | ||
695 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
696 | (void), | |
697 | "Return Inf.") | |
698 | #define FUNC_NAME s_scm_inf | |
699 | { | |
700 | static int initialized = 0; | |
701 | if (! initialized) | |
702 | { | |
703 | guile_ieee_init (); | |
704 | initialized = 1; | |
705 | } | |
55f26379 | 706 | return scm_from_double (guile_Inf); |
7351e207 MV |
707 | } |
708 | #undef FUNC_NAME | |
709 | ||
710 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
711 | (void), | |
712 | "Return NaN.") | |
713 | #define FUNC_NAME s_scm_nan | |
714 | { | |
715 | static int initialized = 0; | |
0aacf84e | 716 | if (!initialized) |
7351e207 MV |
717 | { |
718 | guile_ieee_init (); | |
719 | initialized = 1; | |
720 | } | |
55f26379 | 721 | return scm_from_double (guile_NaN); |
7351e207 MV |
722 | } |
723 | #undef FUNC_NAME | |
724 | ||
4219f20d | 725 | |
a48d60b1 MD |
726 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
727 | (SCM x), | |
728 | "Return the absolute value of @var{x}.") | |
729 | #define FUNC_NAME | |
0f2d19dd | 730 | { |
e11e83f3 | 731 | if (SCM_I_INUMP (x)) |
0aacf84e | 732 | { |
e25f3727 | 733 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
734 | if (xx >= 0) |
735 | return x; | |
736 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 737 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 738 | else |
e25f3727 | 739 | return scm_i_inum2big (-xx); |
4219f20d | 740 | } |
0aacf84e MD |
741 | else if (SCM_BIGP (x)) |
742 | { | |
743 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
744 | if (sgn < 0) | |
745 | return scm_i_clonebig (x, 0); | |
746 | else | |
747 | return x; | |
4219f20d | 748 | } |
0aacf84e | 749 | else if (SCM_REALP (x)) |
ae38324d KR |
750 | { |
751 | /* note that if x is a NaN then xx<0 is false so we return x unchanged */ | |
752 | double xx = SCM_REAL_VALUE (x); | |
753 | if (xx < 0.0) | |
55f26379 | 754 | return scm_from_double (-xx); |
ae38324d KR |
755 | else |
756 | return x; | |
757 | } | |
f92e85f7 MV |
758 | else if (SCM_FRACTIONP (x)) |
759 | { | |
73e4de09 | 760 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 761 | return x; |
cba42c93 | 762 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
763 | SCM_FRACTION_DENOMINATOR (x)); |
764 | } | |
0aacf84e | 765 | else |
a48d60b1 | 766 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 767 | } |
a48d60b1 | 768 | #undef FUNC_NAME |
0f2d19dd | 769 | |
4219f20d | 770 | |
9de33deb | 771 | SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); |
942e5b91 MG |
772 | /* "Return the quotient of the numbers @var{x} and @var{y}." |
773 | */ | |
0f2d19dd | 774 | SCM |
6e8d25a6 | 775 | scm_quotient (SCM x, SCM y) |
0f2d19dd | 776 | { |
e11e83f3 | 777 | if (SCM_I_INUMP (x)) |
0aacf84e | 778 | { |
e25f3727 | 779 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 780 | if (SCM_I_INUMP (y)) |
0aacf84e | 781 | { |
e25f3727 | 782 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
783 | if (yy == 0) |
784 | scm_num_overflow (s_quotient); | |
785 | else | |
786 | { | |
e25f3727 | 787 | scm_t_inum z = xx / yy; |
0aacf84e | 788 | if (SCM_FIXABLE (z)) |
d956fa6f | 789 | return SCM_I_MAKINUM (z); |
0aacf84e | 790 | else |
e25f3727 | 791 | return scm_i_inum2big (z); |
0aacf84e | 792 | } |
828865c3 | 793 | } |
0aacf84e | 794 | else if (SCM_BIGP (y)) |
ac0c002c | 795 | { |
e11e83f3 | 796 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
797 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
798 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
799 | { | |
800 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
801 | scm_remember_upto_here_1 (y); | |
d956fa6f | 802 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 803 | } |
0aacf84e | 804 | else |
cff5fa33 | 805 | return SCM_INUM0; |
ac0c002c DH |
806 | } |
807 | else | |
0aacf84e | 808 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); |
828865c3 | 809 | } |
0aacf84e MD |
810 | else if (SCM_BIGP (x)) |
811 | { | |
e11e83f3 | 812 | if (SCM_I_INUMP (y)) |
0aacf84e | 813 | { |
e25f3727 | 814 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
815 | if (yy == 0) |
816 | scm_num_overflow (s_quotient); | |
817 | else if (yy == 1) | |
818 | return x; | |
819 | else | |
820 | { | |
821 | SCM result = scm_i_mkbig (); | |
822 | if (yy < 0) | |
823 | { | |
824 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
825 | SCM_I_BIG_MPZ (x), | |
826 | - yy); | |
827 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
828 | } | |
829 | else | |
830 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
831 | scm_remember_upto_here_1 (x); | |
832 | return scm_i_normbig (result); | |
833 | } | |
834 | } | |
835 | else if (SCM_BIGP (y)) | |
836 | { | |
837 | SCM result = scm_i_mkbig (); | |
838 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
839 | SCM_I_BIG_MPZ (x), | |
840 | SCM_I_BIG_MPZ (y)); | |
841 | scm_remember_upto_here_2 (x, y); | |
842 | return scm_i_normbig (result); | |
843 | } | |
844 | else | |
845 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); | |
f872b822 | 846 | } |
0aacf84e | 847 | else |
89a7e495 | 848 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient); |
0f2d19dd JB |
849 | } |
850 | ||
9de33deb | 851 | SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); |
942e5b91 MG |
852 | /* "Return the remainder of the numbers @var{x} and @var{y}.\n" |
853 | * "@lisp\n" | |
854 | * "(remainder 13 4) @result{} 1\n" | |
855 | * "(remainder -13 4) @result{} -1\n" | |
856 | * "@end lisp" | |
857 | */ | |
0f2d19dd | 858 | SCM |
6e8d25a6 | 859 | scm_remainder (SCM x, SCM y) |
0f2d19dd | 860 | { |
e11e83f3 | 861 | if (SCM_I_INUMP (x)) |
0aacf84e | 862 | { |
e11e83f3 | 863 | if (SCM_I_INUMP (y)) |
0aacf84e | 864 | { |
e25f3727 | 865 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
866 | if (yy == 0) |
867 | scm_num_overflow (s_remainder); | |
868 | else | |
869 | { | |
e25f3727 | 870 | scm_t_inum z = SCM_I_INUM (x) % yy; |
d956fa6f | 871 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
872 | } |
873 | } | |
874 | else if (SCM_BIGP (y)) | |
ac0c002c | 875 | { |
e11e83f3 | 876 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
877 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
878 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
879 | { | |
880 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
881 | scm_remember_upto_here_1 (y); | |
cff5fa33 | 882 | return SCM_INUM0; |
4dc09ee4 | 883 | } |
0aacf84e MD |
884 | else |
885 | return x; | |
ac0c002c DH |
886 | } |
887 | else | |
0aacf84e | 888 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); |
89a7e495 | 889 | } |
0aacf84e MD |
890 | else if (SCM_BIGP (x)) |
891 | { | |
e11e83f3 | 892 | if (SCM_I_INUMP (y)) |
0aacf84e | 893 | { |
e25f3727 | 894 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
895 | if (yy == 0) |
896 | scm_num_overflow (s_remainder); | |
897 | else | |
898 | { | |
899 | SCM result = scm_i_mkbig (); | |
900 | if (yy < 0) | |
901 | yy = - yy; | |
902 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
903 | scm_remember_upto_here_1 (x); | |
904 | return scm_i_normbig (result); | |
905 | } | |
906 | } | |
907 | else if (SCM_BIGP (y)) | |
908 | { | |
909 | SCM result = scm_i_mkbig (); | |
910 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
911 | SCM_I_BIG_MPZ (x), | |
912 | SCM_I_BIG_MPZ (y)); | |
913 | scm_remember_upto_here_2 (x, y); | |
914 | return scm_i_normbig (result); | |
915 | } | |
916 | else | |
917 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); | |
f872b822 | 918 | } |
0aacf84e | 919 | else |
89a7e495 | 920 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder); |
0f2d19dd JB |
921 | } |
922 | ||
89a7e495 | 923 | |
9de33deb | 924 | SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); |
942e5b91 MG |
925 | /* "Return the modulo of the numbers @var{x} and @var{y}.\n" |
926 | * "@lisp\n" | |
927 | * "(modulo 13 4) @result{} 1\n" | |
928 | * "(modulo -13 4) @result{} 3\n" | |
929 | * "@end lisp" | |
930 | */ | |
0f2d19dd | 931 | SCM |
6e8d25a6 | 932 | scm_modulo (SCM x, SCM y) |
0f2d19dd | 933 | { |
e11e83f3 | 934 | if (SCM_I_INUMP (x)) |
0aacf84e | 935 | { |
e25f3727 | 936 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 937 | if (SCM_I_INUMP (y)) |
0aacf84e | 938 | { |
e25f3727 | 939 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
940 | if (yy == 0) |
941 | scm_num_overflow (s_modulo); | |
942 | else | |
943 | { | |
66b1c775 KR |
944 | /* C99 specifies that "%" is the remainder corresponding to a |
945 | quotient rounded towards zero, and that's also traditional | |
946 | for machine division, so z here should be well defined. */ | |
e25f3727 AW |
947 | scm_t_inum z = xx % yy; |
948 | scm_t_inum result; | |
0aacf84e MD |
949 | |
950 | if (yy < 0) | |
951 | { | |
952 | if (z > 0) | |
953 | result = z + yy; | |
954 | else | |
955 | result = z; | |
956 | } | |
957 | else | |
958 | { | |
959 | if (z < 0) | |
960 | result = z + yy; | |
961 | else | |
962 | result = z; | |
963 | } | |
d956fa6f | 964 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
965 | } |
966 | } | |
967 | else if (SCM_BIGP (y)) | |
968 | { | |
969 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
970 | { |
971 | mpz_t z_x; | |
972 | SCM result; | |
973 | ||
974 | if (sgn_y < 0) | |
975 | { | |
976 | SCM pos_y = scm_i_clonebig (y, 0); | |
977 | /* do this after the last scm_op */ | |
978 | mpz_init_set_si (z_x, xx); | |
979 | result = pos_y; /* re-use this bignum */ | |
980 | mpz_mod (SCM_I_BIG_MPZ (result), | |
981 | z_x, | |
982 | SCM_I_BIG_MPZ (pos_y)); | |
983 | scm_remember_upto_here_1 (pos_y); | |
984 | } | |
985 | else | |
986 | { | |
987 | result = scm_i_mkbig (); | |
988 | /* do this after the last scm_op */ | |
989 | mpz_init_set_si (z_x, xx); | |
990 | mpz_mod (SCM_I_BIG_MPZ (result), | |
991 | z_x, | |
992 | SCM_I_BIG_MPZ (y)); | |
993 | scm_remember_upto_here_1 (y); | |
994 | } | |
ca46fb90 | 995 | |
0aacf84e MD |
996 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
997 | mpz_add (SCM_I_BIG_MPZ (result), | |
998 | SCM_I_BIG_MPZ (y), | |
999 | SCM_I_BIG_MPZ (result)); | |
1000 | scm_remember_upto_here_1 (y); | |
1001 | /* and do this before the next one */ | |
1002 | mpz_clear (z_x); | |
1003 | return scm_i_normbig (result); | |
1004 | } | |
1005 | } | |
1006 | else | |
1007 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
f872b822 | 1008 | } |
0aacf84e MD |
1009 | else if (SCM_BIGP (x)) |
1010 | { | |
e11e83f3 | 1011 | if (SCM_I_INUMP (y)) |
0aacf84e | 1012 | { |
e25f3727 | 1013 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
1014 | if (yy == 0) |
1015 | scm_num_overflow (s_modulo); | |
1016 | else | |
1017 | { | |
1018 | SCM result = scm_i_mkbig (); | |
1019 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
1020 | SCM_I_BIG_MPZ (x), | |
1021 | (yy < 0) ? - yy : yy); | |
1022 | scm_remember_upto_here_1 (x); | |
1023 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1024 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
1025 | SCM_I_BIG_MPZ (result), | |
1026 | - yy); | |
1027 | return scm_i_normbig (result); | |
1028 | } | |
1029 | } | |
1030 | else if (SCM_BIGP (y)) | |
1031 | { | |
0aacf84e MD |
1032 | { |
1033 | SCM result = scm_i_mkbig (); | |
1034 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1035 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
1036 | mpz_mod (SCM_I_BIG_MPZ (result), | |
1037 | SCM_I_BIG_MPZ (x), | |
1038 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 1039 | |
0aacf84e MD |
1040 | scm_remember_upto_here_1 (x); |
1041 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1042 | mpz_add (SCM_I_BIG_MPZ (result), | |
1043 | SCM_I_BIG_MPZ (y), | |
1044 | SCM_I_BIG_MPZ (result)); | |
1045 | scm_remember_upto_here_2 (y, pos_y); | |
1046 | return scm_i_normbig (result); | |
1047 | } | |
1048 | } | |
1049 | else | |
1050 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
828865c3 | 1051 | } |
0aacf84e | 1052 | else |
09fb7599 | 1053 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); |
0f2d19dd JB |
1054 | } |
1055 | ||
78d3deb1 AW |
1056 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
1057 | (SCM x, SCM y, SCM rest), | |
1058 | "Return the greatest common divisor of all parameter values.\n" | |
1059 | "If called without arguments, 0 is returned.") | |
1060 | #define FUNC_NAME s_scm_i_gcd | |
1061 | { | |
1062 | while (!scm_is_null (rest)) | |
1063 | { x = scm_gcd (x, y); | |
1064 | y = scm_car (rest); | |
1065 | rest = scm_cdr (rest); | |
1066 | } | |
1067 | return scm_gcd (x, y); | |
1068 | } | |
1069 | #undef FUNC_NAME | |
1070 | ||
1071 | #define s_gcd s_scm_i_gcd | |
1072 | #define g_gcd g_scm_i_gcd | |
1073 | ||
0f2d19dd | 1074 | SCM |
6e8d25a6 | 1075 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 1076 | { |
ca46fb90 | 1077 | if (SCM_UNBNDP (y)) |
1dd79792 | 1078 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 1079 | |
e11e83f3 | 1080 | if (SCM_I_INUMP (x)) |
ca46fb90 | 1081 | { |
e11e83f3 | 1082 | if (SCM_I_INUMP (y)) |
ca46fb90 | 1083 | { |
e25f3727 AW |
1084 | scm_t_inum xx = SCM_I_INUM (x); |
1085 | scm_t_inum yy = SCM_I_INUM (y); | |
1086 | scm_t_inum u = xx < 0 ? -xx : xx; | |
1087 | scm_t_inum v = yy < 0 ? -yy : yy; | |
1088 | scm_t_inum result; | |
0aacf84e MD |
1089 | if (xx == 0) |
1090 | result = v; | |
1091 | else if (yy == 0) | |
1092 | result = u; | |
1093 | else | |
1094 | { | |
e25f3727 AW |
1095 | scm_t_inum k = 1; |
1096 | scm_t_inum t; | |
0aacf84e MD |
1097 | /* Determine a common factor 2^k */ |
1098 | while (!(1 & (u | v))) | |
1099 | { | |
1100 | k <<= 1; | |
1101 | u >>= 1; | |
1102 | v >>= 1; | |
1103 | } | |
1104 | /* Now, any factor 2^n can be eliminated */ | |
1105 | if (u & 1) | |
1106 | t = -v; | |
1107 | else | |
1108 | { | |
1109 | t = u; | |
1110 | b3: | |
1111 | t = SCM_SRS (t, 1); | |
1112 | } | |
1113 | if (!(1 & t)) | |
1114 | goto b3; | |
1115 | if (t > 0) | |
1116 | u = t; | |
1117 | else | |
1118 | v = -t; | |
1119 | t = u - v; | |
1120 | if (t != 0) | |
1121 | goto b3; | |
1122 | result = u * k; | |
1123 | } | |
1124 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 1125 | ? SCM_I_MAKINUM (result) |
e25f3727 | 1126 | : scm_i_inum2big (result)); |
ca46fb90 RB |
1127 | } |
1128 | else if (SCM_BIGP (y)) | |
1129 | { | |
0bff4dce KR |
1130 | SCM_SWAP (x, y); |
1131 | goto big_inum; | |
ca46fb90 RB |
1132 | } |
1133 | else | |
1134 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 1135 | } |
ca46fb90 RB |
1136 | else if (SCM_BIGP (x)) |
1137 | { | |
e11e83f3 | 1138 | if (SCM_I_INUMP (y)) |
ca46fb90 | 1139 | { |
e25f3727 AW |
1140 | scm_t_bits result; |
1141 | scm_t_inum yy; | |
0bff4dce | 1142 | big_inum: |
e11e83f3 | 1143 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
1144 | if (yy == 0) |
1145 | return scm_abs (x); | |
0aacf84e MD |
1146 | if (yy < 0) |
1147 | yy = -yy; | |
ca46fb90 RB |
1148 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
1149 | scm_remember_upto_here_1 (x); | |
0aacf84e | 1150 | return (SCM_POSFIXABLE (result) |
d956fa6f | 1151 | ? SCM_I_MAKINUM (result) |
e25f3727 | 1152 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
1153 | } |
1154 | else if (SCM_BIGP (y)) | |
1155 | { | |
1156 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
1157 | mpz_gcd (SCM_I_BIG_MPZ (result), |
1158 | SCM_I_BIG_MPZ (x), | |
1159 | SCM_I_BIG_MPZ (y)); | |
1160 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
1161 | return scm_i_normbig (result); |
1162 | } | |
1163 | else | |
1164 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 1165 | } |
ca46fb90 | 1166 | else |
09fb7599 | 1167 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
1168 | } |
1169 | ||
78d3deb1 AW |
1170 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
1171 | (SCM x, SCM y, SCM rest), | |
1172 | "Return the least common multiple of the arguments.\n" | |
1173 | "If called without arguments, 1 is returned.") | |
1174 | #define FUNC_NAME s_scm_i_lcm | |
1175 | { | |
1176 | while (!scm_is_null (rest)) | |
1177 | { x = scm_lcm (x, y); | |
1178 | y = scm_car (rest); | |
1179 | rest = scm_cdr (rest); | |
1180 | } | |
1181 | return scm_lcm (x, y); | |
1182 | } | |
1183 | #undef FUNC_NAME | |
1184 | ||
1185 | #define s_lcm s_scm_i_lcm | |
1186 | #define g_lcm g_scm_i_lcm | |
1187 | ||
0f2d19dd | 1188 | SCM |
6e8d25a6 | 1189 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 1190 | { |
ca46fb90 RB |
1191 | if (SCM_UNBNDP (n2)) |
1192 | { | |
1193 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
1194 | return SCM_I_MAKINUM (1L); |
1195 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 1196 | } |
09fb7599 | 1197 | |
e11e83f3 | 1198 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 1199 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 1200 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 1201 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 1202 | |
e11e83f3 | 1203 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 1204 | { |
e11e83f3 | 1205 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1206 | { |
1207 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 1208 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
1209 | return d; |
1210 | else | |
1211 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
1212 | } | |
1213 | else | |
1214 | { | |
1215 | /* inum n1, big n2 */ | |
1216 | inumbig: | |
1217 | { | |
1218 | SCM result = scm_i_mkbig (); | |
e25f3727 | 1219 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
1220 | if (nn1 == 0) return SCM_INUM0; |
1221 | if (nn1 < 0) nn1 = - nn1; | |
1222 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
1223 | scm_remember_upto_here_1 (n2); | |
1224 | return result; | |
1225 | } | |
1226 | } | |
1227 | } | |
1228 | else | |
1229 | { | |
1230 | /* big n1 */ | |
e11e83f3 | 1231 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1232 | { |
1233 | SCM_SWAP (n1, n2); | |
1234 | goto inumbig; | |
1235 | } | |
1236 | else | |
1237 | { | |
1238 | SCM result = scm_i_mkbig (); | |
1239 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
1240 | SCM_I_BIG_MPZ (n1), | |
1241 | SCM_I_BIG_MPZ (n2)); | |
1242 | scm_remember_upto_here_2(n1, n2); | |
1243 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
1244 | return result; | |
1245 | } | |
f872b822 | 1246 | } |
0f2d19dd JB |
1247 | } |
1248 | ||
8a525303 GB |
1249 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
1250 | ||
1251 | Logand: | |
1252 | X Y Result Method: | |
1253 | (len) | |
1254 | + + + x (map digit:logand X Y) | |
1255 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
1256 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
1257 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
1258 | ||
1259 | Logior: | |
1260 | X Y Result Method: | |
1261 | ||
1262 | + + + (map digit:logior X Y) | |
1263 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
1264 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
1265 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
1266 | ||
1267 | Logxor: | |
1268 | X Y Result Method: | |
1269 | ||
1270 | + + + (map digit:logxor X Y) | |
1271 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
1272 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
1273 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
1274 | ||
1275 | Logtest: | |
1276 | X Y Result | |
1277 | ||
1278 | + + (any digit:logand X Y) | |
1279 | + - (any digit:logand X (lognot (+ -1 Y))) | |
1280 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
1281 | - - #t | |
1282 | ||
1283 | */ | |
1284 | ||
78d3deb1 AW |
1285 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
1286 | (SCM x, SCM y, SCM rest), | |
1287 | "Return the bitwise AND of the integer arguments.\n\n" | |
1288 | "@lisp\n" | |
1289 | "(logand) @result{} -1\n" | |
1290 | "(logand 7) @result{} 7\n" | |
1291 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
1292 | "@end lisp") | |
1293 | #define FUNC_NAME s_scm_i_logand | |
1294 | { | |
1295 | while (!scm_is_null (rest)) | |
1296 | { x = scm_logand (x, y); | |
1297 | y = scm_car (rest); | |
1298 | rest = scm_cdr (rest); | |
1299 | } | |
1300 | return scm_logand (x, y); | |
1301 | } | |
1302 | #undef FUNC_NAME | |
1303 | ||
1304 | #define s_scm_logand s_scm_i_logand | |
1305 | ||
1306 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 1307 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 1308 | { |
e25f3727 | 1309 | scm_t_inum nn1; |
9a00c9fc | 1310 | |
0aacf84e MD |
1311 | if (SCM_UNBNDP (n2)) |
1312 | { | |
1313 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 1314 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
1315 | else if (!SCM_NUMBERP (n1)) |
1316 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1317 | else if (SCM_NUMBERP (n1)) | |
1318 | return n1; | |
1319 | else | |
1320 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1321 | } |
09fb7599 | 1322 | |
e11e83f3 | 1323 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1324 | { |
e11e83f3 MV |
1325 | nn1 = SCM_I_INUM (n1); |
1326 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1327 | { |
e25f3727 | 1328 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 1329 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
1330 | } |
1331 | else if SCM_BIGP (n2) | |
1332 | { | |
1333 | intbig: | |
1334 | if (n1 == 0) | |
1335 | return SCM_INUM0; | |
1336 | { | |
1337 | SCM result_z = scm_i_mkbig (); | |
1338 | mpz_t nn1_z; | |
1339 | mpz_init_set_si (nn1_z, nn1); | |
1340 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1341 | scm_remember_upto_here_1 (n2); | |
1342 | mpz_clear (nn1_z); | |
1343 | return scm_i_normbig (result_z); | |
1344 | } | |
1345 | } | |
1346 | else | |
1347 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1348 | } | |
1349 | else if (SCM_BIGP (n1)) | |
1350 | { | |
e11e83f3 | 1351 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1352 | { |
1353 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1354 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1355 | goto intbig; |
1356 | } | |
1357 | else if (SCM_BIGP (n2)) | |
1358 | { | |
1359 | SCM result_z = scm_i_mkbig (); | |
1360 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
1361 | SCM_I_BIG_MPZ (n1), | |
1362 | SCM_I_BIG_MPZ (n2)); | |
1363 | scm_remember_upto_here_2 (n1, n2); | |
1364 | return scm_i_normbig (result_z); | |
1365 | } | |
1366 | else | |
1367 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1368 | } |
0aacf84e | 1369 | else |
09fb7599 | 1370 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1371 | } |
1bbd0b84 | 1372 | #undef FUNC_NAME |
0f2d19dd | 1373 | |
09fb7599 | 1374 | |
78d3deb1 AW |
1375 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
1376 | (SCM x, SCM y, SCM rest), | |
1377 | "Return the bitwise OR of the integer arguments.\n\n" | |
1378 | "@lisp\n" | |
1379 | "(logior) @result{} 0\n" | |
1380 | "(logior 7) @result{} 7\n" | |
1381 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1382 | "@end lisp") | |
1383 | #define FUNC_NAME s_scm_i_logior | |
1384 | { | |
1385 | while (!scm_is_null (rest)) | |
1386 | { x = scm_logior (x, y); | |
1387 | y = scm_car (rest); | |
1388 | rest = scm_cdr (rest); | |
1389 | } | |
1390 | return scm_logior (x, y); | |
1391 | } | |
1392 | #undef FUNC_NAME | |
1393 | ||
1394 | #define s_scm_logior s_scm_i_logior | |
1395 | ||
1396 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 1397 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 1398 | { |
e25f3727 | 1399 | scm_t_inum nn1; |
9a00c9fc | 1400 | |
0aacf84e MD |
1401 | if (SCM_UNBNDP (n2)) |
1402 | { | |
1403 | if (SCM_UNBNDP (n1)) | |
1404 | return SCM_INUM0; | |
1405 | else if (SCM_NUMBERP (n1)) | |
1406 | return n1; | |
1407 | else | |
1408 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1409 | } |
09fb7599 | 1410 | |
e11e83f3 | 1411 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1412 | { |
e11e83f3 MV |
1413 | nn1 = SCM_I_INUM (n1); |
1414 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1415 | { |
e11e83f3 | 1416 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1417 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
1418 | } |
1419 | else if (SCM_BIGP (n2)) | |
1420 | { | |
1421 | intbig: | |
1422 | if (nn1 == 0) | |
1423 | return n2; | |
1424 | { | |
1425 | SCM result_z = scm_i_mkbig (); | |
1426 | mpz_t nn1_z; | |
1427 | mpz_init_set_si (nn1_z, nn1); | |
1428 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1429 | scm_remember_upto_here_1 (n2); | |
1430 | mpz_clear (nn1_z); | |
9806de0d | 1431 | return scm_i_normbig (result_z); |
0aacf84e MD |
1432 | } |
1433 | } | |
1434 | else | |
1435 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1436 | } | |
1437 | else if (SCM_BIGP (n1)) | |
1438 | { | |
e11e83f3 | 1439 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1440 | { |
1441 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1442 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1443 | goto intbig; |
1444 | } | |
1445 | else if (SCM_BIGP (n2)) | |
1446 | { | |
1447 | SCM result_z = scm_i_mkbig (); | |
1448 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
1449 | SCM_I_BIG_MPZ (n1), | |
1450 | SCM_I_BIG_MPZ (n2)); | |
1451 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 1452 | return scm_i_normbig (result_z); |
0aacf84e MD |
1453 | } |
1454 | else | |
1455 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1456 | } |
0aacf84e | 1457 | else |
09fb7599 | 1458 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1459 | } |
1bbd0b84 | 1460 | #undef FUNC_NAME |
0f2d19dd | 1461 | |
09fb7599 | 1462 | |
78d3deb1 AW |
1463 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
1464 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
1465 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1466 | "set in the result if it is set in an odd number of arguments.\n" | |
1467 | "@lisp\n" | |
1468 | "(logxor) @result{} 0\n" | |
1469 | "(logxor 7) @result{} 7\n" | |
1470 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1471 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1472 | "@end lisp") |
78d3deb1 AW |
1473 | #define FUNC_NAME s_scm_i_logxor |
1474 | { | |
1475 | while (!scm_is_null (rest)) | |
1476 | { x = scm_logxor (x, y); | |
1477 | y = scm_car (rest); | |
1478 | rest = scm_cdr (rest); | |
1479 | } | |
1480 | return scm_logxor (x, y); | |
1481 | } | |
1482 | #undef FUNC_NAME | |
1483 | ||
1484 | #define s_scm_logxor s_scm_i_logxor | |
1485 | ||
1486 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 1487 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1488 | { |
e25f3727 | 1489 | scm_t_inum nn1; |
9a00c9fc | 1490 | |
0aacf84e MD |
1491 | if (SCM_UNBNDP (n2)) |
1492 | { | |
1493 | if (SCM_UNBNDP (n1)) | |
1494 | return SCM_INUM0; | |
1495 | else if (SCM_NUMBERP (n1)) | |
1496 | return n1; | |
1497 | else | |
1498 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1499 | } |
09fb7599 | 1500 | |
e11e83f3 | 1501 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1502 | { |
e11e83f3 MV |
1503 | nn1 = SCM_I_INUM (n1); |
1504 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1505 | { |
e25f3727 | 1506 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 1507 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
1508 | } |
1509 | else if (SCM_BIGP (n2)) | |
1510 | { | |
1511 | intbig: | |
1512 | { | |
1513 | SCM result_z = scm_i_mkbig (); | |
1514 | mpz_t nn1_z; | |
1515 | mpz_init_set_si (nn1_z, nn1); | |
1516 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1517 | scm_remember_upto_here_1 (n2); | |
1518 | mpz_clear (nn1_z); | |
1519 | return scm_i_normbig (result_z); | |
1520 | } | |
1521 | } | |
1522 | else | |
1523 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1524 | } | |
1525 | else if (SCM_BIGP (n1)) | |
1526 | { | |
e11e83f3 | 1527 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1528 | { |
1529 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1530 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1531 | goto intbig; |
1532 | } | |
1533 | else if (SCM_BIGP (n2)) | |
1534 | { | |
1535 | SCM result_z = scm_i_mkbig (); | |
1536 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
1537 | SCM_I_BIG_MPZ (n1), | |
1538 | SCM_I_BIG_MPZ (n2)); | |
1539 | scm_remember_upto_here_2 (n1, n2); | |
1540 | return scm_i_normbig (result_z); | |
1541 | } | |
1542 | else | |
1543 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1544 | } |
0aacf84e | 1545 | else |
09fb7599 | 1546 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1547 | } |
1bbd0b84 | 1548 | #undef FUNC_NAME |
0f2d19dd | 1549 | |
09fb7599 | 1550 | |
a1ec6916 | 1551 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 1552 | (SCM j, SCM k), |
ba6e7231 KR |
1553 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
1554 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
1555 | "without actually calculating the @code{logand}, just testing\n" | |
1556 | "for non-zero.\n" | |
1557 | "\n" | |
1e6808ea | 1558 | "@lisp\n" |
b380b885 MD |
1559 | "(logtest #b0100 #b1011) @result{} #f\n" |
1560 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1561 | "@end lisp") |
1bbd0b84 | 1562 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1563 | { |
e25f3727 | 1564 | scm_t_inum nj; |
9a00c9fc | 1565 | |
e11e83f3 | 1566 | if (SCM_I_INUMP (j)) |
0aacf84e | 1567 | { |
e11e83f3 MV |
1568 | nj = SCM_I_INUM (j); |
1569 | if (SCM_I_INUMP (k)) | |
0aacf84e | 1570 | { |
e25f3727 | 1571 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 1572 | return scm_from_bool (nj & nk); |
0aacf84e MD |
1573 | } |
1574 | else if (SCM_BIGP (k)) | |
1575 | { | |
1576 | intbig: | |
1577 | if (nj == 0) | |
1578 | return SCM_BOOL_F; | |
1579 | { | |
1580 | SCM result; | |
1581 | mpz_t nj_z; | |
1582 | mpz_init_set_si (nj_z, nj); | |
1583 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
1584 | scm_remember_upto_here_1 (k); | |
73e4de09 | 1585 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
1586 | mpz_clear (nj_z); |
1587 | return result; | |
1588 | } | |
1589 | } | |
1590 | else | |
1591 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1592 | } | |
1593 | else if (SCM_BIGP (j)) | |
1594 | { | |
e11e83f3 | 1595 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
1596 | { |
1597 | SCM_SWAP (j, k); | |
e11e83f3 | 1598 | nj = SCM_I_INUM (j); |
0aacf84e MD |
1599 | goto intbig; |
1600 | } | |
1601 | else if (SCM_BIGP (k)) | |
1602 | { | |
1603 | SCM result; | |
1604 | mpz_t result_z; | |
1605 | mpz_init (result_z); | |
1606 | mpz_and (result_z, | |
1607 | SCM_I_BIG_MPZ (j), | |
1608 | SCM_I_BIG_MPZ (k)); | |
1609 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 1610 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
1611 | mpz_clear (result_z); |
1612 | return result; | |
1613 | } | |
1614 | else | |
1615 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1616 | } | |
1617 | else | |
1618 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 1619 | } |
1bbd0b84 | 1620 | #undef FUNC_NAME |
0f2d19dd | 1621 | |
c1bfcf60 | 1622 | |
a1ec6916 | 1623 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1624 | (SCM index, SCM j), |
ba6e7231 KR |
1625 | "Test whether bit number @var{index} in @var{j} is set.\n" |
1626 | "@var{index} starts from 0 for the least significant bit.\n" | |
1627 | "\n" | |
1e6808ea | 1628 | "@lisp\n" |
b380b885 MD |
1629 | "(logbit? 0 #b1101) @result{} #t\n" |
1630 | "(logbit? 1 #b1101) @result{} #f\n" | |
1631 | "(logbit? 2 #b1101) @result{} #t\n" | |
1632 | "(logbit? 3 #b1101) @result{} #t\n" | |
1633 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1634 | "@end lisp") |
1bbd0b84 | 1635 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1636 | { |
78166ad5 | 1637 | unsigned long int iindex; |
5efd3c7d | 1638 | iindex = scm_to_ulong (index); |
78166ad5 | 1639 | |
e11e83f3 | 1640 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
1641 | { |
1642 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 1643 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 1644 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 1645 | } |
0aacf84e MD |
1646 | else if (SCM_BIGP (j)) |
1647 | { | |
1648 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
1649 | scm_remember_upto_here_1 (j); | |
73e4de09 | 1650 | return scm_from_bool (val); |
0aacf84e MD |
1651 | } |
1652 | else | |
78166ad5 | 1653 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 1654 | } |
1bbd0b84 | 1655 | #undef FUNC_NAME |
0f2d19dd | 1656 | |
78166ad5 | 1657 | |
a1ec6916 | 1658 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1659 | (SCM n), |
4d814788 | 1660 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
1661 | "argument.\n" |
1662 | "\n" | |
b380b885 MD |
1663 | "@lisp\n" |
1664 | "(number->string (lognot #b10000000) 2)\n" | |
1665 | " @result{} \"-10000001\"\n" | |
1666 | "(number->string (lognot #b0) 2)\n" | |
1667 | " @result{} \"-1\"\n" | |
1e6808ea | 1668 | "@end lisp") |
1bbd0b84 | 1669 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1670 | { |
e11e83f3 | 1671 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
1672 | /* No overflow here, just need to toggle all the bits making up the inum. |
1673 | Enhancement: No need to strip the tag and add it back, could just xor | |
1674 | a block of 1 bits, if that worked with the various debug versions of | |
1675 | the SCM typedef. */ | |
e11e83f3 | 1676 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
1677 | |
1678 | } else if (SCM_BIGP (n)) { | |
1679 | SCM result = scm_i_mkbig (); | |
1680 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
1681 | scm_remember_upto_here_1 (n); | |
1682 | return result; | |
1683 | ||
1684 | } else { | |
1685 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1686 | } | |
0f2d19dd | 1687 | } |
1bbd0b84 | 1688 | #undef FUNC_NAME |
0f2d19dd | 1689 | |
518b7508 KR |
1690 | /* returns 0 if IN is not an integer. OUT must already be |
1691 | initialized. */ | |
1692 | static int | |
1693 | coerce_to_big (SCM in, mpz_t out) | |
1694 | { | |
1695 | if (SCM_BIGP (in)) | |
1696 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
1697 | else if (SCM_I_INUMP (in)) |
1698 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
1699 | else |
1700 | return 0; | |
1701 | ||
1702 | return 1; | |
1703 | } | |
1704 | ||
d885e204 | 1705 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
1706 | (SCM n, SCM k, SCM m), |
1707 | "Return @var{n} raised to the integer exponent\n" | |
1708 | "@var{k}, modulo @var{m}.\n" | |
1709 | "\n" | |
1710 | "@lisp\n" | |
1711 | "(modulo-expt 2 3 5)\n" | |
1712 | " @result{} 3\n" | |
1713 | "@end lisp") | |
d885e204 | 1714 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
1715 | { |
1716 | mpz_t n_tmp; | |
1717 | mpz_t k_tmp; | |
1718 | mpz_t m_tmp; | |
1719 | ||
1720 | /* There are two classes of error we might encounter -- | |
1721 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
1722 | and | |
1723 | 2) wrong-type errors, which of course we'll report by calling | |
1724 | SCM_WRONG_TYPE_ARG. | |
1725 | We don't report those errors immediately, however; instead we do | |
1726 | some cleanup first. These variables tell us which error (if | |
1727 | any) we should report after cleaning up. | |
1728 | */ | |
1729 | int report_overflow = 0; | |
1730 | ||
1731 | int position_of_wrong_type = 0; | |
1732 | SCM value_of_wrong_type = SCM_INUM0; | |
1733 | ||
1734 | SCM result = SCM_UNDEFINED; | |
1735 | ||
1736 | mpz_init (n_tmp); | |
1737 | mpz_init (k_tmp); | |
1738 | mpz_init (m_tmp); | |
1739 | ||
bc36d050 | 1740 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
1741 | { |
1742 | report_overflow = 1; | |
1743 | goto cleanup; | |
1744 | } | |
1745 | ||
1746 | if (!coerce_to_big (n, n_tmp)) | |
1747 | { | |
1748 | value_of_wrong_type = n; | |
1749 | position_of_wrong_type = 1; | |
1750 | goto cleanup; | |
1751 | } | |
1752 | ||
1753 | if (!coerce_to_big (k, k_tmp)) | |
1754 | { | |
1755 | value_of_wrong_type = k; | |
1756 | position_of_wrong_type = 2; | |
1757 | goto cleanup; | |
1758 | } | |
1759 | ||
1760 | if (!coerce_to_big (m, m_tmp)) | |
1761 | { | |
1762 | value_of_wrong_type = m; | |
1763 | position_of_wrong_type = 3; | |
1764 | goto cleanup; | |
1765 | } | |
1766 | ||
1767 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
1768 | will get a divide-by-zero exception when an inverse 1/n mod m | |
1769 | doesn't exist (or is not unique). Since exceptions are hard to | |
1770 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
1771 | a simple failure code, which is easy to handle. */ | |
1772 | ||
1773 | if (-1 == mpz_sgn (k_tmp)) | |
1774 | { | |
1775 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
1776 | { | |
1777 | report_overflow = 1; | |
1778 | goto cleanup; | |
1779 | } | |
1780 | mpz_neg (k_tmp, k_tmp); | |
1781 | } | |
1782 | ||
1783 | result = scm_i_mkbig (); | |
1784 | mpz_powm (SCM_I_BIG_MPZ (result), | |
1785 | n_tmp, | |
1786 | k_tmp, | |
1787 | m_tmp); | |
b7b8c575 KR |
1788 | |
1789 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
1790 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
1791 | ||
518b7508 KR |
1792 | cleanup: |
1793 | mpz_clear (m_tmp); | |
1794 | mpz_clear (k_tmp); | |
1795 | mpz_clear (n_tmp); | |
1796 | ||
1797 | if (report_overflow) | |
1798 | scm_num_overflow (FUNC_NAME); | |
1799 | ||
1800 | if (position_of_wrong_type) | |
1801 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
1802 | value_of_wrong_type); | |
1803 | ||
1804 | return scm_i_normbig (result); | |
1805 | } | |
1806 | #undef FUNC_NAME | |
1807 | ||
a1ec6916 | 1808 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1809 | (SCM n, SCM k), |
ba6e7231 KR |
1810 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
1811 | "exact integer, @var{n} can be any number.\n" | |
1812 | "\n" | |
1813 | "Negative @var{k} is supported, and results in @math{1/n^abs(k)}\n" | |
1814 | "in the usual way. @math{@var{n}^0} is 1, as usual, and that\n" | |
1815 | "includes @math{0^0} is 1.\n" | |
1e6808ea | 1816 | "\n" |
b380b885 | 1817 | "@lisp\n" |
ba6e7231 KR |
1818 | "(integer-expt 2 5) @result{} 32\n" |
1819 | "(integer-expt -3 3) @result{} -27\n" | |
1820 | "(integer-expt 5 -3) @result{} 1/125\n" | |
1821 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 1822 | "@end lisp") |
1bbd0b84 | 1823 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1824 | { |
e25f3727 | 1825 | scm_t_inum i2 = 0; |
1c35cb19 RB |
1826 | SCM z_i2 = SCM_BOOL_F; |
1827 | int i2_is_big = 0; | |
d956fa6f | 1828 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 1829 | |
5a8fc758 | 1830 | SCM_VALIDATE_NUMBER (SCM_ARG1, n); |
01c7284a MW |
1831 | if (!SCM_I_INUMP (k) && !SCM_BIGP (k)) |
1832 | SCM_WRONG_TYPE_ARG (2, k); | |
5a8fc758 | 1833 | |
01c7284a MW |
1834 | if (scm_is_true (scm_zero_p (n))) |
1835 | { | |
1836 | if (scm_is_true (scm_zero_p (k))) /* 0^0 == 1 per R5RS */ | |
1837 | return acc; /* return exact 1, regardless of n */ | |
1838 | else if (scm_is_true (scm_positive_p (k))) | |
1839 | return n; | |
1840 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
1841 | return scm_nan (); | |
1842 | } | |
1843 | else if (scm_is_eq (n, acc)) | |
1844 | return acc; | |
bc36d050 | 1845 | else if (scm_is_eq (n, SCM_I_MAKINUM (-1L))) |
73e4de09 | 1846 | return scm_is_false (scm_even_p (k)) ? n : acc; |
ca46fb90 | 1847 | |
e11e83f3 MV |
1848 | if (SCM_I_INUMP (k)) |
1849 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
1850 | else if (SCM_BIGP (k)) |
1851 | { | |
1852 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
1853 | scm_remember_upto_here_1 (k); |
1854 | i2_is_big = 1; | |
1855 | } | |
2830fd91 | 1856 | else |
ca46fb90 RB |
1857 | SCM_WRONG_TYPE_ARG (2, k); |
1858 | ||
1859 | if (i2_is_big) | |
f872b822 | 1860 | { |
ca46fb90 RB |
1861 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
1862 | { | |
1863 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
1864 | n = scm_divide (n, SCM_UNDEFINED); | |
1865 | } | |
1866 | while (1) | |
1867 | { | |
1868 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
1869 | { | |
ca46fb90 RB |
1870 | return acc; |
1871 | } | |
1872 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
1873 | { | |
ca46fb90 RB |
1874 | return scm_product (acc, n); |
1875 | } | |
1876 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
1877 | acc = scm_product (acc, n); | |
1878 | n = scm_product (n, n); | |
1879 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
1880 | } | |
f872b822 | 1881 | } |
ca46fb90 | 1882 | else |
f872b822 | 1883 | { |
ca46fb90 RB |
1884 | if (i2 < 0) |
1885 | { | |
1886 | i2 = -i2; | |
1887 | n = scm_divide (n, SCM_UNDEFINED); | |
1888 | } | |
1889 | while (1) | |
1890 | { | |
1891 | if (0 == i2) | |
1892 | return acc; | |
1893 | if (1 == i2) | |
1894 | return scm_product (acc, n); | |
1895 | if (i2 & 1) | |
1896 | acc = scm_product (acc, n); | |
1897 | n = scm_product (n, n); | |
1898 | i2 >>= 1; | |
1899 | } | |
f872b822 | 1900 | } |
0f2d19dd | 1901 | } |
1bbd0b84 | 1902 | #undef FUNC_NAME |
0f2d19dd | 1903 | |
a1ec6916 | 1904 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1905 | (SCM n, SCM cnt), |
32f19569 KR |
1906 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
1907 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 1908 | "\n" |
e7644cb2 | 1909 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
1910 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
1911 | "infinity. (Note that this is not the same rounding as\n" | |
1912 | "@code{quotient} does.)\n" | |
1913 | "\n" | |
1914 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
1915 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
1916 | "shift dropping bits.\n" | |
1e6808ea | 1917 | "\n" |
b380b885 | 1918 | "@lisp\n" |
1e6808ea MG |
1919 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1920 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
1921 | "\n" |
1922 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
1923 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 1924 | "@end lisp") |
1bbd0b84 | 1925 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1926 | { |
3ab9f56e | 1927 | long bits_to_shift; |
5efd3c7d | 1928 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 1929 | |
788aca27 KR |
1930 | if (SCM_I_INUMP (n)) |
1931 | { | |
e25f3727 | 1932 | scm_t_inum nn = SCM_I_INUM (n); |
788aca27 KR |
1933 | |
1934 | if (bits_to_shift > 0) | |
1935 | { | |
1936 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
1937 | overflow a non-zero fixnum. For smaller shifts we check the | |
1938 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
1939 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
1940 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
1941 | bits_to_shift)". */ | |
1942 | ||
1943 | if (nn == 0) | |
1944 | return n; | |
1945 | ||
1946 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 1947 | && ((scm_t_bits) |
788aca27 KR |
1948 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) |
1949 | <= 1)) | |
1950 | { | |
1951 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
1952 | } | |
1953 | else | |
1954 | { | |
e25f3727 | 1955 | SCM result = scm_i_inum2big (nn); |
788aca27 KR |
1956 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
1957 | bits_to_shift); | |
1958 | return result; | |
1959 | } | |
1960 | } | |
1961 | else | |
1962 | { | |
1963 | bits_to_shift = -bits_to_shift; | |
1964 | if (bits_to_shift >= SCM_LONG_BIT) | |
cff5fa33 | 1965 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1)); |
788aca27 KR |
1966 | else |
1967 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
1968 | } | |
1969 | ||
1970 | } | |
1971 | else if (SCM_BIGP (n)) | |
ca46fb90 | 1972 | { |
788aca27 KR |
1973 | SCM result; |
1974 | ||
1975 | if (bits_to_shift == 0) | |
1976 | return n; | |
1977 | ||
1978 | result = scm_i_mkbig (); | |
1979 | if (bits_to_shift >= 0) | |
1980 | { | |
1981 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1982 | bits_to_shift); | |
1983 | return result; | |
1984 | } | |
ca46fb90 | 1985 | else |
788aca27 KR |
1986 | { |
1987 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
1988 | we have to allocate a bignum even if the result is going to be a | |
1989 | fixnum. */ | |
1990 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1991 | -bits_to_shift); | |
1992 | return scm_i_normbig (result); | |
1993 | } | |
1994 | ||
ca46fb90 RB |
1995 | } |
1996 | else | |
788aca27 KR |
1997 | { |
1998 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1999 | } | |
0f2d19dd | 2000 | } |
1bbd0b84 | 2001 | #undef FUNC_NAME |
0f2d19dd | 2002 | |
3c9f20f8 | 2003 | |
a1ec6916 | 2004 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 2005 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
2006 | "Return the integer composed of the @var{start} (inclusive)\n" |
2007 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
2008 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
2009 | "\n" | |
b380b885 MD |
2010 | "@lisp\n" |
2011 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
2012 | " @result{} \"1010\"\n" | |
2013 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
2014 | " @result{} \"10110\"\n" | |
2015 | "@end lisp") | |
1bbd0b84 | 2016 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 2017 | { |
7f848242 | 2018 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
2019 | istart = scm_to_ulong (start); |
2020 | iend = scm_to_ulong (end); | |
c1bfcf60 | 2021 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 2022 | |
7f848242 KR |
2023 | /* how many bits to keep */ |
2024 | bits = iend - istart; | |
2025 | ||
e11e83f3 | 2026 | if (SCM_I_INUMP (n)) |
0aacf84e | 2027 | { |
e25f3727 | 2028 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
2029 | |
2030 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 2031 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 2032 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 2033 | |
0aacf84e MD |
2034 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
2035 | { | |
2036 | /* Since we emulate two's complement encoded numbers, this | |
2037 | * special case requires us to produce a result that has | |
7f848242 | 2038 | * more bits than can be stored in a fixnum. |
0aacf84e | 2039 | */ |
e25f3727 | 2040 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
2041 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
2042 | bits); | |
2043 | return result; | |
0aacf84e | 2044 | } |
ac0c002c | 2045 | |
7f848242 | 2046 | /* mask down to requisite bits */ |
857ae6af | 2047 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 2048 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
2049 | } |
2050 | else if (SCM_BIGP (n)) | |
ac0c002c | 2051 | { |
7f848242 KR |
2052 | SCM result; |
2053 | if (bits == 1) | |
2054 | { | |
d956fa6f | 2055 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
2056 | } |
2057 | else | |
2058 | { | |
2059 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
2060 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
2061 | such bits into a ulong. */ | |
2062 | result = scm_i_mkbig (); | |
2063 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
2064 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
2065 | result = scm_i_normbig (result); | |
2066 | } | |
2067 | scm_remember_upto_here_1 (n); | |
2068 | return result; | |
ac0c002c | 2069 | } |
0aacf84e | 2070 | else |
78166ad5 | 2071 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 2072 | } |
1bbd0b84 | 2073 | #undef FUNC_NAME |
0f2d19dd | 2074 | |
7f848242 | 2075 | |
e4755e5c JB |
2076 | static const char scm_logtab[] = { |
2077 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
2078 | }; | |
1cc91f1b | 2079 | |
a1ec6916 | 2080 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 2081 | (SCM n), |
1e6808ea MG |
2082 | "Return the number of bits in integer @var{n}. If integer is\n" |
2083 | "positive, the 1-bits in its binary representation are counted.\n" | |
2084 | "If negative, the 0-bits in its two's-complement binary\n" | |
2085 | "representation are counted. If 0, 0 is returned.\n" | |
2086 | "\n" | |
b380b885 MD |
2087 | "@lisp\n" |
2088 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
2089 | " @result{} 4\n" |
2090 | "(logcount 0)\n" | |
2091 | " @result{} 0\n" | |
2092 | "(logcount -2)\n" | |
2093 | " @result{} 1\n" | |
2094 | "@end lisp") | |
2095 | #define FUNC_NAME s_scm_logcount | |
2096 | { | |
e11e83f3 | 2097 | if (SCM_I_INUMP (n)) |
f872b822 | 2098 | { |
e25f3727 AW |
2099 | unsigned long c = 0; |
2100 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
2101 | if (nn < 0) |
2102 | nn = -1 - nn; | |
2103 | while (nn) | |
2104 | { | |
2105 | c += scm_logtab[15 & nn]; | |
2106 | nn >>= 4; | |
2107 | } | |
d956fa6f | 2108 | return SCM_I_MAKINUM (c); |
f872b822 | 2109 | } |
ca46fb90 | 2110 | else if (SCM_BIGP (n)) |
f872b822 | 2111 | { |
ca46fb90 | 2112 | unsigned long count; |
713a4259 KR |
2113 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
2114 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 2115 | else |
713a4259 KR |
2116 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
2117 | scm_remember_upto_here_1 (n); | |
d956fa6f | 2118 | return SCM_I_MAKINUM (count); |
f872b822 | 2119 | } |
ca46fb90 RB |
2120 | else |
2121 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 2122 | } |
ca46fb90 | 2123 | #undef FUNC_NAME |
0f2d19dd JB |
2124 | |
2125 | ||
ca46fb90 RB |
2126 | static const char scm_ilentab[] = { |
2127 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
2128 | }; | |
2129 | ||
0f2d19dd | 2130 | |
ca46fb90 RB |
2131 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
2132 | (SCM n), | |
2133 | "Return the number of bits necessary to represent @var{n}.\n" | |
2134 | "\n" | |
2135 | "@lisp\n" | |
2136 | "(integer-length #b10101010)\n" | |
2137 | " @result{} 8\n" | |
2138 | "(integer-length 0)\n" | |
2139 | " @result{} 0\n" | |
2140 | "(integer-length #b1111)\n" | |
2141 | " @result{} 4\n" | |
2142 | "@end lisp") | |
2143 | #define FUNC_NAME s_scm_integer_length | |
2144 | { | |
e11e83f3 | 2145 | if (SCM_I_INUMP (n)) |
0aacf84e | 2146 | { |
e25f3727 | 2147 | unsigned long c = 0; |
0aacf84e | 2148 | unsigned int l = 4; |
e25f3727 | 2149 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
2150 | if (nn < 0) |
2151 | nn = -1 - nn; | |
2152 | while (nn) | |
2153 | { | |
2154 | c += 4; | |
2155 | l = scm_ilentab [15 & nn]; | |
2156 | nn >>= 4; | |
2157 | } | |
d956fa6f | 2158 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
2159 | } |
2160 | else if (SCM_BIGP (n)) | |
2161 | { | |
2162 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
2163 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
2164 | 1 too big, so check for that and adjust. */ | |
2165 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
2166 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
2167 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
2168 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
2169 | size--; | |
2170 | scm_remember_upto_here_1 (n); | |
d956fa6f | 2171 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
2172 | } |
2173 | else | |
ca46fb90 | 2174 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
2175 | } |
2176 | #undef FUNC_NAME | |
0f2d19dd JB |
2177 | |
2178 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
2179 | #define SCM_MAX_DBL_PREC 60 |
2180 | #define SCM_MAX_DBL_RADIX 36 | |
2181 | ||
2182 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
2183 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
2184 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
2185 | ||
2186 | static | |
2187 | void init_dblprec(int *prec, int radix) { | |
2188 | /* determine floating point precision by adding successively | |
2189 | smaller increments to 1.0 until it is considered == 1.0 */ | |
2190 | double f = ((double)1.0)/radix; | |
2191 | double fsum = 1.0 + f; | |
2192 | ||
2193 | *prec = 0; | |
2194 | while (fsum != 1.0) | |
2195 | { | |
2196 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
2197 | fsum = 1.0; | |
2198 | else | |
2199 | { | |
2200 | f /= radix; | |
2201 | fsum = f + 1.0; | |
2202 | } | |
2203 | } | |
2204 | (*prec) -= 1; | |
2205 | } | |
2206 | ||
2207 | static | |
2208 | void init_fx_radix(double *fx_list, int radix) | |
2209 | { | |
2210 | /* initialize a per-radix list of tolerances. When added | |
2211 | to a number < 1.0, we can determine if we should raund | |
2212 | up and quit converting a number to a string. */ | |
2213 | int i; | |
2214 | fx_list[0] = 0.0; | |
2215 | fx_list[1] = 0.5; | |
2216 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
2217 | fx_list[i] = (fx_list[i-1] / radix); | |
2218 | } | |
2219 | ||
2220 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 2221 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 2222 | |
1be6b49c | 2223 | static size_t |
0b799eea | 2224 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 2225 | { |
0b799eea MV |
2226 | int efmt, dpt, d, i, wp; |
2227 | double *fx; | |
2228 | #ifdef DBL_MIN_10_EXP | |
2229 | double f_cpy; | |
2230 | int exp_cpy; | |
2231 | #endif /* DBL_MIN_10_EXP */ | |
2232 | size_t ch = 0; | |
2233 | int exp = 0; | |
2234 | ||
2235 | if(radix < 2 || | |
2236 | radix > SCM_MAX_DBL_RADIX) | |
2237 | { | |
2238 | /* revert to existing behavior */ | |
2239 | radix = 10; | |
2240 | } | |
2241 | ||
2242 | wp = scm_dblprec[radix-2]; | |
2243 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 2244 | |
f872b822 | 2245 | if (f == 0.0) |
abb7e44d MV |
2246 | { |
2247 | #ifdef HAVE_COPYSIGN | |
2248 | double sgn = copysign (1.0, f); | |
2249 | ||
2250 | if (sgn < 0.0) | |
2251 | a[ch++] = '-'; | |
2252 | #endif | |
abb7e44d MV |
2253 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
2254 | } | |
7351e207 | 2255 | |
2e65b52f | 2256 | if (isinf (f)) |
7351e207 MV |
2257 | { |
2258 | if (f < 0) | |
2259 | strcpy (a, "-inf.0"); | |
2260 | else | |
2261 | strcpy (a, "+inf.0"); | |
2262 | return ch+6; | |
2263 | } | |
2e65b52f | 2264 | else if (isnan (f)) |
7351e207 MV |
2265 | { |
2266 | strcpy (a, "+nan.0"); | |
2267 | return ch+6; | |
2268 | } | |
2269 | ||
f872b822 MD |
2270 | if (f < 0.0) |
2271 | { | |
2272 | f = -f; | |
2273 | a[ch++] = '-'; | |
2274 | } | |
7351e207 | 2275 | |
f872b822 MD |
2276 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
2277 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
2278 | /* just do the checking...if it passes, we do the conversion for our |
2279 | radix again below */ | |
2280 | f_cpy = f; | |
2281 | exp_cpy = exp; | |
2282 | ||
2283 | while (f_cpy < 1.0) | |
f872b822 | 2284 | { |
0b799eea MV |
2285 | f_cpy *= 10.0; |
2286 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
2287 | { |
2288 | a[ch++] = '#'; | |
2289 | a[ch++] = '.'; | |
2290 | a[ch++] = '#'; | |
2291 | return ch; | |
2292 | } | |
f872b822 | 2293 | } |
0b799eea | 2294 | while (f_cpy > 10.0) |
f872b822 | 2295 | { |
0b799eea MV |
2296 | f_cpy *= 0.10; |
2297 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
2298 | { |
2299 | a[ch++] = '#'; | |
2300 | a[ch++] = '.'; | |
2301 | a[ch++] = '#'; | |
2302 | return ch; | |
2303 | } | |
f872b822 | 2304 | } |
0b799eea MV |
2305 | #endif |
2306 | ||
f872b822 MD |
2307 | while (f < 1.0) |
2308 | { | |
0b799eea | 2309 | f *= radix; |
f872b822 MD |
2310 | exp--; |
2311 | } | |
0b799eea | 2312 | while (f > radix) |
f872b822 | 2313 | { |
0b799eea | 2314 | f /= radix; |
f872b822 MD |
2315 | exp++; |
2316 | } | |
0b799eea MV |
2317 | |
2318 | if (f + fx[wp] >= radix) | |
f872b822 MD |
2319 | { |
2320 | f = 1.0; | |
2321 | exp++; | |
2322 | } | |
0f2d19dd | 2323 | zero: |
0b799eea MV |
2324 | #ifdef ENGNOT |
2325 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 2326 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
2327 | exp -= dpt++; |
2328 | efmt = 1; | |
f872b822 MD |
2329 | #else |
2330 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 2331 | if (!efmt) |
cda139a7 MD |
2332 | { |
2333 | if (exp < 0) | |
2334 | { | |
2335 | a[ch++] = '0'; | |
2336 | a[ch++] = '.'; | |
2337 | dpt = exp; | |
f872b822 MD |
2338 | while (++dpt) |
2339 | a[ch++] = '0'; | |
cda139a7 MD |
2340 | } |
2341 | else | |
f872b822 | 2342 | dpt = exp + 1; |
cda139a7 | 2343 | } |
0f2d19dd JB |
2344 | else |
2345 | dpt = 1; | |
f872b822 MD |
2346 | #endif |
2347 | ||
2348 | do | |
2349 | { | |
2350 | d = f; | |
2351 | f -= d; | |
0b799eea | 2352 | a[ch++] = number_chars[d]; |
f872b822 MD |
2353 | if (f < fx[wp]) |
2354 | break; | |
2355 | if (f + fx[wp] >= 1.0) | |
2356 | { | |
0b799eea | 2357 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
2358 | break; |
2359 | } | |
0b799eea | 2360 | f *= radix; |
f872b822 MD |
2361 | if (!(--dpt)) |
2362 | a[ch++] = '.'; | |
0f2d19dd | 2363 | } |
f872b822 | 2364 | while (wp--); |
0f2d19dd JB |
2365 | |
2366 | if (dpt > 0) | |
cda139a7 | 2367 | { |
f872b822 | 2368 | #ifndef ENGNOT |
cda139a7 MD |
2369 | if ((dpt > 4) && (exp > 6)) |
2370 | { | |
f872b822 | 2371 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 2372 | for (i = ch++; i > d; i--) |
f872b822 | 2373 | a[i] = a[i - 1]; |
cda139a7 MD |
2374 | a[d] = '.'; |
2375 | efmt = 1; | |
2376 | } | |
2377 | else | |
f872b822 | 2378 | #endif |
cda139a7 | 2379 | { |
f872b822 MD |
2380 | while (--dpt) |
2381 | a[ch++] = '0'; | |
cda139a7 MD |
2382 | a[ch++] = '.'; |
2383 | } | |
2384 | } | |
f872b822 MD |
2385 | if (a[ch - 1] == '.') |
2386 | a[ch++] = '0'; /* trailing zero */ | |
2387 | if (efmt && exp) | |
2388 | { | |
2389 | a[ch++] = 'e'; | |
2390 | if (exp < 0) | |
2391 | { | |
2392 | exp = -exp; | |
2393 | a[ch++] = '-'; | |
2394 | } | |
0b799eea MV |
2395 | for (i = radix; i <= exp; i *= radix); |
2396 | for (i /= radix; i; i /= radix) | |
f872b822 | 2397 | { |
0b799eea | 2398 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
2399 | exp %= i; |
2400 | } | |
0f2d19dd | 2401 | } |
0f2d19dd JB |
2402 | return ch; |
2403 | } | |
2404 | ||
7a1aba42 MV |
2405 | |
2406 | static size_t | |
2407 | icmplx2str (double real, double imag, char *str, int radix) | |
2408 | { | |
2409 | size_t i; | |
2410 | ||
2411 | i = idbl2str (real, str, radix); | |
2412 | if (imag != 0.0) | |
2413 | { | |
2414 | /* Don't output a '+' for negative numbers or for Inf and | |
2415 | NaN. They will provide their own sign. */ | |
2e65b52f | 2416 | if (0 <= imag && !isinf (imag) && !isnan (imag)) |
7a1aba42 MV |
2417 | str[i++] = '+'; |
2418 | i += idbl2str (imag, &str[i], radix); | |
2419 | str[i++] = 'i'; | |
2420 | } | |
2421 | return i; | |
2422 | } | |
2423 | ||
1be6b49c | 2424 | static size_t |
0b799eea | 2425 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 2426 | { |
1be6b49c | 2427 | size_t i; |
3c9a524f | 2428 | if (SCM_REALP (flt)) |
0b799eea | 2429 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 2430 | else |
7a1aba42 MV |
2431 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
2432 | str, radix); | |
0f2d19dd JB |
2433 | return i; |
2434 | } | |
0f2d19dd | 2435 | |
2881e77b | 2436 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
2437 | characters in the result. |
2438 | rad is output base | |
2439 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2440 | size_t |
2881e77b MV |
2441 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
2442 | { | |
2443 | if (num < 0) | |
2444 | { | |
2445 | *p++ = '-'; | |
2446 | return scm_iuint2str (-num, rad, p) + 1; | |
2447 | } | |
2448 | else | |
2449 | return scm_iuint2str (num, rad, p); | |
2450 | } | |
2451 | ||
2452 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
2453 | characters in the result. | |
2454 | rad is output base | |
2455 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
2456 | size_t | |
2457 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 2458 | { |
1be6b49c ML |
2459 | size_t j = 1; |
2460 | size_t i; | |
2881e77b | 2461 | scm_t_uintmax n = num; |
5c11cc9d | 2462 | |
a6f3af16 AW |
2463 | if (rad < 2 || rad > 36) |
2464 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
2465 | ||
f872b822 | 2466 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2467 | j++; |
2468 | ||
2469 | i = j; | |
2881e77b | 2470 | n = num; |
f872b822 MD |
2471 | while (i--) |
2472 | { | |
5c11cc9d GH |
2473 | int d = n % rad; |
2474 | ||
f872b822 | 2475 | n /= rad; |
a6f3af16 | 2476 | p[i] = number_chars[d]; |
f872b822 | 2477 | } |
0f2d19dd JB |
2478 | return j; |
2479 | } | |
2480 | ||
a1ec6916 | 2481 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2482 | (SCM n, SCM radix), |
2483 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2484 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2485 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2486 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2487 | { |
1bbd0b84 | 2488 | int base; |
98cb6e75 | 2489 | |
0aacf84e | 2490 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 2491 | base = 10; |
0aacf84e | 2492 | else |
5efd3c7d | 2493 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 2494 | |
e11e83f3 | 2495 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2496 | { |
2497 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 2498 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 2499 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
2500 | } |
2501 | else if (SCM_BIGP (n)) | |
2502 | { | |
2503 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
2504 | scm_remember_upto_here_1 (n); | |
cc95e00a | 2505 | return scm_take_locale_string (str); |
0aacf84e | 2506 | } |
f92e85f7 MV |
2507 | else if (SCM_FRACTIONP (n)) |
2508 | { | |
f92e85f7 | 2509 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 2510 | scm_from_locale_string ("/"), |
f92e85f7 MV |
2511 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
2512 | } | |
0aacf84e MD |
2513 | else if (SCM_INEXACTP (n)) |
2514 | { | |
2515 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 2516 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
2517 | } |
2518 | else | |
bb628794 | 2519 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 2520 | } |
1bbd0b84 | 2521 | #undef FUNC_NAME |
0f2d19dd JB |
2522 | |
2523 | ||
ca46fb90 RB |
2524 | /* These print routines used to be stubbed here so that scm_repl.c |
2525 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 2526 | |
0f2d19dd | 2527 | int |
e81d98ec | 2528 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2529 | { |
56e55ac7 | 2530 | char num_buf[FLOBUFLEN]; |
0b799eea | 2531 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
2532 | return !0; |
2533 | } | |
2534 | ||
b479fe9a MV |
2535 | void |
2536 | scm_i_print_double (double val, SCM port) | |
2537 | { | |
2538 | char num_buf[FLOBUFLEN]; | |
2539 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
2540 | } | |
2541 | ||
f3ae5d60 | 2542 | int |
e81d98ec | 2543 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 2544 | |
f3ae5d60 | 2545 | { |
56e55ac7 | 2546 | char num_buf[FLOBUFLEN]; |
0b799eea | 2547 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
2548 | return !0; |
2549 | } | |
1cc91f1b | 2550 | |
7a1aba42 MV |
2551 | void |
2552 | scm_i_print_complex (double real, double imag, SCM port) | |
2553 | { | |
2554 | char num_buf[FLOBUFLEN]; | |
2555 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
2556 | } | |
2557 | ||
f92e85f7 MV |
2558 | int |
2559 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
2560 | { | |
2561 | SCM str; | |
f92e85f7 | 2562 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 2563 | scm_display (str, port); |
f92e85f7 MV |
2564 | scm_remember_upto_here_1 (str); |
2565 | return !0; | |
2566 | } | |
2567 | ||
0f2d19dd | 2568 | int |
e81d98ec | 2569 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2570 | { |
ca46fb90 RB |
2571 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
2572 | scm_remember_upto_here_1 (exp); | |
2573 | scm_lfwrite (str, (size_t) strlen (str), port); | |
2574 | free (str); | |
0f2d19dd JB |
2575 | return !0; |
2576 | } | |
2577 | /*** END nums->strs ***/ | |
2578 | ||
3c9a524f | 2579 | |
0f2d19dd | 2580 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2581 | |
3c9a524f DH |
2582 | /* The following functions implement the conversion from strings to numbers. |
2583 | * The implementation somehow follows the grammar for numbers as it is given | |
2584 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2585 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2586 | * points should be noted about the implementation: | |
2587 | * * Each function keeps a local index variable 'idx' that points at the | |
2588 | * current position within the parsed string. The global index is only | |
2589 | * updated if the function could parse the corresponding syntactic unit | |
2590 | * successfully. | |
2591 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2592 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2593 | * global exactness information is only updated after each part has been | |
2594 | * successfully parsed. | |
2595 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2596 | * Only if these fixnums would overflow, the result variables are updated | |
2597 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2598 | * the temporary variables holding the fixnums are cleared, and the process | |
2599 | * starts over again. If for example fixnums were able to store five decimal | |
2600 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2601 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2602 | * only every five digits two bignum operations were performed. | |
2603 | */ | |
2604 | ||
2605 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2606 | ||
2607 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2608 | ||
a6f3af16 AW |
2609 | /* Caller is responsible for checking that the return value is in range |
2610 | for the given radix, which should be <= 36. */ | |
2611 | static unsigned int | |
2612 | char_decimal_value (scm_t_uint32 c) | |
2613 | { | |
2614 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
2615 | that's certainly above any valid decimal, so we take advantage of | |
2616 | that to elide some tests. */ | |
2617 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
2618 | ||
2619 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
2620 | hexadecimals. */ | |
2621 | if (d >= 10U) | |
2622 | { | |
2623 | c = uc_tolower (c); | |
2624 | if (c >= (scm_t_uint32) 'a') | |
2625 | d = c - (scm_t_uint32)'a' + 10U; | |
2626 | } | |
2627 | return d; | |
2628 | } | |
3c9a524f | 2629 | |
2a8fecee | 2630 | static SCM |
3f47e526 | 2631 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 2632 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 2633 | { |
3c9a524f DH |
2634 | unsigned int idx = *p_idx; |
2635 | unsigned int hash_seen = 0; | |
2636 | scm_t_bits shift = 1; | |
2637 | scm_t_bits add = 0; | |
2638 | unsigned int digit_value; | |
2639 | SCM result; | |
2640 | char c; | |
3f47e526 | 2641 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
2642 | |
2643 | if (idx == len) | |
2644 | return SCM_BOOL_F; | |
2a8fecee | 2645 | |
3f47e526 | 2646 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 2647 | digit_value = char_decimal_value (c); |
3c9a524f DH |
2648 | if (digit_value >= radix) |
2649 | return SCM_BOOL_F; | |
2650 | ||
2651 | idx++; | |
d956fa6f | 2652 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 2653 | while (idx != len) |
f872b822 | 2654 | { |
3f47e526 | 2655 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 2656 | if (c == '#') |
3c9a524f DH |
2657 | { |
2658 | hash_seen = 1; | |
2659 | digit_value = 0; | |
2660 | } | |
a6f3af16 AW |
2661 | else if (hash_seen) |
2662 | break; | |
3c9a524f | 2663 | else |
a6f3af16 AW |
2664 | { |
2665 | digit_value = char_decimal_value (c); | |
2666 | /* This check catches non-decimals in addition to out-of-range | |
2667 | decimals. */ | |
2668 | if (digit_value >= radix) | |
2669 | break; | |
2670 | } | |
3c9a524f DH |
2671 | |
2672 | idx++; | |
2673 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2674 | { | |
d956fa6f | 2675 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2676 | if (add > 0) |
d956fa6f | 2677 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2678 | |
2679 | shift = radix; | |
2680 | add = digit_value; | |
2681 | } | |
2682 | else | |
2683 | { | |
2684 | shift = shift * radix; | |
2685 | add = add * radix + digit_value; | |
2686 | } | |
2687 | }; | |
2688 | ||
2689 | if (shift > 1) | |
d956fa6f | 2690 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2691 | if (add > 0) |
d956fa6f | 2692 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2693 | |
2694 | *p_idx = idx; | |
2695 | if (hash_seen) | |
2696 | *p_exactness = INEXACT; | |
2697 | ||
2698 | return result; | |
2a8fecee JB |
2699 | } |
2700 | ||
2701 | ||
3c9a524f DH |
2702 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2703 | * covers the parts of the rules that start at a potential point. The value | |
2704 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2705 | * in variable result. The content of *p_exactness indicates, whether a hash |
2706 | * has already been seen in the digits before the point. | |
3c9a524f | 2707 | */ |
1cc91f1b | 2708 | |
3f47e526 | 2709 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
2710 | |
2711 | static SCM | |
3f47e526 | 2712 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 2713 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2714 | { |
3c9a524f DH |
2715 | unsigned int idx = *p_idx; |
2716 | enum t_exactness x = *p_exactness; | |
3f47e526 | 2717 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
2718 | |
2719 | if (idx == len) | |
79d34f68 | 2720 | return result; |
3c9a524f | 2721 | |
3f47e526 | 2722 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
2723 | { |
2724 | scm_t_bits shift = 1; | |
2725 | scm_t_bits add = 0; | |
2726 | unsigned int digit_value; | |
cff5fa33 | 2727 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
2728 | |
2729 | idx++; | |
2730 | while (idx != len) | |
2731 | { | |
3f47e526 MG |
2732 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
2733 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
2734 | { |
2735 | if (x == INEXACT) | |
2736 | return SCM_BOOL_F; | |
2737 | else | |
2738 | digit_value = DIGIT2UINT (c); | |
2739 | } | |
2740 | else if (c == '#') | |
2741 | { | |
2742 | x = INEXACT; | |
2743 | digit_value = 0; | |
2744 | } | |
2745 | else | |
2746 | break; | |
2747 | ||
2748 | idx++; | |
2749 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2750 | { | |
d956fa6f MV |
2751 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2752 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 2753 | if (add > 0) |
d956fa6f | 2754 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2755 | |
2756 | shift = 10; | |
2757 | add = digit_value; | |
2758 | } | |
2759 | else | |
2760 | { | |
2761 | shift = shift * 10; | |
2762 | add = add * 10 + digit_value; | |
2763 | } | |
2764 | }; | |
2765 | ||
2766 | if (add > 0) | |
2767 | { | |
d956fa6f MV |
2768 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2769 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
2770 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
2771 | } |
2772 | ||
d8592269 | 2773 | result = scm_divide (result, big_shift); |
79d34f68 | 2774 | |
3c9a524f DH |
2775 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2776 | x = INEXACT; | |
f872b822 | 2777 | } |
3c9a524f | 2778 | |
3c9a524f | 2779 | if (idx != len) |
f872b822 | 2780 | { |
3c9a524f DH |
2781 | int sign = 1; |
2782 | unsigned int start; | |
3f47e526 | 2783 | scm_t_wchar c; |
3c9a524f DH |
2784 | int exponent; |
2785 | SCM e; | |
2786 | ||
2787 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2788 | ||
3f47e526 | 2789 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 2790 | { |
3c9a524f DH |
2791 | case 'd': case 'D': |
2792 | case 'e': case 'E': | |
2793 | case 'f': case 'F': | |
2794 | case 'l': case 'L': | |
2795 | case 's': case 'S': | |
2796 | idx++; | |
ee0ddd21 AW |
2797 | if (idx == len) |
2798 | return SCM_BOOL_F; | |
2799 | ||
3c9a524f | 2800 | start = idx; |
3f47e526 | 2801 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2802 | if (c == '-') |
2803 | { | |
2804 | idx++; | |
ee0ddd21 AW |
2805 | if (idx == len) |
2806 | return SCM_BOOL_F; | |
2807 | ||
3c9a524f | 2808 | sign = -1; |
3f47e526 | 2809 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2810 | } |
2811 | else if (c == '+') | |
2812 | { | |
2813 | idx++; | |
ee0ddd21 AW |
2814 | if (idx == len) |
2815 | return SCM_BOOL_F; | |
2816 | ||
3c9a524f | 2817 | sign = 1; |
3f47e526 | 2818 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2819 | } |
2820 | else | |
2821 | sign = 1; | |
2822 | ||
3f47e526 | 2823 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
2824 | return SCM_BOOL_F; |
2825 | ||
2826 | idx++; | |
2827 | exponent = DIGIT2UINT (c); | |
2828 | while (idx != len) | |
f872b822 | 2829 | { |
3f47e526 MG |
2830 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
2831 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
2832 | { |
2833 | idx++; | |
2834 | if (exponent <= SCM_MAXEXP) | |
2835 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2836 | } | |
2837 | else | |
2838 | break; | |
f872b822 | 2839 | } |
3c9a524f DH |
2840 | |
2841 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2842 | { |
3c9a524f | 2843 | size_t exp_len = idx - start; |
3f47e526 | 2844 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
2845 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
2846 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2847 | } |
3c9a524f | 2848 | |
d956fa6f | 2849 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
2850 | if (sign == 1) |
2851 | result = scm_product (result, e); | |
2852 | else | |
f92e85f7 | 2853 | result = scm_divide2real (result, e); |
3c9a524f DH |
2854 | |
2855 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2856 | x = INEXACT; | |
2857 | ||
f872b822 | 2858 | break; |
3c9a524f | 2859 | |
f872b822 | 2860 | default: |
3c9a524f | 2861 | break; |
f872b822 | 2862 | } |
0f2d19dd | 2863 | } |
3c9a524f DH |
2864 | |
2865 | *p_idx = idx; | |
2866 | if (x == INEXACT) | |
2867 | *p_exactness = x; | |
2868 | ||
2869 | return result; | |
0f2d19dd | 2870 | } |
0f2d19dd | 2871 | |
3c9a524f DH |
2872 | |
2873 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2874 | ||
2875 | static SCM | |
3f47e526 | 2876 | mem2ureal (SCM mem, unsigned int *p_idx, |
3c9a524f | 2877 | unsigned int radix, enum t_exactness *p_exactness) |
0f2d19dd | 2878 | { |
3c9a524f | 2879 | unsigned int idx = *p_idx; |
164d2481 | 2880 | SCM result; |
3f47e526 | 2881 | size_t len = scm_i_string_length (mem); |
3c9a524f | 2882 | |
40f89215 NJ |
2883 | /* Start off believing that the number will be exact. This changes |
2884 | to INEXACT if we see a decimal point or a hash. */ | |
2885 | enum t_exactness x = EXACT; | |
2886 | ||
3c9a524f DH |
2887 | if (idx == len) |
2888 | return SCM_BOOL_F; | |
2889 | ||
3f47e526 | 2890 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
2891 | { |
2892 | *p_idx = idx+5; | |
2893 | return scm_inf (); | |
2894 | } | |
2895 | ||
3f47e526 | 2896 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 2897 | { |
d8592269 MV |
2898 | /* Cobble up the fractional part. We might want to set the |
2899 | NaN's mantissa from it. */ | |
7351e207 | 2900 | idx += 4; |
3f47e526 | 2901 | mem2uinteger (mem, &idx, 10, &x); |
7351e207 MV |
2902 | *p_idx = idx; |
2903 | return scm_nan (); | |
2904 | } | |
2905 | ||
3f47e526 | 2906 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
2907 | { |
2908 | if (radix != 10) | |
2909 | return SCM_BOOL_F; | |
2910 | else if (idx + 1 == len) | |
2911 | return SCM_BOOL_F; | |
3f47e526 | 2912 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
2913 | return SCM_BOOL_F; |
2914 | else | |
cff5fa33 | 2915 | result = mem2decimal_from_point (SCM_INUM0, mem, |
40f89215 | 2916 | p_idx, &x); |
f872b822 | 2917 | } |
3c9a524f DH |
2918 | else |
2919 | { | |
3c9a524f | 2920 | SCM uinteger; |
3c9a524f | 2921 | |
3f47e526 | 2922 | uinteger = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 2923 | if (scm_is_false (uinteger)) |
3c9a524f DH |
2924 | return SCM_BOOL_F; |
2925 | ||
2926 | if (idx == len) | |
2927 | result = uinteger; | |
3f47e526 | 2928 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 2929 | { |
3c9a524f DH |
2930 | SCM divisor; |
2931 | ||
2932 | idx++; | |
ee0ddd21 AW |
2933 | if (idx == len) |
2934 | return SCM_BOOL_F; | |
3c9a524f | 2935 | |
3f47e526 | 2936 | divisor = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 2937 | if (scm_is_false (divisor)) |
3c9a524f DH |
2938 | return SCM_BOOL_F; |
2939 | ||
f92e85f7 | 2940 | /* both are int/big here, I assume */ |
cba42c93 | 2941 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 2942 | } |
3c9a524f DH |
2943 | else if (radix == 10) |
2944 | { | |
3f47e526 | 2945 | result = mem2decimal_from_point (uinteger, mem, &idx, &x); |
73e4de09 | 2946 | if (scm_is_false (result)) |
3c9a524f DH |
2947 | return SCM_BOOL_F; |
2948 | } | |
2949 | else | |
2950 | result = uinteger; | |
2951 | ||
2952 | *p_idx = idx; | |
f872b822 | 2953 | } |
164d2481 | 2954 | |
40f89215 NJ |
2955 | /* Update *p_exactness if the number just read was inexact. This is |
2956 | important for complex numbers, so that a complex number is | |
2957 | treated as inexact overall if either its real or imaginary part | |
2958 | is inexact. | |
2959 | */ | |
2960 | if (x == INEXACT) | |
2961 | *p_exactness = x; | |
2962 | ||
164d2481 MV |
2963 | /* When returning an inexact zero, make sure it is represented as a |
2964 | floating point value so that we can change its sign. | |
2965 | */ | |
cff5fa33 | 2966 | if (scm_is_eq (result, SCM_INUM0) && *p_exactness == INEXACT) |
55f26379 | 2967 | result = scm_from_double (0.0); |
164d2481 MV |
2968 | |
2969 | return result; | |
3c9a524f | 2970 | } |
0f2d19dd | 2971 | |
0f2d19dd | 2972 | |
3c9a524f | 2973 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2974 | |
3c9a524f | 2975 | static SCM |
3f47e526 | 2976 | mem2complex (SCM mem, unsigned int idx, |
3c9a524f DH |
2977 | unsigned int radix, enum t_exactness *p_exactness) |
2978 | { | |
3f47e526 | 2979 | scm_t_wchar c; |
3c9a524f DH |
2980 | int sign = 0; |
2981 | SCM ureal; | |
3f47e526 | 2982 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
2983 | |
2984 | if (idx == len) | |
2985 | return SCM_BOOL_F; | |
2986 | ||
3f47e526 | 2987 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2988 | if (c == '+') |
2989 | { | |
2990 | idx++; | |
2991 | sign = 1; | |
2992 | } | |
2993 | else if (c == '-') | |
2994 | { | |
2995 | idx++; | |
2996 | sign = -1; | |
0f2d19dd | 2997 | } |
0f2d19dd | 2998 | |
3c9a524f DH |
2999 | if (idx == len) |
3000 | return SCM_BOOL_F; | |
3001 | ||
3f47e526 | 3002 | ureal = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 3003 | if (scm_is_false (ureal)) |
f872b822 | 3004 | { |
3c9a524f DH |
3005 | /* input must be either +i or -i */ |
3006 | ||
3007 | if (sign == 0) | |
3008 | return SCM_BOOL_F; | |
3009 | ||
3f47e526 MG |
3010 | if (scm_i_string_ref (mem, idx) == 'i' |
3011 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 3012 | { |
3c9a524f DH |
3013 | idx++; |
3014 | if (idx != len) | |
3015 | return SCM_BOOL_F; | |
3016 | ||
cff5fa33 | 3017 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 3018 | } |
3c9a524f DH |
3019 | else |
3020 | return SCM_BOOL_F; | |
0f2d19dd | 3021 | } |
3c9a524f DH |
3022 | else |
3023 | { | |
73e4de09 | 3024 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 3025 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 3026 | |
3c9a524f DH |
3027 | if (idx == len) |
3028 | return ureal; | |
3029 | ||
3f47e526 | 3030 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 3031 | switch (c) |
f872b822 | 3032 | { |
3c9a524f DH |
3033 | case 'i': case 'I': |
3034 | /* either +<ureal>i or -<ureal>i */ | |
3035 | ||
3036 | idx++; | |
3037 | if (sign == 0) | |
3038 | return SCM_BOOL_F; | |
3039 | if (idx != len) | |
3040 | return SCM_BOOL_F; | |
cff5fa33 | 3041 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
3042 | |
3043 | case '@': | |
3044 | /* polar input: <real>@<real>. */ | |
3045 | ||
3046 | idx++; | |
3047 | if (idx == len) | |
3048 | return SCM_BOOL_F; | |
3049 | else | |
f872b822 | 3050 | { |
3c9a524f DH |
3051 | int sign; |
3052 | SCM angle; | |
3053 | SCM result; | |
3054 | ||
3f47e526 | 3055 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
3056 | if (c == '+') |
3057 | { | |
3058 | idx++; | |
ee0ddd21 AW |
3059 | if (idx == len) |
3060 | return SCM_BOOL_F; | |
3c9a524f DH |
3061 | sign = 1; |
3062 | } | |
3063 | else if (c == '-') | |
3064 | { | |
3065 | idx++; | |
ee0ddd21 AW |
3066 | if (idx == len) |
3067 | return SCM_BOOL_F; | |
3c9a524f DH |
3068 | sign = -1; |
3069 | } | |
3070 | else | |
3071 | sign = 1; | |
3072 | ||
3f47e526 | 3073 | angle = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 3074 | if (scm_is_false (angle)) |
3c9a524f DH |
3075 | return SCM_BOOL_F; |
3076 | if (idx != len) | |
3077 | return SCM_BOOL_F; | |
3078 | ||
73e4de09 | 3079 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
3080 | angle = scm_difference (angle, SCM_UNDEFINED); |
3081 | ||
3082 | result = scm_make_polar (ureal, angle); | |
3083 | return result; | |
f872b822 | 3084 | } |
3c9a524f DH |
3085 | case '+': |
3086 | case '-': | |
3087 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 3088 | |
3c9a524f DH |
3089 | idx++; |
3090 | if (idx == len) | |
3091 | return SCM_BOOL_F; | |
3092 | else | |
3093 | { | |
3094 | int sign = (c == '+') ? 1 : -1; | |
3f47e526 | 3095 | SCM imag = mem2ureal (mem, &idx, radix, p_exactness); |
0f2d19dd | 3096 | |
73e4de09 | 3097 | if (scm_is_false (imag)) |
d956fa6f | 3098 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 3099 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 3100 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 3101 | |
3c9a524f DH |
3102 | if (idx == len) |
3103 | return SCM_BOOL_F; | |
3f47e526 MG |
3104 | if (scm_i_string_ref (mem, idx) != 'i' |
3105 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 3106 | return SCM_BOOL_F; |
0f2d19dd | 3107 | |
3c9a524f DH |
3108 | idx++; |
3109 | if (idx != len) | |
3110 | return SCM_BOOL_F; | |
0f2d19dd | 3111 | |
1fe5e088 | 3112 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
3113 | } |
3114 | default: | |
3115 | return SCM_BOOL_F; | |
3116 | } | |
3117 | } | |
0f2d19dd | 3118 | } |
0f2d19dd JB |
3119 | |
3120 | ||
3c9a524f DH |
3121 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
3122 | ||
3123 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 3124 | |
0f2d19dd | 3125 | SCM |
3f47e526 | 3126 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 3127 | { |
3c9a524f DH |
3128 | unsigned int idx = 0; |
3129 | unsigned int radix = NO_RADIX; | |
3130 | enum t_exactness forced_x = NO_EXACTNESS; | |
3131 | enum t_exactness implicit_x = EXACT; | |
3132 | SCM result; | |
3f47e526 | 3133 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
3134 | |
3135 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 3136 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 3137 | { |
3f47e526 | 3138 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
3139 | { |
3140 | case 'b': case 'B': | |
3141 | if (radix != NO_RADIX) | |
3142 | return SCM_BOOL_F; | |
3143 | radix = DUAL; | |
3144 | break; | |
3145 | case 'd': case 'D': | |
3146 | if (radix != NO_RADIX) | |
3147 | return SCM_BOOL_F; | |
3148 | radix = DEC; | |
3149 | break; | |
3150 | case 'i': case 'I': | |
3151 | if (forced_x != NO_EXACTNESS) | |
3152 | return SCM_BOOL_F; | |
3153 | forced_x = INEXACT; | |
3154 | break; | |
3155 | case 'e': case 'E': | |
3156 | if (forced_x != NO_EXACTNESS) | |
3157 | return SCM_BOOL_F; | |
3158 | forced_x = EXACT; | |
3159 | break; | |
3160 | case 'o': case 'O': | |
3161 | if (radix != NO_RADIX) | |
3162 | return SCM_BOOL_F; | |
3163 | radix = OCT; | |
3164 | break; | |
3165 | case 'x': case 'X': | |
3166 | if (radix != NO_RADIX) | |
3167 | return SCM_BOOL_F; | |
3168 | radix = HEX; | |
3169 | break; | |
3170 | default: | |
f872b822 | 3171 | return SCM_BOOL_F; |
3c9a524f DH |
3172 | } |
3173 | idx += 2; | |
3174 | } | |
3175 | ||
3176 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
3177 | if (radix == NO_RADIX) | |
3f47e526 | 3178 | result = mem2complex (mem, idx, default_radix, &implicit_x); |
3c9a524f | 3179 | else |
3f47e526 | 3180 | result = mem2complex (mem, idx, (unsigned int) radix, &implicit_x); |
3c9a524f | 3181 | |
73e4de09 | 3182 | if (scm_is_false (result)) |
3c9a524f | 3183 | return SCM_BOOL_F; |
f872b822 | 3184 | |
3c9a524f | 3185 | switch (forced_x) |
f872b822 | 3186 | { |
3c9a524f DH |
3187 | case EXACT: |
3188 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
3189 | return scm_inexact_to_exact (result); |
3190 | else | |
3191 | return result; | |
3192 | case INEXACT: | |
3193 | if (SCM_INEXACTP (result)) | |
3194 | return result; | |
3195 | else | |
3196 | return scm_exact_to_inexact (result); | |
3197 | case NO_EXACTNESS: | |
3198 | default: | |
3199 | if (implicit_x == INEXACT) | |
3200 | { | |
3201 | if (SCM_INEXACTP (result)) | |
3202 | return result; | |
3203 | else | |
3204 | return scm_exact_to_inexact (result); | |
3205 | } | |
3206 | else | |
3207 | return result; | |
f872b822 | 3208 | } |
0f2d19dd JB |
3209 | } |
3210 | ||
3f47e526 MG |
3211 | SCM |
3212 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
3213 | unsigned int default_radix) | |
3214 | { | |
3215 | SCM str = scm_from_locale_stringn (mem, len); | |
3216 | ||
3217 | return scm_i_string_to_number (str, default_radix); | |
3218 | } | |
3219 | ||
0f2d19dd | 3220 | |
a1ec6916 | 3221 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 3222 | (SCM string, SCM radix), |
1e6808ea | 3223 | "Return a number of the maximally precise representation\n" |
942e5b91 | 3224 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
3225 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
3226 | "is a default radix that may be overridden by an explicit radix\n" | |
3227 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
3228 | "supplied, then the default radix is 10. If string is not a\n" | |
3229 | "syntactically valid notation for a number, then\n" | |
3230 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 3231 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
3232 | { |
3233 | SCM answer; | |
5efd3c7d | 3234 | unsigned int base; |
a6d9e5ab | 3235 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
3236 | |
3237 | if (SCM_UNBNDP (radix)) | |
3238 | base = 10; | |
3239 | else | |
3240 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
3241 | ||
3f47e526 | 3242 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
3243 | scm_remember_upto_here_1 (string); |
3244 | return answer; | |
0f2d19dd | 3245 | } |
1bbd0b84 | 3246 | #undef FUNC_NAME |
3c9a524f DH |
3247 | |
3248 | ||
0f2d19dd JB |
3249 | /*** END strs->nums ***/ |
3250 | ||
5986c47d | 3251 | |
8507ec80 MV |
3252 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
3253 | (SCM x), | |
3254 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
3255 | "otherwise.") | |
3256 | #define FUNC_NAME s_scm_number_p | |
3257 | { | |
3258 | return scm_from_bool (SCM_NUMBERP (x)); | |
3259 | } | |
3260 | #undef FUNC_NAME | |
3261 | ||
3262 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 3263 | (SCM x), |
942e5b91 | 3264 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 3265 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
3266 | "values form subsets of the set of complex numbers, i. e. the\n" |
3267 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
3268 | "rational or integer number.") | |
8507ec80 | 3269 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 3270 | { |
8507ec80 MV |
3271 | /* all numbers are complex. */ |
3272 | return scm_number_p (x); | |
0f2d19dd | 3273 | } |
1bbd0b84 | 3274 | #undef FUNC_NAME |
0f2d19dd | 3275 | |
f92e85f7 MV |
3276 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
3277 | (SCM x), | |
3278 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
3279 | "otherwise. Note that the set of integer values forms a subset of\n" | |
3280 | "the set of real numbers, i. e. the predicate will also be\n" | |
3281 | "fulfilled if @var{x} is an integer number.") | |
3282 | #define FUNC_NAME s_scm_real_p | |
3283 | { | |
c960e556 MW |
3284 | return scm_from_bool |
3285 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
3286 | } |
3287 | #undef FUNC_NAME | |
3288 | ||
3289 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 3290 | (SCM x), |
942e5b91 | 3291 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 3292 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 3293 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
3294 | "fulfilled if @var{x} is an integer number.") |
3295 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 3296 | { |
c960e556 | 3297 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
3298 | return SCM_BOOL_T; |
3299 | else if (SCM_REALP (x)) | |
c960e556 MW |
3300 | /* due to their limited precision, finite floating point numbers are |
3301 | rational as well. (finite means neither infinity nor a NaN) */ | |
3302 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 3303 | else |
bb628794 | 3304 | return SCM_BOOL_F; |
0f2d19dd | 3305 | } |
1bbd0b84 | 3306 | #undef FUNC_NAME |
0f2d19dd | 3307 | |
a1ec6916 | 3308 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 3309 | (SCM x), |
942e5b91 MG |
3310 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
3311 | "else.") | |
1bbd0b84 | 3312 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 3313 | { |
c960e556 | 3314 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 3315 | return SCM_BOOL_T; |
c960e556 MW |
3316 | else if (SCM_REALP (x)) |
3317 | { | |
3318 | double val = SCM_REAL_VALUE (x); | |
3319 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
3320 | } | |
3321 | else | |
8e43ed5d | 3322 | return SCM_BOOL_F; |
0f2d19dd | 3323 | } |
1bbd0b84 | 3324 | #undef FUNC_NAME |
0f2d19dd JB |
3325 | |
3326 | ||
8a1f4f98 AW |
3327 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
3328 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
3329 | (SCM x, SCM y, SCM rest), | |
3330 | "Return @code{#t} if all parameters are numerically equal.") | |
3331 | #define FUNC_NAME s_scm_i_num_eq_p | |
3332 | { | |
3333 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3334 | return SCM_BOOL_T; | |
3335 | while (!scm_is_null (rest)) | |
3336 | { | |
3337 | if (scm_is_false (scm_num_eq_p (x, y))) | |
3338 | return SCM_BOOL_F; | |
3339 | x = y; | |
3340 | y = scm_car (rest); | |
3341 | rest = scm_cdr (rest); | |
3342 | } | |
3343 | return scm_num_eq_p (x, y); | |
3344 | } | |
3345 | #undef FUNC_NAME | |
0f2d19dd | 3346 | SCM |
6e8d25a6 | 3347 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 3348 | { |
d8b95e27 | 3349 | again: |
e11e83f3 | 3350 | if (SCM_I_INUMP (x)) |
0aacf84e | 3351 | { |
e25f3727 | 3352 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 3353 | if (SCM_I_INUMP (y)) |
0aacf84e | 3354 | { |
e25f3727 | 3355 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 3356 | return scm_from_bool (xx == yy); |
0aacf84e MD |
3357 | } |
3358 | else if (SCM_BIGP (y)) | |
3359 | return SCM_BOOL_F; | |
3360 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
3361 | { |
3362 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
3363 | to a double and compare. | |
3364 | ||
3365 | But on a 64-bit system an inum is bigger than a double and | |
3366 | casting it to a double (call that dxx) will round. dxx is at | |
3367 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
3368 | an integer and fits a long. So we cast yy to a long and | |
3369 | compare with plain xx. | |
3370 | ||
3371 | An alternative (for any size system actually) would be to check | |
3372 | yy is an integer (with floor) and is in range of an inum | |
3373 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
3374 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
3375 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
3376 | |
3377 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
3378 | return scm_from_bool ((double) xx == yy |
3379 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 3380 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 3381 | } |
0aacf84e | 3382 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3383 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3384 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
3385 | else if (SCM_FRACTIONP (y)) |
3386 | return SCM_BOOL_F; | |
0aacf84e | 3387 | else |
8a1f4f98 | 3388 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 3389 | } |
0aacf84e MD |
3390 | else if (SCM_BIGP (x)) |
3391 | { | |
e11e83f3 | 3392 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3393 | return SCM_BOOL_F; |
3394 | else if (SCM_BIGP (y)) | |
3395 | { | |
3396 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3397 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3398 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3399 | } |
3400 | else if (SCM_REALP (y)) | |
3401 | { | |
3402 | int cmp; | |
2e65b52f | 3403 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
3404 | return SCM_BOOL_F; |
3405 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3406 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3407 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3408 | } |
3409 | else if (SCM_COMPLEXP (y)) | |
3410 | { | |
3411 | int cmp; | |
3412 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
3413 | return SCM_BOOL_F; | |
2e65b52f | 3414 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
3415 | return SCM_BOOL_F; |
3416 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
3417 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3418 | return scm_from_bool (0 == cmp); |
0aacf84e | 3419 | } |
f92e85f7 MV |
3420 | else if (SCM_FRACTIONP (y)) |
3421 | return SCM_BOOL_F; | |
0aacf84e | 3422 | else |
8a1f4f98 | 3423 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 3424 | } |
0aacf84e MD |
3425 | else if (SCM_REALP (x)) |
3426 | { | |
e8c5b1f2 | 3427 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 3428 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
3429 | { |
3430 | /* see comments with inum/real above */ | |
e25f3727 | 3431 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
3432 | return scm_from_bool (xx == (double) yy |
3433 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 3434 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 3435 | } |
0aacf84e MD |
3436 | else if (SCM_BIGP (y)) |
3437 | { | |
3438 | int cmp; | |
2e65b52f | 3439 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
3440 | return SCM_BOOL_F; |
3441 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3442 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3443 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3444 | } |
3445 | else if (SCM_REALP (y)) | |
73e4de09 | 3446 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 3447 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3448 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3449 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3450 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3451 | { |
3452 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 3453 | if (isnan (xx)) |
d8b95e27 | 3454 | return SCM_BOOL_F; |
2e65b52f | 3455 | if (isinf (xx)) |
73e4de09 | 3456 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3457 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3458 | goto again; | |
3459 | } | |
0aacf84e | 3460 | else |
8a1f4f98 | 3461 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 3462 | } |
0aacf84e MD |
3463 | else if (SCM_COMPLEXP (x)) |
3464 | { | |
e11e83f3 MV |
3465 | if (SCM_I_INUMP (y)) |
3466 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
3467 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3468 | else if (SCM_BIGP (y)) | |
3469 | { | |
3470 | int cmp; | |
3471 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
3472 | return SCM_BOOL_F; | |
2e65b52f | 3473 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
3474 | return SCM_BOOL_F; |
3475 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
3476 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3477 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3478 | } |
3479 | else if (SCM_REALP (y)) | |
73e4de09 | 3480 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
3481 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3482 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 3483 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3484 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3485 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3486 | { |
3487 | double xx; | |
3488 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
3489 | return SCM_BOOL_F; | |
3490 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 3491 | if (isnan (xx)) |
d8b95e27 | 3492 | return SCM_BOOL_F; |
2e65b52f | 3493 | if (isinf (xx)) |
73e4de09 | 3494 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3495 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3496 | goto again; | |
3497 | } | |
f92e85f7 | 3498 | else |
8a1f4f98 | 3499 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
3500 | } |
3501 | else if (SCM_FRACTIONP (x)) | |
3502 | { | |
e11e83f3 | 3503 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
3504 | return SCM_BOOL_F; |
3505 | else if (SCM_BIGP (y)) | |
3506 | return SCM_BOOL_F; | |
3507 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
3508 | { |
3509 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 3510 | if (isnan (yy)) |
d8b95e27 | 3511 | return SCM_BOOL_F; |
2e65b52f | 3512 | if (isinf (yy)) |
73e4de09 | 3513 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3514 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3515 | goto again; | |
3516 | } | |
f92e85f7 | 3517 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
3518 | { |
3519 | double yy; | |
3520 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
3521 | return SCM_BOOL_F; | |
3522 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 3523 | if (isnan (yy)) |
d8b95e27 | 3524 | return SCM_BOOL_F; |
2e65b52f | 3525 | if (isinf (yy)) |
73e4de09 | 3526 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3527 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3528 | goto again; | |
3529 | } | |
f92e85f7 MV |
3530 | else if (SCM_FRACTIONP (y)) |
3531 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 3532 | else |
8a1f4f98 | 3533 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 3534 | } |
0aacf84e | 3535 | else |
8a1f4f98 | 3536 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
3537 | } |
3538 | ||
3539 | ||
a5f0b599 KR |
3540 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
3541 | done are good for inums, but for bignums an answer can almost always be | |
3542 | had by just examining a few high bits of the operands, as done by GMP in | |
3543 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
3544 | of the float exponent to take into account. */ | |
3545 | ||
8c93b597 | 3546 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
3547 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
3548 | (SCM x, SCM y, SCM rest), | |
3549 | "Return @code{#t} if the list of parameters is monotonically\n" | |
3550 | "increasing.") | |
3551 | #define FUNC_NAME s_scm_i_num_less_p | |
3552 | { | |
3553 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3554 | return SCM_BOOL_T; | |
3555 | while (!scm_is_null (rest)) | |
3556 | { | |
3557 | if (scm_is_false (scm_less_p (x, y))) | |
3558 | return SCM_BOOL_F; | |
3559 | x = y; | |
3560 | y = scm_car (rest); | |
3561 | rest = scm_cdr (rest); | |
3562 | } | |
3563 | return scm_less_p (x, y); | |
3564 | } | |
3565 | #undef FUNC_NAME | |
0f2d19dd | 3566 | SCM |
6e8d25a6 | 3567 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3568 | { |
a5f0b599 | 3569 | again: |
e11e83f3 | 3570 | if (SCM_I_INUMP (x)) |
0aacf84e | 3571 | { |
e25f3727 | 3572 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 3573 | if (SCM_I_INUMP (y)) |
0aacf84e | 3574 | { |
e25f3727 | 3575 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 3576 | return scm_from_bool (xx < yy); |
0aacf84e MD |
3577 | } |
3578 | else if (SCM_BIGP (y)) | |
3579 | { | |
3580 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3581 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3582 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3583 | } |
3584 | else if (SCM_REALP (y)) | |
73e4de09 | 3585 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 3586 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3587 | { |
3588 | /* "x < a/b" becomes "x*b < a" */ | |
3589 | int_frac: | |
3590 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
3591 | y = SCM_FRACTION_NUMERATOR (y); | |
3592 | goto again; | |
3593 | } | |
0aacf84e | 3594 | else |
8a1f4f98 | 3595 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 3596 | } |
0aacf84e MD |
3597 | else if (SCM_BIGP (x)) |
3598 | { | |
e11e83f3 | 3599 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3600 | { |
3601 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3602 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3603 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3604 | } |
3605 | else if (SCM_BIGP (y)) | |
3606 | { | |
3607 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3608 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3609 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
3610 | } |
3611 | else if (SCM_REALP (y)) | |
3612 | { | |
3613 | int cmp; | |
2e65b52f | 3614 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
3615 | return SCM_BOOL_F; |
3616 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3617 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3618 | return scm_from_bool (cmp < 0); |
0aacf84e | 3619 | } |
f92e85f7 | 3620 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 3621 | goto int_frac; |
0aacf84e | 3622 | else |
8a1f4f98 | 3623 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 3624 | } |
0aacf84e MD |
3625 | else if (SCM_REALP (x)) |
3626 | { | |
e11e83f3 MV |
3627 | if (SCM_I_INUMP (y)) |
3628 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3629 | else if (SCM_BIGP (y)) |
3630 | { | |
3631 | int cmp; | |
2e65b52f | 3632 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
3633 | return SCM_BOOL_F; |
3634 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3635 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3636 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
3637 | } |
3638 | else if (SCM_REALP (y)) | |
73e4de09 | 3639 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 3640 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3641 | { |
3642 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 3643 | if (isnan (xx)) |
a5f0b599 | 3644 | return SCM_BOOL_F; |
2e65b52f | 3645 | if (isinf (xx)) |
73e4de09 | 3646 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
3647 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3648 | goto again; | |
3649 | } | |
f92e85f7 | 3650 | else |
8a1f4f98 | 3651 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
3652 | } |
3653 | else if (SCM_FRACTIONP (x)) | |
3654 | { | |
e11e83f3 | 3655 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
3656 | { |
3657 | /* "a/b < y" becomes "a < y*b" */ | |
3658 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
3659 | x = SCM_FRACTION_NUMERATOR (x); | |
3660 | goto again; | |
3661 | } | |
f92e85f7 | 3662 | else if (SCM_REALP (y)) |
a5f0b599 KR |
3663 | { |
3664 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 3665 | if (isnan (yy)) |
a5f0b599 | 3666 | return SCM_BOOL_F; |
2e65b52f | 3667 | if (isinf (yy)) |
73e4de09 | 3668 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
3669 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3670 | goto again; | |
3671 | } | |
f92e85f7 | 3672 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3673 | { |
3674 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
3675 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
3676 | SCM_FRACTION_DENOMINATOR (y)); | |
3677 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
3678 | SCM_FRACTION_DENOMINATOR (x)); | |
3679 | x = new_x; | |
3680 | y = new_y; | |
3681 | goto again; | |
3682 | } | |
0aacf84e | 3683 | else |
8a1f4f98 | 3684 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 3685 | } |
0aacf84e | 3686 | else |
8a1f4f98 | 3687 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
3688 | } |
3689 | ||
3690 | ||
8a1f4f98 AW |
3691 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
3692 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
3693 | (SCM x, SCM y, SCM rest), | |
3694 | "Return @code{#t} if the list of parameters is monotonically\n" | |
3695 | "decreasing.") | |
3696 | #define FUNC_NAME s_scm_i_num_gr_p | |
3697 | { | |
3698 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3699 | return SCM_BOOL_T; | |
3700 | while (!scm_is_null (rest)) | |
3701 | { | |
3702 | if (scm_is_false (scm_gr_p (x, y))) | |
3703 | return SCM_BOOL_F; | |
3704 | x = y; | |
3705 | y = scm_car (rest); | |
3706 | rest = scm_cdr (rest); | |
3707 | } | |
3708 | return scm_gr_p (x, y); | |
3709 | } | |
3710 | #undef FUNC_NAME | |
3711 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
3712 | SCM |
3713 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3714 | { |
c76b1eaf | 3715 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 3716 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 3717 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 3718 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
3719 | else |
3720 | return scm_less_p (y, x); | |
0f2d19dd | 3721 | } |
1bbd0b84 | 3722 | #undef FUNC_NAME |
0f2d19dd JB |
3723 | |
3724 | ||
8a1f4f98 AW |
3725 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
3726 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
3727 | (SCM x, SCM y, SCM rest), | |
3728 | "Return @code{#t} if the list of parameters is monotonically\n" | |
3729 | "non-decreasing.") | |
3730 | #define FUNC_NAME s_scm_i_num_leq_p | |
3731 | { | |
3732 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3733 | return SCM_BOOL_T; | |
3734 | while (!scm_is_null (rest)) | |
3735 | { | |
3736 | if (scm_is_false (scm_leq_p (x, y))) | |
3737 | return SCM_BOOL_F; | |
3738 | x = y; | |
3739 | y = scm_car (rest); | |
3740 | rest = scm_cdr (rest); | |
3741 | } | |
3742 | return scm_leq_p (x, y); | |
3743 | } | |
3744 | #undef FUNC_NAME | |
3745 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
3746 | SCM |
3747 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3748 | { |
c76b1eaf | 3749 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 3750 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 3751 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 3752 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 3753 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3754 | return SCM_BOOL_F; |
c76b1eaf | 3755 | else |
73e4de09 | 3756 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 3757 | } |
1bbd0b84 | 3758 | #undef FUNC_NAME |
0f2d19dd JB |
3759 | |
3760 | ||
8a1f4f98 AW |
3761 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
3762 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
3763 | (SCM x, SCM y, SCM rest), | |
3764 | "Return @code{#t} if the list of parameters is monotonically\n" | |
3765 | "non-increasing.") | |
3766 | #define FUNC_NAME s_scm_i_num_geq_p | |
3767 | { | |
3768 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3769 | return SCM_BOOL_T; | |
3770 | while (!scm_is_null (rest)) | |
3771 | { | |
3772 | if (scm_is_false (scm_geq_p (x, y))) | |
3773 | return SCM_BOOL_F; | |
3774 | x = y; | |
3775 | y = scm_car (rest); | |
3776 | rest = scm_cdr (rest); | |
3777 | } | |
3778 | return scm_geq_p (x, y); | |
3779 | } | |
3780 | #undef FUNC_NAME | |
3781 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
3782 | SCM |
3783 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3784 | { |
c76b1eaf | 3785 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 3786 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 3787 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 3788 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 3789 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3790 | return SCM_BOOL_F; |
c76b1eaf | 3791 | else |
73e4de09 | 3792 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 3793 | } |
1bbd0b84 | 3794 | #undef FUNC_NAME |
0f2d19dd JB |
3795 | |
3796 | ||
152f82bf | 3797 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3798 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3799 | * "zero." | |
3800 | */ | |
0f2d19dd | 3801 | SCM |
6e8d25a6 | 3802 | scm_zero_p (SCM z) |
0f2d19dd | 3803 | { |
e11e83f3 | 3804 | if (SCM_I_INUMP (z)) |
bc36d050 | 3805 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 3806 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 3807 | return SCM_BOOL_F; |
0aacf84e | 3808 | else if (SCM_REALP (z)) |
73e4de09 | 3809 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 3810 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 3811 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 3812 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
3813 | else if (SCM_FRACTIONP (z)) |
3814 | return SCM_BOOL_F; | |
0aacf84e | 3815 | else |
c2ff8ab0 | 3816 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); |
0f2d19dd JB |
3817 | } |
3818 | ||
3819 | ||
152f82bf | 3820 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3821 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3822 | * "zero." | |
3823 | */ | |
0f2d19dd | 3824 | SCM |
6e8d25a6 | 3825 | scm_positive_p (SCM x) |
0f2d19dd | 3826 | { |
e11e83f3 MV |
3827 | if (SCM_I_INUMP (x)) |
3828 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
3829 | else if (SCM_BIGP (x)) |
3830 | { | |
3831 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3832 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3833 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3834 | } |
3835 | else if (SCM_REALP (x)) | |
73e4de09 | 3836 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
3837 | else if (SCM_FRACTIONP (x)) |
3838 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3839 | else |
c2ff8ab0 | 3840 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); |
0f2d19dd JB |
3841 | } |
3842 | ||
3843 | ||
152f82bf | 3844 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3845 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3846 | * "zero." | |
3847 | */ | |
0f2d19dd | 3848 | SCM |
6e8d25a6 | 3849 | scm_negative_p (SCM x) |
0f2d19dd | 3850 | { |
e11e83f3 MV |
3851 | if (SCM_I_INUMP (x)) |
3852 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
3853 | else if (SCM_BIGP (x)) |
3854 | { | |
3855 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3856 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3857 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3858 | } |
3859 | else if (SCM_REALP (x)) | |
73e4de09 | 3860 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
3861 | else if (SCM_FRACTIONP (x)) |
3862 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3863 | else |
c2ff8ab0 | 3864 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); |
0f2d19dd JB |
3865 | } |
3866 | ||
3867 | ||
2a06f791 KR |
3868 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
3869 | required by r5rs. On that basis, for exact/inexact combinations the | |
3870 | exact is converted to inexact to compare and possibly return. This is | |
3871 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
3872 | its test, such trouble is not required for min and max. */ | |
3873 | ||
78d3deb1 AW |
3874 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
3875 | (SCM x, SCM y, SCM rest), | |
3876 | "Return the maximum of all parameter values.") | |
3877 | #define FUNC_NAME s_scm_i_max | |
3878 | { | |
3879 | while (!scm_is_null (rest)) | |
3880 | { x = scm_max (x, y); | |
3881 | y = scm_car (rest); | |
3882 | rest = scm_cdr (rest); | |
3883 | } | |
3884 | return scm_max (x, y); | |
3885 | } | |
3886 | #undef FUNC_NAME | |
3887 | ||
3888 | #define s_max s_scm_i_max | |
3889 | #define g_max g_scm_i_max | |
3890 | ||
0f2d19dd | 3891 | SCM |
6e8d25a6 | 3892 | scm_max (SCM x, SCM y) |
0f2d19dd | 3893 | { |
0aacf84e MD |
3894 | if (SCM_UNBNDP (y)) |
3895 | { | |
3896 | if (SCM_UNBNDP (x)) | |
3897 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 3898 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3899 | return x; |
3900 | else | |
3901 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3902 | } |
f4c627b3 | 3903 | |
e11e83f3 | 3904 | if (SCM_I_INUMP (x)) |
0aacf84e | 3905 | { |
e25f3727 | 3906 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 3907 | if (SCM_I_INUMP (y)) |
0aacf84e | 3908 | { |
e25f3727 | 3909 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
3910 | return (xx < yy) ? y : x; |
3911 | } | |
3912 | else if (SCM_BIGP (y)) | |
3913 | { | |
3914 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3915 | scm_remember_upto_here_1 (y); | |
3916 | return (sgn < 0) ? x : y; | |
3917 | } | |
3918 | else if (SCM_REALP (y)) | |
3919 | { | |
3920 | double z = xx; | |
3921 | /* if y==NaN then ">" is false and we return NaN */ | |
55f26379 | 3922 | return (z > SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3923 | } |
f92e85f7 MV |
3924 | else if (SCM_FRACTIONP (y)) |
3925 | { | |
e4bc5d6c | 3926 | use_less: |
73e4de09 | 3927 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 3928 | } |
0aacf84e MD |
3929 | else |
3930 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3931 | } |
0aacf84e MD |
3932 | else if (SCM_BIGP (x)) |
3933 | { | |
e11e83f3 | 3934 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3935 | { |
3936 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3937 | scm_remember_upto_here_1 (x); | |
3938 | return (sgn < 0) ? y : x; | |
3939 | } | |
3940 | else if (SCM_BIGP (y)) | |
3941 | { | |
3942 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3943 | scm_remember_upto_here_2 (x, y); | |
3944 | return (cmp > 0) ? x : y; | |
3945 | } | |
3946 | else if (SCM_REALP (y)) | |
3947 | { | |
2a06f791 KR |
3948 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
3949 | double xx, yy; | |
3950 | big_real: | |
3951 | xx = scm_i_big2dbl (x); | |
3952 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3953 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 3954 | } |
f92e85f7 MV |
3955 | else if (SCM_FRACTIONP (y)) |
3956 | { | |
e4bc5d6c | 3957 | goto use_less; |
f92e85f7 | 3958 | } |
0aacf84e MD |
3959 | else |
3960 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 3961 | } |
0aacf84e MD |
3962 | else if (SCM_REALP (x)) |
3963 | { | |
e11e83f3 | 3964 | if (SCM_I_INUMP (y)) |
0aacf84e | 3965 | { |
e11e83f3 | 3966 | double z = SCM_I_INUM (y); |
0aacf84e | 3967 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3968 | return (SCM_REAL_VALUE (x) < z) ? scm_from_double (z) : x; |
0aacf84e MD |
3969 | } |
3970 | else if (SCM_BIGP (y)) | |
3971 | { | |
b6f8f763 | 3972 | SCM_SWAP (x, y); |
2a06f791 | 3973 | goto big_real; |
0aacf84e MD |
3974 | } |
3975 | else if (SCM_REALP (y)) | |
3976 | { | |
3977 | /* if x==NaN then our explicit check means we return NaN | |
3978 | if y==NaN then ">" is false and we return NaN | |
3979 | calling isnan is unavoidable, since it's the only way to know | |
3980 | which of x or y causes any compares to be false */ | |
3981 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 3982 | return (isnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y; |
0aacf84e | 3983 | } |
f92e85f7 MV |
3984 | else if (SCM_FRACTIONP (y)) |
3985 | { | |
3986 | double yy = scm_i_fraction2double (y); | |
3987 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3988 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
3989 | } |
3990 | else | |
3991 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3992 | } | |
3993 | else if (SCM_FRACTIONP (x)) | |
3994 | { | |
e11e83f3 | 3995 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3996 | { |
e4bc5d6c | 3997 | goto use_less; |
f92e85f7 MV |
3998 | } |
3999 | else if (SCM_BIGP (y)) | |
4000 | { | |
e4bc5d6c | 4001 | goto use_less; |
f92e85f7 MV |
4002 | } |
4003 | else if (SCM_REALP (y)) | |
4004 | { | |
4005 | double xx = scm_i_fraction2double (x); | |
55f26379 | 4006 | return (xx < SCM_REAL_VALUE (y)) ? y : scm_from_double (xx); |
f92e85f7 MV |
4007 | } |
4008 | else if (SCM_FRACTIONP (y)) | |
4009 | { | |
e4bc5d6c | 4010 | goto use_less; |
f92e85f7 | 4011 | } |
0aacf84e MD |
4012 | else |
4013 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 4014 | } |
0aacf84e | 4015 | else |
f4c627b3 | 4016 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
4017 | } |
4018 | ||
4019 | ||
78d3deb1 AW |
4020 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
4021 | (SCM x, SCM y, SCM rest), | |
4022 | "Return the minimum of all parameter values.") | |
4023 | #define FUNC_NAME s_scm_i_min | |
4024 | { | |
4025 | while (!scm_is_null (rest)) | |
4026 | { x = scm_min (x, y); | |
4027 | y = scm_car (rest); | |
4028 | rest = scm_cdr (rest); | |
4029 | } | |
4030 | return scm_min (x, y); | |
4031 | } | |
4032 | #undef FUNC_NAME | |
4033 | ||
4034 | #define s_min s_scm_i_min | |
4035 | #define g_min g_scm_i_min | |
4036 | ||
0f2d19dd | 4037 | SCM |
6e8d25a6 | 4038 | scm_min (SCM x, SCM y) |
0f2d19dd | 4039 | { |
0aacf84e MD |
4040 | if (SCM_UNBNDP (y)) |
4041 | { | |
4042 | if (SCM_UNBNDP (x)) | |
4043 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 4044 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
4045 | return x; |
4046 | else | |
4047 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 4048 | } |
f4c627b3 | 4049 | |
e11e83f3 | 4050 | if (SCM_I_INUMP (x)) |
0aacf84e | 4051 | { |
e25f3727 | 4052 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 4053 | if (SCM_I_INUMP (y)) |
0aacf84e | 4054 | { |
e25f3727 | 4055 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
4056 | return (xx < yy) ? x : y; |
4057 | } | |
4058 | else if (SCM_BIGP (y)) | |
4059 | { | |
4060 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4061 | scm_remember_upto_here_1 (y); | |
4062 | return (sgn < 0) ? y : x; | |
4063 | } | |
4064 | else if (SCM_REALP (y)) | |
4065 | { | |
4066 | double z = xx; | |
4067 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 4068 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 4069 | } |
f92e85f7 MV |
4070 | else if (SCM_FRACTIONP (y)) |
4071 | { | |
e4bc5d6c | 4072 | use_less: |
73e4de09 | 4073 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 4074 | } |
0aacf84e MD |
4075 | else |
4076 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 4077 | } |
0aacf84e MD |
4078 | else if (SCM_BIGP (x)) |
4079 | { | |
e11e83f3 | 4080 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4081 | { |
4082 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4083 | scm_remember_upto_here_1 (x); | |
4084 | return (sgn < 0) ? x : y; | |
4085 | } | |
4086 | else if (SCM_BIGP (y)) | |
4087 | { | |
4088 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4089 | scm_remember_upto_here_2 (x, y); | |
4090 | return (cmp > 0) ? y : x; | |
4091 | } | |
4092 | else if (SCM_REALP (y)) | |
4093 | { | |
2a06f791 KR |
4094 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
4095 | double xx, yy; | |
4096 | big_real: | |
4097 | xx = scm_i_big2dbl (x); | |
4098 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 4099 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 4100 | } |
f92e85f7 MV |
4101 | else if (SCM_FRACTIONP (y)) |
4102 | { | |
e4bc5d6c | 4103 | goto use_less; |
f92e85f7 | 4104 | } |
0aacf84e MD |
4105 | else |
4106 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 4107 | } |
0aacf84e MD |
4108 | else if (SCM_REALP (x)) |
4109 | { | |
e11e83f3 | 4110 | if (SCM_I_INUMP (y)) |
0aacf84e | 4111 | { |
e11e83f3 | 4112 | double z = SCM_I_INUM (y); |
0aacf84e | 4113 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 4114 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
4115 | } |
4116 | else if (SCM_BIGP (y)) | |
4117 | { | |
b6f8f763 | 4118 | SCM_SWAP (x, y); |
2a06f791 | 4119 | goto big_real; |
0aacf84e MD |
4120 | } |
4121 | else if (SCM_REALP (y)) | |
4122 | { | |
4123 | /* if x==NaN then our explicit check means we return NaN | |
4124 | if y==NaN then "<" is false and we return NaN | |
4125 | calling isnan is unavoidable, since it's the only way to know | |
4126 | which of x or y causes any compares to be false */ | |
4127 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4128 | return (isnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y; |
0aacf84e | 4129 | } |
f92e85f7 MV |
4130 | else if (SCM_FRACTIONP (y)) |
4131 | { | |
4132 | double yy = scm_i_fraction2double (y); | |
4133 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 4134 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 4135 | } |
0aacf84e MD |
4136 | else |
4137 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 4138 | } |
f92e85f7 MV |
4139 | else if (SCM_FRACTIONP (x)) |
4140 | { | |
e11e83f3 | 4141 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4142 | { |
e4bc5d6c | 4143 | goto use_less; |
f92e85f7 MV |
4144 | } |
4145 | else if (SCM_BIGP (y)) | |
4146 | { | |
e4bc5d6c | 4147 | goto use_less; |
f92e85f7 MV |
4148 | } |
4149 | else if (SCM_REALP (y)) | |
4150 | { | |
4151 | double xx = scm_i_fraction2double (x); | |
55f26379 | 4152 | return (SCM_REAL_VALUE (y) < xx) ? y : scm_from_double (xx); |
f92e85f7 MV |
4153 | } |
4154 | else if (SCM_FRACTIONP (y)) | |
4155 | { | |
e4bc5d6c | 4156 | goto use_less; |
f92e85f7 MV |
4157 | } |
4158 | else | |
78d3deb1 | 4159 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 4160 | } |
0aacf84e | 4161 | else |
f4c627b3 | 4162 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
4163 | } |
4164 | ||
4165 | ||
8ccd24f7 AW |
4166 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
4167 | (SCM x, SCM y, SCM rest), | |
4168 | "Return the sum of all parameter values. Return 0 if called without\n" | |
4169 | "any parameters." ) | |
4170 | #define FUNC_NAME s_scm_i_sum | |
4171 | { | |
4172 | while (!scm_is_null (rest)) | |
4173 | { x = scm_sum (x, y); | |
4174 | y = scm_car (rest); | |
4175 | rest = scm_cdr (rest); | |
4176 | } | |
4177 | return scm_sum (x, y); | |
4178 | } | |
4179 | #undef FUNC_NAME | |
4180 | ||
4181 | #define s_sum s_scm_i_sum | |
4182 | #define g_sum g_scm_i_sum | |
4183 | ||
0f2d19dd | 4184 | SCM |
6e8d25a6 | 4185 | scm_sum (SCM x, SCM y) |
0f2d19dd | 4186 | { |
9cc37597 | 4187 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
4188 | { |
4189 | if (SCM_NUMBERP (x)) return x; | |
4190 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 4191 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 4192 | } |
c209c88e | 4193 | |
9cc37597 | 4194 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 4195 | { |
9cc37597 | 4196 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 4197 | { |
e25f3727 AW |
4198 | scm_t_inum xx = SCM_I_INUM (x); |
4199 | scm_t_inum yy = SCM_I_INUM (y); | |
4200 | scm_t_inum z = xx + yy; | |
4201 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
4202 | } |
4203 | else if (SCM_BIGP (y)) | |
4204 | { | |
4205 | SCM_SWAP (x, y); | |
4206 | goto add_big_inum; | |
4207 | } | |
4208 | else if (SCM_REALP (y)) | |
4209 | { | |
e25f3727 | 4210 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 4211 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
4212 | } |
4213 | else if (SCM_COMPLEXP (y)) | |
4214 | { | |
e25f3727 | 4215 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 4216 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
4217 | SCM_COMPLEX_IMAG (y)); |
4218 | } | |
f92e85f7 | 4219 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4220 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
4221 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
4222 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
4223 | else |
4224 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
4225 | } else if (SCM_BIGP (x)) |
4226 | { | |
e11e83f3 | 4227 | if (SCM_I_INUMP (y)) |
0aacf84e | 4228 | { |
e25f3727 | 4229 | scm_t_inum inum; |
0aacf84e MD |
4230 | int bigsgn; |
4231 | add_big_inum: | |
e11e83f3 | 4232 | inum = SCM_I_INUM (y); |
0aacf84e MD |
4233 | if (inum == 0) |
4234 | return x; | |
4235 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4236 | if (inum < 0) | |
4237 | { | |
4238 | SCM result = scm_i_mkbig (); | |
4239 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
4240 | scm_remember_upto_here_1 (x); | |
4241 | /* we know the result will have to be a bignum */ | |
4242 | if (bigsgn == -1) | |
4243 | return result; | |
4244 | return scm_i_normbig (result); | |
4245 | } | |
4246 | else | |
4247 | { | |
4248 | SCM result = scm_i_mkbig (); | |
4249 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
4250 | scm_remember_upto_here_1 (x); | |
4251 | /* we know the result will have to be a bignum */ | |
4252 | if (bigsgn == 1) | |
4253 | return result; | |
4254 | return scm_i_normbig (result); | |
4255 | } | |
4256 | } | |
4257 | else if (SCM_BIGP (y)) | |
4258 | { | |
4259 | SCM result = scm_i_mkbig (); | |
4260 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4261 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4262 | mpz_add (SCM_I_BIG_MPZ (result), | |
4263 | SCM_I_BIG_MPZ (x), | |
4264 | SCM_I_BIG_MPZ (y)); | |
4265 | scm_remember_upto_here_2 (x, y); | |
4266 | /* we know the result will have to be a bignum */ | |
4267 | if (sgn_x == sgn_y) | |
4268 | return result; | |
4269 | return scm_i_normbig (result); | |
4270 | } | |
4271 | else if (SCM_REALP (y)) | |
4272 | { | |
4273 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
4274 | scm_remember_upto_here_1 (x); | |
55f26379 | 4275 | return scm_from_double (result); |
0aacf84e MD |
4276 | } |
4277 | else if (SCM_COMPLEXP (y)) | |
4278 | { | |
4279 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4280 | + SCM_COMPLEX_REAL (y)); | |
4281 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4282 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4283 | } |
f92e85f7 | 4284 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4285 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
4286 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
4287 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4288 | else |
4289 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 4290 | } |
0aacf84e MD |
4291 | else if (SCM_REALP (x)) |
4292 | { | |
e11e83f3 | 4293 | if (SCM_I_INUMP (y)) |
55f26379 | 4294 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
4295 | else if (SCM_BIGP (y)) |
4296 | { | |
4297 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
4298 | scm_remember_upto_here_1 (y); | |
55f26379 | 4299 | return scm_from_double (result); |
0aacf84e MD |
4300 | } |
4301 | else if (SCM_REALP (y)) | |
55f26379 | 4302 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 4303 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4304 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4305 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4306 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4307 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
4308 | else |
4309 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 4310 | } |
0aacf84e MD |
4311 | else if (SCM_COMPLEXP (x)) |
4312 | { | |
e11e83f3 | 4313 | if (SCM_I_INUMP (y)) |
8507ec80 | 4314 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
4315 | SCM_COMPLEX_IMAG (x)); |
4316 | else if (SCM_BIGP (y)) | |
4317 | { | |
4318 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
4319 | + SCM_COMPLEX_REAL (x)); | |
4320 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4321 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4322 | } |
4323 | else if (SCM_REALP (y)) | |
8507ec80 | 4324 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
4325 | SCM_COMPLEX_IMAG (x)); |
4326 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4327 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4328 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4329 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4330 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
4331 | SCM_COMPLEX_IMAG (x)); |
4332 | else | |
4333 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
4334 | } | |
4335 | else if (SCM_FRACTIONP (x)) | |
4336 | { | |
e11e83f3 | 4337 | if (SCM_I_INUMP (y)) |
cba42c93 | 4338 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4339 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4340 | SCM_FRACTION_DENOMINATOR (x)); | |
4341 | else if (SCM_BIGP (y)) | |
cba42c93 | 4342 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4343 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4344 | SCM_FRACTION_DENOMINATOR (x)); | |
4345 | else if (SCM_REALP (y)) | |
55f26379 | 4346 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 4347 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4348 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
4349 | SCM_COMPLEX_IMAG (y)); |
4350 | else if (SCM_FRACTIONP (y)) | |
4351 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 4352 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4353 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4354 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4355 | else |
4356 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 4357 | } |
0aacf84e | 4358 | else |
98cb6e75 | 4359 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
4360 | } |
4361 | ||
4362 | ||
40882e3d KR |
4363 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
4364 | (SCM x), | |
4365 | "Return @math{@var{x}+1}.") | |
4366 | #define FUNC_NAME s_scm_oneplus | |
4367 | { | |
cff5fa33 | 4368 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
4369 | } |
4370 | #undef FUNC_NAME | |
4371 | ||
4372 | ||
78d3deb1 AW |
4373 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
4374 | (SCM x, SCM y, SCM rest), | |
4375 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
4376 | "the sum of all but the first argument are subtracted from the first\n" | |
4377 | "argument.") | |
4378 | #define FUNC_NAME s_scm_i_difference | |
4379 | { | |
4380 | while (!scm_is_null (rest)) | |
4381 | { x = scm_difference (x, y); | |
4382 | y = scm_car (rest); | |
4383 | rest = scm_cdr (rest); | |
4384 | } | |
4385 | return scm_difference (x, y); | |
4386 | } | |
4387 | #undef FUNC_NAME | |
4388 | ||
4389 | #define s_difference s_scm_i_difference | |
4390 | #define g_difference g_scm_i_difference | |
4391 | ||
0f2d19dd | 4392 | SCM |
6e8d25a6 | 4393 | scm_difference (SCM x, SCM y) |
78d3deb1 | 4394 | #define FUNC_NAME s_difference |
0f2d19dd | 4395 | { |
9cc37597 | 4396 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
4397 | { |
4398 | if (SCM_UNBNDP (x)) | |
4399 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
4400 | else | |
e11e83f3 | 4401 | if (SCM_I_INUMP (x)) |
ca46fb90 | 4402 | { |
e25f3727 | 4403 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 4404 | if (SCM_FIXABLE (xx)) |
d956fa6f | 4405 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 4406 | else |
e25f3727 | 4407 | return scm_i_inum2big (xx); |
ca46fb90 RB |
4408 | } |
4409 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
4410 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
4411 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
4412 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
4413 | else if (SCM_REALP (x)) | |
55f26379 | 4414 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 4415 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 4416 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 4417 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 4418 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4419 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 4420 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
4421 | else |
4422 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 4423 | } |
ca46fb90 | 4424 | |
9cc37597 | 4425 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 4426 | { |
9cc37597 | 4427 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4428 | { |
e25f3727 AW |
4429 | scm_t_inum xx = SCM_I_INUM (x); |
4430 | scm_t_inum yy = SCM_I_INUM (y); | |
4431 | scm_t_inum z = xx - yy; | |
0aacf84e | 4432 | if (SCM_FIXABLE (z)) |
d956fa6f | 4433 | return SCM_I_MAKINUM (z); |
0aacf84e | 4434 | else |
e25f3727 | 4435 | return scm_i_inum2big (z); |
0aacf84e MD |
4436 | } |
4437 | else if (SCM_BIGP (y)) | |
4438 | { | |
4439 | /* inum-x - big-y */ | |
e25f3727 | 4440 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 4441 | |
0aacf84e | 4442 | if (xx == 0) |
b5c40589 MW |
4443 | { |
4444 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
4445 | bignum, but negating that gives a fixnum. */ | |
4446 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
4447 | } | |
0aacf84e MD |
4448 | else |
4449 | { | |
4450 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4451 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4452 | |
0aacf84e MD |
4453 | if (xx >= 0) |
4454 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
4455 | else | |
4456 | { | |
4457 | /* x - y == -(y + -x) */ | |
4458 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
4459 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4460 | } | |
4461 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 4462 | |
0aacf84e MD |
4463 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
4464 | /* we know the result will have to be a bignum */ | |
4465 | return result; | |
4466 | else | |
4467 | return scm_i_normbig (result); | |
4468 | } | |
4469 | } | |
4470 | else if (SCM_REALP (y)) | |
4471 | { | |
e25f3727 | 4472 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 4473 | return scm_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
4474 | } |
4475 | else if (SCM_COMPLEXP (y)) | |
4476 | { | |
e25f3727 | 4477 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 4478 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4479 | - SCM_COMPLEX_IMAG (y)); |
4480 | } | |
f92e85f7 MV |
4481 | else if (SCM_FRACTIONP (y)) |
4482 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 4483 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4484 | SCM_FRACTION_NUMERATOR (y)), |
4485 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4486 | else |
4487 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 4488 | } |
0aacf84e MD |
4489 | else if (SCM_BIGP (x)) |
4490 | { | |
e11e83f3 | 4491 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4492 | { |
4493 | /* big-x - inum-y */ | |
e25f3727 | 4494 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 4495 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 4496 | |
0aacf84e MD |
4497 | scm_remember_upto_here_1 (x); |
4498 | if (sgn_x == 0) | |
c71b0706 | 4499 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 4500 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
4501 | else |
4502 | { | |
4503 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4504 | |
708f22c6 KR |
4505 | if (yy >= 0) |
4506 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
4507 | else | |
4508 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 4509 | scm_remember_upto_here_1 (x); |
ca46fb90 | 4510 | |
0aacf84e MD |
4511 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
4512 | /* we know the result will have to be a bignum */ | |
4513 | return result; | |
4514 | else | |
4515 | return scm_i_normbig (result); | |
4516 | } | |
4517 | } | |
4518 | else if (SCM_BIGP (y)) | |
4519 | { | |
4520 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4521 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4522 | SCM result = scm_i_mkbig (); | |
4523 | mpz_sub (SCM_I_BIG_MPZ (result), | |
4524 | SCM_I_BIG_MPZ (x), | |
4525 | SCM_I_BIG_MPZ (y)); | |
4526 | scm_remember_upto_here_2 (x, y); | |
4527 | /* we know the result will have to be a bignum */ | |
4528 | if ((sgn_x == 1) && (sgn_y == -1)) | |
4529 | return result; | |
4530 | if ((sgn_x == -1) && (sgn_y == 1)) | |
4531 | return result; | |
4532 | return scm_i_normbig (result); | |
4533 | } | |
4534 | else if (SCM_REALP (y)) | |
4535 | { | |
4536 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
4537 | scm_remember_upto_here_1 (x); | |
55f26379 | 4538 | return scm_from_double (result); |
0aacf84e MD |
4539 | } |
4540 | else if (SCM_COMPLEXP (y)) | |
4541 | { | |
4542 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4543 | - SCM_COMPLEX_REAL (y)); | |
4544 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4545 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4546 | } |
f92e85f7 | 4547 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4548 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4549 | SCM_FRACTION_NUMERATOR (y)), |
4550 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 4551 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 4552 | } |
0aacf84e MD |
4553 | else if (SCM_REALP (x)) |
4554 | { | |
e11e83f3 | 4555 | if (SCM_I_INUMP (y)) |
55f26379 | 4556 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
4557 | else if (SCM_BIGP (y)) |
4558 | { | |
4559 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4560 | scm_remember_upto_here_1 (x); | |
55f26379 | 4561 | return scm_from_double (result); |
0aacf84e MD |
4562 | } |
4563 | else if (SCM_REALP (y)) | |
55f26379 | 4564 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 4565 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4566 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4567 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4568 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4569 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
4570 | else |
4571 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4572 | } |
0aacf84e MD |
4573 | else if (SCM_COMPLEXP (x)) |
4574 | { | |
e11e83f3 | 4575 | if (SCM_I_INUMP (y)) |
8507ec80 | 4576 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
4577 | SCM_COMPLEX_IMAG (x)); |
4578 | else if (SCM_BIGP (y)) | |
4579 | { | |
4580 | double real_part = (SCM_COMPLEX_REAL (x) | |
4581 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
4582 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4583 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
4584 | } |
4585 | else if (SCM_REALP (y)) | |
8507ec80 | 4586 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
4587 | SCM_COMPLEX_IMAG (x)); |
4588 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4589 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4590 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4591 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4592 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
4593 | SCM_COMPLEX_IMAG (x)); |
4594 | else | |
4595 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
4596 | } | |
4597 | else if (SCM_FRACTIONP (x)) | |
4598 | { | |
e11e83f3 | 4599 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4600 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 4601 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4602 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4603 | SCM_FRACTION_DENOMINATOR (x)); | |
4604 | else if (SCM_BIGP (y)) | |
cba42c93 | 4605 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4606 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4607 | SCM_FRACTION_DENOMINATOR (x)); | |
4608 | else if (SCM_REALP (y)) | |
55f26379 | 4609 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 4610 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4611 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4612 | -SCM_COMPLEX_IMAG (y)); |
4613 | else if (SCM_FRACTIONP (y)) | |
4614 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 4615 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4616 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4617 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4618 | else |
4619 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4620 | } |
0aacf84e | 4621 | else |
98cb6e75 | 4622 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 4623 | } |
c05e97b7 | 4624 | #undef FUNC_NAME |
0f2d19dd | 4625 | |
ca46fb90 | 4626 | |
40882e3d KR |
4627 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
4628 | (SCM x), | |
4629 | "Return @math{@var{x}-1}.") | |
4630 | #define FUNC_NAME s_scm_oneminus | |
4631 | { | |
cff5fa33 | 4632 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
4633 | } |
4634 | #undef FUNC_NAME | |
4635 | ||
4636 | ||
78d3deb1 AW |
4637 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
4638 | (SCM x, SCM y, SCM rest), | |
4639 | "Return the product of all arguments. If called without arguments,\n" | |
4640 | "1 is returned.") | |
4641 | #define FUNC_NAME s_scm_i_product | |
4642 | { | |
4643 | while (!scm_is_null (rest)) | |
4644 | { x = scm_product (x, y); | |
4645 | y = scm_car (rest); | |
4646 | rest = scm_cdr (rest); | |
4647 | } | |
4648 | return scm_product (x, y); | |
4649 | } | |
4650 | #undef FUNC_NAME | |
4651 | ||
4652 | #define s_product s_scm_i_product | |
4653 | #define g_product g_scm_i_product | |
4654 | ||
0f2d19dd | 4655 | SCM |
6e8d25a6 | 4656 | scm_product (SCM x, SCM y) |
0f2d19dd | 4657 | { |
9cc37597 | 4658 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
4659 | { |
4660 | if (SCM_UNBNDP (x)) | |
d956fa6f | 4661 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
4662 | else if (SCM_NUMBERP (x)) |
4663 | return x; | |
4664 | else | |
4665 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 4666 | } |
ca46fb90 | 4667 | |
9cc37597 | 4668 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 4669 | { |
e25f3727 | 4670 | scm_t_inum xx; |
f4c627b3 | 4671 | |
0aacf84e | 4672 | intbig: |
e11e83f3 | 4673 | xx = SCM_I_INUM (x); |
f4c627b3 | 4674 | |
0aacf84e MD |
4675 | switch (xx) |
4676 | { | |
ca46fb90 RB |
4677 | case 0: return x; break; |
4678 | case 1: return y; break; | |
b5c40589 MW |
4679 | /* |
4680 | * The following case (x = -1) is important for more than | |
4681 | * just optimization. It handles the case of negating | |
4682 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), | |
4683 | * which is a bignum that must be changed back into a fixnum. | |
4684 | * Failure to do so will cause the following to return #f: | |
4685 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
4686 | */ | |
4687 | case -1: | |
4688 | return scm_difference(y, SCM_UNDEFINED); | |
4689 | break; | |
0aacf84e | 4690 | } |
f4c627b3 | 4691 | |
9cc37597 | 4692 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4693 | { |
e25f3727 AW |
4694 | scm_t_inum yy = SCM_I_INUM (y); |
4695 | scm_t_inum kk = xx * yy; | |
d956fa6f | 4696 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 4697 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
4698 | return k; |
4699 | else | |
4700 | { | |
e25f3727 | 4701 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
4702 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
4703 | return scm_i_normbig (result); | |
4704 | } | |
4705 | } | |
4706 | else if (SCM_BIGP (y)) | |
4707 | { | |
4708 | SCM result = scm_i_mkbig (); | |
4709 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
4710 | scm_remember_upto_here_1 (y); | |
4711 | return result; | |
4712 | } | |
4713 | else if (SCM_REALP (y)) | |
55f26379 | 4714 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 4715 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4716 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 4717 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4718 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4719 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4720 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4721 | else |
4722 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4723 | } |
0aacf84e MD |
4724 | else if (SCM_BIGP (x)) |
4725 | { | |
e11e83f3 | 4726 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4727 | { |
4728 | SCM_SWAP (x, y); | |
4729 | goto intbig; | |
4730 | } | |
4731 | else if (SCM_BIGP (y)) | |
4732 | { | |
4733 | SCM result = scm_i_mkbig (); | |
4734 | mpz_mul (SCM_I_BIG_MPZ (result), | |
4735 | SCM_I_BIG_MPZ (x), | |
4736 | SCM_I_BIG_MPZ (y)); | |
4737 | scm_remember_upto_here_2 (x, y); | |
4738 | return result; | |
4739 | } | |
4740 | else if (SCM_REALP (y)) | |
4741 | { | |
4742 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
4743 | scm_remember_upto_here_1 (x); | |
55f26379 | 4744 | return scm_from_double (result); |
0aacf84e MD |
4745 | } |
4746 | else if (SCM_COMPLEXP (y)) | |
4747 | { | |
4748 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4749 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4750 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4751 | z * SCM_COMPLEX_IMAG (y)); |
4752 | } | |
f92e85f7 | 4753 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4754 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4755 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4756 | else |
4757 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4758 | } |
0aacf84e MD |
4759 | else if (SCM_REALP (x)) |
4760 | { | |
e11e83f3 | 4761 | if (SCM_I_INUMP (y)) |
23d72566 KR |
4762 | { |
4763 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
4764 | if (scm_is_eq (y, SCM_INUM0)) | |
4765 | return y; | |
4766 | return scm_from_double (SCM_I_INUM (y) * SCM_REAL_VALUE (x)); | |
4767 | } | |
0aacf84e MD |
4768 | else if (SCM_BIGP (y)) |
4769 | { | |
4770 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
4771 | scm_remember_upto_here_1 (y); | |
55f26379 | 4772 | return scm_from_double (result); |
0aacf84e MD |
4773 | } |
4774 | else if (SCM_REALP (y)) | |
55f26379 | 4775 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 4776 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4777 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 4778 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4779 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4780 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
4781 | else |
4782 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4783 | } |
0aacf84e MD |
4784 | else if (SCM_COMPLEXP (x)) |
4785 | { | |
e11e83f3 | 4786 | if (SCM_I_INUMP (y)) |
23d72566 KR |
4787 | { |
4788 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
4789 | if (scm_is_eq (y, SCM_INUM0)) | |
4790 | return y; | |
4791 | return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x), | |
4792 | SCM_I_INUM (y) * SCM_COMPLEX_IMAG (x)); | |
4793 | } | |
0aacf84e MD |
4794 | else if (SCM_BIGP (y)) |
4795 | { | |
4796 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4797 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4798 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 4799 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4800 | } |
4801 | else if (SCM_REALP (y)) | |
8507ec80 | 4802 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
4803 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
4804 | else if (SCM_COMPLEXP (y)) | |
4805 | { | |
8507ec80 | 4806 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
4807 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
4808 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
4809 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
4810 | } | |
f92e85f7 MV |
4811 | else if (SCM_FRACTIONP (y)) |
4812 | { | |
4813 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4814 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
4815 | yy * SCM_COMPLEX_IMAG (x)); |
4816 | } | |
4817 | else | |
4818 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
4819 | } | |
4820 | else if (SCM_FRACTIONP (x)) | |
4821 | { | |
e11e83f3 | 4822 | if (SCM_I_INUMP (y)) |
cba42c93 | 4823 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4824 | SCM_FRACTION_DENOMINATOR (x)); |
4825 | else if (SCM_BIGP (y)) | |
cba42c93 | 4826 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4827 | SCM_FRACTION_DENOMINATOR (x)); |
4828 | else if (SCM_REALP (y)) | |
55f26379 | 4829 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
4830 | else if (SCM_COMPLEXP (y)) |
4831 | { | |
4832 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 4833 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4834 | xx * SCM_COMPLEX_IMAG (y)); |
4835 | } | |
4836 | else if (SCM_FRACTIONP (y)) | |
4837 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 4838 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4839 | SCM_FRACTION_NUMERATOR (y)), |
4840 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
4841 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4842 | else |
4843 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4844 | } |
0aacf84e | 4845 | else |
f4c627b3 | 4846 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
4847 | } |
4848 | ||
7351e207 MV |
4849 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
4850 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
4851 | #define ALLOW_DIVIDE_BY_ZERO | |
4852 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
4853 | #endif | |
0f2d19dd | 4854 | |
ba74ef4e MV |
4855 | /* The code below for complex division is adapted from the GNU |
4856 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
4857 | this copyright: */ | |
4858 | ||
4859 | /**************************************************************** | |
4860 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
4861 | ||
4862 | Permission to use, copy, modify, and distribute this software | |
4863 | and its documentation for any purpose and without fee is hereby | |
4864 | granted, provided that the above copyright notice appear in all | |
4865 | copies and that both that the copyright notice and this | |
4866 | permission notice and warranty disclaimer appear in supporting | |
4867 | documentation, and that the names of AT&T Bell Laboratories or | |
4868 | Bellcore or any of their entities not be used in advertising or | |
4869 | publicity pertaining to distribution of the software without | |
4870 | specific, written prior permission. | |
4871 | ||
4872 | AT&T and Bellcore disclaim all warranties with regard to this | |
4873 | software, including all implied warranties of merchantability | |
4874 | and fitness. In no event shall AT&T or Bellcore be liable for | |
4875 | any special, indirect or consequential damages or any damages | |
4876 | whatsoever resulting from loss of use, data or profits, whether | |
4877 | in an action of contract, negligence or other tortious action, | |
4878 | arising out of or in connection with the use or performance of | |
4879 | this software. | |
4880 | ****************************************************************/ | |
4881 | ||
78d3deb1 AW |
4882 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
4883 | (SCM x, SCM y, SCM rest), | |
4884 | "Divide the first argument by the product of the remaining\n" | |
4885 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
4886 | "returned.") | |
4887 | #define FUNC_NAME s_scm_i_divide | |
4888 | { | |
4889 | while (!scm_is_null (rest)) | |
4890 | { x = scm_divide (x, y); | |
4891 | y = scm_car (rest); | |
4892 | rest = scm_cdr (rest); | |
4893 | } | |
4894 | return scm_divide (x, y); | |
4895 | } | |
4896 | #undef FUNC_NAME | |
4897 | ||
4898 | #define s_divide s_scm_i_divide | |
4899 | #define g_divide g_scm_i_divide | |
4900 | ||
f92e85f7 | 4901 | static SCM |
78d3deb1 AW |
4902 | do_divide (SCM x, SCM y, int inexact) |
4903 | #define FUNC_NAME s_divide | |
0f2d19dd | 4904 | { |
f8de44c1 DH |
4905 | double a; |
4906 | ||
9cc37597 | 4907 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
4908 | { |
4909 | if (SCM_UNBNDP (x)) | |
4910 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 4911 | else if (SCM_I_INUMP (x)) |
0aacf84e | 4912 | { |
e25f3727 | 4913 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
4914 | if (xx == 1 || xx == -1) |
4915 | return x; | |
7351e207 | 4916 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4917 | else if (xx == 0) |
4918 | scm_num_overflow (s_divide); | |
7351e207 | 4919 | #endif |
0aacf84e | 4920 | else |
f92e85f7 MV |
4921 | { |
4922 | if (inexact) | |
55f26379 | 4923 | return scm_from_double (1.0 / (double) xx); |
cff5fa33 | 4924 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 4925 | } |
0aacf84e MD |
4926 | } |
4927 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
4928 | { |
4929 | if (inexact) | |
55f26379 | 4930 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cff5fa33 | 4931 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 4932 | } |
0aacf84e MD |
4933 | else if (SCM_REALP (x)) |
4934 | { | |
4935 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 4936 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4937 | if (xx == 0.0) |
4938 | scm_num_overflow (s_divide); | |
4939 | else | |
7351e207 | 4940 | #endif |
55f26379 | 4941 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
4942 | } |
4943 | else if (SCM_COMPLEXP (x)) | |
4944 | { | |
4945 | double r = SCM_COMPLEX_REAL (x); | |
4946 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 4947 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
4948 | { |
4949 | double t = r / i; | |
4950 | double d = i * (1.0 + t * t); | |
8507ec80 | 4951 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
4952 | } |
4953 | else | |
4954 | { | |
4955 | double t = i / r; | |
4956 | double d = r * (1.0 + t * t); | |
8507ec80 | 4957 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
4958 | } |
4959 | } | |
f92e85f7 | 4960 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4961 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 4962 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
4963 | else |
4964 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 4965 | } |
f8de44c1 | 4966 | |
9cc37597 | 4967 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 4968 | { |
e25f3727 | 4969 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 4970 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4971 | { |
e25f3727 | 4972 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
4973 | if (yy == 0) |
4974 | { | |
7351e207 | 4975 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4976 | scm_num_overflow (s_divide); |
7351e207 | 4977 | #else |
55f26379 | 4978 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 4979 | #endif |
0aacf84e MD |
4980 | } |
4981 | else if (xx % yy != 0) | |
f92e85f7 MV |
4982 | { |
4983 | if (inexact) | |
55f26379 | 4984 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 4985 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4986 | } |
0aacf84e MD |
4987 | else |
4988 | { | |
e25f3727 | 4989 | scm_t_inum z = xx / yy; |
0aacf84e | 4990 | if (SCM_FIXABLE (z)) |
d956fa6f | 4991 | return SCM_I_MAKINUM (z); |
0aacf84e | 4992 | else |
e25f3727 | 4993 | return scm_i_inum2big (z); |
0aacf84e | 4994 | } |
f872b822 | 4995 | } |
0aacf84e | 4996 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
4997 | { |
4998 | if (inexact) | |
55f26379 | 4999 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 5000 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 5001 | } |
0aacf84e MD |
5002 | else if (SCM_REALP (y)) |
5003 | { | |
5004 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5005 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5006 | if (yy == 0.0) |
5007 | scm_num_overflow (s_divide); | |
5008 | else | |
7351e207 | 5009 | #endif |
55f26379 | 5010 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 5011 | } |
0aacf84e MD |
5012 | else if (SCM_COMPLEXP (y)) |
5013 | { | |
5014 | a = xx; | |
5015 | complex_div: /* y _must_ be a complex number */ | |
5016 | { | |
5017 | double r = SCM_COMPLEX_REAL (y); | |
5018 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 5019 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
5020 | { |
5021 | double t = r / i; | |
5022 | double d = i * (1.0 + t * t); | |
8507ec80 | 5023 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
5024 | } |
5025 | else | |
5026 | { | |
5027 | double t = i / r; | |
5028 | double d = r * (1.0 + t * t); | |
8507ec80 | 5029 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
5030 | } |
5031 | } | |
5032 | } | |
f92e85f7 MV |
5033 | else if (SCM_FRACTIONP (y)) |
5034 | /* a / b/c = ac / b */ | |
cba42c93 | 5035 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 5036 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
5037 | else |
5038 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 5039 | } |
0aacf84e MD |
5040 | else if (SCM_BIGP (x)) |
5041 | { | |
e11e83f3 | 5042 | if (SCM_I_INUMP (y)) |
0aacf84e | 5043 | { |
e25f3727 | 5044 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
5045 | if (yy == 0) |
5046 | { | |
7351e207 | 5047 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 5048 | scm_num_overflow (s_divide); |
7351e207 | 5049 | #else |
0aacf84e MD |
5050 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
5051 | scm_remember_upto_here_1 (x); | |
5052 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 5053 | #endif |
0aacf84e MD |
5054 | } |
5055 | else if (yy == 1) | |
5056 | return x; | |
5057 | else | |
5058 | { | |
5059 | /* FIXME: HMM, what are the relative performance issues here? | |
5060 | We need to test. Is it faster on average to test | |
5061 | divisible_p, then perform whichever operation, or is it | |
5062 | faster to perform the integer div opportunistically and | |
5063 | switch to real if there's a remainder? For now we take the | |
5064 | middle ground: test, then if divisible, use the faster div | |
5065 | func. */ | |
5066 | ||
e25f3727 | 5067 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
5068 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
5069 | ||
5070 | if (divisible_p) | |
5071 | { | |
5072 | SCM result = scm_i_mkbig (); | |
5073 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
5074 | scm_remember_upto_here_1 (x); | |
5075 | if (yy < 0) | |
5076 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
5077 | return scm_i_normbig (result); | |
5078 | } | |
5079 | else | |
f92e85f7 MV |
5080 | { |
5081 | if (inexact) | |
55f26379 | 5082 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 5083 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 5084 | } |
0aacf84e MD |
5085 | } |
5086 | } | |
5087 | else if (SCM_BIGP (y)) | |
5088 | { | |
a4955a04 MW |
5089 | /* big_x / big_y */ |
5090 | if (inexact) | |
0aacf84e | 5091 | { |
a4955a04 MW |
5092 | /* It's easily possible for the ratio x/y to fit a double |
5093 | but one or both x and y be too big to fit a double, | |
5094 | hence the use of mpq_get_d rather than converting and | |
5095 | dividing. */ | |
5096 | mpq_t q; | |
5097 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
5098 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
5099 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
5100 | } |
5101 | else | |
5102 | { | |
a4955a04 MW |
5103 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
5104 | SCM_I_BIG_MPZ (y)); | |
5105 | if (divisible_p) | |
5106 | { | |
5107 | SCM result = scm_i_mkbig (); | |
5108 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
5109 | SCM_I_BIG_MPZ (x), | |
5110 | SCM_I_BIG_MPZ (y)); | |
5111 | scm_remember_upto_here_2 (x, y); | |
5112 | return scm_i_normbig (result); | |
5113 | } | |
5114 | else | |
5115 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
5116 | } |
5117 | } | |
5118 | else if (SCM_REALP (y)) | |
5119 | { | |
5120 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5121 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5122 | if (yy == 0.0) |
5123 | scm_num_overflow (s_divide); | |
5124 | else | |
7351e207 | 5125 | #endif |
55f26379 | 5126 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
5127 | } |
5128 | else if (SCM_COMPLEXP (y)) | |
5129 | { | |
5130 | a = scm_i_big2dbl (x); | |
5131 | goto complex_div; | |
5132 | } | |
f92e85f7 | 5133 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5134 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 5135 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
5136 | else |
5137 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 5138 | } |
0aacf84e MD |
5139 | else if (SCM_REALP (x)) |
5140 | { | |
5141 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 5142 | if (SCM_I_INUMP (y)) |
0aacf84e | 5143 | { |
e25f3727 | 5144 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 5145 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
5146 | if (yy == 0) |
5147 | scm_num_overflow (s_divide); | |
5148 | else | |
7351e207 | 5149 | #endif |
55f26379 | 5150 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
5151 | } |
5152 | else if (SCM_BIGP (y)) | |
5153 | { | |
5154 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
5155 | scm_remember_upto_here_1 (y); | |
55f26379 | 5156 | return scm_from_double (rx / dby); |
0aacf84e MD |
5157 | } |
5158 | else if (SCM_REALP (y)) | |
5159 | { | |
5160 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5161 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5162 | if (yy == 0.0) |
5163 | scm_num_overflow (s_divide); | |
5164 | else | |
7351e207 | 5165 | #endif |
55f26379 | 5166 | return scm_from_double (rx / yy); |
0aacf84e MD |
5167 | } |
5168 | else if (SCM_COMPLEXP (y)) | |
5169 | { | |
5170 | a = rx; | |
5171 | goto complex_div; | |
5172 | } | |
f92e85f7 | 5173 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5174 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
5175 | else |
5176 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 5177 | } |
0aacf84e MD |
5178 | else if (SCM_COMPLEXP (x)) |
5179 | { | |
5180 | double rx = SCM_COMPLEX_REAL (x); | |
5181 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 5182 | if (SCM_I_INUMP (y)) |
0aacf84e | 5183 | { |
e25f3727 | 5184 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 5185 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
5186 | if (yy == 0) |
5187 | scm_num_overflow (s_divide); | |
5188 | else | |
7351e207 | 5189 | #endif |
0aacf84e MD |
5190 | { |
5191 | double d = yy; | |
8507ec80 | 5192 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
5193 | } |
5194 | } | |
5195 | else if (SCM_BIGP (y)) | |
5196 | { | |
5197 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
5198 | scm_remember_upto_here_1 (y); | |
8507ec80 | 5199 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
5200 | } |
5201 | else if (SCM_REALP (y)) | |
5202 | { | |
5203 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5204 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5205 | if (yy == 0.0) |
5206 | scm_num_overflow (s_divide); | |
5207 | else | |
7351e207 | 5208 | #endif |
8507ec80 | 5209 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
5210 | } |
5211 | else if (SCM_COMPLEXP (y)) | |
5212 | { | |
5213 | double ry = SCM_COMPLEX_REAL (y); | |
5214 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 5215 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
5216 | { |
5217 | double t = ry / iy; | |
5218 | double d = iy * (1.0 + t * t); | |
8507ec80 | 5219 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
5220 | } |
5221 | else | |
5222 | { | |
5223 | double t = iy / ry; | |
5224 | double d = ry * (1.0 + t * t); | |
8507ec80 | 5225 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
5226 | } |
5227 | } | |
f92e85f7 MV |
5228 | else if (SCM_FRACTIONP (y)) |
5229 | { | |
5230 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 5231 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 5232 | } |
0aacf84e MD |
5233 | else |
5234 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 5235 | } |
f92e85f7 MV |
5236 | else if (SCM_FRACTIONP (x)) |
5237 | { | |
e11e83f3 | 5238 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5239 | { |
e25f3727 | 5240 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
5241 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
5242 | if (yy == 0) | |
5243 | scm_num_overflow (s_divide); | |
5244 | else | |
5245 | #endif | |
cba42c93 | 5246 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5247 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
5248 | } | |
5249 | else if (SCM_BIGP (y)) | |
5250 | { | |
cba42c93 | 5251 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5252 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
5253 | } | |
5254 | else if (SCM_REALP (y)) | |
5255 | { | |
5256 | double yy = SCM_REAL_VALUE (y); | |
5257 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
5258 | if (yy == 0.0) | |
5259 | scm_num_overflow (s_divide); | |
5260 | else | |
5261 | #endif | |
55f26379 | 5262 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
5263 | } |
5264 | else if (SCM_COMPLEXP (y)) | |
5265 | { | |
5266 | a = scm_i_fraction2double (x); | |
5267 | goto complex_div; | |
5268 | } | |
5269 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 5270 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5271 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
5272 | else | |
5273 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
5274 | } | |
0aacf84e | 5275 | else |
f8de44c1 | 5276 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 5277 | } |
f92e85f7 MV |
5278 | |
5279 | SCM | |
5280 | scm_divide (SCM x, SCM y) | |
5281 | { | |
78d3deb1 | 5282 | return do_divide (x, y, 0); |
f92e85f7 MV |
5283 | } |
5284 | ||
5285 | static SCM scm_divide2real (SCM x, SCM y) | |
5286 | { | |
78d3deb1 | 5287 | return do_divide (x, y, 1); |
f92e85f7 | 5288 | } |
c05e97b7 | 5289 | #undef FUNC_NAME |
0f2d19dd | 5290 | |
fa605590 | 5291 | |
0f2d19dd | 5292 | double |
3101f40f | 5293 | scm_c_truncate (double x) |
0f2d19dd | 5294 | { |
fa605590 KR |
5295 | #if HAVE_TRUNC |
5296 | return trunc (x); | |
5297 | #else | |
f872b822 MD |
5298 | if (x < 0.0) |
5299 | return -floor (-x); | |
5300 | return floor (x); | |
fa605590 | 5301 | #endif |
0f2d19dd | 5302 | } |
0f2d19dd | 5303 | |
3101f40f MV |
5304 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
5305 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
5306 | Then half-way cases are identified and adjusted down if the | |
5307 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
5308 | |
5309 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
5310 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
5311 | ||
5312 | An odd "result" value is identified with result/2 != floor(result/2). | |
5313 | This is done with plus_half, since that value is ready for use sooner in | |
5314 | a pipelined cpu, and we're already requiring plus_half == result. | |
5315 | ||
5316 | Note however that we need to be careful when x is big and already an | |
5317 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
5318 | us to return such a value, incorrectly. For instance if the hardware is | |
5319 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
5320 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
5321 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
5322 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
5323 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
5324 | ||
5325 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
5326 | x is already an integer. If it is then clearly that's the desired result | |
5327 | already. And if it's not then the exponent must be small enough to allow | |
5328 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
5329 | ||
0f2d19dd | 5330 | double |
3101f40f | 5331 | scm_c_round (double x) |
0f2d19dd | 5332 | { |
6187f48b KR |
5333 | double plus_half, result; |
5334 | ||
5335 | if (x == floor (x)) | |
5336 | return x; | |
5337 | ||
5338 | plus_half = x + 0.5; | |
5339 | result = floor (plus_half); | |
3101f40f | 5340 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
5341 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
5342 | ? result - 1 | |
5343 | : result); | |
0f2d19dd JB |
5344 | } |
5345 | ||
f92e85f7 MV |
5346 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
5347 | (SCM x), | |
5348 | "Round the number @var{x} towards zero.") | |
5349 | #define FUNC_NAME s_scm_truncate_number | |
5350 | { | |
73e4de09 | 5351 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5352 | return scm_floor (x); |
5353 | else | |
5354 | return scm_ceiling (x); | |
5355 | } | |
5356 | #undef FUNC_NAME | |
5357 | ||
5358 | static SCM exactly_one_half; | |
5359 | ||
5360 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, | |
5361 | (SCM x), | |
5362 | "Round the number @var{x} towards the nearest integer. " | |
5363 | "When it is exactly halfway between two integers, " | |
5364 | "round towards the even one.") | |
5365 | #define FUNC_NAME s_scm_round_number | |
5366 | { | |
e11e83f3 | 5367 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
5368 | return x; |
5369 | else if (SCM_REALP (x)) | |
3101f40f | 5370 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 5371 | else |
bae30667 KR |
5372 | { |
5373 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
5374 | single quotient+remainder division then examining to see which way | |
5375 | the rounding should go. */ | |
5376 | SCM plus_half = scm_sum (x, exactly_one_half); | |
5377 | SCM result = scm_floor (plus_half); | |
3101f40f | 5378 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
5379 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
5380 | && scm_is_true (scm_odd_p (result))) | |
cff5fa33 | 5381 | return scm_difference (result, SCM_INUM1); |
bae30667 KR |
5382 | else |
5383 | return result; | |
5384 | } | |
f92e85f7 MV |
5385 | } |
5386 | #undef FUNC_NAME | |
5387 | ||
5388 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
5389 | (SCM x), | |
5390 | "Round the number @var{x} towards minus infinity.") | |
5391 | #define FUNC_NAME s_scm_floor | |
5392 | { | |
e11e83f3 | 5393 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5394 | return x; |
5395 | else if (SCM_REALP (x)) | |
55f26379 | 5396 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5397 | else if (SCM_FRACTIONP (x)) |
5398 | { | |
5399 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5400 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5401 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5402 | { |
5403 | /* For positive x, rounding towards zero is correct. */ | |
5404 | return q; | |
5405 | } | |
5406 | else | |
5407 | { | |
5408 | /* For negative x, we need to return q-1 unless x is an | |
5409 | integer. But fractions are never integer, per our | |
5410 | assumptions. */ | |
cff5fa33 | 5411 | return scm_difference (q, SCM_INUM1); |
f92e85f7 MV |
5412 | } |
5413 | } | |
5414 | else | |
5415 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
5416 | } | |
5417 | #undef FUNC_NAME | |
5418 | ||
5419 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
5420 | (SCM x), | |
5421 | "Round the number @var{x} towards infinity.") | |
5422 | #define FUNC_NAME s_scm_ceiling | |
5423 | { | |
e11e83f3 | 5424 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5425 | return x; |
5426 | else if (SCM_REALP (x)) | |
55f26379 | 5427 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5428 | else if (SCM_FRACTIONP (x)) |
5429 | { | |
5430 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5431 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5432 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
5433 | { |
5434 | /* For negative x, rounding towards zero is correct. */ | |
5435 | return q; | |
5436 | } | |
5437 | else | |
5438 | { | |
5439 | /* For positive x, we need to return q+1 unless x is an | |
5440 | integer. But fractions are never integer, per our | |
5441 | assumptions. */ | |
cff5fa33 | 5442 | return scm_sum (q, SCM_INUM1); |
f92e85f7 MV |
5443 | } |
5444 | } | |
5445 | else | |
5446 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
5447 | } | |
5448 | #undef FUNC_NAME | |
0f2d19dd | 5449 | |
ad79736c AW |
5450 | /* sin/cos/tan/asin/acos/atan |
5451 | sinh/cosh/tanh/asinh/acosh/atanh | |
5452 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
5453 | Written by Jerry D. Hedden, (C) FSF. | |
5454 | See the file `COPYING' for terms applying to this program. */ | |
0f2d19dd | 5455 | |
6fc4d012 | 5456 | SCM_DEFINE (scm_expt, "expt", 2, 0, 0, |
27c37006 | 5457 | (SCM x, SCM y), |
6fc4d012 AW |
5458 | "Return @var{x} raised to the power of @var{y}.") |
5459 | #define FUNC_NAME s_scm_expt | |
0f2d19dd | 5460 | { |
01c7284a MW |
5461 | if (scm_is_integer (y)) |
5462 | { | |
5463 | if (scm_is_true (scm_exact_p (y))) | |
5464 | return scm_integer_expt (x, y); | |
5465 | else | |
5466 | { | |
5467 | /* Here we handle the case where the exponent is an inexact | |
5468 | integer. We make the exponent exact in order to use | |
5469 | scm_integer_expt, and thus avoid the spurious imaginary | |
5470 | parts that may result from round-off errors in the general | |
5471 | e^(y log x) method below (for example when squaring a large | |
5472 | negative number). In this case, we must return an inexact | |
5473 | result for correctness. We also make the base inexact so | |
5474 | that scm_integer_expt will use fast inexact arithmetic | |
5475 | internally. Note that making the base inexact is not | |
5476 | sufficient to guarantee an inexact result, because | |
5477 | scm_integer_expt will return an exact 1 when the exponent | |
5478 | is 0, even if the base is inexact. */ | |
5479 | return scm_exact_to_inexact | |
5480 | (scm_integer_expt (scm_exact_to_inexact (x), | |
5481 | scm_inexact_to_exact (y))); | |
5482 | } | |
5483 | } | |
6fc4d012 AW |
5484 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
5485 | { | |
5486 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
5487 | } | |
5488 | else | |
5489 | return scm_exp (scm_product (scm_log (x), y)); | |
0f2d19dd | 5490 | } |
1bbd0b84 | 5491 | #undef FUNC_NAME |
0f2d19dd | 5492 | |
ad79736c AW |
5493 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
5494 | (SCM z), | |
5495 | "Compute the sine of @var{z}.") | |
5496 | #define FUNC_NAME s_scm_sin | |
5497 | { | |
5498 | if (scm_is_real (z)) | |
5499 | return scm_from_double (sin (scm_to_double (z))); | |
5500 | else if (SCM_COMPLEXP (z)) | |
5501 | { double x, y; | |
5502 | x = SCM_COMPLEX_REAL (z); | |
5503 | y = SCM_COMPLEX_IMAG (z); | |
5504 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
5505 | cos (x) * sinh (y)); | |
5506 | } | |
5507 | else | |
5508 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
5509 | } | |
5510 | #undef FUNC_NAME | |
0f2d19dd | 5511 | |
ad79736c AW |
5512 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
5513 | (SCM z), | |
5514 | "Compute the cosine of @var{z}.") | |
5515 | #define FUNC_NAME s_scm_cos | |
5516 | { | |
5517 | if (scm_is_real (z)) | |
5518 | return scm_from_double (cos (scm_to_double (z))); | |
5519 | else if (SCM_COMPLEXP (z)) | |
5520 | { double x, y; | |
5521 | x = SCM_COMPLEX_REAL (z); | |
5522 | y = SCM_COMPLEX_IMAG (z); | |
5523 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
5524 | -sin (x) * sinh (y)); | |
5525 | } | |
5526 | else | |
5527 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
5528 | } | |
5529 | #undef FUNC_NAME | |
5530 | ||
5531 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
5532 | (SCM z), | |
5533 | "Compute the tangent of @var{z}.") | |
5534 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 5535 | { |
ad79736c AW |
5536 | if (scm_is_real (z)) |
5537 | return scm_from_double (tan (scm_to_double (z))); | |
5538 | else if (SCM_COMPLEXP (z)) | |
5539 | { double x, y, w; | |
5540 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
5541 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
5542 | w = cos (x) + cosh (y); | |
5543 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
5544 | if (w == 0.0) | |
5545 | scm_num_overflow (s_scm_tan); | |
5546 | #endif | |
5547 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
5548 | } | |
5549 | else | |
5550 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
5551 | } | |
5552 | #undef FUNC_NAME | |
5553 | ||
5554 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
5555 | (SCM z), | |
5556 | "Compute the hyperbolic sine of @var{z}.") | |
5557 | #define FUNC_NAME s_scm_sinh | |
5558 | { | |
5559 | if (scm_is_real (z)) | |
5560 | return scm_from_double (sinh (scm_to_double (z))); | |
5561 | else if (SCM_COMPLEXP (z)) | |
5562 | { double x, y; | |
5563 | x = SCM_COMPLEX_REAL (z); | |
5564 | y = SCM_COMPLEX_IMAG (z); | |
5565 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
5566 | cosh (x) * sin (y)); | |
5567 | } | |
5568 | else | |
5569 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
5570 | } | |
5571 | #undef FUNC_NAME | |
5572 | ||
5573 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
5574 | (SCM z), | |
5575 | "Compute the hyperbolic cosine of @var{z}.") | |
5576 | #define FUNC_NAME s_scm_cosh | |
5577 | { | |
5578 | if (scm_is_real (z)) | |
5579 | return scm_from_double (cosh (scm_to_double (z))); | |
5580 | else if (SCM_COMPLEXP (z)) | |
5581 | { double x, y; | |
5582 | x = SCM_COMPLEX_REAL (z); | |
5583 | y = SCM_COMPLEX_IMAG (z); | |
5584 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
5585 | sinh (x) * sin (y)); | |
5586 | } | |
5587 | else | |
5588 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
5589 | } | |
5590 | #undef FUNC_NAME | |
5591 | ||
5592 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
5593 | (SCM z), | |
5594 | "Compute the hyperbolic tangent of @var{z}.") | |
5595 | #define FUNC_NAME s_scm_tanh | |
5596 | { | |
5597 | if (scm_is_real (z)) | |
5598 | return scm_from_double (tanh (scm_to_double (z))); | |
5599 | else if (SCM_COMPLEXP (z)) | |
5600 | { double x, y, w; | |
5601 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
5602 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
5603 | w = cosh (x) + cos (y); | |
5604 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
5605 | if (w == 0.0) | |
5606 | scm_num_overflow (s_scm_tanh); | |
5607 | #endif | |
5608 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
5609 | } | |
5610 | else | |
5611 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
5612 | } | |
5613 | #undef FUNC_NAME | |
5614 | ||
5615 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
5616 | (SCM z), | |
5617 | "Compute the arc sine of @var{z}.") | |
5618 | #define FUNC_NAME s_scm_asin | |
5619 | { | |
5620 | if (scm_is_real (z)) | |
5621 | { | |
5622 | double w = scm_to_double (z); | |
5623 | if (w >= -1.0 && w <= 1.0) | |
5624 | return scm_from_double (asin (w)); | |
5625 | else | |
5626 | return scm_product (scm_c_make_rectangular (0, -1), | |
5627 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
5628 | } | |
5629 | else if (SCM_COMPLEXP (z)) | |
5630 | { double x, y; | |
5631 | x = SCM_COMPLEX_REAL (z); | |
5632 | y = SCM_COMPLEX_IMAG (z); | |
5633 | return scm_product (scm_c_make_rectangular (0, -1), | |
5634 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
5635 | } | |
5636 | else | |
5637 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
5638 | } | |
5639 | #undef FUNC_NAME | |
5640 | ||
5641 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
5642 | (SCM z), | |
5643 | "Compute the arc cosine of @var{z}.") | |
5644 | #define FUNC_NAME s_scm_acos | |
5645 | { | |
5646 | if (scm_is_real (z)) | |
5647 | { | |
5648 | double w = scm_to_double (z); | |
5649 | if (w >= -1.0 && w <= 1.0) | |
5650 | return scm_from_double (acos (w)); | |
5651 | else | |
5652 | return scm_sum (scm_from_double (acos (0.0)), | |
5653 | scm_product (scm_c_make_rectangular (0, 1), | |
5654 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
5655 | } | |
5656 | else if (SCM_COMPLEXP (z)) | |
5657 | { double x, y; | |
5658 | x = SCM_COMPLEX_REAL (z); | |
5659 | y = SCM_COMPLEX_IMAG (z); | |
5660 | return scm_sum (scm_from_double (acos (0.0)), | |
5661 | scm_product (scm_c_make_rectangular (0, 1), | |
5662 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
5663 | } | |
5664 | else | |
5665 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
5666 | } | |
5667 | #undef FUNC_NAME | |
5668 | ||
5669 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
5670 | (SCM z, SCM y), | |
5671 | "With one argument, compute the arc tangent of @var{z}.\n" | |
5672 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
5673 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
5674 | #define FUNC_NAME s_scm_atan | |
5675 | { | |
5676 | if (SCM_UNBNDP (y)) | |
5677 | { | |
5678 | if (scm_is_real (z)) | |
5679 | return scm_from_double (atan (scm_to_double (z))); | |
5680 | else if (SCM_COMPLEXP (z)) | |
5681 | { | |
5682 | double v, w; | |
5683 | v = SCM_COMPLEX_REAL (z); | |
5684 | w = SCM_COMPLEX_IMAG (z); | |
5685 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
5686 | scm_c_make_rectangular (v, w + 1.0))), | |
5687 | scm_c_make_rectangular (0, 2)); | |
5688 | } | |
5689 | else | |
5690 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
5691 | } | |
5692 | else if (scm_is_real (z)) | |
5693 | { | |
5694 | if (scm_is_real (y)) | |
5695 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
5696 | else | |
5697 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
5698 | } | |
5699 | else | |
5700 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
5701 | } | |
5702 | #undef FUNC_NAME | |
5703 | ||
5704 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
5705 | (SCM z), | |
5706 | "Compute the inverse hyperbolic sine of @var{z}.") | |
5707 | #define FUNC_NAME s_scm_sys_asinh | |
5708 | { | |
5709 | if (scm_is_real (z)) | |
5710 | return scm_from_double (asinh (scm_to_double (z))); | |
5711 | else if (scm_is_number (z)) | |
5712 | return scm_log (scm_sum (z, | |
5713 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 5714 | SCM_INUM1)))); |
ad79736c AW |
5715 | else |
5716 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
5717 | } | |
5718 | #undef FUNC_NAME | |
5719 | ||
5720 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
5721 | (SCM z), | |
5722 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
5723 | #define FUNC_NAME s_scm_sys_acosh | |
5724 | { | |
5725 | if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
5726 | return scm_from_double (acosh (scm_to_double (z))); | |
5727 | else if (scm_is_number (z)) | |
5728 | return scm_log (scm_sum (z, | |
5729 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 5730 | SCM_INUM1)))); |
ad79736c AW |
5731 | else |
5732 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
5733 | } | |
5734 | #undef FUNC_NAME | |
5735 | ||
5736 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
5737 | (SCM z), | |
5738 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
5739 | #define FUNC_NAME s_scm_sys_atanh | |
5740 | { | |
5741 | if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
5742 | return scm_from_double (atanh (scm_to_double (z))); | |
5743 | else if (scm_is_number (z)) | |
cff5fa33 MW |
5744 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
5745 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
5746 | SCM_I_MAKINUM (2)); |
5747 | else | |
5748 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 5749 | } |
1bbd0b84 | 5750 | #undef FUNC_NAME |
0f2d19dd | 5751 | |
8507ec80 MV |
5752 | SCM |
5753 | scm_c_make_rectangular (double re, double im) | |
5754 | { | |
5755 | if (im == 0.0) | |
5756 | return scm_from_double (re); | |
5757 | else | |
5758 | { | |
5759 | SCM z; | |
03604fcf LC |
5760 | |
5761 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), | |
92d8fd32 | 5762 | "complex")); |
03604fcf | 5763 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); |
8507ec80 MV |
5764 | SCM_COMPLEX_REAL (z) = re; |
5765 | SCM_COMPLEX_IMAG (z) = im; | |
5766 | return z; | |
5767 | } | |
5768 | } | |
0f2d19dd | 5769 | |
a1ec6916 | 5770 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
5771 | (SCM real_part, SCM imaginary_part), |
5772 | "Return a complex number constructed of the given @var{real-part} " | |
5773 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 5774 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 5775 | { |
ad79736c AW |
5776 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
5777 | SCM_ARG1, FUNC_NAME, "real"); | |
5778 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
5779 | SCM_ARG2, FUNC_NAME, "real"); | |
5780 | return scm_c_make_rectangular (scm_to_double (real_part), | |
5781 | scm_to_double (imaginary_part)); | |
0f2d19dd | 5782 | } |
1bbd0b84 | 5783 | #undef FUNC_NAME |
0f2d19dd | 5784 | |
8507ec80 MV |
5785 | SCM |
5786 | scm_c_make_polar (double mag, double ang) | |
5787 | { | |
5788 | double s, c; | |
5e647d08 LC |
5789 | |
5790 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
5791 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
5792 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
5793 | details. */ | |
5794 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
5795 | sincos (ang, &s, &c); |
5796 | #else | |
5797 | s = sin (ang); | |
5798 | c = cos (ang); | |
5799 | #endif | |
5800 | return scm_c_make_rectangular (mag * c, mag * s); | |
5801 | } | |
0f2d19dd | 5802 | |
a1ec6916 | 5803 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 5804 | (SCM x, SCM y), |
942e5b91 | 5805 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 5806 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 5807 | { |
ad79736c AW |
5808 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
5809 | SCM_ASSERT_TYPE (scm_is_real (y), y, SCM_ARG2, FUNC_NAME, "real"); | |
5810 | return scm_c_make_polar (scm_to_double (x), scm_to_double (y)); | |
0f2d19dd | 5811 | } |
1bbd0b84 | 5812 | #undef FUNC_NAME |
0f2d19dd JB |
5813 | |
5814 | ||
152f82bf | 5815 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
5816 | /* "Return the real part of the number @var{z}." |
5817 | */ | |
0f2d19dd | 5818 | SCM |
6e8d25a6 | 5819 | scm_real_part (SCM z) |
0f2d19dd | 5820 | { |
e11e83f3 | 5821 | if (SCM_I_INUMP (z)) |
c2ff8ab0 | 5822 | return z; |
0aacf84e | 5823 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5824 | return z; |
0aacf84e | 5825 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5826 | return z; |
0aacf84e | 5827 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5828 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
f92e85f7 | 5829 | else if (SCM_FRACTIONP (z)) |
2fa2d879 | 5830 | return z; |
0aacf84e | 5831 | else |
c2ff8ab0 | 5832 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); |
0f2d19dd JB |
5833 | } |
5834 | ||
5835 | ||
152f82bf | 5836 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
5837 | /* "Return the imaginary part of the number @var{z}." |
5838 | */ | |
0f2d19dd | 5839 | SCM |
6e8d25a6 | 5840 | scm_imag_part (SCM z) |
0f2d19dd | 5841 | { |
e11e83f3 | 5842 | if (SCM_I_INUMP (z)) |
f872b822 | 5843 | return SCM_INUM0; |
0aacf84e | 5844 | else if (SCM_BIGP (z)) |
f872b822 | 5845 | return SCM_INUM0; |
0aacf84e | 5846 | else if (SCM_REALP (z)) |
e7efe8e7 | 5847 | return flo0; |
0aacf84e | 5848 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5849 | return scm_from_double (SCM_COMPLEX_IMAG (z)); |
f92e85f7 MV |
5850 | else if (SCM_FRACTIONP (z)) |
5851 | return SCM_INUM0; | |
0aacf84e | 5852 | else |
c2ff8ab0 | 5853 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); |
0f2d19dd JB |
5854 | } |
5855 | ||
f92e85f7 MV |
5856 | SCM_GPROC (s_numerator, "numerator", 1, 0, 0, scm_numerator, g_numerator); |
5857 | /* "Return the numerator of the number @var{z}." | |
5858 | */ | |
5859 | SCM | |
5860 | scm_numerator (SCM z) | |
5861 | { | |
e11e83f3 | 5862 | if (SCM_I_INUMP (z)) |
f92e85f7 MV |
5863 | return z; |
5864 | else if (SCM_BIGP (z)) | |
5865 | return z; | |
5866 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 5867 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
5868 | else if (SCM_REALP (z)) |
5869 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
5870 | else | |
5871 | SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator); | |
5872 | } | |
5873 | ||
5874 | ||
5875 | SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator); | |
5876 | /* "Return the denominator of the number @var{z}." | |
5877 | */ | |
5878 | SCM | |
5879 | scm_denominator (SCM z) | |
5880 | { | |
e11e83f3 | 5881 | if (SCM_I_INUMP (z)) |
cff5fa33 | 5882 | return SCM_INUM1; |
f92e85f7 | 5883 | else if (SCM_BIGP (z)) |
cff5fa33 | 5884 | return SCM_INUM1; |
f92e85f7 | 5885 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 5886 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
5887 | else if (SCM_REALP (z)) |
5888 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
5889 | else | |
5890 | SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator); | |
5891 | } | |
0f2d19dd | 5892 | |
9de33deb | 5893 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
5894 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
5895 | * "@code{abs} for real arguments, but also allows complex numbers." | |
5896 | */ | |
0f2d19dd | 5897 | SCM |
6e8d25a6 | 5898 | scm_magnitude (SCM z) |
0f2d19dd | 5899 | { |
e11e83f3 | 5900 | if (SCM_I_INUMP (z)) |
0aacf84e | 5901 | { |
e25f3727 | 5902 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
5903 | if (zz >= 0) |
5904 | return z; | |
5905 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 5906 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 5907 | else |
e25f3727 | 5908 | return scm_i_inum2big (-zz); |
5986c47d | 5909 | } |
0aacf84e MD |
5910 | else if (SCM_BIGP (z)) |
5911 | { | |
5912 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5913 | scm_remember_upto_here_1 (z); | |
5914 | if (sgn < 0) | |
5915 | return scm_i_clonebig (z, 0); | |
5916 | else | |
5917 | return z; | |
5986c47d | 5918 | } |
0aacf84e | 5919 | else if (SCM_REALP (z)) |
55f26379 | 5920 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 5921 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5922 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
5923 | else if (SCM_FRACTIONP (z)) |
5924 | { | |
73e4de09 | 5925 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5926 | return z; |
cba42c93 | 5927 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
5928 | SCM_FRACTION_DENOMINATOR (z)); |
5929 | } | |
0aacf84e | 5930 | else |
c2ff8ab0 | 5931 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); |
0f2d19dd JB |
5932 | } |
5933 | ||
5934 | ||
9de33deb | 5935 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
5936 | /* "Return the angle of the complex number @var{z}." |
5937 | */ | |
0f2d19dd | 5938 | SCM |
6e8d25a6 | 5939 | scm_angle (SCM z) |
0f2d19dd | 5940 | { |
c8ae173e | 5941 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 5942 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
5943 | But if atan2 follows the floating point rounding mode, then the value |
5944 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 5945 | if (SCM_I_INUMP (z)) |
0aacf84e | 5946 | { |
e11e83f3 | 5947 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 5948 | return flo0; |
0aacf84e | 5949 | else |
55f26379 | 5950 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 5951 | } |
0aacf84e MD |
5952 | else if (SCM_BIGP (z)) |
5953 | { | |
5954 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5955 | scm_remember_upto_here_1 (z); | |
5956 | if (sgn < 0) | |
55f26379 | 5957 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 5958 | else |
e7efe8e7 | 5959 | return flo0; |
0f2d19dd | 5960 | } |
0aacf84e | 5961 | else if (SCM_REALP (z)) |
c8ae173e KR |
5962 | { |
5963 | if (SCM_REAL_VALUE (z) >= 0) | |
e7efe8e7 | 5964 | return flo0; |
c8ae173e | 5965 | else |
55f26379 | 5966 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 5967 | } |
0aacf84e | 5968 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5969 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
5970 | else if (SCM_FRACTIONP (z)) |
5971 | { | |
73e4de09 | 5972 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 5973 | return flo0; |
55f26379 | 5974 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 5975 | } |
0aacf84e | 5976 | else |
f4c627b3 | 5977 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); |
0f2d19dd JB |
5978 | } |
5979 | ||
5980 | ||
3c9a524f DH |
5981 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
5982 | /* Convert the number @var{x} to its inexact representation.\n" | |
5983 | */ | |
5984 | SCM | |
5985 | scm_exact_to_inexact (SCM z) | |
5986 | { | |
e11e83f3 | 5987 | if (SCM_I_INUMP (z)) |
55f26379 | 5988 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 5989 | else if (SCM_BIGP (z)) |
55f26379 | 5990 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 5991 | else if (SCM_FRACTIONP (z)) |
55f26379 | 5992 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
5993 | else if (SCM_INEXACTP (z)) |
5994 | return z; | |
5995 | else | |
5996 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
5997 | } | |
5998 | ||
5999 | ||
a1ec6916 | 6000 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 6001 | (SCM z), |
1e6808ea | 6002 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 6003 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 6004 | { |
e11e83f3 | 6005 | if (SCM_I_INUMP (z)) |
f872b822 | 6006 | return z; |
0aacf84e | 6007 | else if (SCM_BIGP (z)) |
f872b822 | 6008 | return z; |
0aacf84e MD |
6009 | else if (SCM_REALP (z)) |
6010 | { | |
2e65b52f | 6011 | if (isinf (SCM_REAL_VALUE (z)) || isnan (SCM_REAL_VALUE (z))) |
f92e85f7 | 6012 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 6013 | else |
f92e85f7 MV |
6014 | { |
6015 | mpq_t frac; | |
6016 | SCM q; | |
6017 | ||
6018 | mpq_init (frac); | |
6019 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 6020 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
6021 | scm_i_mpz2num (mpq_denref (frac))); |
6022 | ||
cba42c93 | 6023 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
6024 | for frac... |
6025 | */ | |
6026 | mpq_clear (frac); | |
6027 | return q; | |
6028 | } | |
c2ff8ab0 | 6029 | } |
f92e85f7 MV |
6030 | else if (SCM_FRACTIONP (z)) |
6031 | return z; | |
0aacf84e | 6032 | else |
c2ff8ab0 | 6033 | SCM_WRONG_TYPE_ARG (1, z); |
0f2d19dd | 6034 | } |
1bbd0b84 | 6035 | #undef FUNC_NAME |
0f2d19dd | 6036 | |
f92e85f7 | 6037 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
6038 | (SCM x, SCM eps), |
6039 | "Returns the @emph{simplest} rational number differing\n" | |
6040 | "from @var{x} by no more than @var{eps}.\n" | |
6041 | "\n" | |
6042 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
6043 | "exact result when both its arguments are exact. Thus, you might need\n" | |
6044 | "to use @code{inexact->exact} on the arguments.\n" | |
6045 | "\n" | |
6046 | "@lisp\n" | |
6047 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
6048 | "@result{} 6/5\n" | |
6049 | "@end lisp") | |
f92e85f7 MV |
6050 | #define FUNC_NAME s_scm_rationalize |
6051 | { | |
e11e83f3 | 6052 | if (SCM_I_INUMP (x)) |
f92e85f7 MV |
6053 | return x; |
6054 | else if (SCM_BIGP (x)) | |
6055 | return x; | |
6056 | else if ((SCM_REALP (x)) || SCM_FRACTIONP (x)) | |
6057 | { | |
6058 | /* Use continued fractions to find closest ratio. All | |
6059 | arithmetic is done with exact numbers. | |
6060 | */ | |
6061 | ||
6062 | SCM ex = scm_inexact_to_exact (x); | |
6063 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
6064 | SCM tt = SCM_INUM1; |
6065 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
6066 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
6067 | SCM rx; |
6068 | int i = 0; | |
6069 | ||
73e4de09 | 6070 | if (scm_is_true (scm_num_eq_p (ex, int_part))) |
f92e85f7 MV |
6071 | return ex; |
6072 | ||
6073 | ex = scm_difference (ex, int_part); /* x = x-int_part */ | |
6074 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
6075 | ||
6076 | /* We stop after a million iterations just to be absolutely sure | |
6077 | that we don't go into an infinite loop. The process normally | |
6078 | converges after less than a dozen iterations. | |
6079 | */ | |
6080 | ||
76dae881 | 6081 | eps = scm_abs (eps); |
f92e85f7 MV |
6082 | while (++i < 1000000) |
6083 | { | |
6084 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
6085 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
6086 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
6087 | scm_is_false | |
f92e85f7 | 6088 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 6089 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
6090 | { |
6091 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
73e4de09 | 6092 | if (scm_is_false (scm_exact_p (x)) |
76dae881 | 6093 | || scm_is_false (scm_exact_p (eps))) |
02164269 MV |
6094 | return scm_exact_to_inexact (res); |
6095 | else | |
6096 | return res; | |
6097 | } | |
f92e85f7 MV |
6098 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
6099 | SCM_UNDEFINED); | |
6100 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
6101 | a2 = a1; | |
6102 | b2 = b1; | |
6103 | a1 = a; | |
6104 | b1 = b; | |
6105 | } | |
6106 | scm_num_overflow (s_scm_rationalize); | |
6107 | } | |
6108 | else | |
6109 | SCM_WRONG_TYPE_ARG (1, x); | |
6110 | } | |
6111 | #undef FUNC_NAME | |
6112 | ||
73e4de09 MV |
6113 | /* conversion functions */ |
6114 | ||
6115 | int | |
6116 | scm_is_integer (SCM val) | |
6117 | { | |
6118 | return scm_is_true (scm_integer_p (val)); | |
6119 | } | |
6120 | ||
6121 | int | |
6122 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
6123 | { | |
e11e83f3 | 6124 | if (SCM_I_INUMP (val)) |
73e4de09 | 6125 | { |
e11e83f3 | 6126 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
6127 | return n >= min && n <= max; |
6128 | } | |
6129 | else if (SCM_BIGP (val)) | |
6130 | { | |
6131 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
6132 | return 0; | |
6133 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
6134 | { |
6135 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
6136 | { | |
6137 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
6138 | return n >= min && n <= max; | |
6139 | } | |
6140 | else | |
6141 | return 0; | |
6142 | } | |
73e4de09 MV |
6143 | else |
6144 | { | |
d956fa6f MV |
6145 | scm_t_intmax n; |
6146 | size_t count; | |
73e4de09 | 6147 | |
d956fa6f MV |
6148 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
6149 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
6150 | return 0; | |
6151 | ||
6152 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
6153 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 6154 | |
d956fa6f | 6155 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 6156 | { |
d956fa6f MV |
6157 | if (n < 0) |
6158 | return 0; | |
73e4de09 | 6159 | } |
73e4de09 MV |
6160 | else |
6161 | { | |
d956fa6f MV |
6162 | n = -n; |
6163 | if (n >= 0) | |
6164 | return 0; | |
73e4de09 | 6165 | } |
d956fa6f MV |
6166 | |
6167 | return n >= min && n <= max; | |
73e4de09 MV |
6168 | } |
6169 | } | |
73e4de09 MV |
6170 | else |
6171 | return 0; | |
6172 | } | |
6173 | ||
6174 | int | |
6175 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
6176 | { | |
e11e83f3 | 6177 | if (SCM_I_INUMP (val)) |
73e4de09 | 6178 | { |
e11e83f3 | 6179 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
6180 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
6181 | } | |
6182 | else if (SCM_BIGP (val)) | |
6183 | { | |
6184 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
6185 | return 0; | |
6186 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
6187 | { |
6188 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
6189 | { | |
6190 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
6191 | return n >= min && n <= max; | |
6192 | } | |
6193 | else | |
6194 | return 0; | |
6195 | } | |
73e4de09 MV |
6196 | else |
6197 | { | |
d956fa6f MV |
6198 | scm_t_uintmax n; |
6199 | size_t count; | |
73e4de09 | 6200 | |
d956fa6f MV |
6201 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
6202 | return 0; | |
73e4de09 | 6203 | |
d956fa6f MV |
6204 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
6205 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 6206 | return 0; |
d956fa6f MV |
6207 | |
6208 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
6209 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 6210 | |
d956fa6f | 6211 | return n >= min && n <= max; |
73e4de09 MV |
6212 | } |
6213 | } | |
73e4de09 MV |
6214 | else |
6215 | return 0; | |
6216 | } | |
6217 | ||
1713d319 MV |
6218 | static void |
6219 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
6220 | { | |
6221 | scm_error (scm_out_of_range_key, | |
6222 | NULL, | |
6223 | "Value out of range ~S to ~S: ~S", | |
6224 | scm_list_3 (min, max, bad_val), | |
6225 | scm_list_1 (bad_val)); | |
6226 | } | |
6227 | ||
bfd7932e MV |
6228 | #define TYPE scm_t_intmax |
6229 | #define TYPE_MIN min | |
6230 | #define TYPE_MAX max | |
6231 | #define SIZEOF_TYPE 0 | |
6232 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
6233 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
6234 | #include "libguile/conv-integer.i.c" | |
6235 | ||
6236 | #define TYPE scm_t_uintmax | |
6237 | #define TYPE_MIN min | |
6238 | #define TYPE_MAX max | |
6239 | #define SIZEOF_TYPE 0 | |
6240 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
6241 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
6242 | #include "libguile/conv-uinteger.i.c" | |
6243 | ||
6244 | #define TYPE scm_t_int8 | |
6245 | #define TYPE_MIN SCM_T_INT8_MIN | |
6246 | #define TYPE_MAX SCM_T_INT8_MAX | |
6247 | #define SIZEOF_TYPE 1 | |
6248 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
6249 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
6250 | #include "libguile/conv-integer.i.c" | |
6251 | ||
6252 | #define TYPE scm_t_uint8 | |
6253 | #define TYPE_MIN 0 | |
6254 | #define TYPE_MAX SCM_T_UINT8_MAX | |
6255 | #define SIZEOF_TYPE 1 | |
6256 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
6257 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
6258 | #include "libguile/conv-uinteger.i.c" | |
6259 | ||
6260 | #define TYPE scm_t_int16 | |
6261 | #define TYPE_MIN SCM_T_INT16_MIN | |
6262 | #define TYPE_MAX SCM_T_INT16_MAX | |
6263 | #define SIZEOF_TYPE 2 | |
6264 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
6265 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
6266 | #include "libguile/conv-integer.i.c" | |
6267 | ||
6268 | #define TYPE scm_t_uint16 | |
6269 | #define TYPE_MIN 0 | |
6270 | #define TYPE_MAX SCM_T_UINT16_MAX | |
6271 | #define SIZEOF_TYPE 2 | |
6272 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
6273 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
6274 | #include "libguile/conv-uinteger.i.c" | |
6275 | ||
6276 | #define TYPE scm_t_int32 | |
6277 | #define TYPE_MIN SCM_T_INT32_MIN | |
6278 | #define TYPE_MAX SCM_T_INT32_MAX | |
6279 | #define SIZEOF_TYPE 4 | |
6280 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
6281 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
6282 | #include "libguile/conv-integer.i.c" | |
6283 | ||
6284 | #define TYPE scm_t_uint32 | |
6285 | #define TYPE_MIN 0 | |
6286 | #define TYPE_MAX SCM_T_UINT32_MAX | |
6287 | #define SIZEOF_TYPE 4 | |
6288 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
6289 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
6290 | #include "libguile/conv-uinteger.i.c" | |
6291 | ||
904a78f1 MG |
6292 | #define TYPE scm_t_wchar |
6293 | #define TYPE_MIN (scm_t_int32)-1 | |
6294 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
6295 | #define SIZEOF_TYPE 4 | |
6296 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
6297 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
6298 | #include "libguile/conv-integer.i.c" | |
6299 | ||
bfd7932e MV |
6300 | #define TYPE scm_t_int64 |
6301 | #define TYPE_MIN SCM_T_INT64_MIN | |
6302 | #define TYPE_MAX SCM_T_INT64_MAX | |
6303 | #define SIZEOF_TYPE 8 | |
6304 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
6305 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
6306 | #include "libguile/conv-integer.i.c" | |
6307 | ||
6308 | #define TYPE scm_t_uint64 | |
6309 | #define TYPE_MIN 0 | |
6310 | #define TYPE_MAX SCM_T_UINT64_MAX | |
6311 | #define SIZEOF_TYPE 8 | |
6312 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
6313 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
6314 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 6315 | |
cd036260 MV |
6316 | void |
6317 | scm_to_mpz (SCM val, mpz_t rop) | |
6318 | { | |
6319 | if (SCM_I_INUMP (val)) | |
6320 | mpz_set_si (rop, SCM_I_INUM (val)); | |
6321 | else if (SCM_BIGP (val)) | |
6322 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
6323 | else | |
6324 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
6325 | } | |
6326 | ||
6327 | SCM | |
6328 | scm_from_mpz (mpz_t val) | |
6329 | { | |
6330 | return scm_i_mpz2num (val); | |
6331 | } | |
6332 | ||
73e4de09 MV |
6333 | int |
6334 | scm_is_real (SCM val) | |
6335 | { | |
6336 | return scm_is_true (scm_real_p (val)); | |
6337 | } | |
6338 | ||
55f26379 MV |
6339 | int |
6340 | scm_is_rational (SCM val) | |
6341 | { | |
6342 | return scm_is_true (scm_rational_p (val)); | |
6343 | } | |
6344 | ||
73e4de09 MV |
6345 | double |
6346 | scm_to_double (SCM val) | |
6347 | { | |
55f26379 MV |
6348 | if (SCM_I_INUMP (val)) |
6349 | return SCM_I_INUM (val); | |
6350 | else if (SCM_BIGP (val)) | |
6351 | return scm_i_big2dbl (val); | |
6352 | else if (SCM_FRACTIONP (val)) | |
6353 | return scm_i_fraction2double (val); | |
6354 | else if (SCM_REALP (val)) | |
6355 | return SCM_REAL_VALUE (val); | |
6356 | else | |
7a1aba42 | 6357 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
6358 | } |
6359 | ||
6360 | SCM | |
6361 | scm_from_double (double val) | |
6362 | { | |
978c52d1 LC |
6363 | SCM z; |
6364 | ||
6365 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
6366 | ||
6367 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 6368 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 6369 | |
55f26379 | 6370 | return z; |
73e4de09 MV |
6371 | } |
6372 | ||
220058a8 | 6373 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
6374 | |
6375 | float | |
e25f3727 | 6376 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 6377 | { |
220058a8 AW |
6378 | scm_c_issue_deprecation_warning |
6379 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
6380 | ||
55f26379 MV |
6381 | if (SCM_BIGP (num)) |
6382 | { | |
6383 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 6384 | if (!isinf (res)) |
55f26379 MV |
6385 | return res; |
6386 | else | |
6387 | scm_out_of_range (NULL, num); | |
6388 | } | |
6389 | else | |
6390 | return scm_to_double (num); | |
6391 | } | |
6392 | ||
6393 | double | |
e25f3727 | 6394 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 6395 | { |
220058a8 AW |
6396 | scm_c_issue_deprecation_warning |
6397 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
6398 | ||
55f26379 MV |
6399 | if (SCM_BIGP (num)) |
6400 | { | |
6401 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 6402 | if (!isinf (res)) |
55f26379 MV |
6403 | return res; |
6404 | else | |
6405 | scm_out_of_range (NULL, num); | |
6406 | } | |
6407 | else | |
6408 | return scm_to_double (num); | |
6409 | } | |
6410 | ||
6411 | #endif | |
6412 | ||
8507ec80 MV |
6413 | int |
6414 | scm_is_complex (SCM val) | |
6415 | { | |
6416 | return scm_is_true (scm_complex_p (val)); | |
6417 | } | |
6418 | ||
6419 | double | |
6420 | scm_c_real_part (SCM z) | |
6421 | { | |
6422 | if (SCM_COMPLEXP (z)) | |
6423 | return SCM_COMPLEX_REAL (z); | |
6424 | else | |
6425 | { | |
6426 | /* Use the scm_real_part to get proper error checking and | |
6427 | dispatching. | |
6428 | */ | |
6429 | return scm_to_double (scm_real_part (z)); | |
6430 | } | |
6431 | } | |
6432 | ||
6433 | double | |
6434 | scm_c_imag_part (SCM z) | |
6435 | { | |
6436 | if (SCM_COMPLEXP (z)) | |
6437 | return SCM_COMPLEX_IMAG (z); | |
6438 | else | |
6439 | { | |
6440 | /* Use the scm_imag_part to get proper error checking and | |
6441 | dispatching. The result will almost always be 0.0, but not | |
6442 | always. | |
6443 | */ | |
6444 | return scm_to_double (scm_imag_part (z)); | |
6445 | } | |
6446 | } | |
6447 | ||
6448 | double | |
6449 | scm_c_magnitude (SCM z) | |
6450 | { | |
6451 | return scm_to_double (scm_magnitude (z)); | |
6452 | } | |
6453 | ||
6454 | double | |
6455 | scm_c_angle (SCM z) | |
6456 | { | |
6457 | return scm_to_double (scm_angle (z)); | |
6458 | } | |
6459 | ||
6460 | int | |
6461 | scm_is_number (SCM z) | |
6462 | { | |
6463 | return scm_is_true (scm_number_p (z)); | |
6464 | } | |
6465 | ||
8ab3d8a0 KR |
6466 | |
6467 | /* In the following functions we dispatch to the real-arg funcs like log() | |
6468 | when we know the arg is real, instead of just handing everything to | |
6469 | clog() for instance. This is in case clog() doesn't optimize for a | |
6470 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
6471 | well use it to go straight to the applicable C func. */ | |
6472 | ||
6473 | SCM_DEFINE (scm_log, "log", 1, 0, 0, | |
6474 | (SCM z), | |
6475 | "Return the natural logarithm of @var{z}.") | |
6476 | #define FUNC_NAME s_scm_log | |
6477 | { | |
6478 | if (SCM_COMPLEXP (z)) | |
6479 | { | |
4b26c03e | 6480 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6481 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
6482 | #else | |
6483 | double re = SCM_COMPLEX_REAL (z); | |
6484 | double im = SCM_COMPLEX_IMAG (z); | |
6485 | return scm_c_make_rectangular (log (hypot (re, im)), | |
6486 | atan2 (im, re)); | |
6487 | #endif | |
6488 | } | |
6489 | else | |
6490 | { | |
6491 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6492 | although the value itself overflows. */ | |
6493 | double re = scm_to_double (z); | |
6494 | double l = log (fabs (re)); | |
6495 | if (re >= 0.0) | |
6496 | return scm_from_double (l); | |
6497 | else | |
6498 | return scm_c_make_rectangular (l, M_PI); | |
6499 | } | |
6500 | } | |
6501 | #undef FUNC_NAME | |
6502 | ||
6503 | ||
6504 | SCM_DEFINE (scm_log10, "log10", 1, 0, 0, | |
6505 | (SCM z), | |
6506 | "Return the base 10 logarithm of @var{z}.") | |
6507 | #define FUNC_NAME s_scm_log10 | |
6508 | { | |
6509 | if (SCM_COMPLEXP (z)) | |
6510 | { | |
6511 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
6512 | clog() and a multiply by M_LOG10E, rather than the fallback | |
6513 | log10+hypot+atan2.) */ | |
f328f862 LC |
6514 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
6515 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
6516 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
6517 | #else | |
6518 | double re = SCM_COMPLEX_REAL (z); | |
6519 | double im = SCM_COMPLEX_IMAG (z); | |
6520 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
6521 | M_LOG10E * atan2 (im, re)); | |
6522 | #endif | |
6523 | } | |
6524 | else | |
6525 | { | |
6526 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6527 | although the value itself overflows. */ | |
6528 | double re = scm_to_double (z); | |
6529 | double l = log10 (fabs (re)); | |
6530 | if (re >= 0.0) | |
6531 | return scm_from_double (l); | |
6532 | else | |
6533 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
6534 | } | |
6535 | } | |
6536 | #undef FUNC_NAME | |
6537 | ||
6538 | ||
6539 | SCM_DEFINE (scm_exp, "exp", 1, 0, 0, | |
6540 | (SCM z), | |
6541 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
6542 | "base of natural logarithms (2.71828@dots{}).") | |
6543 | #define FUNC_NAME s_scm_exp | |
6544 | { | |
6545 | if (SCM_COMPLEXP (z)) | |
6546 | { | |
4b26c03e | 6547 | #if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6548 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
6549 | #else | |
6550 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
6551 | SCM_COMPLEX_IMAG (z)); | |
6552 | #endif | |
6553 | } | |
6554 | else | |
6555 | { | |
6556 | /* When z is a negative bignum the conversion to double overflows, | |
6557 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
6558 | return scm_from_double (exp (scm_to_double (z))); | |
6559 | } | |
6560 | } | |
6561 | #undef FUNC_NAME | |
6562 | ||
6563 | ||
6564 | SCM_DEFINE (scm_sqrt, "sqrt", 1, 0, 0, | |
6565 | (SCM x), | |
6566 | "Return the square root of @var{z}. Of the two possible roots\n" | |
6567 | "(positive and negative), the one with the a positive real part\n" | |
6568 | "is returned, or if that's zero then a positive imaginary part.\n" | |
6569 | "Thus,\n" | |
6570 | "\n" | |
6571 | "@example\n" | |
6572 | "(sqrt 9.0) @result{} 3.0\n" | |
6573 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
6574 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
6575 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
6576 | "@end example") | |
6577 | #define FUNC_NAME s_scm_sqrt | |
6578 | { | |
6579 | if (SCM_COMPLEXP (x)) | |
6580 | { | |
f328f862 LC |
6581 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
6582 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
6583 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (x))); |
6584 | #else | |
6585 | double re = SCM_COMPLEX_REAL (x); | |
6586 | double im = SCM_COMPLEX_IMAG (x); | |
6587 | return scm_c_make_polar (sqrt (hypot (re, im)), | |
6588 | 0.5 * atan2 (im, re)); | |
6589 | #endif | |
6590 | } | |
6591 | else | |
6592 | { | |
6593 | double xx = scm_to_double (x); | |
6594 | if (xx < 0) | |
6595 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
6596 | else | |
6597 | return scm_from_double (sqrt (xx)); | |
6598 | } | |
6599 | } | |
6600 | #undef FUNC_NAME | |
6601 | ||
6602 | ||
6603 | ||
0f2d19dd JB |
6604 | void |
6605 | scm_init_numbers () | |
0f2d19dd | 6606 | { |
0b799eea MV |
6607 | int i; |
6608 | ||
713a4259 KR |
6609 | mpz_init_set_si (z_negative_one, -1); |
6610 | ||
a261c0e9 DH |
6611 | /* It may be possible to tune the performance of some algorithms by using |
6612 | * the following constants to avoid the creation of bignums. Please, before | |
6613 | * using these values, remember the two rules of program optimization: | |
6614 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 6615 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 6616 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 6617 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 6618 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 6619 | |
f3ae5d60 MD |
6620 | scm_add_feature ("complex"); |
6621 | scm_add_feature ("inexact"); | |
e7efe8e7 | 6622 | flo0 = scm_from_double (0.0); |
0b799eea MV |
6623 | |
6624 | /* determine floating point precision */ | |
55f26379 | 6625 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
6626 | { |
6627 | init_dblprec(&scm_dblprec[i-2],i); | |
6628 | init_fx_radix(fx_per_radix[i-2],i); | |
6629 | } | |
f872b822 | 6630 | #ifdef DBL_DIG |
0b799eea | 6631 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 6632 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 6633 | #endif |
1be6b49c | 6634 | |
cff5fa33 | 6635 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 6636 | #include "libguile/numbers.x" |
0f2d19dd | 6637 | } |
89e00824 ML |
6638 | |
6639 | /* | |
6640 | Local Variables: | |
6641 | c-file-style: "gnu" | |
6642 | End: | |
6643 | */ |