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), | |
603 | "Return @code{#t} if @var{x} is neither infinite\n" | |
604 | "nor a NaN, @code{#f} otherwise.") | |
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))); | |
609 | else if (SCM_COMPLEXP (x)) | |
610 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_COMPLEX_REAL (x)) | |
611 | && DOUBLE_IS_FINITE (SCM_COMPLEX_IMAG (x))); | |
612 | else if (SCM_NUMBERP (x)) | |
613 | return SCM_BOOL_T; | |
614 | else | |
615 | SCM_WRONG_TYPE_ARG (1, x); | |
616 | } | |
617 | #undef FUNC_NAME | |
618 | ||
7351e207 | 619 | SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0, |
b1092b3a MV |
620 | (SCM x), |
621 | "Return @code{#t} if @var{x} is either @samp{+inf.0}\n" | |
622 | "or @samp{-inf.0}, @code{#f} otherwise.") | |
7351e207 MV |
623 | #define FUNC_NAME s_scm_inf_p |
624 | { | |
b1092b3a | 625 | if (SCM_REALP (x)) |
2e65b52f | 626 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
b1092b3a | 627 | else if (SCM_COMPLEXP (x)) |
2e65b52f LC |
628 | return scm_from_bool (isinf (SCM_COMPLEX_REAL (x)) |
629 | || isinf (SCM_COMPLEX_IMAG (x))); | |
0aacf84e | 630 | else |
7351e207 | 631 | return SCM_BOOL_F; |
7351e207 MV |
632 | } |
633 | #undef FUNC_NAME | |
634 | ||
635 | SCM_DEFINE (scm_nan_p, "nan?", 1, 0, 0, | |
636 | (SCM n), | |
637 | "Return @code{#t} if @var{n} is a NaN, @code{#f}\n" | |
638 | "otherwise.") | |
639 | #define FUNC_NAME s_scm_nan_p | |
640 | { | |
0aacf84e | 641 | if (SCM_REALP (n)) |
2e65b52f | 642 | return scm_from_bool (isnan (SCM_REAL_VALUE (n))); |
0aacf84e | 643 | else if (SCM_COMPLEXP (n)) |
2e65b52f LC |
644 | return scm_from_bool (isnan (SCM_COMPLEX_REAL (n)) |
645 | || isnan (SCM_COMPLEX_IMAG (n))); | |
0aacf84e | 646 | else |
7351e207 | 647 | return SCM_BOOL_F; |
7351e207 MV |
648 | } |
649 | #undef FUNC_NAME | |
650 | ||
651 | /* Guile's idea of infinity. */ | |
652 | static double guile_Inf; | |
653 | ||
654 | /* Guile's idea of not a number. */ | |
655 | static double guile_NaN; | |
656 | ||
657 | static void | |
658 | guile_ieee_init (void) | |
659 | { | |
7351e207 MV |
660 | /* Some version of gcc on some old version of Linux used to crash when |
661 | trying to make Inf and NaN. */ | |
662 | ||
240a27d2 KR |
663 | #ifdef INFINITY |
664 | /* C99 INFINITY, when available. | |
665 | FIXME: The standard allows for INFINITY to be something that overflows | |
666 | at compile time. We ought to have a configure test to check for that | |
667 | before trying to use it. (But in practice we believe this is not a | |
668 | problem on any system guile is likely to target.) */ | |
669 | guile_Inf = INFINITY; | |
56a3dcd4 | 670 | #elif defined HAVE_DINFINITY |
240a27d2 | 671 | /* OSF */ |
7351e207 | 672 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 673 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
674 | #else |
675 | double tmp = 1e+10; | |
676 | guile_Inf = tmp; | |
677 | for (;;) | |
678 | { | |
679 | guile_Inf *= 1e+10; | |
680 | if (guile_Inf == tmp) | |
681 | break; | |
682 | tmp = guile_Inf; | |
683 | } | |
684 | #endif | |
685 | ||
240a27d2 KR |
686 | #ifdef NAN |
687 | /* C99 NAN, when available */ | |
688 | guile_NaN = NAN; | |
56a3dcd4 | 689 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
690 | { |
691 | /* OSF */ | |
692 | extern unsigned int DQNAN[2]; | |
693 | guile_NaN = (*((double *)(DQNAN))); | |
694 | } | |
7351e207 MV |
695 | #else |
696 | guile_NaN = guile_Inf / guile_Inf; | |
697 | #endif | |
7351e207 MV |
698 | } |
699 | ||
700 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
701 | (void), | |
702 | "Return Inf.") | |
703 | #define FUNC_NAME s_scm_inf | |
704 | { | |
705 | static int initialized = 0; | |
706 | if (! initialized) | |
707 | { | |
708 | guile_ieee_init (); | |
709 | initialized = 1; | |
710 | } | |
55f26379 | 711 | return scm_from_double (guile_Inf); |
7351e207 MV |
712 | } |
713 | #undef FUNC_NAME | |
714 | ||
715 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
716 | (void), | |
717 | "Return NaN.") | |
718 | #define FUNC_NAME s_scm_nan | |
719 | { | |
720 | static int initialized = 0; | |
0aacf84e | 721 | if (!initialized) |
7351e207 MV |
722 | { |
723 | guile_ieee_init (); | |
724 | initialized = 1; | |
725 | } | |
55f26379 | 726 | return scm_from_double (guile_NaN); |
7351e207 MV |
727 | } |
728 | #undef FUNC_NAME | |
729 | ||
4219f20d | 730 | |
a48d60b1 MD |
731 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
732 | (SCM x), | |
733 | "Return the absolute value of @var{x}.") | |
734 | #define FUNC_NAME | |
0f2d19dd | 735 | { |
e11e83f3 | 736 | if (SCM_I_INUMP (x)) |
0aacf84e | 737 | { |
e25f3727 | 738 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
739 | if (xx >= 0) |
740 | return x; | |
741 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 742 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 743 | else |
e25f3727 | 744 | return scm_i_inum2big (-xx); |
4219f20d | 745 | } |
0aacf84e MD |
746 | else if (SCM_BIGP (x)) |
747 | { | |
748 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
749 | if (sgn < 0) | |
750 | return scm_i_clonebig (x, 0); | |
751 | else | |
752 | return x; | |
4219f20d | 753 | } |
0aacf84e | 754 | else if (SCM_REALP (x)) |
ae38324d KR |
755 | { |
756 | /* note that if x is a NaN then xx<0 is false so we return x unchanged */ | |
757 | double xx = SCM_REAL_VALUE (x); | |
758 | if (xx < 0.0) | |
55f26379 | 759 | return scm_from_double (-xx); |
ae38324d KR |
760 | else |
761 | return x; | |
762 | } | |
f92e85f7 MV |
763 | else if (SCM_FRACTIONP (x)) |
764 | { | |
73e4de09 | 765 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 766 | return x; |
cba42c93 | 767 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
768 | SCM_FRACTION_DENOMINATOR (x)); |
769 | } | |
0aacf84e | 770 | else |
a48d60b1 | 771 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 772 | } |
a48d60b1 | 773 | #undef FUNC_NAME |
0f2d19dd | 774 | |
4219f20d | 775 | |
9de33deb | 776 | SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); |
942e5b91 MG |
777 | /* "Return the quotient of the numbers @var{x} and @var{y}." |
778 | */ | |
0f2d19dd | 779 | SCM |
6e8d25a6 | 780 | scm_quotient (SCM x, SCM y) |
0f2d19dd | 781 | { |
e11e83f3 | 782 | if (SCM_I_INUMP (x)) |
0aacf84e | 783 | { |
e25f3727 | 784 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 785 | if (SCM_I_INUMP (y)) |
0aacf84e | 786 | { |
e25f3727 | 787 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
788 | if (yy == 0) |
789 | scm_num_overflow (s_quotient); | |
790 | else | |
791 | { | |
e25f3727 | 792 | scm_t_inum z = xx / yy; |
0aacf84e | 793 | if (SCM_FIXABLE (z)) |
d956fa6f | 794 | return SCM_I_MAKINUM (z); |
0aacf84e | 795 | else |
e25f3727 | 796 | return scm_i_inum2big (z); |
0aacf84e | 797 | } |
828865c3 | 798 | } |
0aacf84e | 799 | else if (SCM_BIGP (y)) |
ac0c002c | 800 | { |
e11e83f3 | 801 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
802 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
803 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
804 | { | |
805 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
806 | scm_remember_upto_here_1 (y); | |
d956fa6f | 807 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 808 | } |
0aacf84e | 809 | else |
cff5fa33 | 810 | return SCM_INUM0; |
ac0c002c DH |
811 | } |
812 | else | |
0aacf84e | 813 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); |
828865c3 | 814 | } |
0aacf84e MD |
815 | else if (SCM_BIGP (x)) |
816 | { | |
e11e83f3 | 817 | if (SCM_I_INUMP (y)) |
0aacf84e | 818 | { |
e25f3727 | 819 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
820 | if (yy == 0) |
821 | scm_num_overflow (s_quotient); | |
822 | else if (yy == 1) | |
823 | return x; | |
824 | else | |
825 | { | |
826 | SCM result = scm_i_mkbig (); | |
827 | if (yy < 0) | |
828 | { | |
829 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
830 | SCM_I_BIG_MPZ (x), | |
831 | - yy); | |
832 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
833 | } | |
834 | else | |
835 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
836 | scm_remember_upto_here_1 (x); | |
837 | return scm_i_normbig (result); | |
838 | } | |
839 | } | |
840 | else if (SCM_BIGP (y)) | |
841 | { | |
842 | SCM result = scm_i_mkbig (); | |
843 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
844 | SCM_I_BIG_MPZ (x), | |
845 | SCM_I_BIG_MPZ (y)); | |
846 | scm_remember_upto_here_2 (x, y); | |
847 | return scm_i_normbig (result); | |
848 | } | |
849 | else | |
850 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); | |
f872b822 | 851 | } |
0aacf84e | 852 | else |
89a7e495 | 853 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient); |
0f2d19dd JB |
854 | } |
855 | ||
9de33deb | 856 | SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); |
942e5b91 MG |
857 | /* "Return the remainder of the numbers @var{x} and @var{y}.\n" |
858 | * "@lisp\n" | |
859 | * "(remainder 13 4) @result{} 1\n" | |
860 | * "(remainder -13 4) @result{} -1\n" | |
861 | * "@end lisp" | |
862 | */ | |
0f2d19dd | 863 | SCM |
6e8d25a6 | 864 | scm_remainder (SCM x, SCM y) |
0f2d19dd | 865 | { |
e11e83f3 | 866 | if (SCM_I_INUMP (x)) |
0aacf84e | 867 | { |
e11e83f3 | 868 | if (SCM_I_INUMP (y)) |
0aacf84e | 869 | { |
e25f3727 | 870 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
871 | if (yy == 0) |
872 | scm_num_overflow (s_remainder); | |
873 | else | |
874 | { | |
e25f3727 | 875 | scm_t_inum z = SCM_I_INUM (x) % yy; |
d956fa6f | 876 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
877 | } |
878 | } | |
879 | else if (SCM_BIGP (y)) | |
ac0c002c | 880 | { |
e11e83f3 | 881 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
882 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
883 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
884 | { | |
885 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
886 | scm_remember_upto_here_1 (y); | |
cff5fa33 | 887 | return SCM_INUM0; |
4dc09ee4 | 888 | } |
0aacf84e MD |
889 | else |
890 | return x; | |
ac0c002c DH |
891 | } |
892 | else | |
0aacf84e | 893 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); |
89a7e495 | 894 | } |
0aacf84e MD |
895 | else if (SCM_BIGP (x)) |
896 | { | |
e11e83f3 | 897 | if (SCM_I_INUMP (y)) |
0aacf84e | 898 | { |
e25f3727 | 899 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
900 | if (yy == 0) |
901 | scm_num_overflow (s_remainder); | |
902 | else | |
903 | { | |
904 | SCM result = scm_i_mkbig (); | |
905 | if (yy < 0) | |
906 | yy = - yy; | |
907 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
908 | scm_remember_upto_here_1 (x); | |
909 | return scm_i_normbig (result); | |
910 | } | |
911 | } | |
912 | else if (SCM_BIGP (y)) | |
913 | { | |
914 | SCM result = scm_i_mkbig (); | |
915 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
916 | SCM_I_BIG_MPZ (x), | |
917 | SCM_I_BIG_MPZ (y)); | |
918 | scm_remember_upto_here_2 (x, y); | |
919 | return scm_i_normbig (result); | |
920 | } | |
921 | else | |
922 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); | |
f872b822 | 923 | } |
0aacf84e | 924 | else |
89a7e495 | 925 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder); |
0f2d19dd JB |
926 | } |
927 | ||
89a7e495 | 928 | |
9de33deb | 929 | SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); |
942e5b91 MG |
930 | /* "Return the modulo of the numbers @var{x} and @var{y}.\n" |
931 | * "@lisp\n" | |
932 | * "(modulo 13 4) @result{} 1\n" | |
933 | * "(modulo -13 4) @result{} 3\n" | |
934 | * "@end lisp" | |
935 | */ | |
0f2d19dd | 936 | SCM |
6e8d25a6 | 937 | scm_modulo (SCM x, SCM y) |
0f2d19dd | 938 | { |
e11e83f3 | 939 | if (SCM_I_INUMP (x)) |
0aacf84e | 940 | { |
e25f3727 | 941 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 942 | if (SCM_I_INUMP (y)) |
0aacf84e | 943 | { |
e25f3727 | 944 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
945 | if (yy == 0) |
946 | scm_num_overflow (s_modulo); | |
947 | else | |
948 | { | |
66b1c775 KR |
949 | /* C99 specifies that "%" is the remainder corresponding to a |
950 | quotient rounded towards zero, and that's also traditional | |
951 | for machine division, so z here should be well defined. */ | |
e25f3727 AW |
952 | scm_t_inum z = xx % yy; |
953 | scm_t_inum result; | |
0aacf84e MD |
954 | |
955 | if (yy < 0) | |
956 | { | |
957 | if (z > 0) | |
958 | result = z + yy; | |
959 | else | |
960 | result = z; | |
961 | } | |
962 | else | |
963 | { | |
964 | if (z < 0) | |
965 | result = z + yy; | |
966 | else | |
967 | result = z; | |
968 | } | |
d956fa6f | 969 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
970 | } |
971 | } | |
972 | else if (SCM_BIGP (y)) | |
973 | { | |
974 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
975 | { |
976 | mpz_t z_x; | |
977 | SCM result; | |
978 | ||
979 | if (sgn_y < 0) | |
980 | { | |
981 | SCM pos_y = scm_i_clonebig (y, 0); | |
982 | /* do this after the last scm_op */ | |
983 | mpz_init_set_si (z_x, xx); | |
984 | result = pos_y; /* re-use this bignum */ | |
985 | mpz_mod (SCM_I_BIG_MPZ (result), | |
986 | z_x, | |
987 | SCM_I_BIG_MPZ (pos_y)); | |
988 | scm_remember_upto_here_1 (pos_y); | |
989 | } | |
990 | else | |
991 | { | |
992 | result = scm_i_mkbig (); | |
993 | /* do this after the last scm_op */ | |
994 | mpz_init_set_si (z_x, xx); | |
995 | mpz_mod (SCM_I_BIG_MPZ (result), | |
996 | z_x, | |
997 | SCM_I_BIG_MPZ (y)); | |
998 | scm_remember_upto_here_1 (y); | |
999 | } | |
ca46fb90 | 1000 | |
0aacf84e MD |
1001 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
1002 | mpz_add (SCM_I_BIG_MPZ (result), | |
1003 | SCM_I_BIG_MPZ (y), | |
1004 | SCM_I_BIG_MPZ (result)); | |
1005 | scm_remember_upto_here_1 (y); | |
1006 | /* and do this before the next one */ | |
1007 | mpz_clear (z_x); | |
1008 | return scm_i_normbig (result); | |
1009 | } | |
1010 | } | |
1011 | else | |
1012 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
f872b822 | 1013 | } |
0aacf84e MD |
1014 | else if (SCM_BIGP (x)) |
1015 | { | |
e11e83f3 | 1016 | if (SCM_I_INUMP (y)) |
0aacf84e | 1017 | { |
e25f3727 | 1018 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
1019 | if (yy == 0) |
1020 | scm_num_overflow (s_modulo); | |
1021 | else | |
1022 | { | |
1023 | SCM result = scm_i_mkbig (); | |
1024 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
1025 | SCM_I_BIG_MPZ (x), | |
1026 | (yy < 0) ? - yy : yy); | |
1027 | scm_remember_upto_here_1 (x); | |
1028 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1029 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
1030 | SCM_I_BIG_MPZ (result), | |
1031 | - yy); | |
1032 | return scm_i_normbig (result); | |
1033 | } | |
1034 | } | |
1035 | else if (SCM_BIGP (y)) | |
1036 | { | |
0aacf84e MD |
1037 | { |
1038 | SCM result = scm_i_mkbig (); | |
1039 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1040 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
1041 | mpz_mod (SCM_I_BIG_MPZ (result), | |
1042 | SCM_I_BIG_MPZ (x), | |
1043 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 1044 | |
0aacf84e MD |
1045 | scm_remember_upto_here_1 (x); |
1046 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1047 | mpz_add (SCM_I_BIG_MPZ (result), | |
1048 | SCM_I_BIG_MPZ (y), | |
1049 | SCM_I_BIG_MPZ (result)); | |
1050 | scm_remember_upto_here_2 (y, pos_y); | |
1051 | return scm_i_normbig (result); | |
1052 | } | |
1053 | } | |
1054 | else | |
1055 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
828865c3 | 1056 | } |
0aacf84e | 1057 | else |
09fb7599 | 1058 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); |
0f2d19dd JB |
1059 | } |
1060 | ||
78d3deb1 AW |
1061 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
1062 | (SCM x, SCM y, SCM rest), | |
1063 | "Return the greatest common divisor of all parameter values.\n" | |
1064 | "If called without arguments, 0 is returned.") | |
1065 | #define FUNC_NAME s_scm_i_gcd | |
1066 | { | |
1067 | while (!scm_is_null (rest)) | |
1068 | { x = scm_gcd (x, y); | |
1069 | y = scm_car (rest); | |
1070 | rest = scm_cdr (rest); | |
1071 | } | |
1072 | return scm_gcd (x, y); | |
1073 | } | |
1074 | #undef FUNC_NAME | |
1075 | ||
1076 | #define s_gcd s_scm_i_gcd | |
1077 | #define g_gcd g_scm_i_gcd | |
1078 | ||
0f2d19dd | 1079 | SCM |
6e8d25a6 | 1080 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 1081 | { |
ca46fb90 | 1082 | if (SCM_UNBNDP (y)) |
1dd79792 | 1083 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 1084 | |
e11e83f3 | 1085 | if (SCM_I_INUMP (x)) |
ca46fb90 | 1086 | { |
e11e83f3 | 1087 | if (SCM_I_INUMP (y)) |
ca46fb90 | 1088 | { |
e25f3727 AW |
1089 | scm_t_inum xx = SCM_I_INUM (x); |
1090 | scm_t_inum yy = SCM_I_INUM (y); | |
1091 | scm_t_inum u = xx < 0 ? -xx : xx; | |
1092 | scm_t_inum v = yy < 0 ? -yy : yy; | |
1093 | scm_t_inum result; | |
0aacf84e MD |
1094 | if (xx == 0) |
1095 | result = v; | |
1096 | else if (yy == 0) | |
1097 | result = u; | |
1098 | else | |
1099 | { | |
e25f3727 AW |
1100 | scm_t_inum k = 1; |
1101 | scm_t_inum t; | |
0aacf84e MD |
1102 | /* Determine a common factor 2^k */ |
1103 | while (!(1 & (u | v))) | |
1104 | { | |
1105 | k <<= 1; | |
1106 | u >>= 1; | |
1107 | v >>= 1; | |
1108 | } | |
1109 | /* Now, any factor 2^n can be eliminated */ | |
1110 | if (u & 1) | |
1111 | t = -v; | |
1112 | else | |
1113 | { | |
1114 | t = u; | |
1115 | b3: | |
1116 | t = SCM_SRS (t, 1); | |
1117 | } | |
1118 | if (!(1 & t)) | |
1119 | goto b3; | |
1120 | if (t > 0) | |
1121 | u = t; | |
1122 | else | |
1123 | v = -t; | |
1124 | t = u - v; | |
1125 | if (t != 0) | |
1126 | goto b3; | |
1127 | result = u * k; | |
1128 | } | |
1129 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 1130 | ? SCM_I_MAKINUM (result) |
e25f3727 | 1131 | : scm_i_inum2big (result)); |
ca46fb90 RB |
1132 | } |
1133 | else if (SCM_BIGP (y)) | |
1134 | { | |
0bff4dce KR |
1135 | SCM_SWAP (x, y); |
1136 | goto big_inum; | |
ca46fb90 RB |
1137 | } |
1138 | else | |
1139 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 1140 | } |
ca46fb90 RB |
1141 | else if (SCM_BIGP (x)) |
1142 | { | |
e11e83f3 | 1143 | if (SCM_I_INUMP (y)) |
ca46fb90 | 1144 | { |
e25f3727 AW |
1145 | scm_t_bits result; |
1146 | scm_t_inum yy; | |
0bff4dce | 1147 | big_inum: |
e11e83f3 | 1148 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
1149 | if (yy == 0) |
1150 | return scm_abs (x); | |
0aacf84e MD |
1151 | if (yy < 0) |
1152 | yy = -yy; | |
ca46fb90 RB |
1153 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
1154 | scm_remember_upto_here_1 (x); | |
0aacf84e | 1155 | return (SCM_POSFIXABLE (result) |
d956fa6f | 1156 | ? SCM_I_MAKINUM (result) |
e25f3727 | 1157 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
1158 | } |
1159 | else if (SCM_BIGP (y)) | |
1160 | { | |
1161 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
1162 | mpz_gcd (SCM_I_BIG_MPZ (result), |
1163 | SCM_I_BIG_MPZ (x), | |
1164 | SCM_I_BIG_MPZ (y)); | |
1165 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
1166 | return scm_i_normbig (result); |
1167 | } | |
1168 | else | |
1169 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 1170 | } |
ca46fb90 | 1171 | else |
09fb7599 | 1172 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
1173 | } |
1174 | ||
78d3deb1 AW |
1175 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
1176 | (SCM x, SCM y, SCM rest), | |
1177 | "Return the least common multiple of the arguments.\n" | |
1178 | "If called without arguments, 1 is returned.") | |
1179 | #define FUNC_NAME s_scm_i_lcm | |
1180 | { | |
1181 | while (!scm_is_null (rest)) | |
1182 | { x = scm_lcm (x, y); | |
1183 | y = scm_car (rest); | |
1184 | rest = scm_cdr (rest); | |
1185 | } | |
1186 | return scm_lcm (x, y); | |
1187 | } | |
1188 | #undef FUNC_NAME | |
1189 | ||
1190 | #define s_lcm s_scm_i_lcm | |
1191 | #define g_lcm g_scm_i_lcm | |
1192 | ||
0f2d19dd | 1193 | SCM |
6e8d25a6 | 1194 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 1195 | { |
ca46fb90 RB |
1196 | if (SCM_UNBNDP (n2)) |
1197 | { | |
1198 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
1199 | return SCM_I_MAKINUM (1L); |
1200 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 1201 | } |
09fb7599 | 1202 | |
e11e83f3 | 1203 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 1204 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 1205 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 1206 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 1207 | |
e11e83f3 | 1208 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 1209 | { |
e11e83f3 | 1210 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1211 | { |
1212 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 1213 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
1214 | return d; |
1215 | else | |
1216 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
1217 | } | |
1218 | else | |
1219 | { | |
1220 | /* inum n1, big n2 */ | |
1221 | inumbig: | |
1222 | { | |
1223 | SCM result = scm_i_mkbig (); | |
e25f3727 | 1224 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
1225 | if (nn1 == 0) return SCM_INUM0; |
1226 | if (nn1 < 0) nn1 = - nn1; | |
1227 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
1228 | scm_remember_upto_here_1 (n2); | |
1229 | return result; | |
1230 | } | |
1231 | } | |
1232 | } | |
1233 | else | |
1234 | { | |
1235 | /* big n1 */ | |
e11e83f3 | 1236 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1237 | { |
1238 | SCM_SWAP (n1, n2); | |
1239 | goto inumbig; | |
1240 | } | |
1241 | else | |
1242 | { | |
1243 | SCM result = scm_i_mkbig (); | |
1244 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
1245 | SCM_I_BIG_MPZ (n1), | |
1246 | SCM_I_BIG_MPZ (n2)); | |
1247 | scm_remember_upto_here_2(n1, n2); | |
1248 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
1249 | return result; | |
1250 | } | |
f872b822 | 1251 | } |
0f2d19dd JB |
1252 | } |
1253 | ||
8a525303 GB |
1254 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
1255 | ||
1256 | Logand: | |
1257 | X Y Result Method: | |
1258 | (len) | |
1259 | + + + x (map digit:logand X Y) | |
1260 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
1261 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
1262 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
1263 | ||
1264 | Logior: | |
1265 | X Y Result Method: | |
1266 | ||
1267 | + + + (map digit:logior X Y) | |
1268 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
1269 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
1270 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
1271 | ||
1272 | Logxor: | |
1273 | X Y Result Method: | |
1274 | ||
1275 | + + + (map digit:logxor X Y) | |
1276 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
1277 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
1278 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
1279 | ||
1280 | Logtest: | |
1281 | X Y Result | |
1282 | ||
1283 | + + (any digit:logand X Y) | |
1284 | + - (any digit:logand X (lognot (+ -1 Y))) | |
1285 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
1286 | - - #t | |
1287 | ||
1288 | */ | |
1289 | ||
78d3deb1 AW |
1290 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
1291 | (SCM x, SCM y, SCM rest), | |
1292 | "Return the bitwise AND of the integer arguments.\n\n" | |
1293 | "@lisp\n" | |
1294 | "(logand) @result{} -1\n" | |
1295 | "(logand 7) @result{} 7\n" | |
1296 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
1297 | "@end lisp") | |
1298 | #define FUNC_NAME s_scm_i_logand | |
1299 | { | |
1300 | while (!scm_is_null (rest)) | |
1301 | { x = scm_logand (x, y); | |
1302 | y = scm_car (rest); | |
1303 | rest = scm_cdr (rest); | |
1304 | } | |
1305 | return scm_logand (x, y); | |
1306 | } | |
1307 | #undef FUNC_NAME | |
1308 | ||
1309 | #define s_scm_logand s_scm_i_logand | |
1310 | ||
1311 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 1312 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 1313 | { |
e25f3727 | 1314 | scm_t_inum nn1; |
9a00c9fc | 1315 | |
0aacf84e MD |
1316 | if (SCM_UNBNDP (n2)) |
1317 | { | |
1318 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 1319 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
1320 | else if (!SCM_NUMBERP (n1)) |
1321 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1322 | else if (SCM_NUMBERP (n1)) | |
1323 | return n1; | |
1324 | else | |
1325 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1326 | } |
09fb7599 | 1327 | |
e11e83f3 | 1328 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1329 | { |
e11e83f3 MV |
1330 | nn1 = SCM_I_INUM (n1); |
1331 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1332 | { |
e25f3727 | 1333 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 1334 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
1335 | } |
1336 | else if SCM_BIGP (n2) | |
1337 | { | |
1338 | intbig: | |
1339 | if (n1 == 0) | |
1340 | return SCM_INUM0; | |
1341 | { | |
1342 | SCM result_z = scm_i_mkbig (); | |
1343 | mpz_t nn1_z; | |
1344 | mpz_init_set_si (nn1_z, nn1); | |
1345 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1346 | scm_remember_upto_here_1 (n2); | |
1347 | mpz_clear (nn1_z); | |
1348 | return scm_i_normbig (result_z); | |
1349 | } | |
1350 | } | |
1351 | else | |
1352 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1353 | } | |
1354 | else if (SCM_BIGP (n1)) | |
1355 | { | |
e11e83f3 | 1356 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1357 | { |
1358 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1359 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1360 | goto intbig; |
1361 | } | |
1362 | else if (SCM_BIGP (n2)) | |
1363 | { | |
1364 | SCM result_z = scm_i_mkbig (); | |
1365 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
1366 | SCM_I_BIG_MPZ (n1), | |
1367 | SCM_I_BIG_MPZ (n2)); | |
1368 | scm_remember_upto_here_2 (n1, n2); | |
1369 | return scm_i_normbig (result_z); | |
1370 | } | |
1371 | else | |
1372 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1373 | } |
0aacf84e | 1374 | else |
09fb7599 | 1375 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1376 | } |
1bbd0b84 | 1377 | #undef FUNC_NAME |
0f2d19dd | 1378 | |
09fb7599 | 1379 | |
78d3deb1 AW |
1380 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
1381 | (SCM x, SCM y, SCM rest), | |
1382 | "Return the bitwise OR of the integer arguments.\n\n" | |
1383 | "@lisp\n" | |
1384 | "(logior) @result{} 0\n" | |
1385 | "(logior 7) @result{} 7\n" | |
1386 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1387 | "@end lisp") | |
1388 | #define FUNC_NAME s_scm_i_logior | |
1389 | { | |
1390 | while (!scm_is_null (rest)) | |
1391 | { x = scm_logior (x, y); | |
1392 | y = scm_car (rest); | |
1393 | rest = scm_cdr (rest); | |
1394 | } | |
1395 | return scm_logior (x, y); | |
1396 | } | |
1397 | #undef FUNC_NAME | |
1398 | ||
1399 | #define s_scm_logior s_scm_i_logior | |
1400 | ||
1401 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 1402 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 1403 | { |
e25f3727 | 1404 | scm_t_inum nn1; |
9a00c9fc | 1405 | |
0aacf84e MD |
1406 | if (SCM_UNBNDP (n2)) |
1407 | { | |
1408 | if (SCM_UNBNDP (n1)) | |
1409 | return SCM_INUM0; | |
1410 | else if (SCM_NUMBERP (n1)) | |
1411 | return n1; | |
1412 | else | |
1413 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1414 | } |
09fb7599 | 1415 | |
e11e83f3 | 1416 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1417 | { |
e11e83f3 MV |
1418 | nn1 = SCM_I_INUM (n1); |
1419 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1420 | { |
e11e83f3 | 1421 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1422 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
1423 | } |
1424 | else if (SCM_BIGP (n2)) | |
1425 | { | |
1426 | intbig: | |
1427 | if (nn1 == 0) | |
1428 | return n2; | |
1429 | { | |
1430 | SCM result_z = scm_i_mkbig (); | |
1431 | mpz_t nn1_z; | |
1432 | mpz_init_set_si (nn1_z, nn1); | |
1433 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1434 | scm_remember_upto_here_1 (n2); | |
1435 | mpz_clear (nn1_z); | |
9806de0d | 1436 | return scm_i_normbig (result_z); |
0aacf84e MD |
1437 | } |
1438 | } | |
1439 | else | |
1440 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1441 | } | |
1442 | else if (SCM_BIGP (n1)) | |
1443 | { | |
e11e83f3 | 1444 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1445 | { |
1446 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1447 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1448 | goto intbig; |
1449 | } | |
1450 | else if (SCM_BIGP (n2)) | |
1451 | { | |
1452 | SCM result_z = scm_i_mkbig (); | |
1453 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
1454 | SCM_I_BIG_MPZ (n1), | |
1455 | SCM_I_BIG_MPZ (n2)); | |
1456 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 1457 | return scm_i_normbig (result_z); |
0aacf84e MD |
1458 | } |
1459 | else | |
1460 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1461 | } |
0aacf84e | 1462 | else |
09fb7599 | 1463 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1464 | } |
1bbd0b84 | 1465 | #undef FUNC_NAME |
0f2d19dd | 1466 | |
09fb7599 | 1467 | |
78d3deb1 AW |
1468 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
1469 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
1470 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1471 | "set in the result if it is set in an odd number of arguments.\n" | |
1472 | "@lisp\n" | |
1473 | "(logxor) @result{} 0\n" | |
1474 | "(logxor 7) @result{} 7\n" | |
1475 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1476 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1477 | "@end lisp") |
78d3deb1 AW |
1478 | #define FUNC_NAME s_scm_i_logxor |
1479 | { | |
1480 | while (!scm_is_null (rest)) | |
1481 | { x = scm_logxor (x, y); | |
1482 | y = scm_car (rest); | |
1483 | rest = scm_cdr (rest); | |
1484 | } | |
1485 | return scm_logxor (x, y); | |
1486 | } | |
1487 | #undef FUNC_NAME | |
1488 | ||
1489 | #define s_scm_logxor s_scm_i_logxor | |
1490 | ||
1491 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 1492 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1493 | { |
e25f3727 | 1494 | scm_t_inum nn1; |
9a00c9fc | 1495 | |
0aacf84e MD |
1496 | if (SCM_UNBNDP (n2)) |
1497 | { | |
1498 | if (SCM_UNBNDP (n1)) | |
1499 | return SCM_INUM0; | |
1500 | else if (SCM_NUMBERP (n1)) | |
1501 | return n1; | |
1502 | else | |
1503 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1504 | } |
09fb7599 | 1505 | |
e11e83f3 | 1506 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1507 | { |
e11e83f3 MV |
1508 | nn1 = SCM_I_INUM (n1); |
1509 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1510 | { |
e25f3727 | 1511 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 1512 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
1513 | } |
1514 | else if (SCM_BIGP (n2)) | |
1515 | { | |
1516 | intbig: | |
1517 | { | |
1518 | SCM result_z = scm_i_mkbig (); | |
1519 | mpz_t nn1_z; | |
1520 | mpz_init_set_si (nn1_z, nn1); | |
1521 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1522 | scm_remember_upto_here_1 (n2); | |
1523 | mpz_clear (nn1_z); | |
1524 | return scm_i_normbig (result_z); | |
1525 | } | |
1526 | } | |
1527 | else | |
1528 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1529 | } | |
1530 | else if (SCM_BIGP (n1)) | |
1531 | { | |
e11e83f3 | 1532 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1533 | { |
1534 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1535 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1536 | goto intbig; |
1537 | } | |
1538 | else if (SCM_BIGP (n2)) | |
1539 | { | |
1540 | SCM result_z = scm_i_mkbig (); | |
1541 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
1542 | SCM_I_BIG_MPZ (n1), | |
1543 | SCM_I_BIG_MPZ (n2)); | |
1544 | scm_remember_upto_here_2 (n1, n2); | |
1545 | return scm_i_normbig (result_z); | |
1546 | } | |
1547 | else | |
1548 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1549 | } |
0aacf84e | 1550 | else |
09fb7599 | 1551 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1552 | } |
1bbd0b84 | 1553 | #undef FUNC_NAME |
0f2d19dd | 1554 | |
09fb7599 | 1555 | |
a1ec6916 | 1556 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 1557 | (SCM j, SCM k), |
ba6e7231 KR |
1558 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
1559 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
1560 | "without actually calculating the @code{logand}, just testing\n" | |
1561 | "for non-zero.\n" | |
1562 | "\n" | |
1e6808ea | 1563 | "@lisp\n" |
b380b885 MD |
1564 | "(logtest #b0100 #b1011) @result{} #f\n" |
1565 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1566 | "@end lisp") |
1bbd0b84 | 1567 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1568 | { |
e25f3727 | 1569 | scm_t_inum nj; |
9a00c9fc | 1570 | |
e11e83f3 | 1571 | if (SCM_I_INUMP (j)) |
0aacf84e | 1572 | { |
e11e83f3 MV |
1573 | nj = SCM_I_INUM (j); |
1574 | if (SCM_I_INUMP (k)) | |
0aacf84e | 1575 | { |
e25f3727 | 1576 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 1577 | return scm_from_bool (nj & nk); |
0aacf84e MD |
1578 | } |
1579 | else if (SCM_BIGP (k)) | |
1580 | { | |
1581 | intbig: | |
1582 | if (nj == 0) | |
1583 | return SCM_BOOL_F; | |
1584 | { | |
1585 | SCM result; | |
1586 | mpz_t nj_z; | |
1587 | mpz_init_set_si (nj_z, nj); | |
1588 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
1589 | scm_remember_upto_here_1 (k); | |
73e4de09 | 1590 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
1591 | mpz_clear (nj_z); |
1592 | return result; | |
1593 | } | |
1594 | } | |
1595 | else | |
1596 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1597 | } | |
1598 | else if (SCM_BIGP (j)) | |
1599 | { | |
e11e83f3 | 1600 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
1601 | { |
1602 | SCM_SWAP (j, k); | |
e11e83f3 | 1603 | nj = SCM_I_INUM (j); |
0aacf84e MD |
1604 | goto intbig; |
1605 | } | |
1606 | else if (SCM_BIGP (k)) | |
1607 | { | |
1608 | SCM result; | |
1609 | mpz_t result_z; | |
1610 | mpz_init (result_z); | |
1611 | mpz_and (result_z, | |
1612 | SCM_I_BIG_MPZ (j), | |
1613 | SCM_I_BIG_MPZ (k)); | |
1614 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 1615 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
1616 | mpz_clear (result_z); |
1617 | return result; | |
1618 | } | |
1619 | else | |
1620 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1621 | } | |
1622 | else | |
1623 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 1624 | } |
1bbd0b84 | 1625 | #undef FUNC_NAME |
0f2d19dd | 1626 | |
c1bfcf60 | 1627 | |
a1ec6916 | 1628 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1629 | (SCM index, SCM j), |
ba6e7231 KR |
1630 | "Test whether bit number @var{index} in @var{j} is set.\n" |
1631 | "@var{index} starts from 0 for the least significant bit.\n" | |
1632 | "\n" | |
1e6808ea | 1633 | "@lisp\n" |
b380b885 MD |
1634 | "(logbit? 0 #b1101) @result{} #t\n" |
1635 | "(logbit? 1 #b1101) @result{} #f\n" | |
1636 | "(logbit? 2 #b1101) @result{} #t\n" | |
1637 | "(logbit? 3 #b1101) @result{} #t\n" | |
1638 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1639 | "@end lisp") |
1bbd0b84 | 1640 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1641 | { |
78166ad5 | 1642 | unsigned long int iindex; |
5efd3c7d | 1643 | iindex = scm_to_ulong (index); |
78166ad5 | 1644 | |
e11e83f3 | 1645 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
1646 | { |
1647 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 1648 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 1649 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 1650 | } |
0aacf84e MD |
1651 | else if (SCM_BIGP (j)) |
1652 | { | |
1653 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
1654 | scm_remember_upto_here_1 (j); | |
73e4de09 | 1655 | return scm_from_bool (val); |
0aacf84e MD |
1656 | } |
1657 | else | |
78166ad5 | 1658 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 1659 | } |
1bbd0b84 | 1660 | #undef FUNC_NAME |
0f2d19dd | 1661 | |
78166ad5 | 1662 | |
a1ec6916 | 1663 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1664 | (SCM n), |
4d814788 | 1665 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
1666 | "argument.\n" |
1667 | "\n" | |
b380b885 MD |
1668 | "@lisp\n" |
1669 | "(number->string (lognot #b10000000) 2)\n" | |
1670 | " @result{} \"-10000001\"\n" | |
1671 | "(number->string (lognot #b0) 2)\n" | |
1672 | " @result{} \"-1\"\n" | |
1e6808ea | 1673 | "@end lisp") |
1bbd0b84 | 1674 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1675 | { |
e11e83f3 | 1676 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
1677 | /* No overflow here, just need to toggle all the bits making up the inum. |
1678 | Enhancement: No need to strip the tag and add it back, could just xor | |
1679 | a block of 1 bits, if that worked with the various debug versions of | |
1680 | the SCM typedef. */ | |
e11e83f3 | 1681 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
1682 | |
1683 | } else if (SCM_BIGP (n)) { | |
1684 | SCM result = scm_i_mkbig (); | |
1685 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
1686 | scm_remember_upto_here_1 (n); | |
1687 | return result; | |
1688 | ||
1689 | } else { | |
1690 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1691 | } | |
0f2d19dd | 1692 | } |
1bbd0b84 | 1693 | #undef FUNC_NAME |
0f2d19dd | 1694 | |
518b7508 KR |
1695 | /* returns 0 if IN is not an integer. OUT must already be |
1696 | initialized. */ | |
1697 | static int | |
1698 | coerce_to_big (SCM in, mpz_t out) | |
1699 | { | |
1700 | if (SCM_BIGP (in)) | |
1701 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
1702 | else if (SCM_I_INUMP (in)) |
1703 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
1704 | else |
1705 | return 0; | |
1706 | ||
1707 | return 1; | |
1708 | } | |
1709 | ||
d885e204 | 1710 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
1711 | (SCM n, SCM k, SCM m), |
1712 | "Return @var{n} raised to the integer exponent\n" | |
1713 | "@var{k}, modulo @var{m}.\n" | |
1714 | "\n" | |
1715 | "@lisp\n" | |
1716 | "(modulo-expt 2 3 5)\n" | |
1717 | " @result{} 3\n" | |
1718 | "@end lisp") | |
d885e204 | 1719 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
1720 | { |
1721 | mpz_t n_tmp; | |
1722 | mpz_t k_tmp; | |
1723 | mpz_t m_tmp; | |
1724 | ||
1725 | /* There are two classes of error we might encounter -- | |
1726 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
1727 | and | |
1728 | 2) wrong-type errors, which of course we'll report by calling | |
1729 | SCM_WRONG_TYPE_ARG. | |
1730 | We don't report those errors immediately, however; instead we do | |
1731 | some cleanup first. These variables tell us which error (if | |
1732 | any) we should report after cleaning up. | |
1733 | */ | |
1734 | int report_overflow = 0; | |
1735 | ||
1736 | int position_of_wrong_type = 0; | |
1737 | SCM value_of_wrong_type = SCM_INUM0; | |
1738 | ||
1739 | SCM result = SCM_UNDEFINED; | |
1740 | ||
1741 | mpz_init (n_tmp); | |
1742 | mpz_init (k_tmp); | |
1743 | mpz_init (m_tmp); | |
1744 | ||
bc36d050 | 1745 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
1746 | { |
1747 | report_overflow = 1; | |
1748 | goto cleanup; | |
1749 | } | |
1750 | ||
1751 | if (!coerce_to_big (n, n_tmp)) | |
1752 | { | |
1753 | value_of_wrong_type = n; | |
1754 | position_of_wrong_type = 1; | |
1755 | goto cleanup; | |
1756 | } | |
1757 | ||
1758 | if (!coerce_to_big (k, k_tmp)) | |
1759 | { | |
1760 | value_of_wrong_type = k; | |
1761 | position_of_wrong_type = 2; | |
1762 | goto cleanup; | |
1763 | } | |
1764 | ||
1765 | if (!coerce_to_big (m, m_tmp)) | |
1766 | { | |
1767 | value_of_wrong_type = m; | |
1768 | position_of_wrong_type = 3; | |
1769 | goto cleanup; | |
1770 | } | |
1771 | ||
1772 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
1773 | will get a divide-by-zero exception when an inverse 1/n mod m | |
1774 | doesn't exist (or is not unique). Since exceptions are hard to | |
1775 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
1776 | a simple failure code, which is easy to handle. */ | |
1777 | ||
1778 | if (-1 == mpz_sgn (k_tmp)) | |
1779 | { | |
1780 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
1781 | { | |
1782 | report_overflow = 1; | |
1783 | goto cleanup; | |
1784 | } | |
1785 | mpz_neg (k_tmp, k_tmp); | |
1786 | } | |
1787 | ||
1788 | result = scm_i_mkbig (); | |
1789 | mpz_powm (SCM_I_BIG_MPZ (result), | |
1790 | n_tmp, | |
1791 | k_tmp, | |
1792 | m_tmp); | |
b7b8c575 KR |
1793 | |
1794 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
1795 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
1796 | ||
518b7508 KR |
1797 | cleanup: |
1798 | mpz_clear (m_tmp); | |
1799 | mpz_clear (k_tmp); | |
1800 | mpz_clear (n_tmp); | |
1801 | ||
1802 | if (report_overflow) | |
1803 | scm_num_overflow (FUNC_NAME); | |
1804 | ||
1805 | if (position_of_wrong_type) | |
1806 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
1807 | value_of_wrong_type); | |
1808 | ||
1809 | return scm_i_normbig (result); | |
1810 | } | |
1811 | #undef FUNC_NAME | |
1812 | ||
a1ec6916 | 1813 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1814 | (SCM n, SCM k), |
ba6e7231 KR |
1815 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
1816 | "exact integer, @var{n} can be any number.\n" | |
1817 | "\n" | |
1818 | "Negative @var{k} is supported, and results in @math{1/n^abs(k)}\n" | |
1819 | "in the usual way. @math{@var{n}^0} is 1, as usual, and that\n" | |
1820 | "includes @math{0^0} is 1.\n" | |
1e6808ea | 1821 | "\n" |
b380b885 | 1822 | "@lisp\n" |
ba6e7231 KR |
1823 | "(integer-expt 2 5) @result{} 32\n" |
1824 | "(integer-expt -3 3) @result{} -27\n" | |
1825 | "(integer-expt 5 -3) @result{} 1/125\n" | |
1826 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 1827 | "@end lisp") |
1bbd0b84 | 1828 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1829 | { |
e25f3727 | 1830 | scm_t_inum i2 = 0; |
1c35cb19 RB |
1831 | SCM z_i2 = SCM_BOOL_F; |
1832 | int i2_is_big = 0; | |
d956fa6f | 1833 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 1834 | |
5a8fc758 | 1835 | SCM_VALIDATE_NUMBER (SCM_ARG1, n); |
01c7284a MW |
1836 | if (!SCM_I_INUMP (k) && !SCM_BIGP (k)) |
1837 | SCM_WRONG_TYPE_ARG (2, k); | |
5a8fc758 | 1838 | |
01c7284a MW |
1839 | if (scm_is_true (scm_zero_p (n))) |
1840 | { | |
1841 | if (scm_is_true (scm_zero_p (k))) /* 0^0 == 1 per R5RS */ | |
1842 | return acc; /* return exact 1, regardless of n */ | |
1843 | else if (scm_is_true (scm_positive_p (k))) | |
1844 | return n; | |
1845 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
1846 | return scm_nan (); | |
1847 | } | |
1848 | else if (scm_is_eq (n, acc)) | |
1849 | return acc; | |
bc36d050 | 1850 | else if (scm_is_eq (n, SCM_I_MAKINUM (-1L))) |
73e4de09 | 1851 | return scm_is_false (scm_even_p (k)) ? n : acc; |
ca46fb90 | 1852 | |
e11e83f3 MV |
1853 | if (SCM_I_INUMP (k)) |
1854 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
1855 | else if (SCM_BIGP (k)) |
1856 | { | |
1857 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
1858 | scm_remember_upto_here_1 (k); |
1859 | i2_is_big = 1; | |
1860 | } | |
2830fd91 | 1861 | else |
ca46fb90 RB |
1862 | SCM_WRONG_TYPE_ARG (2, k); |
1863 | ||
1864 | if (i2_is_big) | |
f872b822 | 1865 | { |
ca46fb90 RB |
1866 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
1867 | { | |
1868 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
1869 | n = scm_divide (n, SCM_UNDEFINED); | |
1870 | } | |
1871 | while (1) | |
1872 | { | |
1873 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
1874 | { | |
ca46fb90 RB |
1875 | return acc; |
1876 | } | |
1877 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
1878 | { | |
ca46fb90 RB |
1879 | return scm_product (acc, n); |
1880 | } | |
1881 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
1882 | acc = scm_product (acc, n); | |
1883 | n = scm_product (n, n); | |
1884 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
1885 | } | |
f872b822 | 1886 | } |
ca46fb90 | 1887 | else |
f872b822 | 1888 | { |
ca46fb90 RB |
1889 | if (i2 < 0) |
1890 | { | |
1891 | i2 = -i2; | |
1892 | n = scm_divide (n, SCM_UNDEFINED); | |
1893 | } | |
1894 | while (1) | |
1895 | { | |
1896 | if (0 == i2) | |
1897 | return acc; | |
1898 | if (1 == i2) | |
1899 | return scm_product (acc, n); | |
1900 | if (i2 & 1) | |
1901 | acc = scm_product (acc, n); | |
1902 | n = scm_product (n, n); | |
1903 | i2 >>= 1; | |
1904 | } | |
f872b822 | 1905 | } |
0f2d19dd | 1906 | } |
1bbd0b84 | 1907 | #undef FUNC_NAME |
0f2d19dd | 1908 | |
a1ec6916 | 1909 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1910 | (SCM n, SCM cnt), |
32f19569 KR |
1911 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
1912 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 1913 | "\n" |
e7644cb2 | 1914 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
1915 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
1916 | "infinity. (Note that this is not the same rounding as\n" | |
1917 | "@code{quotient} does.)\n" | |
1918 | "\n" | |
1919 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
1920 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
1921 | "shift dropping bits.\n" | |
1e6808ea | 1922 | "\n" |
b380b885 | 1923 | "@lisp\n" |
1e6808ea MG |
1924 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1925 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
1926 | "\n" |
1927 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
1928 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 1929 | "@end lisp") |
1bbd0b84 | 1930 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1931 | { |
3ab9f56e | 1932 | long bits_to_shift; |
5efd3c7d | 1933 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 1934 | |
788aca27 KR |
1935 | if (SCM_I_INUMP (n)) |
1936 | { | |
e25f3727 | 1937 | scm_t_inum nn = SCM_I_INUM (n); |
788aca27 KR |
1938 | |
1939 | if (bits_to_shift > 0) | |
1940 | { | |
1941 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
1942 | overflow a non-zero fixnum. For smaller shifts we check the | |
1943 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
1944 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
1945 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
1946 | bits_to_shift)". */ | |
1947 | ||
1948 | if (nn == 0) | |
1949 | return n; | |
1950 | ||
1951 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 1952 | && ((scm_t_bits) |
788aca27 KR |
1953 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) |
1954 | <= 1)) | |
1955 | { | |
1956 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
1957 | } | |
1958 | else | |
1959 | { | |
e25f3727 | 1960 | SCM result = scm_i_inum2big (nn); |
788aca27 KR |
1961 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
1962 | bits_to_shift); | |
1963 | return result; | |
1964 | } | |
1965 | } | |
1966 | else | |
1967 | { | |
1968 | bits_to_shift = -bits_to_shift; | |
1969 | if (bits_to_shift >= SCM_LONG_BIT) | |
cff5fa33 | 1970 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1)); |
788aca27 KR |
1971 | else |
1972 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
1973 | } | |
1974 | ||
1975 | } | |
1976 | else if (SCM_BIGP (n)) | |
ca46fb90 | 1977 | { |
788aca27 KR |
1978 | SCM result; |
1979 | ||
1980 | if (bits_to_shift == 0) | |
1981 | return n; | |
1982 | ||
1983 | result = scm_i_mkbig (); | |
1984 | if (bits_to_shift >= 0) | |
1985 | { | |
1986 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1987 | bits_to_shift); | |
1988 | return result; | |
1989 | } | |
ca46fb90 | 1990 | else |
788aca27 KR |
1991 | { |
1992 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
1993 | we have to allocate a bignum even if the result is going to be a | |
1994 | fixnum. */ | |
1995 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1996 | -bits_to_shift); | |
1997 | return scm_i_normbig (result); | |
1998 | } | |
1999 | ||
ca46fb90 RB |
2000 | } |
2001 | else | |
788aca27 KR |
2002 | { |
2003 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
2004 | } | |
0f2d19dd | 2005 | } |
1bbd0b84 | 2006 | #undef FUNC_NAME |
0f2d19dd | 2007 | |
3c9f20f8 | 2008 | |
a1ec6916 | 2009 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 2010 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
2011 | "Return the integer composed of the @var{start} (inclusive)\n" |
2012 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
2013 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
2014 | "\n" | |
b380b885 MD |
2015 | "@lisp\n" |
2016 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
2017 | " @result{} \"1010\"\n" | |
2018 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
2019 | " @result{} \"10110\"\n" | |
2020 | "@end lisp") | |
1bbd0b84 | 2021 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 2022 | { |
7f848242 | 2023 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
2024 | istart = scm_to_ulong (start); |
2025 | iend = scm_to_ulong (end); | |
c1bfcf60 | 2026 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 2027 | |
7f848242 KR |
2028 | /* how many bits to keep */ |
2029 | bits = iend - istart; | |
2030 | ||
e11e83f3 | 2031 | if (SCM_I_INUMP (n)) |
0aacf84e | 2032 | { |
e25f3727 | 2033 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
2034 | |
2035 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 2036 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 2037 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 2038 | |
0aacf84e MD |
2039 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
2040 | { | |
2041 | /* Since we emulate two's complement encoded numbers, this | |
2042 | * special case requires us to produce a result that has | |
7f848242 | 2043 | * more bits than can be stored in a fixnum. |
0aacf84e | 2044 | */ |
e25f3727 | 2045 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
2046 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
2047 | bits); | |
2048 | return result; | |
0aacf84e | 2049 | } |
ac0c002c | 2050 | |
7f848242 | 2051 | /* mask down to requisite bits */ |
857ae6af | 2052 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 2053 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
2054 | } |
2055 | else if (SCM_BIGP (n)) | |
ac0c002c | 2056 | { |
7f848242 KR |
2057 | SCM result; |
2058 | if (bits == 1) | |
2059 | { | |
d956fa6f | 2060 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
2061 | } |
2062 | else | |
2063 | { | |
2064 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
2065 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
2066 | such bits into a ulong. */ | |
2067 | result = scm_i_mkbig (); | |
2068 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
2069 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
2070 | result = scm_i_normbig (result); | |
2071 | } | |
2072 | scm_remember_upto_here_1 (n); | |
2073 | return result; | |
ac0c002c | 2074 | } |
0aacf84e | 2075 | else |
78166ad5 | 2076 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 2077 | } |
1bbd0b84 | 2078 | #undef FUNC_NAME |
0f2d19dd | 2079 | |
7f848242 | 2080 | |
e4755e5c JB |
2081 | static const char scm_logtab[] = { |
2082 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
2083 | }; | |
1cc91f1b | 2084 | |
a1ec6916 | 2085 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 2086 | (SCM n), |
1e6808ea MG |
2087 | "Return the number of bits in integer @var{n}. If integer is\n" |
2088 | "positive, the 1-bits in its binary representation are counted.\n" | |
2089 | "If negative, the 0-bits in its two's-complement binary\n" | |
2090 | "representation are counted. If 0, 0 is returned.\n" | |
2091 | "\n" | |
b380b885 MD |
2092 | "@lisp\n" |
2093 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
2094 | " @result{} 4\n" |
2095 | "(logcount 0)\n" | |
2096 | " @result{} 0\n" | |
2097 | "(logcount -2)\n" | |
2098 | " @result{} 1\n" | |
2099 | "@end lisp") | |
2100 | #define FUNC_NAME s_scm_logcount | |
2101 | { | |
e11e83f3 | 2102 | if (SCM_I_INUMP (n)) |
f872b822 | 2103 | { |
e25f3727 AW |
2104 | unsigned long c = 0; |
2105 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
2106 | if (nn < 0) |
2107 | nn = -1 - nn; | |
2108 | while (nn) | |
2109 | { | |
2110 | c += scm_logtab[15 & nn]; | |
2111 | nn >>= 4; | |
2112 | } | |
d956fa6f | 2113 | return SCM_I_MAKINUM (c); |
f872b822 | 2114 | } |
ca46fb90 | 2115 | else if (SCM_BIGP (n)) |
f872b822 | 2116 | { |
ca46fb90 | 2117 | unsigned long count; |
713a4259 KR |
2118 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
2119 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 2120 | else |
713a4259 KR |
2121 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
2122 | scm_remember_upto_here_1 (n); | |
d956fa6f | 2123 | return SCM_I_MAKINUM (count); |
f872b822 | 2124 | } |
ca46fb90 RB |
2125 | else |
2126 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 2127 | } |
ca46fb90 | 2128 | #undef FUNC_NAME |
0f2d19dd JB |
2129 | |
2130 | ||
ca46fb90 RB |
2131 | static const char scm_ilentab[] = { |
2132 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
2133 | }; | |
2134 | ||
0f2d19dd | 2135 | |
ca46fb90 RB |
2136 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
2137 | (SCM n), | |
2138 | "Return the number of bits necessary to represent @var{n}.\n" | |
2139 | "\n" | |
2140 | "@lisp\n" | |
2141 | "(integer-length #b10101010)\n" | |
2142 | " @result{} 8\n" | |
2143 | "(integer-length 0)\n" | |
2144 | " @result{} 0\n" | |
2145 | "(integer-length #b1111)\n" | |
2146 | " @result{} 4\n" | |
2147 | "@end lisp") | |
2148 | #define FUNC_NAME s_scm_integer_length | |
2149 | { | |
e11e83f3 | 2150 | if (SCM_I_INUMP (n)) |
0aacf84e | 2151 | { |
e25f3727 | 2152 | unsigned long c = 0; |
0aacf84e | 2153 | unsigned int l = 4; |
e25f3727 | 2154 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
2155 | if (nn < 0) |
2156 | nn = -1 - nn; | |
2157 | while (nn) | |
2158 | { | |
2159 | c += 4; | |
2160 | l = scm_ilentab [15 & nn]; | |
2161 | nn >>= 4; | |
2162 | } | |
d956fa6f | 2163 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
2164 | } |
2165 | else if (SCM_BIGP (n)) | |
2166 | { | |
2167 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
2168 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
2169 | 1 too big, so check for that and adjust. */ | |
2170 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
2171 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
2172 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
2173 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
2174 | size--; | |
2175 | scm_remember_upto_here_1 (n); | |
d956fa6f | 2176 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
2177 | } |
2178 | else | |
ca46fb90 | 2179 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
2180 | } |
2181 | #undef FUNC_NAME | |
0f2d19dd JB |
2182 | |
2183 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
2184 | #define SCM_MAX_DBL_PREC 60 |
2185 | #define SCM_MAX_DBL_RADIX 36 | |
2186 | ||
2187 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
2188 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
2189 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
2190 | ||
2191 | static | |
2192 | void init_dblprec(int *prec, int radix) { | |
2193 | /* determine floating point precision by adding successively | |
2194 | smaller increments to 1.0 until it is considered == 1.0 */ | |
2195 | double f = ((double)1.0)/radix; | |
2196 | double fsum = 1.0 + f; | |
2197 | ||
2198 | *prec = 0; | |
2199 | while (fsum != 1.0) | |
2200 | { | |
2201 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
2202 | fsum = 1.0; | |
2203 | else | |
2204 | { | |
2205 | f /= radix; | |
2206 | fsum = f + 1.0; | |
2207 | } | |
2208 | } | |
2209 | (*prec) -= 1; | |
2210 | } | |
2211 | ||
2212 | static | |
2213 | void init_fx_radix(double *fx_list, int radix) | |
2214 | { | |
2215 | /* initialize a per-radix list of tolerances. When added | |
2216 | to a number < 1.0, we can determine if we should raund | |
2217 | up and quit converting a number to a string. */ | |
2218 | int i; | |
2219 | fx_list[0] = 0.0; | |
2220 | fx_list[1] = 0.5; | |
2221 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
2222 | fx_list[i] = (fx_list[i-1] / radix); | |
2223 | } | |
2224 | ||
2225 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 2226 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 2227 | |
1be6b49c | 2228 | static size_t |
0b799eea | 2229 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 2230 | { |
0b799eea MV |
2231 | int efmt, dpt, d, i, wp; |
2232 | double *fx; | |
2233 | #ifdef DBL_MIN_10_EXP | |
2234 | double f_cpy; | |
2235 | int exp_cpy; | |
2236 | #endif /* DBL_MIN_10_EXP */ | |
2237 | size_t ch = 0; | |
2238 | int exp = 0; | |
2239 | ||
2240 | if(radix < 2 || | |
2241 | radix > SCM_MAX_DBL_RADIX) | |
2242 | { | |
2243 | /* revert to existing behavior */ | |
2244 | radix = 10; | |
2245 | } | |
2246 | ||
2247 | wp = scm_dblprec[radix-2]; | |
2248 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 2249 | |
f872b822 | 2250 | if (f == 0.0) |
abb7e44d MV |
2251 | { |
2252 | #ifdef HAVE_COPYSIGN | |
2253 | double sgn = copysign (1.0, f); | |
2254 | ||
2255 | if (sgn < 0.0) | |
2256 | a[ch++] = '-'; | |
2257 | #endif | |
abb7e44d MV |
2258 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
2259 | } | |
7351e207 | 2260 | |
2e65b52f | 2261 | if (isinf (f)) |
7351e207 MV |
2262 | { |
2263 | if (f < 0) | |
2264 | strcpy (a, "-inf.0"); | |
2265 | else | |
2266 | strcpy (a, "+inf.0"); | |
2267 | return ch+6; | |
2268 | } | |
2e65b52f | 2269 | else if (isnan (f)) |
7351e207 MV |
2270 | { |
2271 | strcpy (a, "+nan.0"); | |
2272 | return ch+6; | |
2273 | } | |
2274 | ||
f872b822 MD |
2275 | if (f < 0.0) |
2276 | { | |
2277 | f = -f; | |
2278 | a[ch++] = '-'; | |
2279 | } | |
7351e207 | 2280 | |
f872b822 MD |
2281 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
2282 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
2283 | /* just do the checking...if it passes, we do the conversion for our |
2284 | radix again below */ | |
2285 | f_cpy = f; | |
2286 | exp_cpy = exp; | |
2287 | ||
2288 | while (f_cpy < 1.0) | |
f872b822 | 2289 | { |
0b799eea MV |
2290 | f_cpy *= 10.0; |
2291 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
2292 | { |
2293 | a[ch++] = '#'; | |
2294 | a[ch++] = '.'; | |
2295 | a[ch++] = '#'; | |
2296 | return ch; | |
2297 | } | |
f872b822 | 2298 | } |
0b799eea | 2299 | while (f_cpy > 10.0) |
f872b822 | 2300 | { |
0b799eea MV |
2301 | f_cpy *= 0.10; |
2302 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
2303 | { |
2304 | a[ch++] = '#'; | |
2305 | a[ch++] = '.'; | |
2306 | a[ch++] = '#'; | |
2307 | return ch; | |
2308 | } | |
f872b822 | 2309 | } |
0b799eea MV |
2310 | #endif |
2311 | ||
f872b822 MD |
2312 | while (f < 1.0) |
2313 | { | |
0b799eea | 2314 | f *= radix; |
f872b822 MD |
2315 | exp--; |
2316 | } | |
0b799eea | 2317 | while (f > radix) |
f872b822 | 2318 | { |
0b799eea | 2319 | f /= radix; |
f872b822 MD |
2320 | exp++; |
2321 | } | |
0b799eea MV |
2322 | |
2323 | if (f + fx[wp] >= radix) | |
f872b822 MD |
2324 | { |
2325 | f = 1.0; | |
2326 | exp++; | |
2327 | } | |
0f2d19dd | 2328 | zero: |
0b799eea MV |
2329 | #ifdef ENGNOT |
2330 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 2331 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
2332 | exp -= dpt++; |
2333 | efmt = 1; | |
f872b822 MD |
2334 | #else |
2335 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 2336 | if (!efmt) |
cda139a7 MD |
2337 | { |
2338 | if (exp < 0) | |
2339 | { | |
2340 | a[ch++] = '0'; | |
2341 | a[ch++] = '.'; | |
2342 | dpt = exp; | |
f872b822 MD |
2343 | while (++dpt) |
2344 | a[ch++] = '0'; | |
cda139a7 MD |
2345 | } |
2346 | else | |
f872b822 | 2347 | dpt = exp + 1; |
cda139a7 | 2348 | } |
0f2d19dd JB |
2349 | else |
2350 | dpt = 1; | |
f872b822 MD |
2351 | #endif |
2352 | ||
2353 | do | |
2354 | { | |
2355 | d = f; | |
2356 | f -= d; | |
0b799eea | 2357 | a[ch++] = number_chars[d]; |
f872b822 MD |
2358 | if (f < fx[wp]) |
2359 | break; | |
2360 | if (f + fx[wp] >= 1.0) | |
2361 | { | |
0b799eea | 2362 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
2363 | break; |
2364 | } | |
0b799eea | 2365 | f *= radix; |
f872b822 MD |
2366 | if (!(--dpt)) |
2367 | a[ch++] = '.'; | |
0f2d19dd | 2368 | } |
f872b822 | 2369 | while (wp--); |
0f2d19dd JB |
2370 | |
2371 | if (dpt > 0) | |
cda139a7 | 2372 | { |
f872b822 | 2373 | #ifndef ENGNOT |
cda139a7 MD |
2374 | if ((dpt > 4) && (exp > 6)) |
2375 | { | |
f872b822 | 2376 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 2377 | for (i = ch++; i > d; i--) |
f872b822 | 2378 | a[i] = a[i - 1]; |
cda139a7 MD |
2379 | a[d] = '.'; |
2380 | efmt = 1; | |
2381 | } | |
2382 | else | |
f872b822 | 2383 | #endif |
cda139a7 | 2384 | { |
f872b822 MD |
2385 | while (--dpt) |
2386 | a[ch++] = '0'; | |
cda139a7 MD |
2387 | a[ch++] = '.'; |
2388 | } | |
2389 | } | |
f872b822 MD |
2390 | if (a[ch - 1] == '.') |
2391 | a[ch++] = '0'; /* trailing zero */ | |
2392 | if (efmt && exp) | |
2393 | { | |
2394 | a[ch++] = 'e'; | |
2395 | if (exp < 0) | |
2396 | { | |
2397 | exp = -exp; | |
2398 | a[ch++] = '-'; | |
2399 | } | |
0b799eea MV |
2400 | for (i = radix; i <= exp; i *= radix); |
2401 | for (i /= radix; i; i /= radix) | |
f872b822 | 2402 | { |
0b799eea | 2403 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
2404 | exp %= i; |
2405 | } | |
0f2d19dd | 2406 | } |
0f2d19dd JB |
2407 | return ch; |
2408 | } | |
2409 | ||
7a1aba42 MV |
2410 | |
2411 | static size_t | |
2412 | icmplx2str (double real, double imag, char *str, int radix) | |
2413 | { | |
2414 | size_t i; | |
2415 | ||
2416 | i = idbl2str (real, str, radix); | |
2417 | if (imag != 0.0) | |
2418 | { | |
2419 | /* Don't output a '+' for negative numbers or for Inf and | |
2420 | NaN. They will provide their own sign. */ | |
2e65b52f | 2421 | if (0 <= imag && !isinf (imag) && !isnan (imag)) |
7a1aba42 MV |
2422 | str[i++] = '+'; |
2423 | i += idbl2str (imag, &str[i], radix); | |
2424 | str[i++] = 'i'; | |
2425 | } | |
2426 | return i; | |
2427 | } | |
2428 | ||
1be6b49c | 2429 | static size_t |
0b799eea | 2430 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 2431 | { |
1be6b49c | 2432 | size_t i; |
3c9a524f | 2433 | if (SCM_REALP (flt)) |
0b799eea | 2434 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 2435 | else |
7a1aba42 MV |
2436 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
2437 | str, radix); | |
0f2d19dd JB |
2438 | return i; |
2439 | } | |
0f2d19dd | 2440 | |
2881e77b | 2441 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
2442 | characters in the result. |
2443 | rad is output base | |
2444 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2445 | size_t |
2881e77b MV |
2446 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
2447 | { | |
2448 | if (num < 0) | |
2449 | { | |
2450 | *p++ = '-'; | |
2451 | return scm_iuint2str (-num, rad, p) + 1; | |
2452 | } | |
2453 | else | |
2454 | return scm_iuint2str (num, rad, p); | |
2455 | } | |
2456 | ||
2457 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
2458 | characters in the result. | |
2459 | rad is output base | |
2460 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
2461 | size_t | |
2462 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 2463 | { |
1be6b49c ML |
2464 | size_t j = 1; |
2465 | size_t i; | |
2881e77b | 2466 | scm_t_uintmax n = num; |
5c11cc9d | 2467 | |
a6f3af16 AW |
2468 | if (rad < 2 || rad > 36) |
2469 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
2470 | ||
f872b822 | 2471 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2472 | j++; |
2473 | ||
2474 | i = j; | |
2881e77b | 2475 | n = num; |
f872b822 MD |
2476 | while (i--) |
2477 | { | |
5c11cc9d GH |
2478 | int d = n % rad; |
2479 | ||
f872b822 | 2480 | n /= rad; |
a6f3af16 | 2481 | p[i] = number_chars[d]; |
f872b822 | 2482 | } |
0f2d19dd JB |
2483 | return j; |
2484 | } | |
2485 | ||
a1ec6916 | 2486 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2487 | (SCM n, SCM radix), |
2488 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2489 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2490 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2491 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2492 | { |
1bbd0b84 | 2493 | int base; |
98cb6e75 | 2494 | |
0aacf84e | 2495 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 2496 | base = 10; |
0aacf84e | 2497 | else |
5efd3c7d | 2498 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 2499 | |
e11e83f3 | 2500 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2501 | { |
2502 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 2503 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 2504 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
2505 | } |
2506 | else if (SCM_BIGP (n)) | |
2507 | { | |
2508 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
2509 | scm_remember_upto_here_1 (n); | |
cc95e00a | 2510 | return scm_take_locale_string (str); |
0aacf84e | 2511 | } |
f92e85f7 MV |
2512 | else if (SCM_FRACTIONP (n)) |
2513 | { | |
f92e85f7 | 2514 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 2515 | scm_from_locale_string ("/"), |
f92e85f7 MV |
2516 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
2517 | } | |
0aacf84e MD |
2518 | else if (SCM_INEXACTP (n)) |
2519 | { | |
2520 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 2521 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
2522 | } |
2523 | else | |
bb628794 | 2524 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 2525 | } |
1bbd0b84 | 2526 | #undef FUNC_NAME |
0f2d19dd JB |
2527 | |
2528 | ||
ca46fb90 RB |
2529 | /* These print routines used to be stubbed here so that scm_repl.c |
2530 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 2531 | |
0f2d19dd | 2532 | int |
e81d98ec | 2533 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2534 | { |
56e55ac7 | 2535 | char num_buf[FLOBUFLEN]; |
0b799eea | 2536 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
2537 | return !0; |
2538 | } | |
2539 | ||
b479fe9a MV |
2540 | void |
2541 | scm_i_print_double (double val, SCM port) | |
2542 | { | |
2543 | char num_buf[FLOBUFLEN]; | |
2544 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
2545 | } | |
2546 | ||
f3ae5d60 | 2547 | int |
e81d98ec | 2548 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 2549 | |
f3ae5d60 | 2550 | { |
56e55ac7 | 2551 | char num_buf[FLOBUFLEN]; |
0b799eea | 2552 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
2553 | return !0; |
2554 | } | |
1cc91f1b | 2555 | |
7a1aba42 MV |
2556 | void |
2557 | scm_i_print_complex (double real, double imag, SCM port) | |
2558 | { | |
2559 | char num_buf[FLOBUFLEN]; | |
2560 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
2561 | } | |
2562 | ||
f92e85f7 MV |
2563 | int |
2564 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
2565 | { | |
2566 | SCM str; | |
f92e85f7 | 2567 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 2568 | scm_display (str, port); |
f92e85f7 MV |
2569 | scm_remember_upto_here_1 (str); |
2570 | return !0; | |
2571 | } | |
2572 | ||
0f2d19dd | 2573 | int |
e81d98ec | 2574 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2575 | { |
ca46fb90 RB |
2576 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
2577 | scm_remember_upto_here_1 (exp); | |
2578 | scm_lfwrite (str, (size_t) strlen (str), port); | |
2579 | free (str); | |
0f2d19dd JB |
2580 | return !0; |
2581 | } | |
2582 | /*** END nums->strs ***/ | |
2583 | ||
3c9a524f | 2584 | |
0f2d19dd | 2585 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2586 | |
3c9a524f DH |
2587 | /* The following functions implement the conversion from strings to numbers. |
2588 | * The implementation somehow follows the grammar for numbers as it is given | |
2589 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2590 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2591 | * points should be noted about the implementation: | |
2592 | * * Each function keeps a local index variable 'idx' that points at the | |
2593 | * current position within the parsed string. The global index is only | |
2594 | * updated if the function could parse the corresponding syntactic unit | |
2595 | * successfully. | |
2596 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2597 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2598 | * global exactness information is only updated after each part has been | |
2599 | * successfully parsed. | |
2600 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2601 | * Only if these fixnums would overflow, the result variables are updated | |
2602 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2603 | * the temporary variables holding the fixnums are cleared, and the process | |
2604 | * starts over again. If for example fixnums were able to store five decimal | |
2605 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2606 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2607 | * only every five digits two bignum operations were performed. | |
2608 | */ | |
2609 | ||
2610 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2611 | ||
2612 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2613 | ||
a6f3af16 AW |
2614 | /* Caller is responsible for checking that the return value is in range |
2615 | for the given radix, which should be <= 36. */ | |
2616 | static unsigned int | |
2617 | char_decimal_value (scm_t_uint32 c) | |
2618 | { | |
2619 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
2620 | that's certainly above any valid decimal, so we take advantage of | |
2621 | that to elide some tests. */ | |
2622 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
2623 | ||
2624 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
2625 | hexadecimals. */ | |
2626 | if (d >= 10U) | |
2627 | { | |
2628 | c = uc_tolower (c); | |
2629 | if (c >= (scm_t_uint32) 'a') | |
2630 | d = c - (scm_t_uint32)'a' + 10U; | |
2631 | } | |
2632 | return d; | |
2633 | } | |
3c9a524f | 2634 | |
2a8fecee | 2635 | static SCM |
3f47e526 | 2636 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 2637 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 2638 | { |
3c9a524f DH |
2639 | unsigned int idx = *p_idx; |
2640 | unsigned int hash_seen = 0; | |
2641 | scm_t_bits shift = 1; | |
2642 | scm_t_bits add = 0; | |
2643 | unsigned int digit_value; | |
2644 | SCM result; | |
2645 | char c; | |
3f47e526 | 2646 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
2647 | |
2648 | if (idx == len) | |
2649 | return SCM_BOOL_F; | |
2a8fecee | 2650 | |
3f47e526 | 2651 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 2652 | digit_value = char_decimal_value (c); |
3c9a524f DH |
2653 | if (digit_value >= radix) |
2654 | return SCM_BOOL_F; | |
2655 | ||
2656 | idx++; | |
d956fa6f | 2657 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 2658 | while (idx != len) |
f872b822 | 2659 | { |
3f47e526 | 2660 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 2661 | if (c == '#') |
3c9a524f DH |
2662 | { |
2663 | hash_seen = 1; | |
2664 | digit_value = 0; | |
2665 | } | |
a6f3af16 AW |
2666 | else if (hash_seen) |
2667 | break; | |
3c9a524f | 2668 | else |
a6f3af16 AW |
2669 | { |
2670 | digit_value = char_decimal_value (c); | |
2671 | /* This check catches non-decimals in addition to out-of-range | |
2672 | decimals. */ | |
2673 | if (digit_value >= radix) | |
2674 | break; | |
2675 | } | |
3c9a524f DH |
2676 | |
2677 | idx++; | |
2678 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2679 | { | |
d956fa6f | 2680 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2681 | if (add > 0) |
d956fa6f | 2682 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2683 | |
2684 | shift = radix; | |
2685 | add = digit_value; | |
2686 | } | |
2687 | else | |
2688 | { | |
2689 | shift = shift * radix; | |
2690 | add = add * radix + digit_value; | |
2691 | } | |
2692 | }; | |
2693 | ||
2694 | if (shift > 1) | |
d956fa6f | 2695 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2696 | if (add > 0) |
d956fa6f | 2697 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2698 | |
2699 | *p_idx = idx; | |
2700 | if (hash_seen) | |
2701 | *p_exactness = INEXACT; | |
2702 | ||
2703 | return result; | |
2a8fecee JB |
2704 | } |
2705 | ||
2706 | ||
3c9a524f DH |
2707 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2708 | * covers the parts of the rules that start at a potential point. The value | |
2709 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2710 | * in variable result. The content of *p_exactness indicates, whether a hash |
2711 | * has already been seen in the digits before the point. | |
3c9a524f | 2712 | */ |
1cc91f1b | 2713 | |
3f47e526 | 2714 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
2715 | |
2716 | static SCM | |
3f47e526 | 2717 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 2718 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2719 | { |
3c9a524f DH |
2720 | unsigned int idx = *p_idx; |
2721 | enum t_exactness x = *p_exactness; | |
3f47e526 | 2722 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
2723 | |
2724 | if (idx == len) | |
79d34f68 | 2725 | return result; |
3c9a524f | 2726 | |
3f47e526 | 2727 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
2728 | { |
2729 | scm_t_bits shift = 1; | |
2730 | scm_t_bits add = 0; | |
2731 | unsigned int digit_value; | |
cff5fa33 | 2732 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
2733 | |
2734 | idx++; | |
2735 | while (idx != len) | |
2736 | { | |
3f47e526 MG |
2737 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
2738 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
2739 | { |
2740 | if (x == INEXACT) | |
2741 | return SCM_BOOL_F; | |
2742 | else | |
2743 | digit_value = DIGIT2UINT (c); | |
2744 | } | |
2745 | else if (c == '#') | |
2746 | { | |
2747 | x = INEXACT; | |
2748 | digit_value = 0; | |
2749 | } | |
2750 | else | |
2751 | break; | |
2752 | ||
2753 | idx++; | |
2754 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2755 | { | |
d956fa6f MV |
2756 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2757 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 2758 | if (add > 0) |
d956fa6f | 2759 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2760 | |
2761 | shift = 10; | |
2762 | add = digit_value; | |
2763 | } | |
2764 | else | |
2765 | { | |
2766 | shift = shift * 10; | |
2767 | add = add * 10 + digit_value; | |
2768 | } | |
2769 | }; | |
2770 | ||
2771 | if (add > 0) | |
2772 | { | |
d956fa6f MV |
2773 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2774 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
2775 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
2776 | } |
2777 | ||
d8592269 | 2778 | result = scm_divide (result, big_shift); |
79d34f68 | 2779 | |
3c9a524f DH |
2780 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2781 | x = INEXACT; | |
f872b822 | 2782 | } |
3c9a524f | 2783 | |
3c9a524f | 2784 | if (idx != len) |
f872b822 | 2785 | { |
3c9a524f DH |
2786 | int sign = 1; |
2787 | unsigned int start; | |
3f47e526 | 2788 | scm_t_wchar c; |
3c9a524f DH |
2789 | int exponent; |
2790 | SCM e; | |
2791 | ||
2792 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2793 | ||
3f47e526 | 2794 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 2795 | { |
3c9a524f DH |
2796 | case 'd': case 'D': |
2797 | case 'e': case 'E': | |
2798 | case 'f': case 'F': | |
2799 | case 'l': case 'L': | |
2800 | case 's': case 'S': | |
2801 | idx++; | |
ee0ddd21 AW |
2802 | if (idx == len) |
2803 | return SCM_BOOL_F; | |
2804 | ||
3c9a524f | 2805 | start = idx; |
3f47e526 | 2806 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2807 | if (c == '-') |
2808 | { | |
2809 | idx++; | |
ee0ddd21 AW |
2810 | if (idx == len) |
2811 | return SCM_BOOL_F; | |
2812 | ||
3c9a524f | 2813 | sign = -1; |
3f47e526 | 2814 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2815 | } |
2816 | else if (c == '+') | |
2817 | { | |
2818 | idx++; | |
ee0ddd21 AW |
2819 | if (idx == len) |
2820 | return SCM_BOOL_F; | |
2821 | ||
3c9a524f | 2822 | sign = 1; |
3f47e526 | 2823 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2824 | } |
2825 | else | |
2826 | sign = 1; | |
2827 | ||
3f47e526 | 2828 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
2829 | return SCM_BOOL_F; |
2830 | ||
2831 | idx++; | |
2832 | exponent = DIGIT2UINT (c); | |
2833 | while (idx != len) | |
f872b822 | 2834 | { |
3f47e526 MG |
2835 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
2836 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
2837 | { |
2838 | idx++; | |
2839 | if (exponent <= SCM_MAXEXP) | |
2840 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2841 | } | |
2842 | else | |
2843 | break; | |
f872b822 | 2844 | } |
3c9a524f DH |
2845 | |
2846 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2847 | { |
3c9a524f | 2848 | size_t exp_len = idx - start; |
3f47e526 | 2849 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
2850 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
2851 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2852 | } |
3c9a524f | 2853 | |
d956fa6f | 2854 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
2855 | if (sign == 1) |
2856 | result = scm_product (result, e); | |
2857 | else | |
f92e85f7 | 2858 | result = scm_divide2real (result, e); |
3c9a524f DH |
2859 | |
2860 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2861 | x = INEXACT; | |
2862 | ||
f872b822 | 2863 | break; |
3c9a524f | 2864 | |
f872b822 | 2865 | default: |
3c9a524f | 2866 | break; |
f872b822 | 2867 | } |
0f2d19dd | 2868 | } |
3c9a524f DH |
2869 | |
2870 | *p_idx = idx; | |
2871 | if (x == INEXACT) | |
2872 | *p_exactness = x; | |
2873 | ||
2874 | return result; | |
0f2d19dd | 2875 | } |
0f2d19dd | 2876 | |
3c9a524f DH |
2877 | |
2878 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2879 | ||
2880 | static SCM | |
3f47e526 | 2881 | mem2ureal (SCM mem, unsigned int *p_idx, |
3c9a524f | 2882 | unsigned int radix, enum t_exactness *p_exactness) |
0f2d19dd | 2883 | { |
3c9a524f | 2884 | unsigned int idx = *p_idx; |
164d2481 | 2885 | SCM result; |
3f47e526 | 2886 | size_t len = scm_i_string_length (mem); |
3c9a524f | 2887 | |
40f89215 NJ |
2888 | /* Start off believing that the number will be exact. This changes |
2889 | to INEXACT if we see a decimal point or a hash. */ | |
2890 | enum t_exactness x = EXACT; | |
2891 | ||
3c9a524f DH |
2892 | if (idx == len) |
2893 | return SCM_BOOL_F; | |
2894 | ||
3f47e526 | 2895 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
2896 | { |
2897 | *p_idx = idx+5; | |
2898 | return scm_inf (); | |
2899 | } | |
2900 | ||
3f47e526 | 2901 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 2902 | { |
d8592269 MV |
2903 | /* Cobble up the fractional part. We might want to set the |
2904 | NaN's mantissa from it. */ | |
7351e207 | 2905 | idx += 4; |
3f47e526 | 2906 | mem2uinteger (mem, &idx, 10, &x); |
7351e207 MV |
2907 | *p_idx = idx; |
2908 | return scm_nan (); | |
2909 | } | |
2910 | ||
3f47e526 | 2911 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
2912 | { |
2913 | if (radix != 10) | |
2914 | return SCM_BOOL_F; | |
2915 | else if (idx + 1 == len) | |
2916 | return SCM_BOOL_F; | |
3f47e526 | 2917 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
2918 | return SCM_BOOL_F; |
2919 | else | |
cff5fa33 | 2920 | result = mem2decimal_from_point (SCM_INUM0, mem, |
40f89215 | 2921 | p_idx, &x); |
f872b822 | 2922 | } |
3c9a524f DH |
2923 | else |
2924 | { | |
3c9a524f | 2925 | SCM uinteger; |
3c9a524f | 2926 | |
3f47e526 | 2927 | uinteger = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 2928 | if (scm_is_false (uinteger)) |
3c9a524f DH |
2929 | return SCM_BOOL_F; |
2930 | ||
2931 | if (idx == len) | |
2932 | result = uinteger; | |
3f47e526 | 2933 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 2934 | { |
3c9a524f DH |
2935 | SCM divisor; |
2936 | ||
2937 | idx++; | |
ee0ddd21 AW |
2938 | if (idx == len) |
2939 | return SCM_BOOL_F; | |
3c9a524f | 2940 | |
3f47e526 | 2941 | divisor = mem2uinteger (mem, &idx, radix, &x); |
73e4de09 | 2942 | if (scm_is_false (divisor)) |
3c9a524f DH |
2943 | return SCM_BOOL_F; |
2944 | ||
f92e85f7 | 2945 | /* both are int/big here, I assume */ |
cba42c93 | 2946 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 2947 | } |
3c9a524f DH |
2948 | else if (radix == 10) |
2949 | { | |
3f47e526 | 2950 | result = mem2decimal_from_point (uinteger, mem, &idx, &x); |
73e4de09 | 2951 | if (scm_is_false (result)) |
3c9a524f DH |
2952 | return SCM_BOOL_F; |
2953 | } | |
2954 | else | |
2955 | result = uinteger; | |
2956 | ||
2957 | *p_idx = idx; | |
f872b822 | 2958 | } |
164d2481 | 2959 | |
40f89215 NJ |
2960 | /* Update *p_exactness if the number just read was inexact. This is |
2961 | important for complex numbers, so that a complex number is | |
2962 | treated as inexact overall if either its real or imaginary part | |
2963 | is inexact. | |
2964 | */ | |
2965 | if (x == INEXACT) | |
2966 | *p_exactness = x; | |
2967 | ||
164d2481 MV |
2968 | /* When returning an inexact zero, make sure it is represented as a |
2969 | floating point value so that we can change its sign. | |
2970 | */ | |
cff5fa33 | 2971 | if (scm_is_eq (result, SCM_INUM0) && *p_exactness == INEXACT) |
55f26379 | 2972 | result = scm_from_double (0.0); |
164d2481 MV |
2973 | |
2974 | return result; | |
3c9a524f | 2975 | } |
0f2d19dd | 2976 | |
0f2d19dd | 2977 | |
3c9a524f | 2978 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2979 | |
3c9a524f | 2980 | static SCM |
3f47e526 | 2981 | mem2complex (SCM mem, unsigned int idx, |
3c9a524f DH |
2982 | unsigned int radix, enum t_exactness *p_exactness) |
2983 | { | |
3f47e526 | 2984 | scm_t_wchar c; |
3c9a524f DH |
2985 | int sign = 0; |
2986 | SCM ureal; | |
3f47e526 | 2987 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
2988 | |
2989 | if (idx == len) | |
2990 | return SCM_BOOL_F; | |
2991 | ||
3f47e526 | 2992 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
2993 | if (c == '+') |
2994 | { | |
2995 | idx++; | |
2996 | sign = 1; | |
2997 | } | |
2998 | else if (c == '-') | |
2999 | { | |
3000 | idx++; | |
3001 | sign = -1; | |
0f2d19dd | 3002 | } |
0f2d19dd | 3003 | |
3c9a524f DH |
3004 | if (idx == len) |
3005 | return SCM_BOOL_F; | |
3006 | ||
3f47e526 | 3007 | ureal = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 3008 | if (scm_is_false (ureal)) |
f872b822 | 3009 | { |
3c9a524f DH |
3010 | /* input must be either +i or -i */ |
3011 | ||
3012 | if (sign == 0) | |
3013 | return SCM_BOOL_F; | |
3014 | ||
3f47e526 MG |
3015 | if (scm_i_string_ref (mem, idx) == 'i' |
3016 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 3017 | { |
3c9a524f DH |
3018 | idx++; |
3019 | if (idx != len) | |
3020 | return SCM_BOOL_F; | |
3021 | ||
cff5fa33 | 3022 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 3023 | } |
3c9a524f DH |
3024 | else |
3025 | return SCM_BOOL_F; | |
0f2d19dd | 3026 | } |
3c9a524f DH |
3027 | else |
3028 | { | |
73e4de09 | 3029 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 3030 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 3031 | |
3c9a524f DH |
3032 | if (idx == len) |
3033 | return ureal; | |
3034 | ||
3f47e526 | 3035 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 3036 | switch (c) |
f872b822 | 3037 | { |
3c9a524f DH |
3038 | case 'i': case 'I': |
3039 | /* either +<ureal>i or -<ureal>i */ | |
3040 | ||
3041 | idx++; | |
3042 | if (sign == 0) | |
3043 | return SCM_BOOL_F; | |
3044 | if (idx != len) | |
3045 | return SCM_BOOL_F; | |
cff5fa33 | 3046 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
3047 | |
3048 | case '@': | |
3049 | /* polar input: <real>@<real>. */ | |
3050 | ||
3051 | idx++; | |
3052 | if (idx == len) | |
3053 | return SCM_BOOL_F; | |
3054 | else | |
f872b822 | 3055 | { |
3c9a524f DH |
3056 | int sign; |
3057 | SCM angle; | |
3058 | SCM result; | |
3059 | ||
3f47e526 | 3060 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
3061 | if (c == '+') |
3062 | { | |
3063 | idx++; | |
ee0ddd21 AW |
3064 | if (idx == len) |
3065 | return SCM_BOOL_F; | |
3c9a524f DH |
3066 | sign = 1; |
3067 | } | |
3068 | else if (c == '-') | |
3069 | { | |
3070 | idx++; | |
ee0ddd21 AW |
3071 | if (idx == len) |
3072 | return SCM_BOOL_F; | |
3c9a524f DH |
3073 | sign = -1; |
3074 | } | |
3075 | else | |
3076 | sign = 1; | |
3077 | ||
3f47e526 | 3078 | angle = mem2ureal (mem, &idx, radix, p_exactness); |
73e4de09 | 3079 | if (scm_is_false (angle)) |
3c9a524f DH |
3080 | return SCM_BOOL_F; |
3081 | if (idx != len) | |
3082 | return SCM_BOOL_F; | |
3083 | ||
73e4de09 | 3084 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
3085 | angle = scm_difference (angle, SCM_UNDEFINED); |
3086 | ||
3087 | result = scm_make_polar (ureal, angle); | |
3088 | return result; | |
f872b822 | 3089 | } |
3c9a524f DH |
3090 | case '+': |
3091 | case '-': | |
3092 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 3093 | |
3c9a524f DH |
3094 | idx++; |
3095 | if (idx == len) | |
3096 | return SCM_BOOL_F; | |
3097 | else | |
3098 | { | |
3099 | int sign = (c == '+') ? 1 : -1; | |
3f47e526 | 3100 | SCM imag = mem2ureal (mem, &idx, radix, p_exactness); |
0f2d19dd | 3101 | |
73e4de09 | 3102 | if (scm_is_false (imag)) |
d956fa6f | 3103 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 3104 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 3105 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 3106 | |
3c9a524f DH |
3107 | if (idx == len) |
3108 | return SCM_BOOL_F; | |
3f47e526 MG |
3109 | if (scm_i_string_ref (mem, idx) != 'i' |
3110 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 3111 | return SCM_BOOL_F; |
0f2d19dd | 3112 | |
3c9a524f DH |
3113 | idx++; |
3114 | if (idx != len) | |
3115 | return SCM_BOOL_F; | |
0f2d19dd | 3116 | |
1fe5e088 | 3117 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
3118 | } |
3119 | default: | |
3120 | return SCM_BOOL_F; | |
3121 | } | |
3122 | } | |
0f2d19dd | 3123 | } |
0f2d19dd JB |
3124 | |
3125 | ||
3c9a524f DH |
3126 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
3127 | ||
3128 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 3129 | |
0f2d19dd | 3130 | SCM |
3f47e526 | 3131 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 3132 | { |
3c9a524f DH |
3133 | unsigned int idx = 0; |
3134 | unsigned int radix = NO_RADIX; | |
3135 | enum t_exactness forced_x = NO_EXACTNESS; | |
3136 | enum t_exactness implicit_x = EXACT; | |
3137 | SCM result; | |
3f47e526 | 3138 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
3139 | |
3140 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 3141 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 3142 | { |
3f47e526 | 3143 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
3144 | { |
3145 | case 'b': case 'B': | |
3146 | if (radix != NO_RADIX) | |
3147 | return SCM_BOOL_F; | |
3148 | radix = DUAL; | |
3149 | break; | |
3150 | case 'd': case 'D': | |
3151 | if (radix != NO_RADIX) | |
3152 | return SCM_BOOL_F; | |
3153 | radix = DEC; | |
3154 | break; | |
3155 | case 'i': case 'I': | |
3156 | if (forced_x != NO_EXACTNESS) | |
3157 | return SCM_BOOL_F; | |
3158 | forced_x = INEXACT; | |
3159 | break; | |
3160 | case 'e': case 'E': | |
3161 | if (forced_x != NO_EXACTNESS) | |
3162 | return SCM_BOOL_F; | |
3163 | forced_x = EXACT; | |
3164 | break; | |
3165 | case 'o': case 'O': | |
3166 | if (radix != NO_RADIX) | |
3167 | return SCM_BOOL_F; | |
3168 | radix = OCT; | |
3169 | break; | |
3170 | case 'x': case 'X': | |
3171 | if (radix != NO_RADIX) | |
3172 | return SCM_BOOL_F; | |
3173 | radix = HEX; | |
3174 | break; | |
3175 | default: | |
f872b822 | 3176 | return SCM_BOOL_F; |
3c9a524f DH |
3177 | } |
3178 | idx += 2; | |
3179 | } | |
3180 | ||
3181 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
3182 | if (radix == NO_RADIX) | |
3f47e526 | 3183 | result = mem2complex (mem, idx, default_radix, &implicit_x); |
3c9a524f | 3184 | else |
3f47e526 | 3185 | result = mem2complex (mem, idx, (unsigned int) radix, &implicit_x); |
3c9a524f | 3186 | |
73e4de09 | 3187 | if (scm_is_false (result)) |
3c9a524f | 3188 | return SCM_BOOL_F; |
f872b822 | 3189 | |
3c9a524f | 3190 | switch (forced_x) |
f872b822 | 3191 | { |
3c9a524f DH |
3192 | case EXACT: |
3193 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
3194 | return scm_inexact_to_exact (result); |
3195 | else | |
3196 | return result; | |
3197 | case INEXACT: | |
3198 | if (SCM_INEXACTP (result)) | |
3199 | return result; | |
3200 | else | |
3201 | return scm_exact_to_inexact (result); | |
3202 | case NO_EXACTNESS: | |
3203 | default: | |
3204 | if (implicit_x == INEXACT) | |
3205 | { | |
3206 | if (SCM_INEXACTP (result)) | |
3207 | return result; | |
3208 | else | |
3209 | return scm_exact_to_inexact (result); | |
3210 | } | |
3211 | else | |
3212 | return result; | |
f872b822 | 3213 | } |
0f2d19dd JB |
3214 | } |
3215 | ||
3f47e526 MG |
3216 | SCM |
3217 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
3218 | unsigned int default_radix) | |
3219 | { | |
3220 | SCM str = scm_from_locale_stringn (mem, len); | |
3221 | ||
3222 | return scm_i_string_to_number (str, default_radix); | |
3223 | } | |
3224 | ||
0f2d19dd | 3225 | |
a1ec6916 | 3226 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 3227 | (SCM string, SCM radix), |
1e6808ea | 3228 | "Return a number of the maximally precise representation\n" |
942e5b91 | 3229 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
3230 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
3231 | "is a default radix that may be overridden by an explicit radix\n" | |
3232 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
3233 | "supplied, then the default radix is 10. If string is not a\n" | |
3234 | "syntactically valid notation for a number, then\n" | |
3235 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 3236 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
3237 | { |
3238 | SCM answer; | |
5efd3c7d | 3239 | unsigned int base; |
a6d9e5ab | 3240 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
3241 | |
3242 | if (SCM_UNBNDP (radix)) | |
3243 | base = 10; | |
3244 | else | |
3245 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
3246 | ||
3f47e526 | 3247 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
3248 | scm_remember_upto_here_1 (string); |
3249 | return answer; | |
0f2d19dd | 3250 | } |
1bbd0b84 | 3251 | #undef FUNC_NAME |
3c9a524f DH |
3252 | |
3253 | ||
0f2d19dd JB |
3254 | /*** END strs->nums ***/ |
3255 | ||
5986c47d | 3256 | |
0f2d19dd | 3257 | SCM |
1bbd0b84 | 3258 | scm_bigequal (SCM x, SCM y) |
0f2d19dd | 3259 | { |
47ae1f0e | 3260 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
ca46fb90 | 3261 | scm_remember_upto_here_2 (x, y); |
73e4de09 | 3262 | return scm_from_bool (0 == result); |
0f2d19dd JB |
3263 | } |
3264 | ||
0f2d19dd | 3265 | SCM |
f3ae5d60 | 3266 | scm_real_equalp (SCM x, SCM y) |
0f2d19dd | 3267 | { |
73e4de09 | 3268 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0f2d19dd JB |
3269 | } |
3270 | ||
f3ae5d60 MD |
3271 | SCM |
3272 | scm_complex_equalp (SCM x, SCM y) | |
3273 | { | |
73e4de09 | 3274 | return scm_from_bool (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) |
f3ae5d60 MD |
3275 | && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); |
3276 | } | |
0f2d19dd | 3277 | |
f92e85f7 MV |
3278 | SCM |
3279 | scm_i_fraction_equalp (SCM x, SCM y) | |
3280 | { | |
73e4de09 | 3281 | if (scm_is_false (scm_equal_p (SCM_FRACTION_NUMERATOR (x), |
02164269 | 3282 | SCM_FRACTION_NUMERATOR (y))) |
73e4de09 | 3283 | || scm_is_false (scm_equal_p (SCM_FRACTION_DENOMINATOR (x), |
02164269 MV |
3284 | SCM_FRACTION_DENOMINATOR (y)))) |
3285 | return SCM_BOOL_F; | |
3286 | else | |
3287 | return SCM_BOOL_T; | |
f92e85f7 | 3288 | } |
0f2d19dd JB |
3289 | |
3290 | ||
8507ec80 MV |
3291 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
3292 | (SCM x), | |
3293 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
3294 | "otherwise.") | |
3295 | #define FUNC_NAME s_scm_number_p | |
3296 | { | |
3297 | return scm_from_bool (SCM_NUMBERP (x)); | |
3298 | } | |
3299 | #undef FUNC_NAME | |
3300 | ||
3301 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 3302 | (SCM x), |
942e5b91 | 3303 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 3304 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
3305 | "values form subsets of the set of complex numbers, i. e. the\n" |
3306 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
3307 | "rational or integer number.") | |
8507ec80 | 3308 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 3309 | { |
8507ec80 MV |
3310 | /* all numbers are complex. */ |
3311 | return scm_number_p (x); | |
0f2d19dd | 3312 | } |
1bbd0b84 | 3313 | #undef FUNC_NAME |
0f2d19dd | 3314 | |
f92e85f7 MV |
3315 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
3316 | (SCM x), | |
3317 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
3318 | "otherwise. Note that the set of integer values forms a subset of\n" | |
3319 | "the set of real numbers, i. e. the predicate will also be\n" | |
3320 | "fulfilled if @var{x} is an integer number.") | |
3321 | #define FUNC_NAME s_scm_real_p | |
3322 | { | |
3323 | /* we can't represent irrational numbers. */ | |
3324 | return scm_rational_p (x); | |
3325 | } | |
3326 | #undef FUNC_NAME | |
3327 | ||
3328 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 3329 | (SCM x), |
942e5b91 | 3330 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 3331 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 3332 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
3333 | "fulfilled if @var{x} is an integer number.") |
3334 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 3335 | { |
e11e83f3 | 3336 | if (SCM_I_INUMP (x)) |
0f2d19dd | 3337 | return SCM_BOOL_T; |
0aacf84e | 3338 | else if (SCM_IMP (x)) |
0f2d19dd | 3339 | return SCM_BOOL_F; |
0aacf84e | 3340 | else if (SCM_BIGP (x)) |
0f2d19dd | 3341 | return SCM_BOOL_T; |
f92e85f7 MV |
3342 | else if (SCM_FRACTIONP (x)) |
3343 | return SCM_BOOL_T; | |
3344 | else if (SCM_REALP (x)) | |
3345 | /* due to their limited precision, all floating point numbers are | |
3346 | rational as well. */ | |
3347 | return SCM_BOOL_T; | |
0aacf84e | 3348 | else |
bb628794 | 3349 | return SCM_BOOL_F; |
0f2d19dd | 3350 | } |
1bbd0b84 | 3351 | #undef FUNC_NAME |
0f2d19dd | 3352 | |
a1ec6916 | 3353 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 3354 | (SCM x), |
942e5b91 MG |
3355 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
3356 | "else.") | |
1bbd0b84 | 3357 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd JB |
3358 | { |
3359 | double r; | |
e11e83f3 | 3360 | if (SCM_I_INUMP (x)) |
f872b822 MD |
3361 | return SCM_BOOL_T; |
3362 | if (SCM_IMP (x)) | |
3363 | return SCM_BOOL_F; | |
f872b822 MD |
3364 | if (SCM_BIGP (x)) |
3365 | return SCM_BOOL_T; | |
3c9a524f | 3366 | if (!SCM_INEXACTP (x)) |
f872b822 | 3367 | return SCM_BOOL_F; |
3c9a524f | 3368 | if (SCM_COMPLEXP (x)) |
f872b822 | 3369 | return SCM_BOOL_F; |
5986c47d | 3370 | r = SCM_REAL_VALUE (x); |
8e43ed5d AW |
3371 | if (isinf (r)) |
3372 | return SCM_BOOL_F; | |
f872b822 MD |
3373 | if (r == floor (r)) |
3374 | return SCM_BOOL_T; | |
0f2d19dd JB |
3375 | return SCM_BOOL_F; |
3376 | } | |
1bbd0b84 | 3377 | #undef FUNC_NAME |
0f2d19dd JB |
3378 | |
3379 | ||
8a1f4f98 AW |
3380 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
3381 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
3382 | (SCM x, SCM y, SCM rest), | |
3383 | "Return @code{#t} if all parameters are numerically equal.") | |
3384 | #define FUNC_NAME s_scm_i_num_eq_p | |
3385 | { | |
3386 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3387 | return SCM_BOOL_T; | |
3388 | while (!scm_is_null (rest)) | |
3389 | { | |
3390 | if (scm_is_false (scm_num_eq_p (x, y))) | |
3391 | return SCM_BOOL_F; | |
3392 | x = y; | |
3393 | y = scm_car (rest); | |
3394 | rest = scm_cdr (rest); | |
3395 | } | |
3396 | return scm_num_eq_p (x, y); | |
3397 | } | |
3398 | #undef FUNC_NAME | |
0f2d19dd | 3399 | SCM |
6e8d25a6 | 3400 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 3401 | { |
d8b95e27 | 3402 | again: |
e11e83f3 | 3403 | if (SCM_I_INUMP (x)) |
0aacf84e | 3404 | { |
e25f3727 | 3405 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 3406 | if (SCM_I_INUMP (y)) |
0aacf84e | 3407 | { |
e25f3727 | 3408 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 3409 | return scm_from_bool (xx == yy); |
0aacf84e MD |
3410 | } |
3411 | else if (SCM_BIGP (y)) | |
3412 | return SCM_BOOL_F; | |
3413 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
3414 | { |
3415 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
3416 | to a double and compare. | |
3417 | ||
3418 | But on a 64-bit system an inum is bigger than a double and | |
3419 | casting it to a double (call that dxx) will round. dxx is at | |
3420 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
3421 | an integer and fits a long. So we cast yy to a long and | |
3422 | compare with plain xx. | |
3423 | ||
3424 | An alternative (for any size system actually) would be to check | |
3425 | yy is an integer (with floor) and is in range of an inum | |
3426 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
3427 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
3428 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
3429 | |
3430 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
3431 | return scm_from_bool ((double) xx == yy |
3432 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 3433 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 3434 | } |
0aacf84e | 3435 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3436 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3437 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
3438 | else if (SCM_FRACTIONP (y)) |
3439 | return SCM_BOOL_F; | |
0aacf84e | 3440 | else |
8a1f4f98 | 3441 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 3442 | } |
0aacf84e MD |
3443 | else if (SCM_BIGP (x)) |
3444 | { | |
e11e83f3 | 3445 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3446 | return SCM_BOOL_F; |
3447 | else if (SCM_BIGP (y)) | |
3448 | { | |
3449 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3450 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3451 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3452 | } |
3453 | else if (SCM_REALP (y)) | |
3454 | { | |
3455 | int cmp; | |
2e65b52f | 3456 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
3457 | return SCM_BOOL_F; |
3458 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3459 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3460 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3461 | } |
3462 | else if (SCM_COMPLEXP (y)) | |
3463 | { | |
3464 | int cmp; | |
3465 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
3466 | return SCM_BOOL_F; | |
2e65b52f | 3467 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
3468 | return SCM_BOOL_F; |
3469 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
3470 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3471 | return scm_from_bool (0 == cmp); |
0aacf84e | 3472 | } |
f92e85f7 MV |
3473 | else if (SCM_FRACTIONP (y)) |
3474 | return SCM_BOOL_F; | |
0aacf84e | 3475 | else |
8a1f4f98 | 3476 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 3477 | } |
0aacf84e MD |
3478 | else if (SCM_REALP (x)) |
3479 | { | |
e8c5b1f2 | 3480 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 3481 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
3482 | { |
3483 | /* see comments with inum/real above */ | |
e25f3727 | 3484 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
3485 | return scm_from_bool (xx == (double) yy |
3486 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 3487 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 3488 | } |
0aacf84e MD |
3489 | else if (SCM_BIGP (y)) |
3490 | { | |
3491 | int cmp; | |
2e65b52f | 3492 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
3493 | return SCM_BOOL_F; |
3494 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3495 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3496 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3497 | } |
3498 | else if (SCM_REALP (y)) | |
73e4de09 | 3499 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 3500 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3501 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3502 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3503 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3504 | { |
3505 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 3506 | if (isnan (xx)) |
d8b95e27 | 3507 | return SCM_BOOL_F; |
2e65b52f | 3508 | if (isinf (xx)) |
73e4de09 | 3509 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3510 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3511 | goto again; | |
3512 | } | |
0aacf84e | 3513 | else |
8a1f4f98 | 3514 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 3515 | } |
0aacf84e MD |
3516 | else if (SCM_COMPLEXP (x)) |
3517 | { | |
e11e83f3 MV |
3518 | if (SCM_I_INUMP (y)) |
3519 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
3520 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3521 | else if (SCM_BIGP (y)) | |
3522 | { | |
3523 | int cmp; | |
3524 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
3525 | return SCM_BOOL_F; | |
2e65b52f | 3526 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
3527 | return SCM_BOOL_F; |
3528 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
3529 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3530 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3531 | } |
3532 | else if (SCM_REALP (y)) | |
73e4de09 | 3533 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
3534 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3535 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 3536 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3537 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3538 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3539 | { |
3540 | double xx; | |
3541 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
3542 | return SCM_BOOL_F; | |
3543 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 3544 | if (isnan (xx)) |
d8b95e27 | 3545 | return SCM_BOOL_F; |
2e65b52f | 3546 | if (isinf (xx)) |
73e4de09 | 3547 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3548 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3549 | goto again; | |
3550 | } | |
f92e85f7 | 3551 | else |
8a1f4f98 | 3552 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
3553 | } |
3554 | else if (SCM_FRACTIONP (x)) | |
3555 | { | |
e11e83f3 | 3556 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
3557 | return SCM_BOOL_F; |
3558 | else if (SCM_BIGP (y)) | |
3559 | return SCM_BOOL_F; | |
3560 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
3561 | { |
3562 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 3563 | if (isnan (yy)) |
d8b95e27 | 3564 | return SCM_BOOL_F; |
2e65b52f | 3565 | if (isinf (yy)) |
73e4de09 | 3566 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3567 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3568 | goto again; | |
3569 | } | |
f92e85f7 | 3570 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
3571 | { |
3572 | double yy; | |
3573 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
3574 | return SCM_BOOL_F; | |
3575 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 3576 | if (isnan (yy)) |
d8b95e27 | 3577 | return SCM_BOOL_F; |
2e65b52f | 3578 | if (isinf (yy)) |
73e4de09 | 3579 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3580 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3581 | goto again; | |
3582 | } | |
f92e85f7 MV |
3583 | else if (SCM_FRACTIONP (y)) |
3584 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 3585 | else |
8a1f4f98 | 3586 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 3587 | } |
0aacf84e | 3588 | else |
8a1f4f98 | 3589 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
3590 | } |
3591 | ||
3592 | ||
a5f0b599 KR |
3593 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
3594 | done are good for inums, but for bignums an answer can almost always be | |
3595 | had by just examining a few high bits of the operands, as done by GMP in | |
3596 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
3597 | of the float exponent to take into account. */ | |
3598 | ||
8c93b597 | 3599 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
3600 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
3601 | (SCM x, SCM y, SCM rest), | |
3602 | "Return @code{#t} if the list of parameters is monotonically\n" | |
3603 | "increasing.") | |
3604 | #define FUNC_NAME s_scm_i_num_less_p | |
3605 | { | |
3606 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3607 | return SCM_BOOL_T; | |
3608 | while (!scm_is_null (rest)) | |
3609 | { | |
3610 | if (scm_is_false (scm_less_p (x, y))) | |
3611 | return SCM_BOOL_F; | |
3612 | x = y; | |
3613 | y = scm_car (rest); | |
3614 | rest = scm_cdr (rest); | |
3615 | } | |
3616 | return scm_less_p (x, y); | |
3617 | } | |
3618 | #undef FUNC_NAME | |
0f2d19dd | 3619 | SCM |
6e8d25a6 | 3620 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3621 | { |
a5f0b599 | 3622 | again: |
e11e83f3 | 3623 | if (SCM_I_INUMP (x)) |
0aacf84e | 3624 | { |
e25f3727 | 3625 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 3626 | if (SCM_I_INUMP (y)) |
0aacf84e | 3627 | { |
e25f3727 | 3628 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 3629 | return scm_from_bool (xx < yy); |
0aacf84e MD |
3630 | } |
3631 | else if (SCM_BIGP (y)) | |
3632 | { | |
3633 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3634 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3635 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3636 | } |
3637 | else if (SCM_REALP (y)) | |
73e4de09 | 3638 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 3639 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3640 | { |
3641 | /* "x < a/b" becomes "x*b < a" */ | |
3642 | int_frac: | |
3643 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
3644 | y = SCM_FRACTION_NUMERATOR (y); | |
3645 | goto again; | |
3646 | } | |
0aacf84e | 3647 | else |
8a1f4f98 | 3648 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 3649 | } |
0aacf84e MD |
3650 | else if (SCM_BIGP (x)) |
3651 | { | |
e11e83f3 | 3652 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3653 | { |
3654 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3655 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3656 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3657 | } |
3658 | else if (SCM_BIGP (y)) | |
3659 | { | |
3660 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3661 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3662 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
3663 | } |
3664 | else if (SCM_REALP (y)) | |
3665 | { | |
3666 | int cmp; | |
2e65b52f | 3667 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
3668 | return SCM_BOOL_F; |
3669 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3670 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3671 | return scm_from_bool (cmp < 0); |
0aacf84e | 3672 | } |
f92e85f7 | 3673 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 3674 | goto int_frac; |
0aacf84e | 3675 | else |
8a1f4f98 | 3676 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 3677 | } |
0aacf84e MD |
3678 | else if (SCM_REALP (x)) |
3679 | { | |
e11e83f3 MV |
3680 | if (SCM_I_INUMP (y)) |
3681 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3682 | else if (SCM_BIGP (y)) |
3683 | { | |
3684 | int cmp; | |
2e65b52f | 3685 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
3686 | return SCM_BOOL_F; |
3687 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3688 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3689 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
3690 | } |
3691 | else if (SCM_REALP (y)) | |
73e4de09 | 3692 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 3693 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3694 | { |
3695 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 3696 | if (isnan (xx)) |
a5f0b599 | 3697 | return SCM_BOOL_F; |
2e65b52f | 3698 | if (isinf (xx)) |
73e4de09 | 3699 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
3700 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3701 | goto again; | |
3702 | } | |
f92e85f7 | 3703 | else |
8a1f4f98 | 3704 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
3705 | } |
3706 | else if (SCM_FRACTIONP (x)) | |
3707 | { | |
e11e83f3 | 3708 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
3709 | { |
3710 | /* "a/b < y" becomes "a < y*b" */ | |
3711 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
3712 | x = SCM_FRACTION_NUMERATOR (x); | |
3713 | goto again; | |
3714 | } | |
f92e85f7 | 3715 | else if (SCM_REALP (y)) |
a5f0b599 KR |
3716 | { |
3717 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 3718 | if (isnan (yy)) |
a5f0b599 | 3719 | return SCM_BOOL_F; |
2e65b52f | 3720 | if (isinf (yy)) |
73e4de09 | 3721 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
3722 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3723 | goto again; | |
3724 | } | |
f92e85f7 | 3725 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3726 | { |
3727 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
3728 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
3729 | SCM_FRACTION_DENOMINATOR (y)); | |
3730 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
3731 | SCM_FRACTION_DENOMINATOR (x)); | |
3732 | x = new_x; | |
3733 | y = new_y; | |
3734 | goto again; | |
3735 | } | |
0aacf84e | 3736 | else |
8a1f4f98 | 3737 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 3738 | } |
0aacf84e | 3739 | else |
8a1f4f98 | 3740 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
3741 | } |
3742 | ||
3743 | ||
8a1f4f98 AW |
3744 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
3745 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
3746 | (SCM x, SCM y, SCM rest), | |
3747 | "Return @code{#t} if the list of parameters is monotonically\n" | |
3748 | "decreasing.") | |
3749 | #define FUNC_NAME s_scm_i_num_gr_p | |
3750 | { | |
3751 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3752 | return SCM_BOOL_T; | |
3753 | while (!scm_is_null (rest)) | |
3754 | { | |
3755 | if (scm_is_false (scm_gr_p (x, y))) | |
3756 | return SCM_BOOL_F; | |
3757 | x = y; | |
3758 | y = scm_car (rest); | |
3759 | rest = scm_cdr (rest); | |
3760 | } | |
3761 | return scm_gr_p (x, y); | |
3762 | } | |
3763 | #undef FUNC_NAME | |
3764 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
3765 | SCM |
3766 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3767 | { |
c76b1eaf | 3768 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 3769 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 3770 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 3771 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
3772 | else |
3773 | return scm_less_p (y, x); | |
0f2d19dd | 3774 | } |
1bbd0b84 | 3775 | #undef FUNC_NAME |
0f2d19dd JB |
3776 | |
3777 | ||
8a1f4f98 AW |
3778 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
3779 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
3780 | (SCM x, SCM y, SCM rest), | |
3781 | "Return @code{#t} if the list of parameters is monotonically\n" | |
3782 | "non-decreasing.") | |
3783 | #define FUNC_NAME s_scm_i_num_leq_p | |
3784 | { | |
3785 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3786 | return SCM_BOOL_T; | |
3787 | while (!scm_is_null (rest)) | |
3788 | { | |
3789 | if (scm_is_false (scm_leq_p (x, y))) | |
3790 | return SCM_BOOL_F; | |
3791 | x = y; | |
3792 | y = scm_car (rest); | |
3793 | rest = scm_cdr (rest); | |
3794 | } | |
3795 | return scm_leq_p (x, y); | |
3796 | } | |
3797 | #undef FUNC_NAME | |
3798 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
3799 | SCM |
3800 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3801 | { |
c76b1eaf | 3802 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 3803 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 3804 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 3805 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 3806 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3807 | return SCM_BOOL_F; |
c76b1eaf | 3808 | else |
73e4de09 | 3809 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 3810 | } |
1bbd0b84 | 3811 | #undef FUNC_NAME |
0f2d19dd JB |
3812 | |
3813 | ||
8a1f4f98 AW |
3814 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
3815 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
3816 | (SCM x, SCM y, SCM rest), | |
3817 | "Return @code{#t} if the list of parameters is monotonically\n" | |
3818 | "non-increasing.") | |
3819 | #define FUNC_NAME s_scm_i_num_geq_p | |
3820 | { | |
3821 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
3822 | return SCM_BOOL_T; | |
3823 | while (!scm_is_null (rest)) | |
3824 | { | |
3825 | if (scm_is_false (scm_geq_p (x, y))) | |
3826 | return SCM_BOOL_F; | |
3827 | x = y; | |
3828 | y = scm_car (rest); | |
3829 | rest = scm_cdr (rest); | |
3830 | } | |
3831 | return scm_geq_p (x, y); | |
3832 | } | |
3833 | #undef FUNC_NAME | |
3834 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
3835 | SCM |
3836 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3837 | { |
c76b1eaf | 3838 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 3839 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 3840 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 3841 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 3842 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3843 | return SCM_BOOL_F; |
c76b1eaf | 3844 | else |
73e4de09 | 3845 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 3846 | } |
1bbd0b84 | 3847 | #undef FUNC_NAME |
0f2d19dd JB |
3848 | |
3849 | ||
152f82bf | 3850 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3851 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3852 | * "zero." | |
3853 | */ | |
0f2d19dd | 3854 | SCM |
6e8d25a6 | 3855 | scm_zero_p (SCM z) |
0f2d19dd | 3856 | { |
e11e83f3 | 3857 | if (SCM_I_INUMP (z)) |
bc36d050 | 3858 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 3859 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 3860 | return SCM_BOOL_F; |
0aacf84e | 3861 | else if (SCM_REALP (z)) |
73e4de09 | 3862 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 3863 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 3864 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 3865 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
3866 | else if (SCM_FRACTIONP (z)) |
3867 | return SCM_BOOL_F; | |
0aacf84e | 3868 | else |
c2ff8ab0 | 3869 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); |
0f2d19dd JB |
3870 | } |
3871 | ||
3872 | ||
152f82bf | 3873 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3874 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3875 | * "zero." | |
3876 | */ | |
0f2d19dd | 3877 | SCM |
6e8d25a6 | 3878 | scm_positive_p (SCM x) |
0f2d19dd | 3879 | { |
e11e83f3 MV |
3880 | if (SCM_I_INUMP (x)) |
3881 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
3882 | else if (SCM_BIGP (x)) |
3883 | { | |
3884 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3885 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3886 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3887 | } |
3888 | else if (SCM_REALP (x)) | |
73e4de09 | 3889 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
3890 | else if (SCM_FRACTIONP (x)) |
3891 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3892 | else |
c2ff8ab0 | 3893 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); |
0f2d19dd JB |
3894 | } |
3895 | ||
3896 | ||
152f82bf | 3897 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3898 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3899 | * "zero." | |
3900 | */ | |
0f2d19dd | 3901 | SCM |
6e8d25a6 | 3902 | scm_negative_p (SCM x) |
0f2d19dd | 3903 | { |
e11e83f3 MV |
3904 | if (SCM_I_INUMP (x)) |
3905 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
3906 | else if (SCM_BIGP (x)) |
3907 | { | |
3908 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3909 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3910 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3911 | } |
3912 | else if (SCM_REALP (x)) | |
73e4de09 | 3913 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
3914 | else if (SCM_FRACTIONP (x)) |
3915 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3916 | else |
c2ff8ab0 | 3917 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); |
0f2d19dd JB |
3918 | } |
3919 | ||
3920 | ||
2a06f791 KR |
3921 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
3922 | required by r5rs. On that basis, for exact/inexact combinations the | |
3923 | exact is converted to inexact to compare and possibly return. This is | |
3924 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
3925 | its test, such trouble is not required for min and max. */ | |
3926 | ||
78d3deb1 AW |
3927 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
3928 | (SCM x, SCM y, SCM rest), | |
3929 | "Return the maximum of all parameter values.") | |
3930 | #define FUNC_NAME s_scm_i_max | |
3931 | { | |
3932 | while (!scm_is_null (rest)) | |
3933 | { x = scm_max (x, y); | |
3934 | y = scm_car (rest); | |
3935 | rest = scm_cdr (rest); | |
3936 | } | |
3937 | return scm_max (x, y); | |
3938 | } | |
3939 | #undef FUNC_NAME | |
3940 | ||
3941 | #define s_max s_scm_i_max | |
3942 | #define g_max g_scm_i_max | |
3943 | ||
0f2d19dd | 3944 | SCM |
6e8d25a6 | 3945 | scm_max (SCM x, SCM y) |
0f2d19dd | 3946 | { |
0aacf84e MD |
3947 | if (SCM_UNBNDP (y)) |
3948 | { | |
3949 | if (SCM_UNBNDP (x)) | |
3950 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 3951 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3952 | return x; |
3953 | else | |
3954 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3955 | } |
f4c627b3 | 3956 | |
e11e83f3 | 3957 | if (SCM_I_INUMP (x)) |
0aacf84e | 3958 | { |
e25f3727 | 3959 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 3960 | if (SCM_I_INUMP (y)) |
0aacf84e | 3961 | { |
e25f3727 | 3962 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
3963 | return (xx < yy) ? y : x; |
3964 | } | |
3965 | else if (SCM_BIGP (y)) | |
3966 | { | |
3967 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3968 | scm_remember_upto_here_1 (y); | |
3969 | return (sgn < 0) ? x : y; | |
3970 | } | |
3971 | else if (SCM_REALP (y)) | |
3972 | { | |
3973 | double z = xx; | |
3974 | /* if y==NaN then ">" is false and we return NaN */ | |
55f26379 | 3975 | return (z > SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3976 | } |
f92e85f7 MV |
3977 | else if (SCM_FRACTIONP (y)) |
3978 | { | |
e4bc5d6c | 3979 | use_less: |
73e4de09 | 3980 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 3981 | } |
0aacf84e MD |
3982 | else |
3983 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3984 | } |
0aacf84e MD |
3985 | else if (SCM_BIGP (x)) |
3986 | { | |
e11e83f3 | 3987 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3988 | { |
3989 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3990 | scm_remember_upto_here_1 (x); | |
3991 | return (sgn < 0) ? y : x; | |
3992 | } | |
3993 | else if (SCM_BIGP (y)) | |
3994 | { | |
3995 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3996 | scm_remember_upto_here_2 (x, y); | |
3997 | return (cmp > 0) ? x : y; | |
3998 | } | |
3999 | else if (SCM_REALP (y)) | |
4000 | { | |
2a06f791 KR |
4001 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
4002 | double xx, yy; | |
4003 | big_real: | |
4004 | xx = scm_i_big2dbl (x); | |
4005 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 4006 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 4007 | } |
f92e85f7 MV |
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); | |
f4c627b3 | 4014 | } |
0aacf84e MD |
4015 | else if (SCM_REALP (x)) |
4016 | { | |
e11e83f3 | 4017 | if (SCM_I_INUMP (y)) |
0aacf84e | 4018 | { |
e11e83f3 | 4019 | double z = SCM_I_INUM (y); |
0aacf84e | 4020 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 4021 | return (SCM_REAL_VALUE (x) < z) ? scm_from_double (z) : x; |
0aacf84e MD |
4022 | } |
4023 | else if (SCM_BIGP (y)) | |
4024 | { | |
b6f8f763 | 4025 | SCM_SWAP (x, y); |
2a06f791 | 4026 | goto big_real; |
0aacf84e MD |
4027 | } |
4028 | else if (SCM_REALP (y)) | |
4029 | { | |
4030 | /* if x==NaN then our explicit check means we return NaN | |
4031 | if y==NaN then ">" is false and we return NaN | |
4032 | calling isnan is unavoidable, since it's the only way to know | |
4033 | which of x or y causes any compares to be false */ | |
4034 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4035 | return (isnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y; |
0aacf84e | 4036 | } |
f92e85f7 MV |
4037 | else if (SCM_FRACTIONP (y)) |
4038 | { | |
4039 | double yy = scm_i_fraction2double (y); | |
4040 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 4041 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
4042 | } |
4043 | else | |
4044 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
4045 | } | |
4046 | else if (SCM_FRACTIONP (x)) | |
4047 | { | |
e11e83f3 | 4048 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4049 | { |
e4bc5d6c | 4050 | goto use_less; |
f92e85f7 MV |
4051 | } |
4052 | else if (SCM_BIGP (y)) | |
4053 | { | |
e4bc5d6c | 4054 | goto use_less; |
f92e85f7 MV |
4055 | } |
4056 | else if (SCM_REALP (y)) | |
4057 | { | |
4058 | double xx = scm_i_fraction2double (x); | |
55f26379 | 4059 | return (xx < SCM_REAL_VALUE (y)) ? y : scm_from_double (xx); |
f92e85f7 MV |
4060 | } |
4061 | else if (SCM_FRACTIONP (y)) | |
4062 | { | |
e4bc5d6c | 4063 | goto use_less; |
f92e85f7 | 4064 | } |
0aacf84e MD |
4065 | else |
4066 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 4067 | } |
0aacf84e | 4068 | else |
f4c627b3 | 4069 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
4070 | } |
4071 | ||
4072 | ||
78d3deb1 AW |
4073 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
4074 | (SCM x, SCM y, SCM rest), | |
4075 | "Return the minimum of all parameter values.") | |
4076 | #define FUNC_NAME s_scm_i_min | |
4077 | { | |
4078 | while (!scm_is_null (rest)) | |
4079 | { x = scm_min (x, y); | |
4080 | y = scm_car (rest); | |
4081 | rest = scm_cdr (rest); | |
4082 | } | |
4083 | return scm_min (x, y); | |
4084 | } | |
4085 | #undef FUNC_NAME | |
4086 | ||
4087 | #define s_min s_scm_i_min | |
4088 | #define g_min g_scm_i_min | |
4089 | ||
0f2d19dd | 4090 | SCM |
6e8d25a6 | 4091 | scm_min (SCM x, SCM y) |
0f2d19dd | 4092 | { |
0aacf84e MD |
4093 | if (SCM_UNBNDP (y)) |
4094 | { | |
4095 | if (SCM_UNBNDP (x)) | |
4096 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 4097 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
4098 | return x; |
4099 | else | |
4100 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 4101 | } |
f4c627b3 | 4102 | |
e11e83f3 | 4103 | if (SCM_I_INUMP (x)) |
0aacf84e | 4104 | { |
e25f3727 | 4105 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 4106 | if (SCM_I_INUMP (y)) |
0aacf84e | 4107 | { |
e25f3727 | 4108 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
4109 | return (xx < yy) ? x : y; |
4110 | } | |
4111 | else if (SCM_BIGP (y)) | |
4112 | { | |
4113 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4114 | scm_remember_upto_here_1 (y); | |
4115 | return (sgn < 0) ? y : x; | |
4116 | } | |
4117 | else if (SCM_REALP (y)) | |
4118 | { | |
4119 | double z = xx; | |
4120 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 4121 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 4122 | } |
f92e85f7 MV |
4123 | else if (SCM_FRACTIONP (y)) |
4124 | { | |
e4bc5d6c | 4125 | use_less: |
73e4de09 | 4126 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 4127 | } |
0aacf84e MD |
4128 | else |
4129 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 4130 | } |
0aacf84e MD |
4131 | else if (SCM_BIGP (x)) |
4132 | { | |
e11e83f3 | 4133 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4134 | { |
4135 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4136 | scm_remember_upto_here_1 (x); | |
4137 | return (sgn < 0) ? x : y; | |
4138 | } | |
4139 | else if (SCM_BIGP (y)) | |
4140 | { | |
4141 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4142 | scm_remember_upto_here_2 (x, y); | |
4143 | return (cmp > 0) ? y : x; | |
4144 | } | |
4145 | else if (SCM_REALP (y)) | |
4146 | { | |
2a06f791 KR |
4147 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
4148 | double xx, yy; | |
4149 | big_real: | |
4150 | xx = scm_i_big2dbl (x); | |
4151 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 4152 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 4153 | } |
f92e85f7 MV |
4154 | else if (SCM_FRACTIONP (y)) |
4155 | { | |
e4bc5d6c | 4156 | goto use_less; |
f92e85f7 | 4157 | } |
0aacf84e MD |
4158 | else |
4159 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 4160 | } |
0aacf84e MD |
4161 | else if (SCM_REALP (x)) |
4162 | { | |
e11e83f3 | 4163 | if (SCM_I_INUMP (y)) |
0aacf84e | 4164 | { |
e11e83f3 | 4165 | double z = SCM_I_INUM (y); |
0aacf84e | 4166 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 4167 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
4168 | } |
4169 | else if (SCM_BIGP (y)) | |
4170 | { | |
b6f8f763 | 4171 | SCM_SWAP (x, y); |
2a06f791 | 4172 | goto big_real; |
0aacf84e MD |
4173 | } |
4174 | else if (SCM_REALP (y)) | |
4175 | { | |
4176 | /* if x==NaN then our explicit check means we return NaN | |
4177 | if y==NaN then "<" is false and we return NaN | |
4178 | calling isnan is unavoidable, since it's the only way to know | |
4179 | which of x or y causes any compares to be false */ | |
4180 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4181 | return (isnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y; |
0aacf84e | 4182 | } |
f92e85f7 MV |
4183 | else if (SCM_FRACTIONP (y)) |
4184 | { | |
4185 | double yy = scm_i_fraction2double (y); | |
4186 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 4187 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 4188 | } |
0aacf84e MD |
4189 | else |
4190 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 4191 | } |
f92e85f7 MV |
4192 | else if (SCM_FRACTIONP (x)) |
4193 | { | |
e11e83f3 | 4194 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4195 | { |
e4bc5d6c | 4196 | goto use_less; |
f92e85f7 MV |
4197 | } |
4198 | else if (SCM_BIGP (y)) | |
4199 | { | |
e4bc5d6c | 4200 | goto use_less; |
f92e85f7 MV |
4201 | } |
4202 | else if (SCM_REALP (y)) | |
4203 | { | |
4204 | double xx = scm_i_fraction2double (x); | |
55f26379 | 4205 | return (SCM_REAL_VALUE (y) < xx) ? y : scm_from_double (xx); |
f92e85f7 MV |
4206 | } |
4207 | else if (SCM_FRACTIONP (y)) | |
4208 | { | |
e4bc5d6c | 4209 | goto use_less; |
f92e85f7 MV |
4210 | } |
4211 | else | |
78d3deb1 | 4212 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 4213 | } |
0aacf84e | 4214 | else |
f4c627b3 | 4215 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
4216 | } |
4217 | ||
4218 | ||
8ccd24f7 AW |
4219 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
4220 | (SCM x, SCM y, SCM rest), | |
4221 | "Return the sum of all parameter values. Return 0 if called without\n" | |
4222 | "any parameters." ) | |
4223 | #define FUNC_NAME s_scm_i_sum | |
4224 | { | |
4225 | while (!scm_is_null (rest)) | |
4226 | { x = scm_sum (x, y); | |
4227 | y = scm_car (rest); | |
4228 | rest = scm_cdr (rest); | |
4229 | } | |
4230 | return scm_sum (x, y); | |
4231 | } | |
4232 | #undef FUNC_NAME | |
4233 | ||
4234 | #define s_sum s_scm_i_sum | |
4235 | #define g_sum g_scm_i_sum | |
4236 | ||
0f2d19dd | 4237 | SCM |
6e8d25a6 | 4238 | scm_sum (SCM x, SCM y) |
0f2d19dd | 4239 | { |
9cc37597 | 4240 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
4241 | { |
4242 | if (SCM_NUMBERP (x)) return x; | |
4243 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 4244 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 4245 | } |
c209c88e | 4246 | |
9cc37597 | 4247 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 4248 | { |
9cc37597 | 4249 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 4250 | { |
e25f3727 AW |
4251 | scm_t_inum xx = SCM_I_INUM (x); |
4252 | scm_t_inum yy = SCM_I_INUM (y); | |
4253 | scm_t_inum z = xx + yy; | |
4254 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
4255 | } |
4256 | else if (SCM_BIGP (y)) | |
4257 | { | |
4258 | SCM_SWAP (x, y); | |
4259 | goto add_big_inum; | |
4260 | } | |
4261 | else if (SCM_REALP (y)) | |
4262 | { | |
e25f3727 | 4263 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 4264 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
4265 | } |
4266 | else if (SCM_COMPLEXP (y)) | |
4267 | { | |
e25f3727 | 4268 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 4269 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
4270 | SCM_COMPLEX_IMAG (y)); |
4271 | } | |
f92e85f7 | 4272 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4273 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
4274 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
4275 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
4276 | else |
4277 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
4278 | } else if (SCM_BIGP (x)) |
4279 | { | |
e11e83f3 | 4280 | if (SCM_I_INUMP (y)) |
0aacf84e | 4281 | { |
e25f3727 | 4282 | scm_t_inum inum; |
0aacf84e MD |
4283 | int bigsgn; |
4284 | add_big_inum: | |
e11e83f3 | 4285 | inum = SCM_I_INUM (y); |
0aacf84e MD |
4286 | if (inum == 0) |
4287 | return x; | |
4288 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4289 | if (inum < 0) | |
4290 | { | |
4291 | SCM result = scm_i_mkbig (); | |
4292 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
4293 | scm_remember_upto_here_1 (x); | |
4294 | /* we know the result will have to be a bignum */ | |
4295 | if (bigsgn == -1) | |
4296 | return result; | |
4297 | return scm_i_normbig (result); | |
4298 | } | |
4299 | else | |
4300 | { | |
4301 | SCM result = scm_i_mkbig (); | |
4302 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
4303 | scm_remember_upto_here_1 (x); | |
4304 | /* we know the result will have to be a bignum */ | |
4305 | if (bigsgn == 1) | |
4306 | return result; | |
4307 | return scm_i_normbig (result); | |
4308 | } | |
4309 | } | |
4310 | else if (SCM_BIGP (y)) | |
4311 | { | |
4312 | SCM result = scm_i_mkbig (); | |
4313 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4314 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4315 | mpz_add (SCM_I_BIG_MPZ (result), | |
4316 | SCM_I_BIG_MPZ (x), | |
4317 | SCM_I_BIG_MPZ (y)); | |
4318 | scm_remember_upto_here_2 (x, y); | |
4319 | /* we know the result will have to be a bignum */ | |
4320 | if (sgn_x == sgn_y) | |
4321 | return result; | |
4322 | return scm_i_normbig (result); | |
4323 | } | |
4324 | else if (SCM_REALP (y)) | |
4325 | { | |
4326 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
4327 | scm_remember_upto_here_1 (x); | |
55f26379 | 4328 | return scm_from_double (result); |
0aacf84e MD |
4329 | } |
4330 | else if (SCM_COMPLEXP (y)) | |
4331 | { | |
4332 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4333 | + SCM_COMPLEX_REAL (y)); | |
4334 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4335 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4336 | } |
f92e85f7 | 4337 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4338 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
4339 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
4340 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4341 | else |
4342 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 4343 | } |
0aacf84e MD |
4344 | else if (SCM_REALP (x)) |
4345 | { | |
e11e83f3 | 4346 | if (SCM_I_INUMP (y)) |
55f26379 | 4347 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
4348 | else if (SCM_BIGP (y)) |
4349 | { | |
4350 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
4351 | scm_remember_upto_here_1 (y); | |
55f26379 | 4352 | return scm_from_double (result); |
0aacf84e MD |
4353 | } |
4354 | else if (SCM_REALP (y)) | |
55f26379 | 4355 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 4356 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4357 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4358 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4359 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4360 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
4361 | else |
4362 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 4363 | } |
0aacf84e MD |
4364 | else if (SCM_COMPLEXP (x)) |
4365 | { | |
e11e83f3 | 4366 | if (SCM_I_INUMP (y)) |
8507ec80 | 4367 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
4368 | SCM_COMPLEX_IMAG (x)); |
4369 | else if (SCM_BIGP (y)) | |
4370 | { | |
4371 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
4372 | + SCM_COMPLEX_REAL (x)); | |
4373 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4374 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4375 | } |
4376 | else if (SCM_REALP (y)) | |
8507ec80 | 4377 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
4378 | SCM_COMPLEX_IMAG (x)); |
4379 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4380 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4381 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4382 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4383 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
4384 | SCM_COMPLEX_IMAG (x)); |
4385 | else | |
4386 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
4387 | } | |
4388 | else if (SCM_FRACTIONP (x)) | |
4389 | { | |
e11e83f3 | 4390 | if (SCM_I_INUMP (y)) |
cba42c93 | 4391 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4392 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4393 | SCM_FRACTION_DENOMINATOR (x)); | |
4394 | else if (SCM_BIGP (y)) | |
cba42c93 | 4395 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4396 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4397 | SCM_FRACTION_DENOMINATOR (x)); | |
4398 | else if (SCM_REALP (y)) | |
55f26379 | 4399 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 4400 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4401 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
4402 | SCM_COMPLEX_IMAG (y)); |
4403 | else if (SCM_FRACTIONP (y)) | |
4404 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 4405 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4406 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4407 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4408 | else |
4409 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 4410 | } |
0aacf84e | 4411 | else |
98cb6e75 | 4412 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
4413 | } |
4414 | ||
4415 | ||
40882e3d KR |
4416 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
4417 | (SCM x), | |
4418 | "Return @math{@var{x}+1}.") | |
4419 | #define FUNC_NAME s_scm_oneplus | |
4420 | { | |
cff5fa33 | 4421 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
4422 | } |
4423 | #undef FUNC_NAME | |
4424 | ||
4425 | ||
78d3deb1 AW |
4426 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
4427 | (SCM x, SCM y, SCM rest), | |
4428 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
4429 | "the sum of all but the first argument are subtracted from the first\n" | |
4430 | "argument.") | |
4431 | #define FUNC_NAME s_scm_i_difference | |
4432 | { | |
4433 | while (!scm_is_null (rest)) | |
4434 | { x = scm_difference (x, y); | |
4435 | y = scm_car (rest); | |
4436 | rest = scm_cdr (rest); | |
4437 | } | |
4438 | return scm_difference (x, y); | |
4439 | } | |
4440 | #undef FUNC_NAME | |
4441 | ||
4442 | #define s_difference s_scm_i_difference | |
4443 | #define g_difference g_scm_i_difference | |
4444 | ||
0f2d19dd | 4445 | SCM |
6e8d25a6 | 4446 | scm_difference (SCM x, SCM y) |
78d3deb1 | 4447 | #define FUNC_NAME s_difference |
0f2d19dd | 4448 | { |
9cc37597 | 4449 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
4450 | { |
4451 | if (SCM_UNBNDP (x)) | |
4452 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
4453 | else | |
e11e83f3 | 4454 | if (SCM_I_INUMP (x)) |
ca46fb90 | 4455 | { |
e25f3727 | 4456 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 4457 | if (SCM_FIXABLE (xx)) |
d956fa6f | 4458 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 4459 | else |
e25f3727 | 4460 | return scm_i_inum2big (xx); |
ca46fb90 RB |
4461 | } |
4462 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
4463 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
4464 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
4465 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
4466 | else if (SCM_REALP (x)) | |
55f26379 | 4467 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 4468 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 4469 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 4470 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 4471 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4472 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 4473 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
4474 | else |
4475 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 4476 | } |
ca46fb90 | 4477 | |
9cc37597 | 4478 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 4479 | { |
9cc37597 | 4480 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4481 | { |
e25f3727 AW |
4482 | scm_t_inum xx = SCM_I_INUM (x); |
4483 | scm_t_inum yy = SCM_I_INUM (y); | |
4484 | scm_t_inum z = xx - yy; | |
0aacf84e | 4485 | if (SCM_FIXABLE (z)) |
d956fa6f | 4486 | return SCM_I_MAKINUM (z); |
0aacf84e | 4487 | else |
e25f3727 | 4488 | return scm_i_inum2big (z); |
0aacf84e MD |
4489 | } |
4490 | else if (SCM_BIGP (y)) | |
4491 | { | |
4492 | /* inum-x - big-y */ | |
e25f3727 | 4493 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 4494 | |
0aacf84e MD |
4495 | if (xx == 0) |
4496 | return scm_i_clonebig (y, 0); | |
4497 | else | |
4498 | { | |
4499 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4500 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4501 | |
0aacf84e MD |
4502 | if (xx >= 0) |
4503 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
4504 | else | |
4505 | { | |
4506 | /* x - y == -(y + -x) */ | |
4507 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
4508 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4509 | } | |
4510 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 4511 | |
0aacf84e MD |
4512 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
4513 | /* we know the result will have to be a bignum */ | |
4514 | return result; | |
4515 | else | |
4516 | return scm_i_normbig (result); | |
4517 | } | |
4518 | } | |
4519 | else if (SCM_REALP (y)) | |
4520 | { | |
e25f3727 | 4521 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 4522 | return scm_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
4523 | } |
4524 | else if (SCM_COMPLEXP (y)) | |
4525 | { | |
e25f3727 | 4526 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 4527 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4528 | - SCM_COMPLEX_IMAG (y)); |
4529 | } | |
f92e85f7 MV |
4530 | else if (SCM_FRACTIONP (y)) |
4531 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 4532 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4533 | SCM_FRACTION_NUMERATOR (y)), |
4534 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4535 | else |
4536 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 4537 | } |
0aacf84e MD |
4538 | else if (SCM_BIGP (x)) |
4539 | { | |
e11e83f3 | 4540 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4541 | { |
4542 | /* big-x - inum-y */ | |
e25f3727 | 4543 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 4544 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 4545 | |
0aacf84e MD |
4546 | scm_remember_upto_here_1 (x); |
4547 | if (sgn_x == 0) | |
c71b0706 | 4548 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 4549 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
4550 | else |
4551 | { | |
4552 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4553 | |
708f22c6 KR |
4554 | if (yy >= 0) |
4555 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
4556 | else | |
4557 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 4558 | scm_remember_upto_here_1 (x); |
ca46fb90 | 4559 | |
0aacf84e MD |
4560 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
4561 | /* we know the result will have to be a bignum */ | |
4562 | return result; | |
4563 | else | |
4564 | return scm_i_normbig (result); | |
4565 | } | |
4566 | } | |
4567 | else if (SCM_BIGP (y)) | |
4568 | { | |
4569 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4570 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4571 | SCM result = scm_i_mkbig (); | |
4572 | mpz_sub (SCM_I_BIG_MPZ (result), | |
4573 | SCM_I_BIG_MPZ (x), | |
4574 | SCM_I_BIG_MPZ (y)); | |
4575 | scm_remember_upto_here_2 (x, y); | |
4576 | /* we know the result will have to be a bignum */ | |
4577 | if ((sgn_x == 1) && (sgn_y == -1)) | |
4578 | return result; | |
4579 | if ((sgn_x == -1) && (sgn_y == 1)) | |
4580 | return result; | |
4581 | return scm_i_normbig (result); | |
4582 | } | |
4583 | else if (SCM_REALP (y)) | |
4584 | { | |
4585 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
4586 | scm_remember_upto_here_1 (x); | |
55f26379 | 4587 | return scm_from_double (result); |
0aacf84e MD |
4588 | } |
4589 | else if (SCM_COMPLEXP (y)) | |
4590 | { | |
4591 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4592 | - SCM_COMPLEX_REAL (y)); | |
4593 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4594 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4595 | } |
f92e85f7 | 4596 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4597 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4598 | SCM_FRACTION_NUMERATOR (y)), |
4599 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 4600 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 4601 | } |
0aacf84e MD |
4602 | else if (SCM_REALP (x)) |
4603 | { | |
e11e83f3 | 4604 | if (SCM_I_INUMP (y)) |
55f26379 | 4605 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
4606 | else if (SCM_BIGP (y)) |
4607 | { | |
4608 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4609 | scm_remember_upto_here_1 (x); | |
55f26379 | 4610 | return scm_from_double (result); |
0aacf84e MD |
4611 | } |
4612 | else if (SCM_REALP (y)) | |
55f26379 | 4613 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 4614 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4615 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4616 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4617 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4618 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
4619 | else |
4620 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4621 | } |
0aacf84e MD |
4622 | else if (SCM_COMPLEXP (x)) |
4623 | { | |
e11e83f3 | 4624 | if (SCM_I_INUMP (y)) |
8507ec80 | 4625 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
4626 | SCM_COMPLEX_IMAG (x)); |
4627 | else if (SCM_BIGP (y)) | |
4628 | { | |
4629 | double real_part = (SCM_COMPLEX_REAL (x) | |
4630 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
4631 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4632 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
4633 | } |
4634 | else if (SCM_REALP (y)) | |
8507ec80 | 4635 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
4636 | SCM_COMPLEX_IMAG (x)); |
4637 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4638 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4639 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4640 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4641 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
4642 | SCM_COMPLEX_IMAG (x)); |
4643 | else | |
4644 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
4645 | } | |
4646 | else if (SCM_FRACTIONP (x)) | |
4647 | { | |
e11e83f3 | 4648 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4649 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 4650 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4651 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4652 | SCM_FRACTION_DENOMINATOR (x)); | |
4653 | else if (SCM_BIGP (y)) | |
cba42c93 | 4654 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4655 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4656 | SCM_FRACTION_DENOMINATOR (x)); | |
4657 | else if (SCM_REALP (y)) | |
55f26379 | 4658 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 4659 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4660 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4661 | -SCM_COMPLEX_IMAG (y)); |
4662 | else if (SCM_FRACTIONP (y)) | |
4663 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 4664 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4665 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4666 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4667 | else |
4668 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4669 | } |
0aacf84e | 4670 | else |
98cb6e75 | 4671 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 4672 | } |
c05e97b7 | 4673 | #undef FUNC_NAME |
0f2d19dd | 4674 | |
ca46fb90 | 4675 | |
40882e3d KR |
4676 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
4677 | (SCM x), | |
4678 | "Return @math{@var{x}-1}.") | |
4679 | #define FUNC_NAME s_scm_oneminus | |
4680 | { | |
cff5fa33 | 4681 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
4682 | } |
4683 | #undef FUNC_NAME | |
4684 | ||
4685 | ||
78d3deb1 AW |
4686 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
4687 | (SCM x, SCM y, SCM rest), | |
4688 | "Return the product of all arguments. If called without arguments,\n" | |
4689 | "1 is returned.") | |
4690 | #define FUNC_NAME s_scm_i_product | |
4691 | { | |
4692 | while (!scm_is_null (rest)) | |
4693 | { x = scm_product (x, y); | |
4694 | y = scm_car (rest); | |
4695 | rest = scm_cdr (rest); | |
4696 | } | |
4697 | return scm_product (x, y); | |
4698 | } | |
4699 | #undef FUNC_NAME | |
4700 | ||
4701 | #define s_product s_scm_i_product | |
4702 | #define g_product g_scm_i_product | |
4703 | ||
0f2d19dd | 4704 | SCM |
6e8d25a6 | 4705 | scm_product (SCM x, SCM y) |
0f2d19dd | 4706 | { |
9cc37597 | 4707 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
4708 | { |
4709 | if (SCM_UNBNDP (x)) | |
d956fa6f | 4710 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
4711 | else if (SCM_NUMBERP (x)) |
4712 | return x; | |
4713 | else | |
4714 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 4715 | } |
ca46fb90 | 4716 | |
9cc37597 | 4717 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 4718 | { |
e25f3727 | 4719 | scm_t_inum xx; |
f4c627b3 | 4720 | |
0aacf84e | 4721 | intbig: |
e11e83f3 | 4722 | xx = SCM_I_INUM (x); |
f4c627b3 | 4723 | |
0aacf84e MD |
4724 | switch (xx) |
4725 | { | |
ca46fb90 RB |
4726 | case 0: return x; break; |
4727 | case 1: return y; break; | |
0aacf84e | 4728 | } |
f4c627b3 | 4729 | |
9cc37597 | 4730 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4731 | { |
e25f3727 AW |
4732 | scm_t_inum yy = SCM_I_INUM (y); |
4733 | scm_t_inum kk = xx * yy; | |
d956fa6f | 4734 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 4735 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
4736 | return k; |
4737 | else | |
4738 | { | |
e25f3727 | 4739 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
4740 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
4741 | return scm_i_normbig (result); | |
4742 | } | |
4743 | } | |
4744 | else if (SCM_BIGP (y)) | |
4745 | { | |
4746 | SCM result = scm_i_mkbig (); | |
4747 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
4748 | scm_remember_upto_here_1 (y); | |
4749 | return result; | |
4750 | } | |
4751 | else if (SCM_REALP (y)) | |
55f26379 | 4752 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 4753 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4754 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 4755 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4756 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4757 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4758 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4759 | else |
4760 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4761 | } |
0aacf84e MD |
4762 | else if (SCM_BIGP (x)) |
4763 | { | |
e11e83f3 | 4764 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4765 | { |
4766 | SCM_SWAP (x, y); | |
4767 | goto intbig; | |
4768 | } | |
4769 | else if (SCM_BIGP (y)) | |
4770 | { | |
4771 | SCM result = scm_i_mkbig (); | |
4772 | mpz_mul (SCM_I_BIG_MPZ (result), | |
4773 | SCM_I_BIG_MPZ (x), | |
4774 | SCM_I_BIG_MPZ (y)); | |
4775 | scm_remember_upto_here_2 (x, y); | |
4776 | return result; | |
4777 | } | |
4778 | else if (SCM_REALP (y)) | |
4779 | { | |
4780 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
4781 | scm_remember_upto_here_1 (x); | |
55f26379 | 4782 | return scm_from_double (result); |
0aacf84e MD |
4783 | } |
4784 | else if (SCM_COMPLEXP (y)) | |
4785 | { | |
4786 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4787 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4788 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4789 | z * SCM_COMPLEX_IMAG (y)); |
4790 | } | |
f92e85f7 | 4791 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4792 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4793 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4794 | else |
4795 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4796 | } |
0aacf84e MD |
4797 | else if (SCM_REALP (x)) |
4798 | { | |
e11e83f3 | 4799 | if (SCM_I_INUMP (y)) |
23d72566 KR |
4800 | { |
4801 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
4802 | if (scm_is_eq (y, SCM_INUM0)) | |
4803 | return y; | |
4804 | return scm_from_double (SCM_I_INUM (y) * SCM_REAL_VALUE (x)); | |
4805 | } | |
0aacf84e MD |
4806 | else if (SCM_BIGP (y)) |
4807 | { | |
4808 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
4809 | scm_remember_upto_here_1 (y); | |
55f26379 | 4810 | return scm_from_double (result); |
0aacf84e MD |
4811 | } |
4812 | else if (SCM_REALP (y)) | |
55f26379 | 4813 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 4814 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4815 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 4816 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4817 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4818 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
4819 | else |
4820 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4821 | } |
0aacf84e MD |
4822 | else if (SCM_COMPLEXP (x)) |
4823 | { | |
e11e83f3 | 4824 | if (SCM_I_INUMP (y)) |
23d72566 KR |
4825 | { |
4826 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
4827 | if (scm_is_eq (y, SCM_INUM0)) | |
4828 | return y; | |
4829 | return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x), | |
4830 | SCM_I_INUM (y) * SCM_COMPLEX_IMAG (x)); | |
4831 | } | |
0aacf84e MD |
4832 | else if (SCM_BIGP (y)) |
4833 | { | |
4834 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4835 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4836 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 4837 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4838 | } |
4839 | else if (SCM_REALP (y)) | |
8507ec80 | 4840 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
4841 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
4842 | else if (SCM_COMPLEXP (y)) | |
4843 | { | |
8507ec80 | 4844 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
4845 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
4846 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
4847 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
4848 | } | |
f92e85f7 MV |
4849 | else if (SCM_FRACTIONP (y)) |
4850 | { | |
4851 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4852 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
4853 | yy * SCM_COMPLEX_IMAG (x)); |
4854 | } | |
4855 | else | |
4856 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
4857 | } | |
4858 | else if (SCM_FRACTIONP (x)) | |
4859 | { | |
e11e83f3 | 4860 | if (SCM_I_INUMP (y)) |
cba42c93 | 4861 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4862 | SCM_FRACTION_DENOMINATOR (x)); |
4863 | else if (SCM_BIGP (y)) | |
cba42c93 | 4864 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4865 | SCM_FRACTION_DENOMINATOR (x)); |
4866 | else if (SCM_REALP (y)) | |
55f26379 | 4867 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
4868 | else if (SCM_COMPLEXP (y)) |
4869 | { | |
4870 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 4871 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4872 | xx * SCM_COMPLEX_IMAG (y)); |
4873 | } | |
4874 | else if (SCM_FRACTIONP (y)) | |
4875 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 4876 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4877 | SCM_FRACTION_NUMERATOR (y)), |
4878 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
4879 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4880 | else |
4881 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4882 | } |
0aacf84e | 4883 | else |
f4c627b3 | 4884 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
4885 | } |
4886 | ||
7351e207 MV |
4887 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
4888 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
4889 | #define ALLOW_DIVIDE_BY_ZERO | |
4890 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
4891 | #endif | |
0f2d19dd | 4892 | |
ba74ef4e MV |
4893 | /* The code below for complex division is adapted from the GNU |
4894 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
4895 | this copyright: */ | |
4896 | ||
4897 | /**************************************************************** | |
4898 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
4899 | ||
4900 | Permission to use, copy, modify, and distribute this software | |
4901 | and its documentation for any purpose and without fee is hereby | |
4902 | granted, provided that the above copyright notice appear in all | |
4903 | copies and that both that the copyright notice and this | |
4904 | permission notice and warranty disclaimer appear in supporting | |
4905 | documentation, and that the names of AT&T Bell Laboratories or | |
4906 | Bellcore or any of their entities not be used in advertising or | |
4907 | publicity pertaining to distribution of the software without | |
4908 | specific, written prior permission. | |
4909 | ||
4910 | AT&T and Bellcore disclaim all warranties with regard to this | |
4911 | software, including all implied warranties of merchantability | |
4912 | and fitness. In no event shall AT&T or Bellcore be liable for | |
4913 | any special, indirect or consequential damages or any damages | |
4914 | whatsoever resulting from loss of use, data or profits, whether | |
4915 | in an action of contract, negligence or other tortious action, | |
4916 | arising out of or in connection with the use or performance of | |
4917 | this software. | |
4918 | ****************************************************************/ | |
4919 | ||
78d3deb1 AW |
4920 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
4921 | (SCM x, SCM y, SCM rest), | |
4922 | "Divide the first argument by the product of the remaining\n" | |
4923 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
4924 | "returned.") | |
4925 | #define FUNC_NAME s_scm_i_divide | |
4926 | { | |
4927 | while (!scm_is_null (rest)) | |
4928 | { x = scm_divide (x, y); | |
4929 | y = scm_car (rest); | |
4930 | rest = scm_cdr (rest); | |
4931 | } | |
4932 | return scm_divide (x, y); | |
4933 | } | |
4934 | #undef FUNC_NAME | |
4935 | ||
4936 | #define s_divide s_scm_i_divide | |
4937 | #define g_divide g_scm_i_divide | |
4938 | ||
f92e85f7 | 4939 | static SCM |
78d3deb1 AW |
4940 | do_divide (SCM x, SCM y, int inexact) |
4941 | #define FUNC_NAME s_divide | |
0f2d19dd | 4942 | { |
f8de44c1 DH |
4943 | double a; |
4944 | ||
9cc37597 | 4945 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
4946 | { |
4947 | if (SCM_UNBNDP (x)) | |
4948 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 4949 | else if (SCM_I_INUMP (x)) |
0aacf84e | 4950 | { |
e25f3727 | 4951 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
4952 | if (xx == 1 || xx == -1) |
4953 | return x; | |
7351e207 | 4954 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4955 | else if (xx == 0) |
4956 | scm_num_overflow (s_divide); | |
7351e207 | 4957 | #endif |
0aacf84e | 4958 | else |
f92e85f7 MV |
4959 | { |
4960 | if (inexact) | |
55f26379 | 4961 | return scm_from_double (1.0 / (double) xx); |
cff5fa33 | 4962 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 4963 | } |
0aacf84e MD |
4964 | } |
4965 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
4966 | { |
4967 | if (inexact) | |
55f26379 | 4968 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cff5fa33 | 4969 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 4970 | } |
0aacf84e MD |
4971 | else if (SCM_REALP (x)) |
4972 | { | |
4973 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 4974 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4975 | if (xx == 0.0) |
4976 | scm_num_overflow (s_divide); | |
4977 | else | |
7351e207 | 4978 | #endif |
55f26379 | 4979 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
4980 | } |
4981 | else if (SCM_COMPLEXP (x)) | |
4982 | { | |
4983 | double r = SCM_COMPLEX_REAL (x); | |
4984 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 4985 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
4986 | { |
4987 | double t = r / i; | |
4988 | double d = i * (1.0 + t * t); | |
8507ec80 | 4989 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
4990 | } |
4991 | else | |
4992 | { | |
4993 | double t = i / r; | |
4994 | double d = r * (1.0 + t * t); | |
8507ec80 | 4995 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
4996 | } |
4997 | } | |
f92e85f7 | 4998 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4999 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 5000 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
5001 | else |
5002 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 5003 | } |
f8de44c1 | 5004 | |
9cc37597 | 5005 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 5006 | { |
e25f3727 | 5007 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 5008 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 5009 | { |
e25f3727 | 5010 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
5011 | if (yy == 0) |
5012 | { | |
7351e207 | 5013 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 5014 | scm_num_overflow (s_divide); |
7351e207 | 5015 | #else |
55f26379 | 5016 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 5017 | #endif |
0aacf84e MD |
5018 | } |
5019 | else if (xx % yy != 0) | |
f92e85f7 MV |
5020 | { |
5021 | if (inexact) | |
55f26379 | 5022 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 5023 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 5024 | } |
0aacf84e MD |
5025 | else |
5026 | { | |
e25f3727 | 5027 | scm_t_inum z = xx / yy; |
0aacf84e | 5028 | if (SCM_FIXABLE (z)) |
d956fa6f | 5029 | return SCM_I_MAKINUM (z); |
0aacf84e | 5030 | else |
e25f3727 | 5031 | return scm_i_inum2big (z); |
0aacf84e | 5032 | } |
f872b822 | 5033 | } |
0aacf84e | 5034 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
5035 | { |
5036 | if (inexact) | |
55f26379 | 5037 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 5038 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 5039 | } |
0aacf84e MD |
5040 | else if (SCM_REALP (y)) |
5041 | { | |
5042 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5043 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5044 | if (yy == 0.0) |
5045 | scm_num_overflow (s_divide); | |
5046 | else | |
7351e207 | 5047 | #endif |
55f26379 | 5048 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 5049 | } |
0aacf84e MD |
5050 | else if (SCM_COMPLEXP (y)) |
5051 | { | |
5052 | a = xx; | |
5053 | complex_div: /* y _must_ be a complex number */ | |
5054 | { | |
5055 | double r = SCM_COMPLEX_REAL (y); | |
5056 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 5057 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
5058 | { |
5059 | double t = r / i; | |
5060 | double d = i * (1.0 + t * t); | |
8507ec80 | 5061 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
5062 | } |
5063 | else | |
5064 | { | |
5065 | double t = i / r; | |
5066 | double d = r * (1.0 + t * t); | |
8507ec80 | 5067 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
5068 | } |
5069 | } | |
5070 | } | |
f92e85f7 MV |
5071 | else if (SCM_FRACTIONP (y)) |
5072 | /* a / b/c = ac / b */ | |
cba42c93 | 5073 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 5074 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
5075 | else |
5076 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 5077 | } |
0aacf84e MD |
5078 | else if (SCM_BIGP (x)) |
5079 | { | |
e11e83f3 | 5080 | if (SCM_I_INUMP (y)) |
0aacf84e | 5081 | { |
e25f3727 | 5082 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
5083 | if (yy == 0) |
5084 | { | |
7351e207 | 5085 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 5086 | scm_num_overflow (s_divide); |
7351e207 | 5087 | #else |
0aacf84e MD |
5088 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
5089 | scm_remember_upto_here_1 (x); | |
5090 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 5091 | #endif |
0aacf84e MD |
5092 | } |
5093 | else if (yy == 1) | |
5094 | return x; | |
5095 | else | |
5096 | { | |
5097 | /* FIXME: HMM, what are the relative performance issues here? | |
5098 | We need to test. Is it faster on average to test | |
5099 | divisible_p, then perform whichever operation, or is it | |
5100 | faster to perform the integer div opportunistically and | |
5101 | switch to real if there's a remainder? For now we take the | |
5102 | middle ground: test, then if divisible, use the faster div | |
5103 | func. */ | |
5104 | ||
e25f3727 | 5105 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
5106 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
5107 | ||
5108 | if (divisible_p) | |
5109 | { | |
5110 | SCM result = scm_i_mkbig (); | |
5111 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
5112 | scm_remember_upto_here_1 (x); | |
5113 | if (yy < 0) | |
5114 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
5115 | return scm_i_normbig (result); | |
5116 | } | |
5117 | else | |
f92e85f7 MV |
5118 | { |
5119 | if (inexact) | |
55f26379 | 5120 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 5121 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 5122 | } |
0aacf84e MD |
5123 | } |
5124 | } | |
5125 | else if (SCM_BIGP (y)) | |
5126 | { | |
a4955a04 MW |
5127 | /* big_x / big_y */ |
5128 | if (inexact) | |
0aacf84e | 5129 | { |
a4955a04 MW |
5130 | /* It's easily possible for the ratio x/y to fit a double |
5131 | but one or both x and y be too big to fit a double, | |
5132 | hence the use of mpq_get_d rather than converting and | |
5133 | dividing. */ | |
5134 | mpq_t q; | |
5135 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
5136 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
5137 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
5138 | } |
5139 | else | |
5140 | { | |
a4955a04 MW |
5141 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
5142 | SCM_I_BIG_MPZ (y)); | |
5143 | if (divisible_p) | |
5144 | { | |
5145 | SCM result = scm_i_mkbig (); | |
5146 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
5147 | SCM_I_BIG_MPZ (x), | |
5148 | SCM_I_BIG_MPZ (y)); | |
5149 | scm_remember_upto_here_2 (x, y); | |
5150 | return scm_i_normbig (result); | |
5151 | } | |
5152 | else | |
5153 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
5154 | } |
5155 | } | |
5156 | else if (SCM_REALP (y)) | |
5157 | { | |
5158 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5159 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5160 | if (yy == 0.0) |
5161 | scm_num_overflow (s_divide); | |
5162 | else | |
7351e207 | 5163 | #endif |
55f26379 | 5164 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
5165 | } |
5166 | else if (SCM_COMPLEXP (y)) | |
5167 | { | |
5168 | a = scm_i_big2dbl (x); | |
5169 | goto complex_div; | |
5170 | } | |
f92e85f7 | 5171 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5172 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 5173 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
5174 | else |
5175 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 5176 | } |
0aacf84e MD |
5177 | else if (SCM_REALP (x)) |
5178 | { | |
5179 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 5180 | if (SCM_I_INUMP (y)) |
0aacf84e | 5181 | { |
e25f3727 | 5182 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 5183 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
5184 | if (yy == 0) |
5185 | scm_num_overflow (s_divide); | |
5186 | else | |
7351e207 | 5187 | #endif |
55f26379 | 5188 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
5189 | } |
5190 | else if (SCM_BIGP (y)) | |
5191 | { | |
5192 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
5193 | scm_remember_upto_here_1 (y); | |
55f26379 | 5194 | return scm_from_double (rx / dby); |
0aacf84e MD |
5195 | } |
5196 | else if (SCM_REALP (y)) | |
5197 | { | |
5198 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5199 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5200 | if (yy == 0.0) |
5201 | scm_num_overflow (s_divide); | |
5202 | else | |
7351e207 | 5203 | #endif |
55f26379 | 5204 | return scm_from_double (rx / yy); |
0aacf84e MD |
5205 | } |
5206 | else if (SCM_COMPLEXP (y)) | |
5207 | { | |
5208 | a = rx; | |
5209 | goto complex_div; | |
5210 | } | |
f92e85f7 | 5211 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5212 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
5213 | else |
5214 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 5215 | } |
0aacf84e MD |
5216 | else if (SCM_COMPLEXP (x)) |
5217 | { | |
5218 | double rx = SCM_COMPLEX_REAL (x); | |
5219 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 5220 | if (SCM_I_INUMP (y)) |
0aacf84e | 5221 | { |
e25f3727 | 5222 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 5223 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
5224 | if (yy == 0) |
5225 | scm_num_overflow (s_divide); | |
5226 | else | |
7351e207 | 5227 | #endif |
0aacf84e MD |
5228 | { |
5229 | double d = yy; | |
8507ec80 | 5230 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
5231 | } |
5232 | } | |
5233 | else if (SCM_BIGP (y)) | |
5234 | { | |
5235 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
5236 | scm_remember_upto_here_1 (y); | |
8507ec80 | 5237 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
5238 | } |
5239 | else if (SCM_REALP (y)) | |
5240 | { | |
5241 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 5242 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
5243 | if (yy == 0.0) |
5244 | scm_num_overflow (s_divide); | |
5245 | else | |
7351e207 | 5246 | #endif |
8507ec80 | 5247 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
5248 | } |
5249 | else if (SCM_COMPLEXP (y)) | |
5250 | { | |
5251 | double ry = SCM_COMPLEX_REAL (y); | |
5252 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 5253 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
5254 | { |
5255 | double t = ry / iy; | |
5256 | double d = iy * (1.0 + t * t); | |
8507ec80 | 5257 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
5258 | } |
5259 | else | |
5260 | { | |
5261 | double t = iy / ry; | |
5262 | double d = ry * (1.0 + t * t); | |
8507ec80 | 5263 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
5264 | } |
5265 | } | |
f92e85f7 MV |
5266 | else if (SCM_FRACTIONP (y)) |
5267 | { | |
5268 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 5269 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 5270 | } |
0aacf84e MD |
5271 | else |
5272 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 5273 | } |
f92e85f7 MV |
5274 | else if (SCM_FRACTIONP (x)) |
5275 | { | |
e11e83f3 | 5276 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5277 | { |
e25f3727 | 5278 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
5279 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
5280 | if (yy == 0) | |
5281 | scm_num_overflow (s_divide); | |
5282 | else | |
5283 | #endif | |
cba42c93 | 5284 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5285 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
5286 | } | |
5287 | else if (SCM_BIGP (y)) | |
5288 | { | |
cba42c93 | 5289 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5290 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
5291 | } | |
5292 | else if (SCM_REALP (y)) | |
5293 | { | |
5294 | double yy = SCM_REAL_VALUE (y); | |
5295 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
5296 | if (yy == 0.0) | |
5297 | scm_num_overflow (s_divide); | |
5298 | else | |
5299 | #endif | |
55f26379 | 5300 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
5301 | } |
5302 | else if (SCM_COMPLEXP (y)) | |
5303 | { | |
5304 | a = scm_i_fraction2double (x); | |
5305 | goto complex_div; | |
5306 | } | |
5307 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 5308 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5309 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
5310 | else | |
5311 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
5312 | } | |
0aacf84e | 5313 | else |
f8de44c1 | 5314 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 5315 | } |
f92e85f7 MV |
5316 | |
5317 | SCM | |
5318 | scm_divide (SCM x, SCM y) | |
5319 | { | |
78d3deb1 | 5320 | return do_divide (x, y, 0); |
f92e85f7 MV |
5321 | } |
5322 | ||
5323 | static SCM scm_divide2real (SCM x, SCM y) | |
5324 | { | |
78d3deb1 | 5325 | return do_divide (x, y, 1); |
f92e85f7 | 5326 | } |
c05e97b7 | 5327 | #undef FUNC_NAME |
0f2d19dd | 5328 | |
fa605590 | 5329 | |
0f2d19dd | 5330 | double |
3101f40f | 5331 | scm_c_truncate (double x) |
0f2d19dd | 5332 | { |
fa605590 KR |
5333 | #if HAVE_TRUNC |
5334 | return trunc (x); | |
5335 | #else | |
f872b822 MD |
5336 | if (x < 0.0) |
5337 | return -floor (-x); | |
5338 | return floor (x); | |
fa605590 | 5339 | #endif |
0f2d19dd | 5340 | } |
0f2d19dd | 5341 | |
3101f40f MV |
5342 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
5343 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
5344 | Then half-way cases are identified and adjusted down if the | |
5345 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
5346 | |
5347 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
5348 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
5349 | ||
5350 | An odd "result" value is identified with result/2 != floor(result/2). | |
5351 | This is done with plus_half, since that value is ready for use sooner in | |
5352 | a pipelined cpu, and we're already requiring plus_half == result. | |
5353 | ||
5354 | Note however that we need to be careful when x is big and already an | |
5355 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
5356 | us to return such a value, incorrectly. For instance if the hardware is | |
5357 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
5358 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
5359 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
5360 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
5361 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
5362 | ||
5363 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
5364 | x is already an integer. If it is then clearly that's the desired result | |
5365 | already. And if it's not then the exponent must be small enough to allow | |
5366 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
5367 | ||
0f2d19dd | 5368 | double |
3101f40f | 5369 | scm_c_round (double x) |
0f2d19dd | 5370 | { |
6187f48b KR |
5371 | double plus_half, result; |
5372 | ||
5373 | if (x == floor (x)) | |
5374 | return x; | |
5375 | ||
5376 | plus_half = x + 0.5; | |
5377 | result = floor (plus_half); | |
3101f40f | 5378 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
5379 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
5380 | ? result - 1 | |
5381 | : result); | |
0f2d19dd JB |
5382 | } |
5383 | ||
f92e85f7 MV |
5384 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
5385 | (SCM x), | |
5386 | "Round the number @var{x} towards zero.") | |
5387 | #define FUNC_NAME s_scm_truncate_number | |
5388 | { | |
73e4de09 | 5389 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5390 | return scm_floor (x); |
5391 | else | |
5392 | return scm_ceiling (x); | |
5393 | } | |
5394 | #undef FUNC_NAME | |
5395 | ||
5396 | static SCM exactly_one_half; | |
5397 | ||
5398 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, | |
5399 | (SCM x), | |
5400 | "Round the number @var{x} towards the nearest integer. " | |
5401 | "When it is exactly halfway between two integers, " | |
5402 | "round towards the even one.") | |
5403 | #define FUNC_NAME s_scm_round_number | |
5404 | { | |
e11e83f3 | 5405 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
5406 | return x; |
5407 | else if (SCM_REALP (x)) | |
3101f40f | 5408 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 5409 | else |
bae30667 KR |
5410 | { |
5411 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
5412 | single quotient+remainder division then examining to see which way | |
5413 | the rounding should go. */ | |
5414 | SCM plus_half = scm_sum (x, exactly_one_half); | |
5415 | SCM result = scm_floor (plus_half); | |
3101f40f | 5416 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
5417 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
5418 | && scm_is_true (scm_odd_p (result))) | |
cff5fa33 | 5419 | return scm_difference (result, SCM_INUM1); |
bae30667 KR |
5420 | else |
5421 | return result; | |
5422 | } | |
f92e85f7 MV |
5423 | } |
5424 | #undef FUNC_NAME | |
5425 | ||
5426 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
5427 | (SCM x), | |
5428 | "Round the number @var{x} towards minus infinity.") | |
5429 | #define FUNC_NAME s_scm_floor | |
5430 | { | |
e11e83f3 | 5431 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5432 | return x; |
5433 | else if (SCM_REALP (x)) | |
55f26379 | 5434 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5435 | else if (SCM_FRACTIONP (x)) |
5436 | { | |
5437 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5438 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5439 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5440 | { |
5441 | /* For positive x, rounding towards zero is correct. */ | |
5442 | return q; | |
5443 | } | |
5444 | else | |
5445 | { | |
5446 | /* For negative x, we need to return q-1 unless x is an | |
5447 | integer. But fractions are never integer, per our | |
5448 | assumptions. */ | |
cff5fa33 | 5449 | return scm_difference (q, SCM_INUM1); |
f92e85f7 MV |
5450 | } |
5451 | } | |
5452 | else | |
5453 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
5454 | } | |
5455 | #undef FUNC_NAME | |
5456 | ||
5457 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
5458 | (SCM x), | |
5459 | "Round the number @var{x} towards infinity.") | |
5460 | #define FUNC_NAME s_scm_ceiling | |
5461 | { | |
e11e83f3 | 5462 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5463 | return x; |
5464 | else if (SCM_REALP (x)) | |
55f26379 | 5465 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5466 | else if (SCM_FRACTIONP (x)) |
5467 | { | |
5468 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5469 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5470 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
5471 | { |
5472 | /* For negative x, rounding towards zero is correct. */ | |
5473 | return q; | |
5474 | } | |
5475 | else | |
5476 | { | |
5477 | /* For positive x, we need to return q+1 unless x is an | |
5478 | integer. But fractions are never integer, per our | |
5479 | assumptions. */ | |
cff5fa33 | 5480 | return scm_sum (q, SCM_INUM1); |
f92e85f7 MV |
5481 | } |
5482 | } | |
5483 | else | |
5484 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
5485 | } | |
5486 | #undef FUNC_NAME | |
0f2d19dd | 5487 | |
ad79736c AW |
5488 | /* sin/cos/tan/asin/acos/atan |
5489 | sinh/cosh/tanh/asinh/acosh/atanh | |
5490 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
5491 | Written by Jerry D. Hedden, (C) FSF. | |
5492 | See the file `COPYING' for terms applying to this program. */ | |
0f2d19dd | 5493 | |
6fc4d012 | 5494 | SCM_DEFINE (scm_expt, "expt", 2, 0, 0, |
27c37006 | 5495 | (SCM x, SCM y), |
6fc4d012 AW |
5496 | "Return @var{x} raised to the power of @var{y}.") |
5497 | #define FUNC_NAME s_scm_expt | |
0f2d19dd | 5498 | { |
01c7284a MW |
5499 | if (scm_is_integer (y)) |
5500 | { | |
5501 | if (scm_is_true (scm_exact_p (y))) | |
5502 | return scm_integer_expt (x, y); | |
5503 | else | |
5504 | { | |
5505 | /* Here we handle the case where the exponent is an inexact | |
5506 | integer. We make the exponent exact in order to use | |
5507 | scm_integer_expt, and thus avoid the spurious imaginary | |
5508 | parts that may result from round-off errors in the general | |
5509 | e^(y log x) method below (for example when squaring a large | |
5510 | negative number). In this case, we must return an inexact | |
5511 | result for correctness. We also make the base inexact so | |
5512 | that scm_integer_expt will use fast inexact arithmetic | |
5513 | internally. Note that making the base inexact is not | |
5514 | sufficient to guarantee an inexact result, because | |
5515 | scm_integer_expt will return an exact 1 when the exponent | |
5516 | is 0, even if the base is inexact. */ | |
5517 | return scm_exact_to_inexact | |
5518 | (scm_integer_expt (scm_exact_to_inexact (x), | |
5519 | scm_inexact_to_exact (y))); | |
5520 | } | |
5521 | } | |
6fc4d012 AW |
5522 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
5523 | { | |
5524 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
5525 | } | |
5526 | else | |
5527 | return scm_exp (scm_product (scm_log (x), y)); | |
0f2d19dd | 5528 | } |
1bbd0b84 | 5529 | #undef FUNC_NAME |
0f2d19dd | 5530 | |
ad79736c AW |
5531 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
5532 | (SCM z), | |
5533 | "Compute the sine of @var{z}.") | |
5534 | #define FUNC_NAME s_scm_sin | |
5535 | { | |
5536 | if (scm_is_real (z)) | |
5537 | return scm_from_double (sin (scm_to_double (z))); | |
5538 | else if (SCM_COMPLEXP (z)) | |
5539 | { double x, y; | |
5540 | x = SCM_COMPLEX_REAL (z); | |
5541 | y = SCM_COMPLEX_IMAG (z); | |
5542 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
5543 | cos (x) * sinh (y)); | |
5544 | } | |
5545 | else | |
5546 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
5547 | } | |
5548 | #undef FUNC_NAME | |
0f2d19dd | 5549 | |
ad79736c AW |
5550 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
5551 | (SCM z), | |
5552 | "Compute the cosine of @var{z}.") | |
5553 | #define FUNC_NAME s_scm_cos | |
5554 | { | |
5555 | if (scm_is_real (z)) | |
5556 | return scm_from_double (cos (scm_to_double (z))); | |
5557 | else if (SCM_COMPLEXP (z)) | |
5558 | { double x, y; | |
5559 | x = SCM_COMPLEX_REAL (z); | |
5560 | y = SCM_COMPLEX_IMAG (z); | |
5561 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
5562 | -sin (x) * sinh (y)); | |
5563 | } | |
5564 | else | |
5565 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
5566 | } | |
5567 | #undef FUNC_NAME | |
5568 | ||
5569 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
5570 | (SCM z), | |
5571 | "Compute the tangent of @var{z}.") | |
5572 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 5573 | { |
ad79736c AW |
5574 | if (scm_is_real (z)) |
5575 | return scm_from_double (tan (scm_to_double (z))); | |
5576 | else if (SCM_COMPLEXP (z)) | |
5577 | { double x, y, w; | |
5578 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
5579 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
5580 | w = cos (x) + cosh (y); | |
5581 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
5582 | if (w == 0.0) | |
5583 | scm_num_overflow (s_scm_tan); | |
5584 | #endif | |
5585 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
5586 | } | |
5587 | else | |
5588 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
5589 | } | |
5590 | #undef FUNC_NAME | |
5591 | ||
5592 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
5593 | (SCM z), | |
5594 | "Compute the hyperbolic sine of @var{z}.") | |
5595 | #define FUNC_NAME s_scm_sinh | |
5596 | { | |
5597 | if (scm_is_real (z)) | |
5598 | return scm_from_double (sinh (scm_to_double (z))); | |
5599 | else if (SCM_COMPLEXP (z)) | |
5600 | { double x, y; | |
5601 | x = SCM_COMPLEX_REAL (z); | |
5602 | y = SCM_COMPLEX_IMAG (z); | |
5603 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
5604 | cosh (x) * sin (y)); | |
5605 | } | |
5606 | else | |
5607 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
5608 | } | |
5609 | #undef FUNC_NAME | |
5610 | ||
5611 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
5612 | (SCM z), | |
5613 | "Compute the hyperbolic cosine of @var{z}.") | |
5614 | #define FUNC_NAME s_scm_cosh | |
5615 | { | |
5616 | if (scm_is_real (z)) | |
5617 | return scm_from_double (cosh (scm_to_double (z))); | |
5618 | else if (SCM_COMPLEXP (z)) | |
5619 | { double x, y; | |
5620 | x = SCM_COMPLEX_REAL (z); | |
5621 | y = SCM_COMPLEX_IMAG (z); | |
5622 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
5623 | sinh (x) * sin (y)); | |
5624 | } | |
5625 | else | |
5626 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
5627 | } | |
5628 | #undef FUNC_NAME | |
5629 | ||
5630 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
5631 | (SCM z), | |
5632 | "Compute the hyperbolic tangent of @var{z}.") | |
5633 | #define FUNC_NAME s_scm_tanh | |
5634 | { | |
5635 | if (scm_is_real (z)) | |
5636 | return scm_from_double (tanh (scm_to_double (z))); | |
5637 | else if (SCM_COMPLEXP (z)) | |
5638 | { double x, y, w; | |
5639 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
5640 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
5641 | w = cosh (x) + cos (y); | |
5642 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
5643 | if (w == 0.0) | |
5644 | scm_num_overflow (s_scm_tanh); | |
5645 | #endif | |
5646 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
5647 | } | |
5648 | else | |
5649 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
5650 | } | |
5651 | #undef FUNC_NAME | |
5652 | ||
5653 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
5654 | (SCM z), | |
5655 | "Compute the arc sine of @var{z}.") | |
5656 | #define FUNC_NAME s_scm_asin | |
5657 | { | |
5658 | if (scm_is_real (z)) | |
5659 | { | |
5660 | double w = scm_to_double (z); | |
5661 | if (w >= -1.0 && w <= 1.0) | |
5662 | return scm_from_double (asin (w)); | |
5663 | else | |
5664 | return scm_product (scm_c_make_rectangular (0, -1), | |
5665 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
5666 | } | |
5667 | else if (SCM_COMPLEXP (z)) | |
5668 | { double x, y; | |
5669 | x = SCM_COMPLEX_REAL (z); | |
5670 | y = SCM_COMPLEX_IMAG (z); | |
5671 | return scm_product (scm_c_make_rectangular (0, -1), | |
5672 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
5673 | } | |
5674 | else | |
5675 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
5676 | } | |
5677 | #undef FUNC_NAME | |
5678 | ||
5679 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
5680 | (SCM z), | |
5681 | "Compute the arc cosine of @var{z}.") | |
5682 | #define FUNC_NAME s_scm_acos | |
5683 | { | |
5684 | if (scm_is_real (z)) | |
5685 | { | |
5686 | double w = scm_to_double (z); | |
5687 | if (w >= -1.0 && w <= 1.0) | |
5688 | return scm_from_double (acos (w)); | |
5689 | else | |
5690 | return scm_sum (scm_from_double (acos (0.0)), | |
5691 | scm_product (scm_c_make_rectangular (0, 1), | |
5692 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
5693 | } | |
5694 | else if (SCM_COMPLEXP (z)) | |
5695 | { double x, y; | |
5696 | x = SCM_COMPLEX_REAL (z); | |
5697 | y = SCM_COMPLEX_IMAG (z); | |
5698 | return scm_sum (scm_from_double (acos (0.0)), | |
5699 | scm_product (scm_c_make_rectangular (0, 1), | |
5700 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
5701 | } | |
5702 | else | |
5703 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
5704 | } | |
5705 | #undef FUNC_NAME | |
5706 | ||
5707 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
5708 | (SCM z, SCM y), | |
5709 | "With one argument, compute the arc tangent of @var{z}.\n" | |
5710 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
5711 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
5712 | #define FUNC_NAME s_scm_atan | |
5713 | { | |
5714 | if (SCM_UNBNDP (y)) | |
5715 | { | |
5716 | if (scm_is_real (z)) | |
5717 | return scm_from_double (atan (scm_to_double (z))); | |
5718 | else if (SCM_COMPLEXP (z)) | |
5719 | { | |
5720 | double v, w; | |
5721 | v = SCM_COMPLEX_REAL (z); | |
5722 | w = SCM_COMPLEX_IMAG (z); | |
5723 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
5724 | scm_c_make_rectangular (v, w + 1.0))), | |
5725 | scm_c_make_rectangular (0, 2)); | |
5726 | } | |
5727 | else | |
5728 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
5729 | } | |
5730 | else if (scm_is_real (z)) | |
5731 | { | |
5732 | if (scm_is_real (y)) | |
5733 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
5734 | else | |
5735 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
5736 | } | |
5737 | else | |
5738 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
5739 | } | |
5740 | #undef FUNC_NAME | |
5741 | ||
5742 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
5743 | (SCM z), | |
5744 | "Compute the inverse hyperbolic sine of @var{z}.") | |
5745 | #define FUNC_NAME s_scm_sys_asinh | |
5746 | { | |
5747 | if (scm_is_real (z)) | |
5748 | return scm_from_double (asinh (scm_to_double (z))); | |
5749 | else if (scm_is_number (z)) | |
5750 | return scm_log (scm_sum (z, | |
5751 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 5752 | SCM_INUM1)))); |
ad79736c AW |
5753 | else |
5754 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
5755 | } | |
5756 | #undef FUNC_NAME | |
5757 | ||
5758 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
5759 | (SCM z), | |
5760 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
5761 | #define FUNC_NAME s_scm_sys_acosh | |
5762 | { | |
5763 | if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
5764 | return scm_from_double (acosh (scm_to_double (z))); | |
5765 | else if (scm_is_number (z)) | |
5766 | return scm_log (scm_sum (z, | |
5767 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 5768 | SCM_INUM1)))); |
ad79736c AW |
5769 | else |
5770 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
5771 | } | |
5772 | #undef FUNC_NAME | |
5773 | ||
5774 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
5775 | (SCM z), | |
5776 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
5777 | #define FUNC_NAME s_scm_sys_atanh | |
5778 | { | |
5779 | if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
5780 | return scm_from_double (atanh (scm_to_double (z))); | |
5781 | else if (scm_is_number (z)) | |
cff5fa33 MW |
5782 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
5783 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
5784 | SCM_I_MAKINUM (2)); |
5785 | else | |
5786 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 5787 | } |
1bbd0b84 | 5788 | #undef FUNC_NAME |
0f2d19dd | 5789 | |
8507ec80 MV |
5790 | SCM |
5791 | scm_c_make_rectangular (double re, double im) | |
5792 | { | |
5793 | if (im == 0.0) | |
5794 | return scm_from_double (re); | |
5795 | else | |
5796 | { | |
5797 | SCM z; | |
03604fcf LC |
5798 | |
5799 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), | |
92d8fd32 | 5800 | "complex")); |
03604fcf | 5801 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); |
8507ec80 MV |
5802 | SCM_COMPLEX_REAL (z) = re; |
5803 | SCM_COMPLEX_IMAG (z) = im; | |
5804 | return z; | |
5805 | } | |
5806 | } | |
0f2d19dd | 5807 | |
a1ec6916 | 5808 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
5809 | (SCM real_part, SCM imaginary_part), |
5810 | "Return a complex number constructed of the given @var{real-part} " | |
5811 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 5812 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 5813 | { |
ad79736c AW |
5814 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
5815 | SCM_ARG1, FUNC_NAME, "real"); | |
5816 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
5817 | SCM_ARG2, FUNC_NAME, "real"); | |
5818 | return scm_c_make_rectangular (scm_to_double (real_part), | |
5819 | scm_to_double (imaginary_part)); | |
0f2d19dd | 5820 | } |
1bbd0b84 | 5821 | #undef FUNC_NAME |
0f2d19dd | 5822 | |
8507ec80 MV |
5823 | SCM |
5824 | scm_c_make_polar (double mag, double ang) | |
5825 | { | |
5826 | double s, c; | |
5e647d08 LC |
5827 | |
5828 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
5829 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
5830 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
5831 | details. */ | |
5832 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
5833 | sincos (ang, &s, &c); |
5834 | #else | |
5835 | s = sin (ang); | |
5836 | c = cos (ang); | |
5837 | #endif | |
5838 | return scm_c_make_rectangular (mag * c, mag * s); | |
5839 | } | |
0f2d19dd | 5840 | |
a1ec6916 | 5841 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 5842 | (SCM x, SCM y), |
942e5b91 | 5843 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 5844 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 5845 | { |
ad79736c AW |
5846 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
5847 | SCM_ASSERT_TYPE (scm_is_real (y), y, SCM_ARG2, FUNC_NAME, "real"); | |
5848 | return scm_c_make_polar (scm_to_double (x), scm_to_double (y)); | |
0f2d19dd | 5849 | } |
1bbd0b84 | 5850 | #undef FUNC_NAME |
0f2d19dd JB |
5851 | |
5852 | ||
152f82bf | 5853 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
5854 | /* "Return the real part of the number @var{z}." |
5855 | */ | |
0f2d19dd | 5856 | SCM |
6e8d25a6 | 5857 | scm_real_part (SCM z) |
0f2d19dd | 5858 | { |
e11e83f3 | 5859 | if (SCM_I_INUMP (z)) |
c2ff8ab0 | 5860 | return z; |
0aacf84e | 5861 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5862 | return z; |
0aacf84e | 5863 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5864 | return z; |
0aacf84e | 5865 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5866 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
f92e85f7 | 5867 | else if (SCM_FRACTIONP (z)) |
2fa2d879 | 5868 | return z; |
0aacf84e | 5869 | else |
c2ff8ab0 | 5870 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); |
0f2d19dd JB |
5871 | } |
5872 | ||
5873 | ||
152f82bf | 5874 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
5875 | /* "Return the imaginary part of the number @var{z}." |
5876 | */ | |
0f2d19dd | 5877 | SCM |
6e8d25a6 | 5878 | scm_imag_part (SCM z) |
0f2d19dd | 5879 | { |
e11e83f3 | 5880 | if (SCM_I_INUMP (z)) |
f872b822 | 5881 | return SCM_INUM0; |
0aacf84e | 5882 | else if (SCM_BIGP (z)) |
f872b822 | 5883 | return SCM_INUM0; |
0aacf84e | 5884 | else if (SCM_REALP (z)) |
e7efe8e7 | 5885 | return flo0; |
0aacf84e | 5886 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5887 | return scm_from_double (SCM_COMPLEX_IMAG (z)); |
f92e85f7 MV |
5888 | else if (SCM_FRACTIONP (z)) |
5889 | return SCM_INUM0; | |
0aacf84e | 5890 | else |
c2ff8ab0 | 5891 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); |
0f2d19dd JB |
5892 | } |
5893 | ||
f92e85f7 MV |
5894 | SCM_GPROC (s_numerator, "numerator", 1, 0, 0, scm_numerator, g_numerator); |
5895 | /* "Return the numerator of the number @var{z}." | |
5896 | */ | |
5897 | SCM | |
5898 | scm_numerator (SCM z) | |
5899 | { | |
e11e83f3 | 5900 | if (SCM_I_INUMP (z)) |
f92e85f7 MV |
5901 | return z; |
5902 | else if (SCM_BIGP (z)) | |
5903 | return z; | |
5904 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 5905 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
5906 | else if (SCM_REALP (z)) |
5907 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
5908 | else | |
5909 | SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator); | |
5910 | } | |
5911 | ||
5912 | ||
5913 | SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator); | |
5914 | /* "Return the denominator of the number @var{z}." | |
5915 | */ | |
5916 | SCM | |
5917 | scm_denominator (SCM z) | |
5918 | { | |
e11e83f3 | 5919 | if (SCM_I_INUMP (z)) |
cff5fa33 | 5920 | return SCM_INUM1; |
f92e85f7 | 5921 | else if (SCM_BIGP (z)) |
cff5fa33 | 5922 | return SCM_INUM1; |
f92e85f7 | 5923 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 5924 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
5925 | else if (SCM_REALP (z)) |
5926 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
5927 | else | |
5928 | SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator); | |
5929 | } | |
0f2d19dd | 5930 | |
9de33deb | 5931 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
5932 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
5933 | * "@code{abs} for real arguments, but also allows complex numbers." | |
5934 | */ | |
0f2d19dd | 5935 | SCM |
6e8d25a6 | 5936 | scm_magnitude (SCM z) |
0f2d19dd | 5937 | { |
e11e83f3 | 5938 | if (SCM_I_INUMP (z)) |
0aacf84e | 5939 | { |
e25f3727 | 5940 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
5941 | if (zz >= 0) |
5942 | return z; | |
5943 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 5944 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 5945 | else |
e25f3727 | 5946 | return scm_i_inum2big (-zz); |
5986c47d | 5947 | } |
0aacf84e MD |
5948 | else if (SCM_BIGP (z)) |
5949 | { | |
5950 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5951 | scm_remember_upto_here_1 (z); | |
5952 | if (sgn < 0) | |
5953 | return scm_i_clonebig (z, 0); | |
5954 | else | |
5955 | return z; | |
5986c47d | 5956 | } |
0aacf84e | 5957 | else if (SCM_REALP (z)) |
55f26379 | 5958 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 5959 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5960 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
5961 | else if (SCM_FRACTIONP (z)) |
5962 | { | |
73e4de09 | 5963 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5964 | return z; |
cba42c93 | 5965 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
5966 | SCM_FRACTION_DENOMINATOR (z)); |
5967 | } | |
0aacf84e | 5968 | else |
c2ff8ab0 | 5969 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); |
0f2d19dd JB |
5970 | } |
5971 | ||
5972 | ||
9de33deb | 5973 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
5974 | /* "Return the angle of the complex number @var{z}." |
5975 | */ | |
0f2d19dd | 5976 | SCM |
6e8d25a6 | 5977 | scm_angle (SCM z) |
0f2d19dd | 5978 | { |
c8ae173e | 5979 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 5980 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
5981 | But if atan2 follows the floating point rounding mode, then the value |
5982 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 5983 | if (SCM_I_INUMP (z)) |
0aacf84e | 5984 | { |
e11e83f3 | 5985 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 5986 | return flo0; |
0aacf84e | 5987 | else |
55f26379 | 5988 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 5989 | } |
0aacf84e MD |
5990 | else if (SCM_BIGP (z)) |
5991 | { | |
5992 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5993 | scm_remember_upto_here_1 (z); | |
5994 | if (sgn < 0) | |
55f26379 | 5995 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 5996 | else |
e7efe8e7 | 5997 | return flo0; |
0f2d19dd | 5998 | } |
0aacf84e | 5999 | else if (SCM_REALP (z)) |
c8ae173e KR |
6000 | { |
6001 | if (SCM_REAL_VALUE (z) >= 0) | |
e7efe8e7 | 6002 | return flo0; |
c8ae173e | 6003 | else |
55f26379 | 6004 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 6005 | } |
0aacf84e | 6006 | else if (SCM_COMPLEXP (z)) |
55f26379 | 6007 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
6008 | else if (SCM_FRACTIONP (z)) |
6009 | { | |
73e4de09 | 6010 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 6011 | return flo0; |
55f26379 | 6012 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 6013 | } |
0aacf84e | 6014 | else |
f4c627b3 | 6015 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); |
0f2d19dd JB |
6016 | } |
6017 | ||
6018 | ||
3c9a524f DH |
6019 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
6020 | /* Convert the number @var{x} to its inexact representation.\n" | |
6021 | */ | |
6022 | SCM | |
6023 | scm_exact_to_inexact (SCM z) | |
6024 | { | |
e11e83f3 | 6025 | if (SCM_I_INUMP (z)) |
55f26379 | 6026 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 6027 | else if (SCM_BIGP (z)) |
55f26379 | 6028 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 6029 | else if (SCM_FRACTIONP (z)) |
55f26379 | 6030 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
6031 | else if (SCM_INEXACTP (z)) |
6032 | return z; | |
6033 | else | |
6034 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
6035 | } | |
6036 | ||
6037 | ||
a1ec6916 | 6038 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 6039 | (SCM z), |
1e6808ea | 6040 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 6041 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 6042 | { |
e11e83f3 | 6043 | if (SCM_I_INUMP (z)) |
f872b822 | 6044 | return z; |
0aacf84e | 6045 | else if (SCM_BIGP (z)) |
f872b822 | 6046 | return z; |
0aacf84e MD |
6047 | else if (SCM_REALP (z)) |
6048 | { | |
2e65b52f | 6049 | if (isinf (SCM_REAL_VALUE (z)) || isnan (SCM_REAL_VALUE (z))) |
f92e85f7 | 6050 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 6051 | else |
f92e85f7 MV |
6052 | { |
6053 | mpq_t frac; | |
6054 | SCM q; | |
6055 | ||
6056 | mpq_init (frac); | |
6057 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 6058 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
6059 | scm_i_mpz2num (mpq_denref (frac))); |
6060 | ||
cba42c93 | 6061 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
6062 | for frac... |
6063 | */ | |
6064 | mpq_clear (frac); | |
6065 | return q; | |
6066 | } | |
c2ff8ab0 | 6067 | } |
f92e85f7 MV |
6068 | else if (SCM_FRACTIONP (z)) |
6069 | return z; | |
0aacf84e | 6070 | else |
c2ff8ab0 | 6071 | SCM_WRONG_TYPE_ARG (1, z); |
0f2d19dd | 6072 | } |
1bbd0b84 | 6073 | #undef FUNC_NAME |
0f2d19dd | 6074 | |
f92e85f7 | 6075 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
6076 | (SCM x, SCM eps), |
6077 | "Returns the @emph{simplest} rational number differing\n" | |
6078 | "from @var{x} by no more than @var{eps}.\n" | |
6079 | "\n" | |
6080 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
6081 | "exact result when both its arguments are exact. Thus, you might need\n" | |
6082 | "to use @code{inexact->exact} on the arguments.\n" | |
6083 | "\n" | |
6084 | "@lisp\n" | |
6085 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
6086 | "@result{} 6/5\n" | |
6087 | "@end lisp") | |
f92e85f7 MV |
6088 | #define FUNC_NAME s_scm_rationalize |
6089 | { | |
e11e83f3 | 6090 | if (SCM_I_INUMP (x)) |
f92e85f7 MV |
6091 | return x; |
6092 | else if (SCM_BIGP (x)) | |
6093 | return x; | |
6094 | else if ((SCM_REALP (x)) || SCM_FRACTIONP (x)) | |
6095 | { | |
6096 | /* Use continued fractions to find closest ratio. All | |
6097 | arithmetic is done with exact numbers. | |
6098 | */ | |
6099 | ||
6100 | SCM ex = scm_inexact_to_exact (x); | |
6101 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
6102 | SCM tt = SCM_INUM1; |
6103 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
6104 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
6105 | SCM rx; |
6106 | int i = 0; | |
6107 | ||
73e4de09 | 6108 | if (scm_is_true (scm_num_eq_p (ex, int_part))) |
f92e85f7 MV |
6109 | return ex; |
6110 | ||
6111 | ex = scm_difference (ex, int_part); /* x = x-int_part */ | |
6112 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
6113 | ||
6114 | /* We stop after a million iterations just to be absolutely sure | |
6115 | that we don't go into an infinite loop. The process normally | |
6116 | converges after less than a dozen iterations. | |
6117 | */ | |
6118 | ||
76dae881 | 6119 | eps = scm_abs (eps); |
f92e85f7 MV |
6120 | while (++i < 1000000) |
6121 | { | |
6122 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
6123 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
6124 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
6125 | scm_is_false | |
f92e85f7 | 6126 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 6127 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
6128 | { |
6129 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
73e4de09 | 6130 | if (scm_is_false (scm_exact_p (x)) |
76dae881 | 6131 | || scm_is_false (scm_exact_p (eps))) |
02164269 MV |
6132 | return scm_exact_to_inexact (res); |
6133 | else | |
6134 | return res; | |
6135 | } | |
f92e85f7 MV |
6136 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
6137 | SCM_UNDEFINED); | |
6138 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
6139 | a2 = a1; | |
6140 | b2 = b1; | |
6141 | a1 = a; | |
6142 | b1 = b; | |
6143 | } | |
6144 | scm_num_overflow (s_scm_rationalize); | |
6145 | } | |
6146 | else | |
6147 | SCM_WRONG_TYPE_ARG (1, x); | |
6148 | } | |
6149 | #undef FUNC_NAME | |
6150 | ||
73e4de09 MV |
6151 | /* conversion functions */ |
6152 | ||
6153 | int | |
6154 | scm_is_integer (SCM val) | |
6155 | { | |
6156 | return scm_is_true (scm_integer_p (val)); | |
6157 | } | |
6158 | ||
6159 | int | |
6160 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
6161 | { | |
e11e83f3 | 6162 | if (SCM_I_INUMP (val)) |
73e4de09 | 6163 | { |
e11e83f3 | 6164 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
6165 | return n >= min && n <= max; |
6166 | } | |
6167 | else if (SCM_BIGP (val)) | |
6168 | { | |
6169 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
6170 | return 0; | |
6171 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
6172 | { |
6173 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
6174 | { | |
6175 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
6176 | return n >= min && n <= max; | |
6177 | } | |
6178 | else | |
6179 | return 0; | |
6180 | } | |
73e4de09 MV |
6181 | else |
6182 | { | |
d956fa6f MV |
6183 | scm_t_intmax n; |
6184 | size_t count; | |
73e4de09 | 6185 | |
d956fa6f MV |
6186 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
6187 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
6188 | return 0; | |
6189 | ||
6190 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
6191 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 6192 | |
d956fa6f | 6193 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 6194 | { |
d956fa6f MV |
6195 | if (n < 0) |
6196 | return 0; | |
73e4de09 | 6197 | } |
73e4de09 MV |
6198 | else |
6199 | { | |
d956fa6f MV |
6200 | n = -n; |
6201 | if (n >= 0) | |
6202 | return 0; | |
73e4de09 | 6203 | } |
d956fa6f MV |
6204 | |
6205 | return n >= min && n <= max; | |
73e4de09 MV |
6206 | } |
6207 | } | |
73e4de09 MV |
6208 | else |
6209 | return 0; | |
6210 | } | |
6211 | ||
6212 | int | |
6213 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
6214 | { | |
e11e83f3 | 6215 | if (SCM_I_INUMP (val)) |
73e4de09 | 6216 | { |
e11e83f3 | 6217 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
6218 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
6219 | } | |
6220 | else if (SCM_BIGP (val)) | |
6221 | { | |
6222 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
6223 | return 0; | |
6224 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
6225 | { |
6226 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
6227 | { | |
6228 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
6229 | return n >= min && n <= max; | |
6230 | } | |
6231 | else | |
6232 | return 0; | |
6233 | } | |
73e4de09 MV |
6234 | else |
6235 | { | |
d956fa6f MV |
6236 | scm_t_uintmax n; |
6237 | size_t count; | |
73e4de09 | 6238 | |
d956fa6f MV |
6239 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
6240 | return 0; | |
73e4de09 | 6241 | |
d956fa6f MV |
6242 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
6243 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 6244 | return 0; |
d956fa6f MV |
6245 | |
6246 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
6247 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 6248 | |
d956fa6f | 6249 | return n >= min && n <= max; |
73e4de09 MV |
6250 | } |
6251 | } | |
73e4de09 MV |
6252 | else |
6253 | return 0; | |
6254 | } | |
6255 | ||
1713d319 MV |
6256 | static void |
6257 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
6258 | { | |
6259 | scm_error (scm_out_of_range_key, | |
6260 | NULL, | |
6261 | "Value out of range ~S to ~S: ~S", | |
6262 | scm_list_3 (min, max, bad_val), | |
6263 | scm_list_1 (bad_val)); | |
6264 | } | |
6265 | ||
bfd7932e MV |
6266 | #define TYPE scm_t_intmax |
6267 | #define TYPE_MIN min | |
6268 | #define TYPE_MAX max | |
6269 | #define SIZEOF_TYPE 0 | |
6270 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
6271 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
6272 | #include "libguile/conv-integer.i.c" | |
6273 | ||
6274 | #define TYPE scm_t_uintmax | |
6275 | #define TYPE_MIN min | |
6276 | #define TYPE_MAX max | |
6277 | #define SIZEOF_TYPE 0 | |
6278 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
6279 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
6280 | #include "libguile/conv-uinteger.i.c" | |
6281 | ||
6282 | #define TYPE scm_t_int8 | |
6283 | #define TYPE_MIN SCM_T_INT8_MIN | |
6284 | #define TYPE_MAX SCM_T_INT8_MAX | |
6285 | #define SIZEOF_TYPE 1 | |
6286 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
6287 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
6288 | #include "libguile/conv-integer.i.c" | |
6289 | ||
6290 | #define TYPE scm_t_uint8 | |
6291 | #define TYPE_MIN 0 | |
6292 | #define TYPE_MAX SCM_T_UINT8_MAX | |
6293 | #define SIZEOF_TYPE 1 | |
6294 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
6295 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
6296 | #include "libguile/conv-uinteger.i.c" | |
6297 | ||
6298 | #define TYPE scm_t_int16 | |
6299 | #define TYPE_MIN SCM_T_INT16_MIN | |
6300 | #define TYPE_MAX SCM_T_INT16_MAX | |
6301 | #define SIZEOF_TYPE 2 | |
6302 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
6303 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
6304 | #include "libguile/conv-integer.i.c" | |
6305 | ||
6306 | #define TYPE scm_t_uint16 | |
6307 | #define TYPE_MIN 0 | |
6308 | #define TYPE_MAX SCM_T_UINT16_MAX | |
6309 | #define SIZEOF_TYPE 2 | |
6310 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
6311 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
6312 | #include "libguile/conv-uinteger.i.c" | |
6313 | ||
6314 | #define TYPE scm_t_int32 | |
6315 | #define TYPE_MIN SCM_T_INT32_MIN | |
6316 | #define TYPE_MAX SCM_T_INT32_MAX | |
6317 | #define SIZEOF_TYPE 4 | |
6318 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
6319 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
6320 | #include "libguile/conv-integer.i.c" | |
6321 | ||
6322 | #define TYPE scm_t_uint32 | |
6323 | #define TYPE_MIN 0 | |
6324 | #define TYPE_MAX SCM_T_UINT32_MAX | |
6325 | #define SIZEOF_TYPE 4 | |
6326 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
6327 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
6328 | #include "libguile/conv-uinteger.i.c" | |
6329 | ||
904a78f1 MG |
6330 | #define TYPE scm_t_wchar |
6331 | #define TYPE_MIN (scm_t_int32)-1 | |
6332 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
6333 | #define SIZEOF_TYPE 4 | |
6334 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
6335 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
6336 | #include "libguile/conv-integer.i.c" | |
6337 | ||
bfd7932e MV |
6338 | #define TYPE scm_t_int64 |
6339 | #define TYPE_MIN SCM_T_INT64_MIN | |
6340 | #define TYPE_MAX SCM_T_INT64_MAX | |
6341 | #define SIZEOF_TYPE 8 | |
6342 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
6343 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
6344 | #include "libguile/conv-integer.i.c" | |
6345 | ||
6346 | #define TYPE scm_t_uint64 | |
6347 | #define TYPE_MIN 0 | |
6348 | #define TYPE_MAX SCM_T_UINT64_MAX | |
6349 | #define SIZEOF_TYPE 8 | |
6350 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
6351 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
6352 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 6353 | |
cd036260 MV |
6354 | void |
6355 | scm_to_mpz (SCM val, mpz_t rop) | |
6356 | { | |
6357 | if (SCM_I_INUMP (val)) | |
6358 | mpz_set_si (rop, SCM_I_INUM (val)); | |
6359 | else if (SCM_BIGP (val)) | |
6360 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
6361 | else | |
6362 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
6363 | } | |
6364 | ||
6365 | SCM | |
6366 | scm_from_mpz (mpz_t val) | |
6367 | { | |
6368 | return scm_i_mpz2num (val); | |
6369 | } | |
6370 | ||
73e4de09 MV |
6371 | int |
6372 | scm_is_real (SCM val) | |
6373 | { | |
6374 | return scm_is_true (scm_real_p (val)); | |
6375 | } | |
6376 | ||
55f26379 MV |
6377 | int |
6378 | scm_is_rational (SCM val) | |
6379 | { | |
6380 | return scm_is_true (scm_rational_p (val)); | |
6381 | } | |
6382 | ||
73e4de09 MV |
6383 | double |
6384 | scm_to_double (SCM val) | |
6385 | { | |
55f26379 MV |
6386 | if (SCM_I_INUMP (val)) |
6387 | return SCM_I_INUM (val); | |
6388 | else if (SCM_BIGP (val)) | |
6389 | return scm_i_big2dbl (val); | |
6390 | else if (SCM_FRACTIONP (val)) | |
6391 | return scm_i_fraction2double (val); | |
6392 | else if (SCM_REALP (val)) | |
6393 | return SCM_REAL_VALUE (val); | |
6394 | else | |
7a1aba42 | 6395 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
6396 | } |
6397 | ||
6398 | SCM | |
6399 | scm_from_double (double val) | |
6400 | { | |
978c52d1 LC |
6401 | SCM z; |
6402 | ||
6403 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
6404 | ||
6405 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 6406 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 6407 | |
55f26379 | 6408 | return z; |
73e4de09 MV |
6409 | } |
6410 | ||
220058a8 | 6411 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
6412 | |
6413 | float | |
e25f3727 | 6414 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 6415 | { |
220058a8 AW |
6416 | scm_c_issue_deprecation_warning |
6417 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
6418 | ||
55f26379 MV |
6419 | if (SCM_BIGP (num)) |
6420 | { | |
6421 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 6422 | if (!isinf (res)) |
55f26379 MV |
6423 | return res; |
6424 | else | |
6425 | scm_out_of_range (NULL, num); | |
6426 | } | |
6427 | else | |
6428 | return scm_to_double (num); | |
6429 | } | |
6430 | ||
6431 | double | |
e25f3727 | 6432 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 6433 | { |
220058a8 AW |
6434 | scm_c_issue_deprecation_warning |
6435 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
6436 | ||
55f26379 MV |
6437 | if (SCM_BIGP (num)) |
6438 | { | |
6439 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 6440 | if (!isinf (res)) |
55f26379 MV |
6441 | return res; |
6442 | else | |
6443 | scm_out_of_range (NULL, num); | |
6444 | } | |
6445 | else | |
6446 | return scm_to_double (num); | |
6447 | } | |
6448 | ||
6449 | #endif | |
6450 | ||
8507ec80 MV |
6451 | int |
6452 | scm_is_complex (SCM val) | |
6453 | { | |
6454 | return scm_is_true (scm_complex_p (val)); | |
6455 | } | |
6456 | ||
6457 | double | |
6458 | scm_c_real_part (SCM z) | |
6459 | { | |
6460 | if (SCM_COMPLEXP (z)) | |
6461 | return SCM_COMPLEX_REAL (z); | |
6462 | else | |
6463 | { | |
6464 | /* Use the scm_real_part to get proper error checking and | |
6465 | dispatching. | |
6466 | */ | |
6467 | return scm_to_double (scm_real_part (z)); | |
6468 | } | |
6469 | } | |
6470 | ||
6471 | double | |
6472 | scm_c_imag_part (SCM z) | |
6473 | { | |
6474 | if (SCM_COMPLEXP (z)) | |
6475 | return SCM_COMPLEX_IMAG (z); | |
6476 | else | |
6477 | { | |
6478 | /* Use the scm_imag_part to get proper error checking and | |
6479 | dispatching. The result will almost always be 0.0, but not | |
6480 | always. | |
6481 | */ | |
6482 | return scm_to_double (scm_imag_part (z)); | |
6483 | } | |
6484 | } | |
6485 | ||
6486 | double | |
6487 | scm_c_magnitude (SCM z) | |
6488 | { | |
6489 | return scm_to_double (scm_magnitude (z)); | |
6490 | } | |
6491 | ||
6492 | double | |
6493 | scm_c_angle (SCM z) | |
6494 | { | |
6495 | return scm_to_double (scm_angle (z)); | |
6496 | } | |
6497 | ||
6498 | int | |
6499 | scm_is_number (SCM z) | |
6500 | { | |
6501 | return scm_is_true (scm_number_p (z)); | |
6502 | } | |
6503 | ||
8ab3d8a0 KR |
6504 | |
6505 | /* In the following functions we dispatch to the real-arg funcs like log() | |
6506 | when we know the arg is real, instead of just handing everything to | |
6507 | clog() for instance. This is in case clog() doesn't optimize for a | |
6508 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
6509 | well use it to go straight to the applicable C func. */ | |
6510 | ||
6511 | SCM_DEFINE (scm_log, "log", 1, 0, 0, | |
6512 | (SCM z), | |
6513 | "Return the natural logarithm of @var{z}.") | |
6514 | #define FUNC_NAME s_scm_log | |
6515 | { | |
6516 | if (SCM_COMPLEXP (z)) | |
6517 | { | |
4b26c03e | 6518 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6519 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
6520 | #else | |
6521 | double re = SCM_COMPLEX_REAL (z); | |
6522 | double im = SCM_COMPLEX_IMAG (z); | |
6523 | return scm_c_make_rectangular (log (hypot (re, im)), | |
6524 | atan2 (im, re)); | |
6525 | #endif | |
6526 | } | |
6527 | else | |
6528 | { | |
6529 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6530 | although the value itself overflows. */ | |
6531 | double re = scm_to_double (z); | |
6532 | double l = log (fabs (re)); | |
6533 | if (re >= 0.0) | |
6534 | return scm_from_double (l); | |
6535 | else | |
6536 | return scm_c_make_rectangular (l, M_PI); | |
6537 | } | |
6538 | } | |
6539 | #undef FUNC_NAME | |
6540 | ||
6541 | ||
6542 | SCM_DEFINE (scm_log10, "log10", 1, 0, 0, | |
6543 | (SCM z), | |
6544 | "Return the base 10 logarithm of @var{z}.") | |
6545 | #define FUNC_NAME s_scm_log10 | |
6546 | { | |
6547 | if (SCM_COMPLEXP (z)) | |
6548 | { | |
6549 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
6550 | clog() and a multiply by M_LOG10E, rather than the fallback | |
6551 | log10+hypot+atan2.) */ | |
f328f862 LC |
6552 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
6553 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
6554 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
6555 | #else | |
6556 | double re = SCM_COMPLEX_REAL (z); | |
6557 | double im = SCM_COMPLEX_IMAG (z); | |
6558 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
6559 | M_LOG10E * atan2 (im, re)); | |
6560 | #endif | |
6561 | } | |
6562 | else | |
6563 | { | |
6564 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6565 | although the value itself overflows. */ | |
6566 | double re = scm_to_double (z); | |
6567 | double l = log10 (fabs (re)); | |
6568 | if (re >= 0.0) | |
6569 | return scm_from_double (l); | |
6570 | else | |
6571 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
6572 | } | |
6573 | } | |
6574 | #undef FUNC_NAME | |
6575 | ||
6576 | ||
6577 | SCM_DEFINE (scm_exp, "exp", 1, 0, 0, | |
6578 | (SCM z), | |
6579 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
6580 | "base of natural logarithms (2.71828@dots{}).") | |
6581 | #define FUNC_NAME s_scm_exp | |
6582 | { | |
6583 | if (SCM_COMPLEXP (z)) | |
6584 | { | |
4b26c03e | 6585 | #if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6586 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
6587 | #else | |
6588 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
6589 | SCM_COMPLEX_IMAG (z)); | |
6590 | #endif | |
6591 | } | |
6592 | else | |
6593 | { | |
6594 | /* When z is a negative bignum the conversion to double overflows, | |
6595 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
6596 | return scm_from_double (exp (scm_to_double (z))); | |
6597 | } | |
6598 | } | |
6599 | #undef FUNC_NAME | |
6600 | ||
6601 | ||
6602 | SCM_DEFINE (scm_sqrt, "sqrt", 1, 0, 0, | |
6603 | (SCM x), | |
6604 | "Return the square root of @var{z}. Of the two possible roots\n" | |
6605 | "(positive and negative), the one with the a positive real part\n" | |
6606 | "is returned, or if that's zero then a positive imaginary part.\n" | |
6607 | "Thus,\n" | |
6608 | "\n" | |
6609 | "@example\n" | |
6610 | "(sqrt 9.0) @result{} 3.0\n" | |
6611 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
6612 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
6613 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
6614 | "@end example") | |
6615 | #define FUNC_NAME s_scm_sqrt | |
6616 | { | |
6617 | if (SCM_COMPLEXP (x)) | |
6618 | { | |
f328f862 LC |
6619 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
6620 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
6621 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (x))); |
6622 | #else | |
6623 | double re = SCM_COMPLEX_REAL (x); | |
6624 | double im = SCM_COMPLEX_IMAG (x); | |
6625 | return scm_c_make_polar (sqrt (hypot (re, im)), | |
6626 | 0.5 * atan2 (im, re)); | |
6627 | #endif | |
6628 | } | |
6629 | else | |
6630 | { | |
6631 | double xx = scm_to_double (x); | |
6632 | if (xx < 0) | |
6633 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
6634 | else | |
6635 | return scm_from_double (sqrt (xx)); | |
6636 | } | |
6637 | } | |
6638 | #undef FUNC_NAME | |
6639 | ||
6640 | ||
6641 | ||
0f2d19dd JB |
6642 | void |
6643 | scm_init_numbers () | |
0f2d19dd | 6644 | { |
0b799eea MV |
6645 | int i; |
6646 | ||
713a4259 KR |
6647 | mpz_init_set_si (z_negative_one, -1); |
6648 | ||
a261c0e9 DH |
6649 | /* It may be possible to tune the performance of some algorithms by using |
6650 | * the following constants to avoid the creation of bignums. Please, before | |
6651 | * using these values, remember the two rules of program optimization: | |
6652 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 6653 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 6654 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 6655 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 6656 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 6657 | |
f3ae5d60 MD |
6658 | scm_add_feature ("complex"); |
6659 | scm_add_feature ("inexact"); | |
e7efe8e7 | 6660 | flo0 = scm_from_double (0.0); |
0b799eea MV |
6661 | |
6662 | /* determine floating point precision */ | |
55f26379 | 6663 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
6664 | { |
6665 | init_dblprec(&scm_dblprec[i-2],i); | |
6666 | init_fx_radix(fx_per_radix[i-2],i); | |
6667 | } | |
f872b822 | 6668 | #ifdef DBL_DIG |
0b799eea | 6669 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 6670 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 6671 | #endif |
1be6b49c | 6672 | |
cff5fa33 | 6673 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 6674 | #include "libguile/numbers.x" |
0f2d19dd | 6675 | } |
89e00824 ML |
6676 | |
6677 | /* | |
6678 | Local Variables: | |
6679 | c-file-style: "gnu" | |
6680 | End: | |
6681 | */ |