Commit | Line | Data |
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8e43ed5d | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc. |
ba74ef4e MV |
2 | * |
3 | * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories | |
4 | * and Bellcore. See scm_divide. | |
5 | * | |
f81e080b | 6 | * |
73be1d9e | 7 | * This library is free software; you can redistribute it and/or |
53befeb7 NJ |
8 | * modify it under the terms of the GNU Lesser General Public License |
9 | * as published by the Free Software Foundation; either version 3 of | |
10 | * the License, or (at your option) any later version. | |
0f2d19dd | 11 | * |
53befeb7 NJ |
12 | * This library is distributed in the hope that it will be useful, but |
13 | * WITHOUT ANY WARRANTY; without even the implied warranty of | |
73be1d9e MV |
14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
15 | * Lesser General Public License for more details. | |
0f2d19dd | 16 | * |
73be1d9e MV |
17 | * You should have received a copy of the GNU Lesser General Public |
18 | * License along with this library; if not, write to the Free Software | |
53befeb7 NJ |
19 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
20 | * 02110-1301 USA | |
73be1d9e | 21 | */ |
1bbd0b84 | 22 | |
0f2d19dd | 23 | \f |
ca46fb90 | 24 | /* General assumptions: |
ca46fb90 RB |
25 | * All objects satisfying SCM_BIGP() are too large to fit in a fixnum. |
26 | * If an object satisfies integer?, it's either an inum, a bignum, or a real. | |
27 | * If floor (r) == r, r is an int, and mpz_set_d will DTRT. | |
c7218482 | 28 | * XXX What about infinities? They are equal to their own floor! -mhw |
f92e85f7 | 29 | * All objects satisfying SCM_FRACTIONP are never an integer. |
ca46fb90 RB |
30 | */ |
31 | ||
32 | /* TODO: | |
33 | ||
34 | - see if special casing bignums and reals in integer-exponent when | |
35 | possible (to use mpz_pow and mpf_pow_ui) is faster. | |
36 | ||
37 | - look in to better short-circuiting of common cases in | |
38 | integer-expt and elsewhere. | |
39 | ||
40 | - see if direct mpz operations can help in ash and elsewhere. | |
41 | ||
42 | */ | |
0f2d19dd | 43 | |
dbb605f5 | 44 | #ifdef HAVE_CONFIG_H |
ee33d62a RB |
45 | # include <config.h> |
46 | #endif | |
47 | ||
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 | ||
041fccf6 MW |
86 | /* On some platforms, isinf(x) returns 0, 1 or -1, indicating the sign |
87 | of the infinity, but other platforms return a boolean only. */ | |
88 | #define DOUBLE_IS_POSITIVE_INFINITY(x) (isinf(x) && ((x) > 0)) | |
89 | #define DOUBLE_IS_NEGATIVE_INFINITY(x) (isinf(x) && ((x) < 0)) | |
90 | ||
0f2d19dd | 91 | \f |
f4c627b3 | 92 | |
ca46fb90 RB |
93 | /* |
94 | Wonder if this might be faster for some of our code? A switch on | |
95 | the numtag would jump directly to the right case, and the | |
96 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
97 | ||
98 | #define SCM_I_NUMTAG_NOTNUM 0 | |
99 | #define SCM_I_NUMTAG_INUM 1 | |
100 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
101 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
102 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
103 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 104 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 105 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 106 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
107 | : SCM_I_NUMTAG_NOTNUM))) |
108 | */ | |
f92e85f7 | 109 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
110 | |
111 | ||
e7efe8e7 | 112 | static SCM flo0; |
ff62c168 | 113 | static SCM exactly_one_half; |
e7efe8e7 | 114 | |
34d19ef6 | 115 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 116 | |
56e55ac7 | 117 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
118 | * printed or scm_string representation of an inexact number. |
119 | */ | |
0b799eea | 120 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 121 | |
b127c712 | 122 | |
ad79736c AW |
123 | #if !defined (HAVE_ASINH) |
124 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } | |
125 | #endif | |
126 | #if !defined (HAVE_ACOSH) | |
127 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } | |
128 | #endif | |
129 | #if !defined (HAVE_ATANH) | |
130 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } | |
131 | #endif | |
132 | ||
f8a8200b KR |
133 | /* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses |
134 | an explicit check. In some future gmp (don't know what version number), | |
135 | mpz_cmp_d is supposed to do this itself. */ | |
136 | #if 1 | |
b127c712 | 137 | #define xmpz_cmp_d(z, d) \ |
2e65b52f | 138 | (isinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) |
b127c712 KR |
139 | #else |
140 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
141 | #endif | |
142 | ||
f92e85f7 | 143 | |
4b26c03e | 144 | #if defined (GUILE_I) |
bca69a9f | 145 | #if HAVE_COMPLEX_DOUBLE |
8ab3d8a0 KR |
146 | |
147 | /* For an SCM object Z which is a complex number (ie. satisfies | |
148 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
149 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 150 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 151 | |
7a35784c | 152 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
8ab3d8a0 KR |
153 | |
154 | /* Convert a C "complex double" to an SCM value. */ | |
7a35784c | 155 | static inline SCM |
8ab3d8a0 KR |
156 | scm_from_complex_double (complex double z) |
157 | { | |
158 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
159 | } | |
bca69a9f | 160 | |
8ab3d8a0 | 161 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 162 | #endif /* GUILE_I */ |
8ab3d8a0 | 163 | |
0f2d19dd JB |
164 | \f |
165 | ||
713a4259 | 166 | static mpz_t z_negative_one; |
ac0c002c DH |
167 | |
168 | \f | |
864e7d42 LC |
169 | /* Clear the `mpz_t' embedded in bignum PTR. */ |
170 | static void | |
171 | finalize_bignum (GC_PTR ptr, GC_PTR data) | |
172 | { | |
173 | SCM bignum; | |
174 | ||
175 | bignum = PTR2SCM (ptr); | |
176 | mpz_clear (SCM_I_BIG_MPZ (bignum)); | |
177 | } | |
178 | ||
d017fcdf LC |
179 | /* Return a new uninitialized bignum. */ |
180 | static inline SCM | |
181 | make_bignum (void) | |
182 | { | |
183 | scm_t_bits *p; | |
864e7d42 LC |
184 | GC_finalization_proc prev_finalizer; |
185 | GC_PTR prev_finalizer_data; | |
d017fcdf LC |
186 | |
187 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ | |
188 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), | |
189 | "bignum"); | |
190 | p[0] = scm_tc16_big; | |
191 | ||
864e7d42 LC |
192 | GC_REGISTER_FINALIZER_NO_ORDER (p, finalize_bignum, NULL, |
193 | &prev_finalizer, | |
194 | &prev_finalizer_data); | |
195 | ||
d017fcdf LC |
196 | return SCM_PACK (p); |
197 | } | |
ac0c002c | 198 | |
864e7d42 | 199 | |
189171c5 | 200 | SCM |
ca46fb90 RB |
201 | scm_i_mkbig () |
202 | { | |
203 | /* Return a newly created bignum. */ | |
d017fcdf | 204 | SCM z = make_bignum (); |
ca46fb90 RB |
205 | mpz_init (SCM_I_BIG_MPZ (z)); |
206 | return z; | |
207 | } | |
208 | ||
e25f3727 AW |
209 | static SCM |
210 | scm_i_inum2big (scm_t_inum x) | |
211 | { | |
212 | /* Return a newly created bignum initialized to X. */ | |
213 | SCM z = make_bignum (); | |
214 | #if SIZEOF_VOID_P == SIZEOF_LONG | |
215 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
216 | #else | |
217 | /* Note that in this case, you'll also have to check all mpz_*_ui and | |
218 | mpz_*_si invocations in Guile. */ | |
219 | #error creation of mpz not implemented for this inum size | |
220 | #endif | |
221 | return z; | |
222 | } | |
223 | ||
189171c5 | 224 | SCM |
c71b0706 MV |
225 | scm_i_long2big (long x) |
226 | { | |
227 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 228 | SCM z = make_bignum (); |
c71b0706 MV |
229 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
230 | return z; | |
231 | } | |
232 | ||
189171c5 | 233 | SCM |
c71b0706 MV |
234 | scm_i_ulong2big (unsigned long x) |
235 | { | |
236 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 237 | SCM z = make_bignum (); |
c71b0706 MV |
238 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
239 | return z; | |
240 | } | |
241 | ||
189171c5 | 242 | SCM |
ca46fb90 RB |
243 | scm_i_clonebig (SCM src_big, int same_sign_p) |
244 | { | |
245 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
d017fcdf | 246 | SCM z = make_bignum (); |
ca46fb90 | 247 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
0aacf84e MD |
248 | if (!same_sign_p) |
249 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
250 | return z; |
251 | } | |
252 | ||
189171c5 | 253 | int |
ca46fb90 RB |
254 | scm_i_bigcmp (SCM x, SCM y) |
255 | { | |
256 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
257 | /* presume we already know x and y are bignums */ | |
258 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
259 | scm_remember_upto_here_2 (x, y); | |
260 | return result; | |
261 | } | |
262 | ||
189171c5 | 263 | SCM |
ca46fb90 RB |
264 | scm_i_dbl2big (double d) |
265 | { | |
266 | /* results are only defined if d is an integer */ | |
d017fcdf | 267 | SCM z = make_bignum (); |
ca46fb90 RB |
268 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
269 | return z; | |
270 | } | |
271 | ||
f92e85f7 MV |
272 | /* Convert a integer in double representation to a SCM number. */ |
273 | ||
189171c5 | 274 | SCM |
f92e85f7 MV |
275 | scm_i_dbl2num (double u) |
276 | { | |
277 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
278 | powers of 2, so there's no rounding when making "double" values | |
279 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
280 | get rounded on a 64-bit machine, hence the "+1". | |
281 | ||
282 | The use of floor() to force to an integer value ensures we get a | |
283 | "numerically closest" value without depending on how a | |
284 | double->long cast or how mpz_set_d will round. For reference, | |
285 | double->long probably follows the hardware rounding mode, | |
286 | mpz_set_d truncates towards zero. */ | |
287 | ||
288 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
289 | representable as a double? */ | |
290 | ||
291 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
292 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
e25f3727 | 293 | return SCM_I_MAKINUM ((scm_t_inum) u); |
f92e85f7 MV |
294 | else |
295 | return scm_i_dbl2big (u); | |
296 | } | |
297 | ||
089c9a59 KR |
298 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
299 | with R5RS exact->inexact. | |
300 | ||
301 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
302 | (ie. truncate towards zero), then adjust to get the closest double by |
303 | examining the next lower bit and adding 1 (to the absolute value) if | |
304 | necessary. | |
305 | ||
306 | Bignums exactly half way between representable doubles are rounded to the | |
307 | next higher absolute value (ie. away from zero). This seems like an | |
308 | adequate interpretation of R5RS "numerically closest", and it's easier | |
309 | and faster than a full "nearest-even" style. | |
310 | ||
311 | The bit test must be done on the absolute value of the mpz_t, which means | |
312 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
313 | negatives as twos complement. | |
314 | ||
315 | In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up | |
316 | following the hardware rounding mode, but applied to the absolute value | |
317 | of the mpz_t operand. This is not what we want so we put the high | |
318 | DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when, | |
319 | mpz_get_d is supposed to always truncate towards zero. | |
320 | ||
321 | ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3 | |
322 | is a slowdown. It'd be faster to pick out the relevant high bits with | |
323 | mpz_getlimbn if we could be bothered coding that, and if the new | |
324 | truncating gmp doesn't come out. */ | |
089c9a59 KR |
325 | |
326 | double | |
ca46fb90 RB |
327 | scm_i_big2dbl (SCM b) |
328 | { | |
089c9a59 KR |
329 | double result; |
330 | size_t bits; | |
331 | ||
332 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
333 | ||
f8a8200b | 334 | #if 1 |
089c9a59 | 335 | { |
f8a8200b | 336 | /* Current GMP, eg. 4.1.3, force truncation towards zero */ |
089c9a59 KR |
337 | mpz_t tmp; |
338 | if (bits > DBL_MANT_DIG) | |
339 | { | |
340 | size_t shift = bits - DBL_MANT_DIG; | |
341 | mpz_init2 (tmp, DBL_MANT_DIG); | |
342 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
343 | result = ldexp (mpz_get_d (tmp), shift); | |
344 | mpz_clear (tmp); | |
345 | } | |
346 | else | |
347 | { | |
348 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
349 | } | |
350 | } | |
351 | #else | |
f8a8200b | 352 | /* Future GMP */ |
089c9a59 KR |
353 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
354 | #endif | |
355 | ||
356 | if (bits > DBL_MANT_DIG) | |
357 | { | |
358 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
359 | /* test bit number "pos" in absolute value */ | |
360 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
361 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
362 | { | |
363 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
364 | } | |
365 | } | |
366 | ||
ca46fb90 RB |
367 | scm_remember_upto_here_1 (b); |
368 | return result; | |
369 | } | |
370 | ||
189171c5 | 371 | SCM |
ca46fb90 RB |
372 | scm_i_normbig (SCM b) |
373 | { | |
374 | /* convert a big back to a fixnum if it'll fit */ | |
375 | /* presume b is a bignum */ | |
376 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
377 | { | |
e25f3727 | 378 | scm_t_inum val = mpz_get_si (SCM_I_BIG_MPZ (b)); |
ca46fb90 | 379 | if (SCM_FIXABLE (val)) |
d956fa6f | 380 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
381 | } |
382 | return b; | |
383 | } | |
f872b822 | 384 | |
f92e85f7 MV |
385 | static SCM_C_INLINE_KEYWORD SCM |
386 | scm_i_mpz2num (mpz_t b) | |
387 | { | |
388 | /* convert a mpz number to a SCM number. */ | |
389 | if (mpz_fits_slong_p (b)) | |
390 | { | |
e25f3727 | 391 | scm_t_inum val = mpz_get_si (b); |
f92e85f7 | 392 | if (SCM_FIXABLE (val)) |
d956fa6f | 393 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
394 | } |
395 | ||
396 | { | |
d017fcdf | 397 | SCM z = make_bignum (); |
f92e85f7 MV |
398 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
399 | return z; | |
400 | } | |
401 | } | |
402 | ||
403 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
404 | static SCM scm_divide2real (SCM x, SCM y); | |
405 | ||
cba42c93 MV |
406 | static SCM |
407 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 408 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 409 | { |
c60e130c MV |
410 | /* First make sure the arguments are proper. |
411 | */ | |
e11e83f3 | 412 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 413 | { |
bc36d050 | 414 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 415 | scm_num_overflow ("make-ratio"); |
cff5fa33 | 416 | if (scm_is_eq (denominator, SCM_INUM1)) |
f92e85f7 MV |
417 | return numerator; |
418 | } | |
419 | else | |
420 | { | |
421 | if (!(SCM_BIGP(denominator))) | |
422 | SCM_WRONG_TYPE_ARG (2, denominator); | |
423 | } | |
e11e83f3 | 424 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
425 | SCM_WRONG_TYPE_ARG (1, numerator); |
426 | ||
427 | /* Then flip signs so that the denominator is positive. | |
428 | */ | |
73e4de09 | 429 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
430 | { |
431 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
432 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
433 | } | |
434 | ||
435 | /* Now consider for each of the four fixnum/bignum combinations | |
436 | whether the rational number is really an integer. | |
437 | */ | |
e11e83f3 | 438 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 439 | { |
e25f3727 | 440 | scm_t_inum x = SCM_I_INUM (numerator); |
bc36d050 | 441 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 442 | return SCM_INUM0; |
e11e83f3 | 443 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 444 | { |
e25f3727 | 445 | scm_t_inum y; |
e11e83f3 | 446 | y = SCM_I_INUM (denominator); |
f92e85f7 | 447 | if (x == y) |
cff5fa33 | 448 | return SCM_INUM1; |
f92e85f7 | 449 | if ((x % y) == 0) |
d956fa6f | 450 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 451 | } |
dd5130ca KR |
452 | else |
453 | { | |
454 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
455 | of that value for the denominator, as a bignum. Apart from |
456 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
457 | integer. */ | |
458 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
459 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
460 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 461 | return SCM_I_MAKINUM(-1); |
dd5130ca | 462 | } |
f92e85f7 | 463 | } |
c60e130c | 464 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 465 | { |
e11e83f3 | 466 | if (SCM_I_INUMP (denominator)) |
c60e130c | 467 | { |
e25f3727 | 468 | scm_t_inum yy = SCM_I_INUM (denominator); |
c60e130c MV |
469 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
470 | return scm_divide (numerator, denominator); | |
471 | } | |
472 | else | |
f92e85f7 | 473 | { |
bc36d050 | 474 | if (scm_is_eq (numerator, denominator)) |
cff5fa33 | 475 | return SCM_INUM1; |
c60e130c MV |
476 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
477 | SCM_I_BIG_MPZ (denominator))) | |
478 | return scm_divide(numerator, denominator); | |
f92e85f7 | 479 | } |
f92e85f7 | 480 | } |
c60e130c MV |
481 | |
482 | /* No, it's a proper fraction. | |
483 | */ | |
e2bf3b19 HWN |
484 | { |
485 | SCM divisor = scm_gcd (numerator, denominator); | |
cff5fa33 | 486 | if (!(scm_is_eq (divisor, SCM_INUM1))) |
e2bf3b19 HWN |
487 | { |
488 | numerator = scm_divide (numerator, divisor); | |
489 | denominator = scm_divide (denominator, divisor); | |
490 | } | |
491 | ||
492 | return scm_double_cell (scm_tc16_fraction, | |
493 | SCM_UNPACK (numerator), | |
494 | SCM_UNPACK (denominator), 0); | |
495 | } | |
f92e85f7 | 496 | } |
c60e130c | 497 | #undef FUNC_NAME |
f92e85f7 | 498 | |
f92e85f7 MV |
499 | double |
500 | scm_i_fraction2double (SCM z) | |
501 | { | |
55f26379 MV |
502 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
503 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
504 | } |
505 | ||
2e274311 MW |
506 | static int |
507 | double_is_non_negative_zero (double x) | |
508 | { | |
509 | static double zero = 0.0; | |
510 | ||
511 | return !memcmp (&x, &zero, sizeof(double)); | |
512 | } | |
513 | ||
2519490c MW |
514 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
515 | (SCM x), | |
942e5b91 MG |
516 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
517 | "otherwise.") | |
1bbd0b84 | 518 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 519 | { |
41df63cf MW |
520 | if (SCM_INEXACTP (x)) |
521 | return SCM_BOOL_F; | |
522 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 523 | return SCM_BOOL_T; |
41df63cf | 524 | else |
2519490c | 525 | SCM_WTA_DISPATCH_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
526 | } |
527 | #undef FUNC_NAME | |
528 | ||
529 | ||
2519490c | 530 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
531 | (SCM x), |
532 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
533 | "else.") | |
534 | #define FUNC_NAME s_scm_inexact_p | |
535 | { | |
536 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 537 | return SCM_BOOL_T; |
41df63cf | 538 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 539 | return SCM_BOOL_F; |
41df63cf | 540 | else |
2519490c | 541 | SCM_WTA_DISPATCH_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 542 | } |
1bbd0b84 | 543 | #undef FUNC_NAME |
0f2d19dd | 544 | |
4219f20d | 545 | |
2519490c | 546 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 547 | (SCM n), |
942e5b91 MG |
548 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
549 | "otherwise.") | |
1bbd0b84 | 550 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 551 | { |
e11e83f3 | 552 | if (SCM_I_INUMP (n)) |
0aacf84e | 553 | { |
e25f3727 | 554 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 555 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
556 | } |
557 | else if (SCM_BIGP (n)) | |
558 | { | |
559 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
560 | scm_remember_upto_here_1 (n); | |
73e4de09 | 561 | return scm_from_bool (odd_p); |
0aacf84e | 562 | } |
f92e85f7 MV |
563 | else if (SCM_REALP (n)) |
564 | { | |
2519490c MW |
565 | double val = SCM_REAL_VALUE (n); |
566 | if (DOUBLE_IS_FINITE (val)) | |
567 | { | |
568 | double rem = fabs (fmod (val, 2.0)); | |
569 | if (rem == 1.0) | |
570 | return SCM_BOOL_T; | |
571 | else if (rem == 0.0) | |
572 | return SCM_BOOL_F; | |
573 | } | |
f92e85f7 | 574 | } |
2519490c | 575 | SCM_WTA_DISPATCH_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 576 | } |
1bbd0b84 | 577 | #undef FUNC_NAME |
0f2d19dd | 578 | |
4219f20d | 579 | |
2519490c | 580 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 581 | (SCM n), |
942e5b91 MG |
582 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
583 | "otherwise.") | |
1bbd0b84 | 584 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 585 | { |
e11e83f3 | 586 | if (SCM_I_INUMP (n)) |
0aacf84e | 587 | { |
e25f3727 | 588 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 589 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
590 | } |
591 | else if (SCM_BIGP (n)) | |
592 | { | |
593 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
594 | scm_remember_upto_here_1 (n); | |
73e4de09 | 595 | return scm_from_bool (even_p); |
0aacf84e | 596 | } |
f92e85f7 MV |
597 | else if (SCM_REALP (n)) |
598 | { | |
2519490c MW |
599 | double val = SCM_REAL_VALUE (n); |
600 | if (DOUBLE_IS_FINITE (val)) | |
601 | { | |
602 | double rem = fabs (fmod (val, 2.0)); | |
603 | if (rem == 1.0) | |
604 | return SCM_BOOL_F; | |
605 | else if (rem == 0.0) | |
606 | return SCM_BOOL_T; | |
607 | } | |
f92e85f7 | 608 | } |
2519490c | 609 | SCM_WTA_DISPATCH_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 610 | } |
1bbd0b84 | 611 | #undef FUNC_NAME |
0f2d19dd | 612 | |
2519490c MW |
613 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
614 | (SCM x), | |
10391e06 AW |
615 | "Return @code{#t} if the real number @var{x} is neither\n" |
616 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
617 | #define FUNC_NAME s_scm_finite_p |
618 | { | |
619 | if (SCM_REALP (x)) | |
620 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 621 | else if (scm_is_real (x)) |
7112615f MW |
622 | return SCM_BOOL_T; |
623 | else | |
2519490c | 624 | SCM_WTA_DISPATCH_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
625 | } |
626 | #undef FUNC_NAME | |
627 | ||
2519490c MW |
628 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
629 | (SCM x), | |
630 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
631 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
632 | #define FUNC_NAME s_scm_inf_p |
633 | { | |
b1092b3a | 634 | if (SCM_REALP (x)) |
2e65b52f | 635 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 636 | else if (scm_is_real (x)) |
7351e207 | 637 | return SCM_BOOL_F; |
10391e06 | 638 | else |
2519490c | 639 | SCM_WTA_DISPATCH_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
640 | } |
641 | #undef FUNC_NAME | |
642 | ||
2519490c MW |
643 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
644 | (SCM x), | |
10391e06 AW |
645 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
646 | "or @code{#f} otherwise.") | |
7351e207 MV |
647 | #define FUNC_NAME s_scm_nan_p |
648 | { | |
10391e06 AW |
649 | if (SCM_REALP (x)) |
650 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
651 | else if (scm_is_real (x)) | |
7351e207 | 652 | return SCM_BOOL_F; |
10391e06 | 653 | else |
2519490c | 654 | SCM_WTA_DISPATCH_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
655 | } |
656 | #undef FUNC_NAME | |
657 | ||
658 | /* Guile's idea of infinity. */ | |
659 | static double guile_Inf; | |
660 | ||
661 | /* Guile's idea of not a number. */ | |
662 | static double guile_NaN; | |
663 | ||
664 | static void | |
665 | guile_ieee_init (void) | |
666 | { | |
7351e207 MV |
667 | /* Some version of gcc on some old version of Linux used to crash when |
668 | trying to make Inf and NaN. */ | |
669 | ||
240a27d2 KR |
670 | #ifdef INFINITY |
671 | /* C99 INFINITY, when available. | |
672 | FIXME: The standard allows for INFINITY to be something that overflows | |
673 | at compile time. We ought to have a configure test to check for that | |
674 | before trying to use it. (But in practice we believe this is not a | |
675 | problem on any system guile is likely to target.) */ | |
676 | guile_Inf = INFINITY; | |
56a3dcd4 | 677 | #elif defined HAVE_DINFINITY |
240a27d2 | 678 | /* OSF */ |
7351e207 | 679 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 680 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
681 | #else |
682 | double tmp = 1e+10; | |
683 | guile_Inf = tmp; | |
684 | for (;;) | |
685 | { | |
686 | guile_Inf *= 1e+10; | |
687 | if (guile_Inf == tmp) | |
688 | break; | |
689 | tmp = guile_Inf; | |
690 | } | |
691 | #endif | |
692 | ||
240a27d2 KR |
693 | #ifdef NAN |
694 | /* C99 NAN, when available */ | |
695 | guile_NaN = NAN; | |
56a3dcd4 | 696 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
697 | { |
698 | /* OSF */ | |
699 | extern unsigned int DQNAN[2]; | |
700 | guile_NaN = (*((double *)(DQNAN))); | |
701 | } | |
7351e207 MV |
702 | #else |
703 | guile_NaN = guile_Inf / guile_Inf; | |
704 | #endif | |
7351e207 MV |
705 | } |
706 | ||
707 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
708 | (void), | |
709 | "Return Inf.") | |
710 | #define FUNC_NAME s_scm_inf | |
711 | { | |
712 | static int initialized = 0; | |
713 | if (! initialized) | |
714 | { | |
715 | guile_ieee_init (); | |
716 | initialized = 1; | |
717 | } | |
55f26379 | 718 | return scm_from_double (guile_Inf); |
7351e207 MV |
719 | } |
720 | #undef FUNC_NAME | |
721 | ||
722 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
723 | (void), | |
724 | "Return NaN.") | |
725 | #define FUNC_NAME s_scm_nan | |
726 | { | |
727 | static int initialized = 0; | |
0aacf84e | 728 | if (!initialized) |
7351e207 MV |
729 | { |
730 | guile_ieee_init (); | |
731 | initialized = 1; | |
732 | } | |
55f26379 | 733 | return scm_from_double (guile_NaN); |
7351e207 MV |
734 | } |
735 | #undef FUNC_NAME | |
736 | ||
4219f20d | 737 | |
a48d60b1 MD |
738 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
739 | (SCM x), | |
740 | "Return the absolute value of @var{x}.") | |
2519490c | 741 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 742 | { |
e11e83f3 | 743 | if (SCM_I_INUMP (x)) |
0aacf84e | 744 | { |
e25f3727 | 745 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
746 | if (xx >= 0) |
747 | return x; | |
748 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 749 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 750 | else |
e25f3727 | 751 | return scm_i_inum2big (-xx); |
4219f20d | 752 | } |
9b9ef10c MW |
753 | else if (SCM_LIKELY (SCM_REALP (x))) |
754 | { | |
755 | double xx = SCM_REAL_VALUE (x); | |
756 | /* If x is a NaN then xx<0 is false so we return x unchanged */ | |
757 | if (xx < 0.0) | |
758 | return scm_from_double (-xx); | |
759 | /* Handle signed zeroes properly */ | |
760 | else if (SCM_UNLIKELY (xx == 0.0)) | |
761 | return flo0; | |
762 | else | |
763 | return x; | |
764 | } | |
0aacf84e MD |
765 | else if (SCM_BIGP (x)) |
766 | { | |
767 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
768 | if (sgn < 0) | |
769 | return scm_i_clonebig (x, 0); | |
770 | else | |
771 | return x; | |
4219f20d | 772 | } |
f92e85f7 MV |
773 | else if (SCM_FRACTIONP (x)) |
774 | { | |
73e4de09 | 775 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 776 | return x; |
cba42c93 | 777 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
778 | SCM_FRACTION_DENOMINATOR (x)); |
779 | } | |
0aacf84e | 780 | else |
a48d60b1 | 781 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 782 | } |
a48d60b1 | 783 | #undef FUNC_NAME |
0f2d19dd | 784 | |
4219f20d | 785 | |
2519490c MW |
786 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
787 | (SCM x, SCM y), | |
788 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
789 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 790 | { |
a16982ca | 791 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 792 | { |
e25f3727 | 793 | scm_t_inum xx = SCM_I_INUM (x); |
a16982ca | 794 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 795 | { |
e25f3727 | 796 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 797 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 798 | scm_num_overflow (s_scm_quotient); |
0aacf84e MD |
799 | else |
800 | { | |
e25f3727 | 801 | scm_t_inum z = xx / yy; |
a16982ca | 802 | if (SCM_LIKELY (SCM_FIXABLE (z))) |
d956fa6f | 803 | return SCM_I_MAKINUM (z); |
0aacf84e | 804 | else |
e25f3727 | 805 | return scm_i_inum2big (z); |
0aacf84e | 806 | } |
828865c3 | 807 | } |
0aacf84e | 808 | else if (SCM_BIGP (y)) |
ac0c002c | 809 | { |
e11e83f3 | 810 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
811 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
812 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
813 | { | |
814 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
815 | scm_remember_upto_here_1 (y); | |
d956fa6f | 816 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 817 | } |
0aacf84e | 818 | else |
cff5fa33 | 819 | return SCM_INUM0; |
ac0c002c DH |
820 | } |
821 | else | |
2519490c | 822 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
828865c3 | 823 | } |
0aacf84e MD |
824 | else if (SCM_BIGP (x)) |
825 | { | |
a16982ca | 826 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 827 | { |
e25f3727 | 828 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 829 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 830 | scm_num_overflow (s_scm_quotient); |
a16982ca | 831 | else if (SCM_UNLIKELY (yy == 1)) |
0aacf84e MD |
832 | return x; |
833 | else | |
834 | { | |
835 | SCM result = scm_i_mkbig (); | |
836 | if (yy < 0) | |
837 | { | |
838 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
839 | SCM_I_BIG_MPZ (x), | |
840 | - yy); | |
841 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
842 | } | |
843 | else | |
844 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
845 | scm_remember_upto_here_1 (x); | |
846 | return scm_i_normbig (result); | |
847 | } | |
848 | } | |
849 | else if (SCM_BIGP (y)) | |
850 | { | |
851 | SCM result = scm_i_mkbig (); | |
852 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
853 | SCM_I_BIG_MPZ (x), | |
854 | SCM_I_BIG_MPZ (y)); | |
855 | scm_remember_upto_here_2 (x, y); | |
856 | return scm_i_normbig (result); | |
857 | } | |
858 | else | |
2519490c | 859 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 860 | } |
0aacf84e | 861 | else |
2519490c | 862 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 863 | } |
2519490c | 864 | #undef FUNC_NAME |
0f2d19dd | 865 | |
2519490c MW |
866 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
867 | (SCM x, SCM y), | |
868 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
869 | "@lisp\n" | |
870 | "(remainder 13 4) @result{} 1\n" | |
871 | "(remainder -13 4) @result{} -1\n" | |
872 | "@end lisp") | |
873 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 874 | { |
a16982ca | 875 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 876 | { |
a16982ca | 877 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 878 | { |
e25f3727 | 879 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 880 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 881 | scm_num_overflow (s_scm_remainder); |
0aacf84e MD |
882 | else |
883 | { | |
a16982ca MW |
884 | /* C99 specifies that "%" is the remainder corresponding to a |
885 | quotient rounded towards zero, and that's also traditional | |
886 | for machine division, so z here should be well defined. */ | |
e25f3727 | 887 | scm_t_inum z = SCM_I_INUM (x) % yy; |
d956fa6f | 888 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
889 | } |
890 | } | |
891 | else if (SCM_BIGP (y)) | |
ac0c002c | 892 | { |
e11e83f3 | 893 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
894 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
895 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
896 | { | |
897 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
898 | scm_remember_upto_here_1 (y); | |
cff5fa33 | 899 | return SCM_INUM0; |
4dc09ee4 | 900 | } |
0aacf84e MD |
901 | else |
902 | return x; | |
ac0c002c DH |
903 | } |
904 | else | |
2519490c | 905 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
89a7e495 | 906 | } |
0aacf84e MD |
907 | else if (SCM_BIGP (x)) |
908 | { | |
a16982ca | 909 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 910 | { |
e25f3727 | 911 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 912 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 913 | scm_num_overflow (s_scm_remainder); |
0aacf84e MD |
914 | else |
915 | { | |
916 | SCM result = scm_i_mkbig (); | |
917 | if (yy < 0) | |
918 | yy = - yy; | |
919 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
920 | scm_remember_upto_here_1 (x); | |
921 | return scm_i_normbig (result); | |
922 | } | |
923 | } | |
924 | else if (SCM_BIGP (y)) | |
925 | { | |
926 | SCM result = scm_i_mkbig (); | |
927 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
928 | SCM_I_BIG_MPZ (x), | |
929 | SCM_I_BIG_MPZ (y)); | |
930 | scm_remember_upto_here_2 (x, y); | |
931 | return scm_i_normbig (result); | |
932 | } | |
933 | else | |
2519490c | 934 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 935 | } |
0aacf84e | 936 | else |
2519490c | 937 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 938 | } |
2519490c | 939 | #undef FUNC_NAME |
0f2d19dd | 940 | |
89a7e495 | 941 | |
2519490c MW |
942 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
943 | (SCM x, SCM y), | |
944 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
945 | "@lisp\n" | |
946 | "(modulo 13 4) @result{} 1\n" | |
947 | "(modulo -13 4) @result{} 3\n" | |
948 | "@end lisp") | |
949 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 950 | { |
a16982ca | 951 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 952 | { |
e25f3727 | 953 | scm_t_inum xx = SCM_I_INUM (x); |
a16982ca | 954 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 955 | { |
e25f3727 | 956 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 957 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 958 | scm_num_overflow (s_scm_modulo); |
0aacf84e MD |
959 | else |
960 | { | |
66b1c775 KR |
961 | /* C99 specifies that "%" is the remainder corresponding to a |
962 | quotient rounded towards zero, and that's also traditional | |
963 | for machine division, so z here should be well defined. */ | |
e25f3727 AW |
964 | scm_t_inum z = xx % yy; |
965 | scm_t_inum result; | |
0aacf84e MD |
966 | |
967 | if (yy < 0) | |
968 | { | |
969 | if (z > 0) | |
970 | result = z + yy; | |
971 | else | |
972 | result = z; | |
973 | } | |
974 | else | |
975 | { | |
976 | if (z < 0) | |
977 | result = z + yy; | |
978 | else | |
979 | result = z; | |
980 | } | |
d956fa6f | 981 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
982 | } |
983 | } | |
984 | else if (SCM_BIGP (y)) | |
985 | { | |
986 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
987 | { |
988 | mpz_t z_x; | |
989 | SCM result; | |
990 | ||
991 | if (sgn_y < 0) | |
992 | { | |
993 | SCM pos_y = scm_i_clonebig (y, 0); | |
994 | /* do this after the last scm_op */ | |
995 | mpz_init_set_si (z_x, xx); | |
996 | result = pos_y; /* re-use this bignum */ | |
997 | mpz_mod (SCM_I_BIG_MPZ (result), | |
998 | z_x, | |
999 | SCM_I_BIG_MPZ (pos_y)); | |
1000 | scm_remember_upto_here_1 (pos_y); | |
1001 | } | |
1002 | else | |
1003 | { | |
1004 | result = scm_i_mkbig (); | |
1005 | /* do this after the last scm_op */ | |
1006 | mpz_init_set_si (z_x, xx); | |
1007 | mpz_mod (SCM_I_BIG_MPZ (result), | |
1008 | z_x, | |
1009 | SCM_I_BIG_MPZ (y)); | |
1010 | scm_remember_upto_here_1 (y); | |
1011 | } | |
ca46fb90 | 1012 | |
0aacf84e MD |
1013 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
1014 | mpz_add (SCM_I_BIG_MPZ (result), | |
1015 | SCM_I_BIG_MPZ (y), | |
1016 | SCM_I_BIG_MPZ (result)); | |
1017 | scm_remember_upto_here_1 (y); | |
1018 | /* and do this before the next one */ | |
1019 | mpz_clear (z_x); | |
1020 | return scm_i_normbig (result); | |
1021 | } | |
1022 | } | |
1023 | else | |
2519490c | 1024 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
f872b822 | 1025 | } |
0aacf84e MD |
1026 | else if (SCM_BIGP (x)) |
1027 | { | |
a16982ca | 1028 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 1029 | { |
e25f3727 | 1030 | scm_t_inum yy = SCM_I_INUM (y); |
a16982ca | 1031 | if (SCM_UNLIKELY (yy == 0)) |
2519490c | 1032 | scm_num_overflow (s_scm_modulo); |
0aacf84e MD |
1033 | else |
1034 | { | |
1035 | SCM result = scm_i_mkbig (); | |
1036 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
1037 | SCM_I_BIG_MPZ (x), | |
1038 | (yy < 0) ? - yy : yy); | |
1039 | scm_remember_upto_here_1 (x); | |
1040 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1041 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
1042 | SCM_I_BIG_MPZ (result), | |
1043 | - yy); | |
1044 | return scm_i_normbig (result); | |
1045 | } | |
1046 | } | |
1047 | else if (SCM_BIGP (y)) | |
1048 | { | |
a16982ca MW |
1049 | SCM result = scm_i_mkbig (); |
1050 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1051 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
1052 | mpz_mod (SCM_I_BIG_MPZ (result), | |
1053 | SCM_I_BIG_MPZ (x), | |
1054 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 1055 | |
a16982ca MW |
1056 | scm_remember_upto_here_1 (x); |
1057 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1058 | mpz_add (SCM_I_BIG_MPZ (result), | |
1059 | SCM_I_BIG_MPZ (y), | |
1060 | SCM_I_BIG_MPZ (result)); | |
1061 | scm_remember_upto_here_2 (y, pos_y); | |
1062 | return scm_i_normbig (result); | |
0aacf84e MD |
1063 | } |
1064 | else | |
2519490c | 1065 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 1066 | } |
0aacf84e | 1067 | else |
2519490c | 1068 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 1069 | } |
2519490c | 1070 | #undef FUNC_NAME |
0f2d19dd | 1071 | |
ff62c168 MW |
1072 | static SCM scm_i_inexact_euclidean_quotient (double x, double y); |
1073 | static SCM scm_i_slow_exact_euclidean_quotient (SCM x, SCM y); | |
1074 | ||
1075 | SCM_PRIMITIVE_GENERIC (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, | |
1076 | (SCM x, SCM y), | |
1077 | "Return the integer @var{q} such that\n" | |
1078 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1079 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1080 | "@lisp\n" | |
1081 | "(euclidean-quotient 123 10) @result{} 12\n" | |
1082 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
1083 | "(euclidean-quotient -123 10) @result{} -13\n" | |
1084 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
1085 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
1086 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
1087 | "@end lisp") | |
1088 | #define FUNC_NAME s_scm_euclidean_quotient | |
1089 | { | |
1090 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1091 | { | |
1092 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1093 | { | |
1094 | scm_t_inum yy = SCM_I_INUM (y); | |
1095 | if (SCM_UNLIKELY (yy == 0)) | |
1096 | scm_num_overflow (s_scm_euclidean_quotient); | |
1097 | else | |
1098 | { | |
1099 | scm_t_inum xx = SCM_I_INUM (x); | |
1100 | scm_t_inum qq = xx / yy; | |
1101 | if (xx < qq * yy) | |
1102 | { | |
1103 | if (yy > 0) | |
1104 | qq--; | |
1105 | else | |
1106 | qq++; | |
1107 | } | |
1108 | return SCM_I_MAKINUM (qq); | |
1109 | } | |
1110 | } | |
1111 | else if (SCM_BIGP (y)) | |
1112 | { | |
1113 | if (SCM_I_INUM (x) >= 0) | |
1114 | return SCM_INUM0; | |
1115 | else | |
1116 | return SCM_I_MAKINUM (- mpz_sgn (SCM_I_BIG_MPZ (y))); | |
1117 | } | |
1118 | else if (SCM_REALP (y)) | |
1119 | return scm_i_inexact_euclidean_quotient | |
1120 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1121 | else if (SCM_FRACTIONP (y)) | |
1122 | return scm_i_slow_exact_euclidean_quotient (x, y); | |
1123 | else | |
1124 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1125 | s_scm_euclidean_quotient); | |
1126 | } | |
1127 | else if (SCM_BIGP (x)) | |
1128 | { | |
1129 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1130 | { | |
1131 | scm_t_inum yy = SCM_I_INUM (y); | |
1132 | if (SCM_UNLIKELY (yy == 0)) | |
1133 | scm_num_overflow (s_scm_euclidean_quotient); | |
1134 | else | |
1135 | { | |
1136 | SCM q = scm_i_mkbig (); | |
1137 | if (yy > 0) | |
1138 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1139 | else | |
1140 | { | |
1141 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1142 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1143 | } | |
1144 | scm_remember_upto_here_1 (x); | |
1145 | return scm_i_normbig (q); | |
1146 | } | |
1147 | } | |
1148 | else if (SCM_BIGP (y)) | |
1149 | { | |
1150 | SCM q = scm_i_mkbig (); | |
1151 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1152 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1153 | SCM_I_BIG_MPZ (x), | |
1154 | SCM_I_BIG_MPZ (y)); | |
1155 | else | |
1156 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1157 | SCM_I_BIG_MPZ (x), | |
1158 | SCM_I_BIG_MPZ (y)); | |
1159 | scm_remember_upto_here_2 (x, y); | |
1160 | return scm_i_normbig (q); | |
1161 | } | |
1162 | else if (SCM_REALP (y)) | |
1163 | return scm_i_inexact_euclidean_quotient | |
1164 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1165 | else if (SCM_FRACTIONP (y)) | |
1166 | return scm_i_slow_exact_euclidean_quotient (x, y); | |
1167 | else | |
1168 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1169 | s_scm_euclidean_quotient); | |
1170 | } | |
1171 | else if (SCM_REALP (x)) | |
1172 | { | |
1173 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1174 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1175 | return scm_i_inexact_euclidean_quotient | |
1176 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1177 | else | |
1178 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1179 | s_scm_euclidean_quotient); | |
1180 | } | |
1181 | else if (SCM_FRACTIONP (x)) | |
1182 | { | |
1183 | if (SCM_REALP (y)) | |
1184 | return scm_i_inexact_euclidean_quotient | |
1185 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1186 | else | |
1187 | return scm_i_slow_exact_euclidean_quotient (x, y); | |
1188 | } | |
1189 | else | |
1190 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG1, | |
1191 | s_scm_euclidean_quotient); | |
1192 | } | |
1193 | #undef FUNC_NAME | |
1194 | ||
1195 | static SCM | |
1196 | scm_i_inexact_euclidean_quotient (double x, double y) | |
1197 | { | |
1198 | if (SCM_LIKELY (y > 0)) | |
1199 | return scm_from_double (floor (x / y)); | |
1200 | else if (SCM_LIKELY (y < 0)) | |
1201 | return scm_from_double (ceil (x / y)); | |
1202 | else if (y == 0) | |
1203 | scm_num_overflow (s_scm_euclidean_quotient); /* or return a NaN? */ | |
1204 | else | |
1205 | return scm_nan (); | |
1206 | } | |
1207 | ||
1208 | /* Compute exact euclidean_quotient the slow way. | |
1209 | We use this only if both arguments are exact, | |
1210 | and at least one of them is a fraction */ | |
1211 | static SCM | |
1212 | scm_i_slow_exact_euclidean_quotient (SCM x, SCM y) | |
1213 | { | |
1214 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
1215 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG1, | |
1216 | s_scm_euclidean_quotient); | |
1217 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
1218 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1219 | s_scm_euclidean_quotient); | |
1220 | else if (scm_is_true (scm_positive_p (y))) | |
1221 | return scm_floor (scm_divide (x, y)); | |
1222 | else if (scm_is_true (scm_negative_p (y))) | |
1223 | return scm_ceiling (scm_divide (x, y)); | |
1224 | else | |
1225 | scm_num_overflow (s_scm_euclidean_quotient); | |
1226 | } | |
1227 | ||
1228 | static SCM scm_i_inexact_euclidean_remainder (double x, double y); | |
1229 | static SCM scm_i_slow_exact_euclidean_remainder (SCM x, SCM y); | |
1230 | ||
1231 | SCM_PRIMITIVE_GENERIC (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, | |
1232 | (SCM x, SCM y), | |
1233 | "Return the real number @var{r} such that\n" | |
1234 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
1235 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1236 | "for some integer @var{q}.\n" | |
1237 | "@lisp\n" | |
1238 | "(euclidean-remainder 123 10) @result{} 3\n" | |
1239 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
1240 | "(euclidean-remainder -123 10) @result{} 7\n" | |
1241 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
1242 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
1243 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
1244 | "@end lisp") | |
1245 | #define FUNC_NAME s_scm_euclidean_remainder | |
1246 | { | |
1247 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1248 | { | |
1249 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1250 | { | |
1251 | scm_t_inum yy = SCM_I_INUM (y); | |
1252 | if (SCM_UNLIKELY (yy == 0)) | |
1253 | scm_num_overflow (s_scm_euclidean_remainder); | |
1254 | else | |
1255 | { | |
1256 | scm_t_inum rr = SCM_I_INUM (x) % yy; | |
1257 | if (rr >= 0) | |
1258 | return SCM_I_MAKINUM (rr); | |
1259 | else if (yy > 0) | |
1260 | return SCM_I_MAKINUM (rr + yy); | |
1261 | else | |
1262 | return SCM_I_MAKINUM (rr - yy); | |
1263 | } | |
1264 | } | |
1265 | else if (SCM_BIGP (y)) | |
1266 | { | |
1267 | scm_t_inum xx = SCM_I_INUM (x); | |
1268 | if (xx >= 0) | |
1269 | return x; | |
1270 | else if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1271 | { | |
1272 | SCM r = scm_i_mkbig (); | |
1273 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1274 | scm_remember_upto_here_1 (y); | |
1275 | return scm_i_normbig (r); | |
1276 | } | |
1277 | else | |
1278 | { | |
1279 | SCM r = scm_i_mkbig (); | |
1280 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1281 | scm_remember_upto_here_1 (y); | |
1282 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1283 | return scm_i_normbig (r); | |
1284 | } | |
1285 | } | |
1286 | else if (SCM_REALP (y)) | |
1287 | return scm_i_inexact_euclidean_remainder | |
1288 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1289 | else if (SCM_FRACTIONP (y)) | |
1290 | return scm_i_slow_exact_euclidean_remainder (x, y); | |
1291 | else | |
1292 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1293 | s_scm_euclidean_remainder); | |
1294 | } | |
1295 | else if (SCM_BIGP (x)) | |
1296 | { | |
1297 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1298 | { | |
1299 | scm_t_inum yy = SCM_I_INUM (y); | |
1300 | if (SCM_UNLIKELY (yy == 0)) | |
1301 | scm_num_overflow (s_scm_euclidean_remainder); | |
1302 | else | |
1303 | { | |
1304 | scm_t_inum rr; | |
1305 | if (yy < 0) | |
1306 | yy = -yy; | |
1307 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1308 | scm_remember_upto_here_1 (x); | |
1309 | return SCM_I_MAKINUM (rr); | |
1310 | } | |
1311 | } | |
1312 | else if (SCM_BIGP (y)) | |
1313 | { | |
1314 | SCM r = scm_i_mkbig (); | |
1315 | mpz_mod (SCM_I_BIG_MPZ (r), | |
1316 | SCM_I_BIG_MPZ (x), | |
1317 | SCM_I_BIG_MPZ (y)); | |
1318 | scm_remember_upto_here_2 (x, y); | |
1319 | return scm_i_normbig (r); | |
1320 | } | |
1321 | else if (SCM_REALP (y)) | |
1322 | return scm_i_inexact_euclidean_remainder | |
1323 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1324 | else if (SCM_FRACTIONP (y)) | |
1325 | return scm_i_slow_exact_euclidean_remainder (x, y); | |
1326 | else | |
1327 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1328 | s_scm_euclidean_remainder); | |
1329 | } | |
1330 | else if (SCM_REALP (x)) | |
1331 | { | |
1332 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1333 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1334 | return scm_i_inexact_euclidean_remainder | |
1335 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1336 | else | |
1337 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1338 | s_scm_euclidean_remainder); | |
1339 | } | |
1340 | else if (SCM_FRACTIONP (x)) | |
1341 | { | |
1342 | if (SCM_REALP (y)) | |
1343 | return scm_i_inexact_euclidean_remainder | |
1344 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1345 | else | |
1346 | return scm_i_slow_exact_euclidean_remainder (x, y); | |
1347 | } | |
1348 | else | |
1349 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG1, | |
1350 | s_scm_euclidean_remainder); | |
1351 | } | |
1352 | #undef FUNC_NAME | |
1353 | ||
1354 | static SCM | |
1355 | scm_i_inexact_euclidean_remainder (double x, double y) | |
1356 | { | |
1357 | double q; | |
1358 | ||
1359 | /* Although it would be more efficient to use fmod here, we can't | |
1360 | because it would in some cases produce results inconsistent with | |
1361 | scm_i_inexact_euclidean_quotient, such that x != q * y + r (not | |
1362 | even close). In particular, when x is very close to a multiple of | |
1363 | y, then r might be either 0.0 or abs(y)-epsilon, but those two | |
1364 | cases must correspond to different choices of q. If r = 0.0 then q | |
1365 | must be x/y, and if r = abs(y) then q must be (x-r)/y. If quotient | |
1366 | chooses one and remainder chooses the other, it would be bad. This | |
1367 | problem was observed with x = 130.0 and y = 10/7. */ | |
1368 | if (SCM_LIKELY (y > 0)) | |
1369 | q = floor (x / y); | |
1370 | else if (SCM_LIKELY (y < 0)) | |
1371 | q = ceil (x / y); | |
1372 | else if (y == 0) | |
1373 | scm_num_overflow (s_scm_euclidean_remainder); /* or return a NaN? */ | |
1374 | else | |
1375 | return scm_nan (); | |
1376 | return scm_from_double (x - q * y); | |
1377 | } | |
1378 | ||
1379 | /* Compute exact euclidean_remainder the slow way. | |
1380 | We use this only if both arguments are exact, | |
1381 | and at least one of them is a fraction */ | |
1382 | static SCM | |
1383 | scm_i_slow_exact_euclidean_remainder (SCM x, SCM y) | |
1384 | { | |
1385 | SCM q; | |
1386 | ||
1387 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
1388 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG1, | |
1389 | s_scm_euclidean_remainder); | |
1390 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
1391 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1392 | s_scm_euclidean_remainder); | |
1393 | else if (scm_is_true (scm_positive_p (y))) | |
1394 | q = scm_floor (scm_divide (x, y)); | |
1395 | else if (scm_is_true (scm_negative_p (y))) | |
1396 | q = scm_ceiling (scm_divide (x, y)); | |
1397 | else | |
1398 | scm_num_overflow (s_scm_euclidean_remainder); | |
1399 | return scm_difference (x, scm_product (y, q)); | |
1400 | } | |
1401 | ||
1402 | ||
ac6ce16b MW |
1403 | static SCM scm_i_inexact_euclidean_divide (double x, double y); |
1404 | static SCM scm_i_slow_exact_euclidean_divide (SCM x, SCM y); | |
ff62c168 | 1405 | |
ac6ce16b | 1406 | SCM_PRIMITIVE_GENERIC (scm_euclidean_divide, "euclidean/", 2, 0, 0, |
ff62c168 MW |
1407 | (SCM x, SCM y), |
1408 | "Return the integer @var{q} and the real number @var{r}\n" | |
1409 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1410 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1411 | "@lisp\n" | |
1412 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
1413 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
1414 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
1415 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
1416 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1417 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1418 | "@end lisp") | |
ac6ce16b | 1419 | #define FUNC_NAME s_scm_euclidean_divide |
ff62c168 MW |
1420 | { |
1421 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1422 | { | |
1423 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1424 | { | |
1425 | scm_t_inum yy = SCM_I_INUM (y); | |
1426 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 1427 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1428 | else |
1429 | { | |
1430 | scm_t_inum xx = SCM_I_INUM (x); | |
1431 | scm_t_inum qq = xx / yy; | |
1432 | scm_t_inum rr = xx - qq * yy; | |
1433 | if (rr < 0) | |
1434 | { | |
1435 | if (yy > 0) | |
1436 | { rr += yy; qq--; } | |
1437 | else | |
1438 | { rr -= yy; qq++; } | |
1439 | } | |
1440 | return scm_values (scm_list_2 (SCM_I_MAKINUM (qq), | |
1441 | SCM_I_MAKINUM (rr))); | |
1442 | } | |
1443 | } | |
1444 | else if (SCM_BIGP (y)) | |
1445 | { | |
1446 | scm_t_inum xx = SCM_I_INUM (x); | |
1447 | if (xx >= 0) | |
1448 | return scm_values (scm_list_2 (SCM_INUM0, x)); | |
1449 | else if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1450 | { | |
1451 | SCM r = scm_i_mkbig (); | |
1452 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1453 | scm_remember_upto_here_1 (y); | |
1454 | return scm_values | |
1455 | (scm_list_2 (SCM_I_MAKINUM (-1), scm_i_normbig (r))); | |
1456 | } | |
1457 | else | |
1458 | { | |
1459 | SCM r = scm_i_mkbig (); | |
1460 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1461 | scm_remember_upto_here_1 (y); | |
1462 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1463 | return scm_values (scm_list_2 (SCM_INUM1, scm_i_normbig (r))); | |
1464 | } | |
1465 | } | |
1466 | else if (SCM_REALP (y)) | |
ac6ce16b | 1467 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1468 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); |
1469 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 1470 | return scm_i_slow_exact_euclidean_divide (x, y); |
ff62c168 | 1471 | else |
ac6ce16b MW |
1472 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1473 | s_scm_euclidean_divide); | |
ff62c168 MW |
1474 | } |
1475 | else if (SCM_BIGP (x)) | |
1476 | { | |
1477 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1478 | { | |
1479 | scm_t_inum yy = SCM_I_INUM (y); | |
1480 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 1481 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1482 | else |
1483 | { | |
1484 | SCM q = scm_i_mkbig (); | |
1485 | SCM r = scm_i_mkbig (); | |
1486 | if (yy > 0) | |
1487 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1488 | SCM_I_BIG_MPZ (x), yy); | |
1489 | else | |
1490 | { | |
1491 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1492 | SCM_I_BIG_MPZ (x), -yy); | |
1493 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1494 | } | |
1495 | scm_remember_upto_here_1 (x); | |
1496 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
1497 | scm_i_normbig (r))); | |
1498 | } | |
1499 | } | |
1500 | else if (SCM_BIGP (y)) | |
1501 | { | |
1502 | SCM q = scm_i_mkbig (); | |
1503 | SCM r = scm_i_mkbig (); | |
1504 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1505 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1506 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1507 | else | |
1508 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1509 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1510 | scm_remember_upto_here_2 (x, y); | |
1511 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
1512 | scm_i_normbig (r))); | |
1513 | } | |
1514 | else if (SCM_REALP (y)) | |
ac6ce16b | 1515 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1516 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
1517 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 1518 | return scm_i_slow_exact_euclidean_divide (x, y); |
ff62c168 | 1519 | else |
ac6ce16b MW |
1520 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1521 | s_scm_euclidean_divide); | |
ff62c168 MW |
1522 | } |
1523 | else if (SCM_REALP (x)) | |
1524 | { | |
1525 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1526 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
ac6ce16b | 1527 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1528 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
1529 | else | |
ac6ce16b MW |
1530 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1531 | s_scm_euclidean_divide); | |
ff62c168 MW |
1532 | } |
1533 | else if (SCM_FRACTIONP (x)) | |
1534 | { | |
1535 | if (SCM_REALP (y)) | |
ac6ce16b | 1536 | return scm_i_inexact_euclidean_divide |
ff62c168 MW |
1537 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
1538 | else | |
ac6ce16b | 1539 | return scm_i_slow_exact_euclidean_divide (x, y); |
ff62c168 MW |
1540 | } |
1541 | else | |
ac6ce16b MW |
1542 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG1, |
1543 | s_scm_euclidean_divide); | |
ff62c168 MW |
1544 | } |
1545 | #undef FUNC_NAME | |
1546 | ||
1547 | static SCM | |
ac6ce16b | 1548 | scm_i_inexact_euclidean_divide (double x, double y) |
ff62c168 MW |
1549 | { |
1550 | double q, r; | |
1551 | ||
1552 | if (SCM_LIKELY (y > 0)) | |
1553 | q = floor (x / y); | |
1554 | else if (SCM_LIKELY (y < 0)) | |
1555 | q = ceil (x / y); | |
1556 | else if (y == 0) | |
ac6ce16b | 1557 | scm_num_overflow (s_scm_euclidean_divide); /* or return a NaN? */ |
ff62c168 MW |
1558 | else |
1559 | q = guile_NaN; | |
1560 | r = x - q * y; | |
1561 | return scm_values (scm_list_2 (scm_from_double (q), | |
1562 | scm_from_double (r))); | |
1563 | } | |
1564 | ||
1565 | /* Compute exact euclidean quotient and remainder the slow way. | |
1566 | We use this only if both arguments are exact, | |
1567 | and at least one of them is a fraction */ | |
1568 | static SCM | |
ac6ce16b | 1569 | scm_i_slow_exact_euclidean_divide (SCM x, SCM y) |
ff62c168 MW |
1570 | { |
1571 | SCM q, r; | |
1572 | ||
1573 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
ac6ce16b MW |
1574 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG1, |
1575 | s_scm_euclidean_divide); | |
ff62c168 | 1576 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) |
ac6ce16b MW |
1577 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_divide, x, y, SCM_ARG2, |
1578 | s_scm_euclidean_divide); | |
ff62c168 MW |
1579 | else if (scm_is_true (scm_positive_p (y))) |
1580 | q = scm_floor (scm_divide (x, y)); | |
1581 | else if (scm_is_true (scm_negative_p (y))) | |
1582 | q = scm_ceiling (scm_divide (x, y)); | |
1583 | else | |
ac6ce16b | 1584 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1585 | r = scm_difference (x, scm_product (q, y)); |
1586 | return scm_values (scm_list_2 (q, r)); | |
1587 | } | |
1588 | ||
1589 | static SCM scm_i_inexact_centered_quotient (double x, double y); | |
1590 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
1591 | static SCM scm_i_slow_exact_centered_quotient (SCM x, SCM y); | |
1592 | ||
1593 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, | |
1594 | (SCM x, SCM y), | |
1595 | "Return the integer @var{q} such that\n" | |
1596 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
1597 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
1598 | "@lisp\n" | |
1599 | "(centered-quotient 123 10) @result{} 12\n" | |
1600 | "(centered-quotient 123 -10) @result{} -12\n" | |
1601 | "(centered-quotient -123 10) @result{} -12\n" | |
1602 | "(centered-quotient -123 -10) @result{} 12\n" | |
1603 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
1604 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
1605 | "@end lisp") | |
1606 | #define FUNC_NAME s_scm_centered_quotient | |
1607 | { | |
1608 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1609 | { | |
1610 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1611 | { | |
1612 | scm_t_inum yy = SCM_I_INUM (y); | |
1613 | if (SCM_UNLIKELY (yy == 0)) | |
1614 | scm_num_overflow (s_scm_centered_quotient); | |
1615 | else | |
1616 | { | |
1617 | scm_t_inum xx = SCM_I_INUM (x); | |
1618 | scm_t_inum qq = xx / yy; | |
1619 | scm_t_inum rr = xx - qq * yy; | |
1620 | if (SCM_LIKELY (xx > 0)) | |
1621 | { | |
1622 | if (SCM_LIKELY (yy > 0)) | |
1623 | { | |
1624 | if (rr >= (yy + 1) / 2) | |
1625 | qq++; | |
1626 | } | |
1627 | else | |
1628 | { | |
1629 | if (rr >= (1 - yy) / 2) | |
1630 | qq--; | |
1631 | } | |
1632 | } | |
1633 | else | |
1634 | { | |
1635 | if (SCM_LIKELY (yy > 0)) | |
1636 | { | |
1637 | if (rr < -yy / 2) | |
1638 | qq--; | |
1639 | } | |
1640 | else | |
1641 | { | |
1642 | if (rr < yy / 2) | |
1643 | qq++; | |
1644 | } | |
1645 | } | |
1646 | return SCM_I_MAKINUM (qq); | |
1647 | } | |
1648 | } | |
1649 | else if (SCM_BIGP (y)) | |
1650 | { | |
1651 | /* Pass a denormalized bignum version of x (even though it | |
1652 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
1653 | return scm_i_bigint_centered_quotient | |
1654 | (scm_i_long2big (SCM_I_INUM (x)), y); | |
1655 | } | |
1656 | else if (SCM_REALP (y)) | |
1657 | return scm_i_inexact_centered_quotient | |
1658 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1659 | else if (SCM_FRACTIONP (y)) | |
1660 | return scm_i_slow_exact_centered_quotient (x, y); | |
1661 | else | |
1662 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1663 | s_scm_centered_quotient); | |
1664 | } | |
1665 | else if (SCM_BIGP (x)) | |
1666 | { | |
1667 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1668 | { | |
1669 | scm_t_inum yy = SCM_I_INUM (y); | |
1670 | if (SCM_UNLIKELY (yy == 0)) | |
1671 | scm_num_overflow (s_scm_centered_quotient); | |
1672 | else | |
1673 | { | |
1674 | SCM q = scm_i_mkbig (); | |
1675 | scm_t_inum rr; | |
1676 | /* Arrange for rr to initially be non-positive, | |
1677 | because that simplifies the test to see | |
1678 | if it is within the needed bounds. */ | |
1679 | if (yy > 0) | |
1680 | { | |
1681 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
1682 | SCM_I_BIG_MPZ (x), yy); | |
1683 | scm_remember_upto_here_1 (x); | |
1684 | if (rr < -yy / 2) | |
1685 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
1686 | SCM_I_BIG_MPZ (q), 1); | |
1687 | } | |
1688 | else | |
1689 | { | |
1690 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
1691 | SCM_I_BIG_MPZ (x), -yy); | |
1692 | scm_remember_upto_here_1 (x); | |
1693 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1694 | if (rr < yy / 2) | |
1695 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
1696 | SCM_I_BIG_MPZ (q), 1); | |
1697 | } | |
1698 | return scm_i_normbig (q); | |
1699 | } | |
1700 | } | |
1701 | else if (SCM_BIGP (y)) | |
1702 | return scm_i_bigint_centered_quotient (x, y); | |
1703 | else if (SCM_REALP (y)) | |
1704 | return scm_i_inexact_centered_quotient | |
1705 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1706 | else if (SCM_FRACTIONP (y)) | |
1707 | return scm_i_slow_exact_centered_quotient (x, y); | |
1708 | else | |
1709 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1710 | s_scm_centered_quotient); | |
1711 | } | |
1712 | else if (SCM_REALP (x)) | |
1713 | { | |
1714 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1715 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1716 | return scm_i_inexact_centered_quotient | |
1717 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1718 | else | |
1719 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1720 | s_scm_centered_quotient); | |
1721 | } | |
1722 | else if (SCM_FRACTIONP (x)) | |
1723 | { | |
1724 | if (SCM_REALP (y)) | |
1725 | return scm_i_inexact_centered_quotient | |
1726 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1727 | else | |
1728 | return scm_i_slow_exact_centered_quotient (x, y); | |
1729 | } | |
1730 | else | |
1731 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
1732 | s_scm_centered_quotient); | |
1733 | } | |
1734 | #undef FUNC_NAME | |
1735 | ||
1736 | static SCM | |
1737 | scm_i_inexact_centered_quotient (double x, double y) | |
1738 | { | |
1739 | if (SCM_LIKELY (y > 0)) | |
1740 | return scm_from_double (floor (x/y + 0.5)); | |
1741 | else if (SCM_LIKELY (y < 0)) | |
1742 | return scm_from_double (ceil (x/y - 0.5)); | |
1743 | else if (y == 0) | |
1744 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
1745 | else | |
1746 | return scm_nan (); | |
1747 | } | |
1748 | ||
1749 | /* Assumes that both x and y are bigints, though | |
1750 | x might be able to fit into a fixnum. */ | |
1751 | static SCM | |
1752 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
1753 | { | |
1754 | SCM q, r, min_r; | |
1755 | ||
1756 | /* Note that x might be small enough to fit into a | |
1757 | fixnum, so we must not let it escape into the wild */ | |
1758 | q = scm_i_mkbig (); | |
1759 | r = scm_i_mkbig (); | |
1760 | ||
1761 | /* min_r will eventually become -abs(y)/2 */ | |
1762 | min_r = scm_i_mkbig (); | |
1763 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
1764 | SCM_I_BIG_MPZ (y), 1); | |
1765 | ||
1766 | /* Arrange for rr to initially be non-positive, | |
1767 | because that simplifies the test to see | |
1768 | if it is within the needed bounds. */ | |
1769 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1770 | { | |
1771 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1772 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1773 | scm_remember_upto_here_2 (x, y); | |
1774 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
1775 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1776 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
1777 | SCM_I_BIG_MPZ (q), 1); | |
1778 | } | |
1779 | else | |
1780 | { | |
1781 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1782 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1783 | scm_remember_upto_here_2 (x, y); | |
1784 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1785 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
1786 | SCM_I_BIG_MPZ (q), 1); | |
1787 | } | |
1788 | scm_remember_upto_here_2 (r, min_r); | |
1789 | return scm_i_normbig (q); | |
1790 | } | |
1791 | ||
1792 | /* Compute exact centered quotient the slow way. | |
1793 | We use this only if both arguments are exact, | |
1794 | and at least one of them is a fraction */ | |
1795 | static SCM | |
1796 | scm_i_slow_exact_centered_quotient (SCM x, SCM y) | |
1797 | { | |
1798 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
1799 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
1800 | s_scm_centered_quotient); | |
1801 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
1802 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1803 | s_scm_centered_quotient); | |
1804 | else if (scm_is_true (scm_positive_p (y))) | |
1805 | return scm_floor (scm_sum (scm_divide (x, y), | |
1806 | exactly_one_half)); | |
1807 | else if (scm_is_true (scm_negative_p (y))) | |
1808 | return scm_ceiling (scm_difference (scm_divide (x, y), | |
1809 | exactly_one_half)); | |
1810 | else | |
1811 | scm_num_overflow (s_scm_centered_quotient); | |
1812 | } | |
1813 | ||
1814 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
1815 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
1816 | static SCM scm_i_slow_exact_centered_remainder (SCM x, SCM y); | |
1817 | ||
1818 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
1819 | (SCM x, SCM y), | |
1820 | "Return the real number @var{r} such that\n" | |
1821 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
1822 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1823 | "for some integer @var{q}.\n" | |
1824 | "@lisp\n" | |
1825 | "(centered-remainder 123 10) @result{} 3\n" | |
1826 | "(centered-remainder 123 -10) @result{} 3\n" | |
1827 | "(centered-remainder -123 10) @result{} -3\n" | |
1828 | "(centered-remainder -123 -10) @result{} -3\n" | |
1829 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
1830 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
1831 | "@end lisp") | |
1832 | #define FUNC_NAME s_scm_centered_remainder | |
1833 | { | |
1834 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1835 | { | |
1836 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1837 | { | |
1838 | scm_t_inum yy = SCM_I_INUM (y); | |
1839 | if (SCM_UNLIKELY (yy == 0)) | |
1840 | scm_num_overflow (s_scm_centered_remainder); | |
1841 | else | |
1842 | { | |
1843 | scm_t_inum xx = SCM_I_INUM (x); | |
1844 | scm_t_inum rr = xx % yy; | |
1845 | if (SCM_LIKELY (xx > 0)) | |
1846 | { | |
1847 | if (SCM_LIKELY (yy > 0)) | |
1848 | { | |
1849 | if (rr >= (yy + 1) / 2) | |
1850 | rr -= yy; | |
1851 | } | |
1852 | else | |
1853 | { | |
1854 | if (rr >= (1 - yy) / 2) | |
1855 | rr += yy; | |
1856 | } | |
1857 | } | |
1858 | else | |
1859 | { | |
1860 | if (SCM_LIKELY (yy > 0)) | |
1861 | { | |
1862 | if (rr < -yy / 2) | |
1863 | rr += yy; | |
1864 | } | |
1865 | else | |
1866 | { | |
1867 | if (rr < yy / 2) | |
1868 | rr -= yy; | |
1869 | } | |
1870 | } | |
1871 | return SCM_I_MAKINUM (rr); | |
1872 | } | |
1873 | } | |
1874 | else if (SCM_BIGP (y)) | |
1875 | { | |
1876 | /* Pass a denormalized bignum version of x (even though it | |
1877 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
1878 | return scm_i_bigint_centered_remainder | |
1879 | (scm_i_long2big (SCM_I_INUM (x)), y); | |
1880 | } | |
1881 | else if (SCM_REALP (y)) | |
1882 | return scm_i_inexact_centered_remainder | |
1883 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); | |
1884 | else if (SCM_FRACTIONP (y)) | |
1885 | return scm_i_slow_exact_centered_remainder (x, y); | |
1886 | else | |
1887 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1888 | s_scm_centered_remainder); | |
1889 | } | |
1890 | else if (SCM_BIGP (x)) | |
1891 | { | |
1892 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1893 | { | |
1894 | scm_t_inum yy = SCM_I_INUM (y); | |
1895 | if (SCM_UNLIKELY (yy == 0)) | |
1896 | scm_num_overflow (s_scm_centered_remainder); | |
1897 | else | |
1898 | { | |
1899 | scm_t_inum rr; | |
1900 | /* Arrange for rr to initially be non-positive, | |
1901 | because that simplifies the test to see | |
1902 | if it is within the needed bounds. */ | |
1903 | if (yy > 0) | |
1904 | { | |
1905 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1906 | scm_remember_upto_here_1 (x); | |
1907 | if (rr < -yy / 2) | |
1908 | rr += yy; | |
1909 | } | |
1910 | else | |
1911 | { | |
1912 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1913 | scm_remember_upto_here_1 (x); | |
1914 | if (rr < yy / 2) | |
1915 | rr -= yy; | |
1916 | } | |
1917 | return SCM_I_MAKINUM (rr); | |
1918 | } | |
1919 | } | |
1920 | else if (SCM_BIGP (y)) | |
1921 | return scm_i_bigint_centered_remainder (x, y); | |
1922 | else if (SCM_REALP (y)) | |
1923 | return scm_i_inexact_centered_remainder | |
1924 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1925 | else if (SCM_FRACTIONP (y)) | |
1926 | return scm_i_slow_exact_centered_remainder (x, y); | |
1927 | else | |
1928 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1929 | s_scm_centered_remainder); | |
1930 | } | |
1931 | else if (SCM_REALP (x)) | |
1932 | { | |
1933 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1934 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1935 | return scm_i_inexact_centered_remainder | |
1936 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1937 | else | |
1938 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1939 | s_scm_centered_remainder); | |
1940 | } | |
1941 | else if (SCM_FRACTIONP (x)) | |
1942 | { | |
1943 | if (SCM_REALP (y)) | |
1944 | return scm_i_inexact_centered_remainder | |
1945 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1946 | else | |
1947 | return scm_i_slow_exact_centered_remainder (x, y); | |
1948 | } | |
1949 | else | |
1950 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
1951 | s_scm_centered_remainder); | |
1952 | } | |
1953 | #undef FUNC_NAME | |
1954 | ||
1955 | static SCM | |
1956 | scm_i_inexact_centered_remainder (double x, double y) | |
1957 | { | |
1958 | double q; | |
1959 | ||
1960 | /* Although it would be more efficient to use fmod here, we can't | |
1961 | because it would in some cases produce results inconsistent with | |
1962 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
1963 | close). In particular, when x-y/2 is very close to a multiple of | |
1964 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
1965 | two cases must correspond to different choices of q. If quotient | |
1966 | chooses one and remainder chooses the other, it would be bad. */ | |
1967 | if (SCM_LIKELY (y > 0)) | |
1968 | q = floor (x/y + 0.5); | |
1969 | else if (SCM_LIKELY (y < 0)) | |
1970 | q = ceil (x/y - 0.5); | |
1971 | else if (y == 0) | |
1972 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
1973 | else | |
1974 | return scm_nan (); | |
1975 | return scm_from_double (x - q * y); | |
1976 | } | |
1977 | ||
1978 | /* Assumes that both x and y are bigints, though | |
1979 | x might be able to fit into a fixnum. */ | |
1980 | static SCM | |
1981 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
1982 | { | |
1983 | SCM r, min_r; | |
1984 | ||
1985 | /* Note that x might be small enough to fit into a | |
1986 | fixnum, so we must not let it escape into the wild */ | |
1987 | r = scm_i_mkbig (); | |
1988 | ||
1989 | /* min_r will eventually become -abs(y)/2 */ | |
1990 | min_r = scm_i_mkbig (); | |
1991 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
1992 | SCM_I_BIG_MPZ (y), 1); | |
1993 | ||
1994 | /* Arrange for rr to initially be non-positive, | |
1995 | because that simplifies the test to see | |
1996 | if it is within the needed bounds. */ | |
1997 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1998 | { | |
1999 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
2000 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2001 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2002 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2003 | mpz_add (SCM_I_BIG_MPZ (r), | |
2004 | SCM_I_BIG_MPZ (r), | |
2005 | SCM_I_BIG_MPZ (y)); | |
2006 | } | |
2007 | else | |
2008 | { | |
2009 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
2010 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2011 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2012 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2013 | SCM_I_BIG_MPZ (r), | |
2014 | SCM_I_BIG_MPZ (y)); | |
2015 | } | |
2016 | scm_remember_upto_here_2 (x, y); | |
2017 | return scm_i_normbig (r); | |
2018 | } | |
2019 | ||
2020 | /* Compute exact centered_remainder the slow way. | |
2021 | We use this only if both arguments are exact, | |
2022 | and at least one of them is a fraction */ | |
2023 | static SCM | |
2024 | scm_i_slow_exact_centered_remainder (SCM x, SCM y) | |
2025 | { | |
2026 | SCM q; | |
2027 | ||
2028 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
2029 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
2030 | s_scm_centered_remainder); | |
2031 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) | |
2032 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2033 | s_scm_centered_remainder); | |
2034 | else if (scm_is_true (scm_positive_p (y))) | |
2035 | q = scm_floor (scm_sum (scm_divide (x, y), exactly_one_half)); | |
2036 | else if (scm_is_true (scm_negative_p (y))) | |
2037 | q = scm_ceiling (scm_difference (scm_divide (x, y), exactly_one_half)); | |
2038 | else | |
2039 | scm_num_overflow (s_scm_centered_remainder); | |
2040 | return scm_difference (x, scm_product (y, q)); | |
2041 | } | |
2042 | ||
2043 | ||
ac6ce16b MW |
2044 | static SCM scm_i_inexact_centered_divide (double x, double y); |
2045 | static SCM scm_i_bigint_centered_divide (SCM x, SCM y); | |
2046 | static SCM scm_i_slow_exact_centered_divide (SCM x, SCM y); | |
ff62c168 | 2047 | |
ac6ce16b | 2048 | SCM_PRIMITIVE_GENERIC (scm_centered_divide, "centered/", 2, 0, 0, |
ff62c168 MW |
2049 | (SCM x, SCM y), |
2050 | "Return the integer @var{q} and the real number @var{r}\n" | |
2051 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2052 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2053 | "@lisp\n" | |
2054 | "(centered/ 123 10) @result{} 12 and 3\n" | |
2055 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
2056 | "(centered/ -123 10) @result{} -12 and -3\n" | |
2057 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
2058 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2059 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
2060 | "@end lisp") | |
ac6ce16b | 2061 | #define FUNC_NAME s_scm_centered_divide |
ff62c168 MW |
2062 | { |
2063 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2064 | { | |
2065 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2066 | { | |
2067 | scm_t_inum yy = SCM_I_INUM (y); | |
2068 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 2069 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2070 | else |
2071 | { | |
2072 | scm_t_inum xx = SCM_I_INUM (x); | |
2073 | scm_t_inum qq = xx / yy; | |
2074 | scm_t_inum rr = xx - qq * yy; | |
2075 | if (SCM_LIKELY (xx > 0)) | |
2076 | { | |
2077 | if (SCM_LIKELY (yy > 0)) | |
2078 | { | |
2079 | if (rr >= (yy + 1) / 2) | |
2080 | { qq++; rr -= yy; } | |
2081 | } | |
2082 | else | |
2083 | { | |
2084 | if (rr >= (1 - yy) / 2) | |
2085 | { qq--; rr += yy; } | |
2086 | } | |
2087 | } | |
2088 | else | |
2089 | { | |
2090 | if (SCM_LIKELY (yy > 0)) | |
2091 | { | |
2092 | if (rr < -yy / 2) | |
2093 | { qq--; rr += yy; } | |
2094 | } | |
2095 | else | |
2096 | { | |
2097 | if (rr < yy / 2) | |
2098 | { qq++; rr -= yy; } | |
2099 | } | |
2100 | } | |
2101 | return scm_values (scm_list_2 (SCM_I_MAKINUM (qq), | |
2102 | SCM_I_MAKINUM (rr))); | |
2103 | } | |
2104 | } | |
2105 | else if (SCM_BIGP (y)) | |
2106 | { | |
2107 | /* Pass a denormalized bignum version of x (even though it | |
ac6ce16b MW |
2108 | can fit in a fixnum) to scm_i_bigint_centered_divide */ |
2109 | return scm_i_bigint_centered_divide | |
ff62c168 MW |
2110 | (scm_i_long2big (SCM_I_INUM (x)), y); |
2111 | } | |
2112 | else if (SCM_REALP (y)) | |
ac6ce16b | 2113 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2114 | (SCM_I_INUM (x), SCM_REAL_VALUE (y)); |
2115 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 2116 | return scm_i_slow_exact_centered_divide (x, y); |
ff62c168 | 2117 | else |
ac6ce16b MW |
2118 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2119 | s_scm_centered_divide); | |
ff62c168 MW |
2120 | } |
2121 | else if (SCM_BIGP (x)) | |
2122 | { | |
2123 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2124 | { | |
2125 | scm_t_inum yy = SCM_I_INUM (y); | |
2126 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 2127 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2128 | else |
2129 | { | |
2130 | SCM q = scm_i_mkbig (); | |
2131 | scm_t_inum rr; | |
2132 | /* Arrange for rr to initially be non-positive, | |
2133 | because that simplifies the test to see | |
2134 | if it is within the needed bounds. */ | |
2135 | if (yy > 0) | |
2136 | { | |
2137 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2138 | SCM_I_BIG_MPZ (x), yy); | |
2139 | scm_remember_upto_here_1 (x); | |
2140 | if (rr < -yy / 2) | |
2141 | { | |
2142 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2143 | SCM_I_BIG_MPZ (q), 1); | |
2144 | rr += yy; | |
2145 | } | |
2146 | } | |
2147 | else | |
2148 | { | |
2149 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2150 | SCM_I_BIG_MPZ (x), -yy); | |
2151 | scm_remember_upto_here_1 (x); | |
2152 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2153 | if (rr < yy / 2) | |
2154 | { | |
2155 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2156 | SCM_I_BIG_MPZ (q), 1); | |
2157 | rr -= yy; | |
2158 | } | |
2159 | } | |
2160 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
2161 | SCM_I_MAKINUM (rr))); | |
2162 | } | |
2163 | } | |
2164 | else if (SCM_BIGP (y)) | |
ac6ce16b | 2165 | return scm_i_bigint_centered_divide (x, y); |
ff62c168 | 2166 | else if (SCM_REALP (y)) |
ac6ce16b | 2167 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2168 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
2169 | else if (SCM_FRACTIONP (y)) | |
ac6ce16b | 2170 | return scm_i_slow_exact_centered_divide (x, y); |
ff62c168 | 2171 | else |
ac6ce16b MW |
2172 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2173 | s_scm_centered_divide); | |
ff62c168 MW |
2174 | } |
2175 | else if (SCM_REALP (x)) | |
2176 | { | |
2177 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2178 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
ac6ce16b | 2179 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2180 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
2181 | else | |
ac6ce16b MW |
2182 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2183 | s_scm_centered_divide); | |
ff62c168 MW |
2184 | } |
2185 | else if (SCM_FRACTIONP (x)) | |
2186 | { | |
2187 | if (SCM_REALP (y)) | |
ac6ce16b | 2188 | return scm_i_inexact_centered_divide |
ff62c168 MW |
2189 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
2190 | else | |
ac6ce16b | 2191 | return scm_i_slow_exact_centered_divide (x, y); |
ff62c168 MW |
2192 | } |
2193 | else | |
ac6ce16b MW |
2194 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG1, |
2195 | s_scm_centered_divide); | |
ff62c168 MW |
2196 | } |
2197 | #undef FUNC_NAME | |
2198 | ||
2199 | static SCM | |
ac6ce16b | 2200 | scm_i_inexact_centered_divide (double x, double y) |
ff62c168 MW |
2201 | { |
2202 | double q, r; | |
2203 | ||
2204 | if (SCM_LIKELY (y > 0)) | |
2205 | q = floor (x/y + 0.5); | |
2206 | else if (SCM_LIKELY (y < 0)) | |
2207 | q = ceil (x/y - 0.5); | |
2208 | else if (y == 0) | |
ac6ce16b | 2209 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ |
ff62c168 MW |
2210 | else |
2211 | q = guile_NaN; | |
2212 | r = x - q * y; | |
2213 | return scm_values (scm_list_2 (scm_from_double (q), | |
2214 | scm_from_double (r))); | |
2215 | } | |
2216 | ||
2217 | /* Assumes that both x and y are bigints, though | |
2218 | x might be able to fit into a fixnum. */ | |
2219 | static SCM | |
ac6ce16b | 2220 | scm_i_bigint_centered_divide (SCM x, SCM y) |
ff62c168 MW |
2221 | { |
2222 | SCM q, r, min_r; | |
2223 | ||
2224 | /* Note that x might be small enough to fit into a | |
2225 | fixnum, so we must not let it escape into the wild */ | |
2226 | q = scm_i_mkbig (); | |
2227 | r = scm_i_mkbig (); | |
2228 | ||
2229 | /* min_r will eventually become -abs(y/2) */ | |
2230 | min_r = scm_i_mkbig (); | |
2231 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2232 | SCM_I_BIG_MPZ (y), 1); | |
2233 | ||
2234 | /* Arrange for rr to initially be non-positive, | |
2235 | because that simplifies the test to see | |
2236 | if it is within the needed bounds. */ | |
2237 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2238 | { | |
2239 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2240 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2241 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2242 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2243 | { | |
2244 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2245 | SCM_I_BIG_MPZ (q), 1); | |
2246 | mpz_add (SCM_I_BIG_MPZ (r), | |
2247 | SCM_I_BIG_MPZ (r), | |
2248 | SCM_I_BIG_MPZ (y)); | |
2249 | } | |
2250 | } | |
2251 | else | |
2252 | { | |
2253 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2254 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2255 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2256 | { | |
2257 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2258 | SCM_I_BIG_MPZ (q), 1); | |
2259 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2260 | SCM_I_BIG_MPZ (r), | |
2261 | SCM_I_BIG_MPZ (y)); | |
2262 | } | |
2263 | } | |
2264 | scm_remember_upto_here_2 (x, y); | |
2265 | return scm_values (scm_list_2 (scm_i_normbig (q), | |
2266 | scm_i_normbig (r))); | |
2267 | } | |
2268 | ||
2269 | /* Compute exact centered quotient and remainder the slow way. | |
2270 | We use this only if both arguments are exact, | |
2271 | and at least one of them is a fraction */ | |
2272 | static SCM | |
ac6ce16b | 2273 | scm_i_slow_exact_centered_divide (SCM x, SCM y) |
ff62c168 MW |
2274 | { |
2275 | SCM q, r; | |
2276 | ||
2277 | if (!(SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x))) | |
ac6ce16b MW |
2278 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG1, |
2279 | s_scm_centered_divide); | |
ff62c168 | 2280 | else if (!(SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y))) |
ac6ce16b MW |
2281 | SCM_WTA_DISPATCH_2 (g_scm_centered_divide, x, y, SCM_ARG2, |
2282 | s_scm_centered_divide); | |
ff62c168 MW |
2283 | else if (scm_is_true (scm_positive_p (y))) |
2284 | q = scm_floor (scm_sum (scm_divide (x, y), | |
2285 | exactly_one_half)); | |
2286 | else if (scm_is_true (scm_negative_p (y))) | |
2287 | q = scm_ceiling (scm_difference (scm_divide (x, y), | |
2288 | exactly_one_half)); | |
2289 | else | |
ac6ce16b | 2290 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2291 | r = scm_difference (x, scm_product (q, y)); |
2292 | return scm_values (scm_list_2 (q, r)); | |
2293 | } | |
2294 | ||
2295 | ||
78d3deb1 AW |
2296 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
2297 | (SCM x, SCM y, SCM rest), | |
2298 | "Return the greatest common divisor of all parameter values.\n" | |
2299 | "If called without arguments, 0 is returned.") | |
2300 | #define FUNC_NAME s_scm_i_gcd | |
2301 | { | |
2302 | while (!scm_is_null (rest)) | |
2303 | { x = scm_gcd (x, y); | |
2304 | y = scm_car (rest); | |
2305 | rest = scm_cdr (rest); | |
2306 | } | |
2307 | return scm_gcd (x, y); | |
2308 | } | |
2309 | #undef FUNC_NAME | |
2310 | ||
2311 | #define s_gcd s_scm_i_gcd | |
2312 | #define g_gcd g_scm_i_gcd | |
2313 | ||
0f2d19dd | 2314 | SCM |
6e8d25a6 | 2315 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 2316 | { |
ca46fb90 | 2317 | if (SCM_UNBNDP (y)) |
1dd79792 | 2318 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 2319 | |
e11e83f3 | 2320 | if (SCM_I_INUMP (x)) |
ca46fb90 | 2321 | { |
e11e83f3 | 2322 | if (SCM_I_INUMP (y)) |
ca46fb90 | 2323 | { |
e25f3727 AW |
2324 | scm_t_inum xx = SCM_I_INUM (x); |
2325 | scm_t_inum yy = SCM_I_INUM (y); | |
2326 | scm_t_inum u = xx < 0 ? -xx : xx; | |
2327 | scm_t_inum v = yy < 0 ? -yy : yy; | |
2328 | scm_t_inum result; | |
0aacf84e MD |
2329 | if (xx == 0) |
2330 | result = v; | |
2331 | else if (yy == 0) | |
2332 | result = u; | |
2333 | else | |
2334 | { | |
e25f3727 AW |
2335 | scm_t_inum k = 1; |
2336 | scm_t_inum t; | |
0aacf84e MD |
2337 | /* Determine a common factor 2^k */ |
2338 | while (!(1 & (u | v))) | |
2339 | { | |
2340 | k <<= 1; | |
2341 | u >>= 1; | |
2342 | v >>= 1; | |
2343 | } | |
2344 | /* Now, any factor 2^n can be eliminated */ | |
2345 | if (u & 1) | |
2346 | t = -v; | |
2347 | else | |
2348 | { | |
2349 | t = u; | |
2350 | b3: | |
2351 | t = SCM_SRS (t, 1); | |
2352 | } | |
2353 | if (!(1 & t)) | |
2354 | goto b3; | |
2355 | if (t > 0) | |
2356 | u = t; | |
2357 | else | |
2358 | v = -t; | |
2359 | t = u - v; | |
2360 | if (t != 0) | |
2361 | goto b3; | |
2362 | result = u * k; | |
2363 | } | |
2364 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 2365 | ? SCM_I_MAKINUM (result) |
e25f3727 | 2366 | : scm_i_inum2big (result)); |
ca46fb90 RB |
2367 | } |
2368 | else if (SCM_BIGP (y)) | |
2369 | { | |
0bff4dce KR |
2370 | SCM_SWAP (x, y); |
2371 | goto big_inum; | |
ca46fb90 RB |
2372 | } |
2373 | else | |
2374 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 2375 | } |
ca46fb90 RB |
2376 | else if (SCM_BIGP (x)) |
2377 | { | |
e11e83f3 | 2378 | if (SCM_I_INUMP (y)) |
ca46fb90 | 2379 | { |
e25f3727 AW |
2380 | scm_t_bits result; |
2381 | scm_t_inum yy; | |
0bff4dce | 2382 | big_inum: |
e11e83f3 | 2383 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
2384 | if (yy == 0) |
2385 | return scm_abs (x); | |
0aacf84e MD |
2386 | if (yy < 0) |
2387 | yy = -yy; | |
ca46fb90 RB |
2388 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
2389 | scm_remember_upto_here_1 (x); | |
0aacf84e | 2390 | return (SCM_POSFIXABLE (result) |
d956fa6f | 2391 | ? SCM_I_MAKINUM (result) |
e25f3727 | 2392 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
2393 | } |
2394 | else if (SCM_BIGP (y)) | |
2395 | { | |
2396 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
2397 | mpz_gcd (SCM_I_BIG_MPZ (result), |
2398 | SCM_I_BIG_MPZ (x), | |
2399 | SCM_I_BIG_MPZ (y)); | |
2400 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
2401 | return scm_i_normbig (result); |
2402 | } | |
2403 | else | |
2404 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 2405 | } |
ca46fb90 | 2406 | else |
09fb7599 | 2407 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
2408 | } |
2409 | ||
78d3deb1 AW |
2410 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
2411 | (SCM x, SCM y, SCM rest), | |
2412 | "Return the least common multiple of the arguments.\n" | |
2413 | "If called without arguments, 1 is returned.") | |
2414 | #define FUNC_NAME s_scm_i_lcm | |
2415 | { | |
2416 | while (!scm_is_null (rest)) | |
2417 | { x = scm_lcm (x, y); | |
2418 | y = scm_car (rest); | |
2419 | rest = scm_cdr (rest); | |
2420 | } | |
2421 | return scm_lcm (x, y); | |
2422 | } | |
2423 | #undef FUNC_NAME | |
2424 | ||
2425 | #define s_lcm s_scm_i_lcm | |
2426 | #define g_lcm g_scm_i_lcm | |
2427 | ||
0f2d19dd | 2428 | SCM |
6e8d25a6 | 2429 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 2430 | { |
ca46fb90 RB |
2431 | if (SCM_UNBNDP (n2)) |
2432 | { | |
2433 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
2434 | return SCM_I_MAKINUM (1L); |
2435 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 2436 | } |
09fb7599 | 2437 | |
e11e83f3 | 2438 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 2439 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 2440 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 2441 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 2442 | |
e11e83f3 | 2443 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 2444 | { |
e11e83f3 | 2445 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
2446 | { |
2447 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 2448 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
2449 | return d; |
2450 | else | |
2451 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
2452 | } | |
2453 | else | |
2454 | { | |
2455 | /* inum n1, big n2 */ | |
2456 | inumbig: | |
2457 | { | |
2458 | SCM result = scm_i_mkbig (); | |
e25f3727 | 2459 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
2460 | if (nn1 == 0) return SCM_INUM0; |
2461 | if (nn1 < 0) nn1 = - nn1; | |
2462 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
2463 | scm_remember_upto_here_1 (n2); | |
2464 | return result; | |
2465 | } | |
2466 | } | |
2467 | } | |
2468 | else | |
2469 | { | |
2470 | /* big n1 */ | |
e11e83f3 | 2471 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
2472 | { |
2473 | SCM_SWAP (n1, n2); | |
2474 | goto inumbig; | |
2475 | } | |
2476 | else | |
2477 | { | |
2478 | SCM result = scm_i_mkbig (); | |
2479 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
2480 | SCM_I_BIG_MPZ (n1), | |
2481 | SCM_I_BIG_MPZ (n2)); | |
2482 | scm_remember_upto_here_2(n1, n2); | |
2483 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
2484 | return result; | |
2485 | } | |
f872b822 | 2486 | } |
0f2d19dd JB |
2487 | } |
2488 | ||
8a525303 GB |
2489 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
2490 | ||
2491 | Logand: | |
2492 | X Y Result Method: | |
2493 | (len) | |
2494 | + + + x (map digit:logand X Y) | |
2495 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
2496 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
2497 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
2498 | ||
2499 | Logior: | |
2500 | X Y Result Method: | |
2501 | ||
2502 | + + + (map digit:logior X Y) | |
2503 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
2504 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
2505 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
2506 | ||
2507 | Logxor: | |
2508 | X Y Result Method: | |
2509 | ||
2510 | + + + (map digit:logxor X Y) | |
2511 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
2512 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
2513 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
2514 | ||
2515 | Logtest: | |
2516 | X Y Result | |
2517 | ||
2518 | + + (any digit:logand X Y) | |
2519 | + - (any digit:logand X (lognot (+ -1 Y))) | |
2520 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
2521 | - - #t | |
2522 | ||
2523 | */ | |
2524 | ||
78d3deb1 AW |
2525 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
2526 | (SCM x, SCM y, SCM rest), | |
2527 | "Return the bitwise AND of the integer arguments.\n\n" | |
2528 | "@lisp\n" | |
2529 | "(logand) @result{} -1\n" | |
2530 | "(logand 7) @result{} 7\n" | |
2531 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
2532 | "@end lisp") | |
2533 | #define FUNC_NAME s_scm_i_logand | |
2534 | { | |
2535 | while (!scm_is_null (rest)) | |
2536 | { x = scm_logand (x, y); | |
2537 | y = scm_car (rest); | |
2538 | rest = scm_cdr (rest); | |
2539 | } | |
2540 | return scm_logand (x, y); | |
2541 | } | |
2542 | #undef FUNC_NAME | |
2543 | ||
2544 | #define s_scm_logand s_scm_i_logand | |
2545 | ||
2546 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 2547 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 2548 | { |
e25f3727 | 2549 | scm_t_inum nn1; |
9a00c9fc | 2550 | |
0aacf84e MD |
2551 | if (SCM_UNBNDP (n2)) |
2552 | { | |
2553 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 2554 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
2555 | else if (!SCM_NUMBERP (n1)) |
2556 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
2557 | else if (SCM_NUMBERP (n1)) | |
2558 | return n1; | |
2559 | else | |
2560 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2561 | } |
09fb7599 | 2562 | |
e11e83f3 | 2563 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2564 | { |
e11e83f3 MV |
2565 | nn1 = SCM_I_INUM (n1); |
2566 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2567 | { |
e25f3727 | 2568 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 2569 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
2570 | } |
2571 | else if SCM_BIGP (n2) | |
2572 | { | |
2573 | intbig: | |
2574 | if (n1 == 0) | |
2575 | return SCM_INUM0; | |
2576 | { | |
2577 | SCM result_z = scm_i_mkbig (); | |
2578 | mpz_t nn1_z; | |
2579 | mpz_init_set_si (nn1_z, nn1); | |
2580 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2581 | scm_remember_upto_here_1 (n2); | |
2582 | mpz_clear (nn1_z); | |
2583 | return scm_i_normbig (result_z); | |
2584 | } | |
2585 | } | |
2586 | else | |
2587 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2588 | } | |
2589 | else if (SCM_BIGP (n1)) | |
2590 | { | |
e11e83f3 | 2591 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2592 | { |
2593 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2594 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2595 | goto intbig; |
2596 | } | |
2597 | else if (SCM_BIGP (n2)) | |
2598 | { | |
2599 | SCM result_z = scm_i_mkbig (); | |
2600 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
2601 | SCM_I_BIG_MPZ (n1), | |
2602 | SCM_I_BIG_MPZ (n2)); | |
2603 | scm_remember_upto_here_2 (n1, n2); | |
2604 | return scm_i_normbig (result_z); | |
2605 | } | |
2606 | else | |
2607 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2608 | } |
0aacf84e | 2609 | else |
09fb7599 | 2610 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2611 | } |
1bbd0b84 | 2612 | #undef FUNC_NAME |
0f2d19dd | 2613 | |
09fb7599 | 2614 | |
78d3deb1 AW |
2615 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
2616 | (SCM x, SCM y, SCM rest), | |
2617 | "Return the bitwise OR of the integer arguments.\n\n" | |
2618 | "@lisp\n" | |
2619 | "(logior) @result{} 0\n" | |
2620 | "(logior 7) @result{} 7\n" | |
2621 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
2622 | "@end lisp") | |
2623 | #define FUNC_NAME s_scm_i_logior | |
2624 | { | |
2625 | while (!scm_is_null (rest)) | |
2626 | { x = scm_logior (x, y); | |
2627 | y = scm_car (rest); | |
2628 | rest = scm_cdr (rest); | |
2629 | } | |
2630 | return scm_logior (x, y); | |
2631 | } | |
2632 | #undef FUNC_NAME | |
2633 | ||
2634 | #define s_scm_logior s_scm_i_logior | |
2635 | ||
2636 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 2637 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 2638 | { |
e25f3727 | 2639 | scm_t_inum nn1; |
9a00c9fc | 2640 | |
0aacf84e MD |
2641 | if (SCM_UNBNDP (n2)) |
2642 | { | |
2643 | if (SCM_UNBNDP (n1)) | |
2644 | return SCM_INUM0; | |
2645 | else if (SCM_NUMBERP (n1)) | |
2646 | return n1; | |
2647 | else | |
2648 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2649 | } |
09fb7599 | 2650 | |
e11e83f3 | 2651 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2652 | { |
e11e83f3 MV |
2653 | nn1 = SCM_I_INUM (n1); |
2654 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2655 | { |
e11e83f3 | 2656 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 2657 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
2658 | } |
2659 | else if (SCM_BIGP (n2)) | |
2660 | { | |
2661 | intbig: | |
2662 | if (nn1 == 0) | |
2663 | return n2; | |
2664 | { | |
2665 | SCM result_z = scm_i_mkbig (); | |
2666 | mpz_t nn1_z; | |
2667 | mpz_init_set_si (nn1_z, nn1); | |
2668 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2669 | scm_remember_upto_here_1 (n2); | |
2670 | mpz_clear (nn1_z); | |
9806de0d | 2671 | return scm_i_normbig (result_z); |
0aacf84e MD |
2672 | } |
2673 | } | |
2674 | else | |
2675 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2676 | } | |
2677 | else if (SCM_BIGP (n1)) | |
2678 | { | |
e11e83f3 | 2679 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2680 | { |
2681 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2682 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2683 | goto intbig; |
2684 | } | |
2685 | else if (SCM_BIGP (n2)) | |
2686 | { | |
2687 | SCM result_z = scm_i_mkbig (); | |
2688 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
2689 | SCM_I_BIG_MPZ (n1), | |
2690 | SCM_I_BIG_MPZ (n2)); | |
2691 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 2692 | return scm_i_normbig (result_z); |
0aacf84e MD |
2693 | } |
2694 | else | |
2695 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2696 | } |
0aacf84e | 2697 | else |
09fb7599 | 2698 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2699 | } |
1bbd0b84 | 2700 | #undef FUNC_NAME |
0f2d19dd | 2701 | |
09fb7599 | 2702 | |
78d3deb1 AW |
2703 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
2704 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
2705 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
2706 | "set in the result if it is set in an odd number of arguments.\n" | |
2707 | "@lisp\n" | |
2708 | "(logxor) @result{} 0\n" | |
2709 | "(logxor 7) @result{} 7\n" | |
2710 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
2711 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 2712 | "@end lisp") |
78d3deb1 AW |
2713 | #define FUNC_NAME s_scm_i_logxor |
2714 | { | |
2715 | while (!scm_is_null (rest)) | |
2716 | { x = scm_logxor (x, y); | |
2717 | y = scm_car (rest); | |
2718 | rest = scm_cdr (rest); | |
2719 | } | |
2720 | return scm_logxor (x, y); | |
2721 | } | |
2722 | #undef FUNC_NAME | |
2723 | ||
2724 | #define s_scm_logxor s_scm_i_logxor | |
2725 | ||
2726 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 2727 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 2728 | { |
e25f3727 | 2729 | scm_t_inum nn1; |
9a00c9fc | 2730 | |
0aacf84e MD |
2731 | if (SCM_UNBNDP (n2)) |
2732 | { | |
2733 | if (SCM_UNBNDP (n1)) | |
2734 | return SCM_INUM0; | |
2735 | else if (SCM_NUMBERP (n1)) | |
2736 | return n1; | |
2737 | else | |
2738 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2739 | } |
09fb7599 | 2740 | |
e11e83f3 | 2741 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2742 | { |
e11e83f3 MV |
2743 | nn1 = SCM_I_INUM (n1); |
2744 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2745 | { |
e25f3727 | 2746 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 2747 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
2748 | } |
2749 | else if (SCM_BIGP (n2)) | |
2750 | { | |
2751 | intbig: | |
2752 | { | |
2753 | SCM result_z = scm_i_mkbig (); | |
2754 | mpz_t nn1_z; | |
2755 | mpz_init_set_si (nn1_z, nn1); | |
2756 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2757 | scm_remember_upto_here_1 (n2); | |
2758 | mpz_clear (nn1_z); | |
2759 | return scm_i_normbig (result_z); | |
2760 | } | |
2761 | } | |
2762 | else | |
2763 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2764 | } | |
2765 | else if (SCM_BIGP (n1)) | |
2766 | { | |
e11e83f3 | 2767 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2768 | { |
2769 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2770 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2771 | goto intbig; |
2772 | } | |
2773 | else if (SCM_BIGP (n2)) | |
2774 | { | |
2775 | SCM result_z = scm_i_mkbig (); | |
2776 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
2777 | SCM_I_BIG_MPZ (n1), | |
2778 | SCM_I_BIG_MPZ (n2)); | |
2779 | scm_remember_upto_here_2 (n1, n2); | |
2780 | return scm_i_normbig (result_z); | |
2781 | } | |
2782 | else | |
2783 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2784 | } |
0aacf84e | 2785 | else |
09fb7599 | 2786 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2787 | } |
1bbd0b84 | 2788 | #undef FUNC_NAME |
0f2d19dd | 2789 | |
09fb7599 | 2790 | |
a1ec6916 | 2791 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 2792 | (SCM j, SCM k), |
ba6e7231 KR |
2793 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
2794 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
2795 | "without actually calculating the @code{logand}, just testing\n" | |
2796 | "for non-zero.\n" | |
2797 | "\n" | |
1e6808ea | 2798 | "@lisp\n" |
b380b885 MD |
2799 | "(logtest #b0100 #b1011) @result{} #f\n" |
2800 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 2801 | "@end lisp") |
1bbd0b84 | 2802 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 2803 | { |
e25f3727 | 2804 | scm_t_inum nj; |
9a00c9fc | 2805 | |
e11e83f3 | 2806 | if (SCM_I_INUMP (j)) |
0aacf84e | 2807 | { |
e11e83f3 MV |
2808 | nj = SCM_I_INUM (j); |
2809 | if (SCM_I_INUMP (k)) | |
0aacf84e | 2810 | { |
e25f3727 | 2811 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 2812 | return scm_from_bool (nj & nk); |
0aacf84e MD |
2813 | } |
2814 | else if (SCM_BIGP (k)) | |
2815 | { | |
2816 | intbig: | |
2817 | if (nj == 0) | |
2818 | return SCM_BOOL_F; | |
2819 | { | |
2820 | SCM result; | |
2821 | mpz_t nj_z; | |
2822 | mpz_init_set_si (nj_z, nj); | |
2823 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
2824 | scm_remember_upto_here_1 (k); | |
73e4de09 | 2825 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
2826 | mpz_clear (nj_z); |
2827 | return result; | |
2828 | } | |
2829 | } | |
2830 | else | |
2831 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
2832 | } | |
2833 | else if (SCM_BIGP (j)) | |
2834 | { | |
e11e83f3 | 2835 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
2836 | { |
2837 | SCM_SWAP (j, k); | |
e11e83f3 | 2838 | nj = SCM_I_INUM (j); |
0aacf84e MD |
2839 | goto intbig; |
2840 | } | |
2841 | else if (SCM_BIGP (k)) | |
2842 | { | |
2843 | SCM result; | |
2844 | mpz_t result_z; | |
2845 | mpz_init (result_z); | |
2846 | mpz_and (result_z, | |
2847 | SCM_I_BIG_MPZ (j), | |
2848 | SCM_I_BIG_MPZ (k)); | |
2849 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 2850 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
2851 | mpz_clear (result_z); |
2852 | return result; | |
2853 | } | |
2854 | else | |
2855 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
2856 | } | |
2857 | else | |
2858 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 2859 | } |
1bbd0b84 | 2860 | #undef FUNC_NAME |
0f2d19dd | 2861 | |
c1bfcf60 | 2862 | |
a1ec6916 | 2863 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 2864 | (SCM index, SCM j), |
ba6e7231 KR |
2865 | "Test whether bit number @var{index} in @var{j} is set.\n" |
2866 | "@var{index} starts from 0 for the least significant bit.\n" | |
2867 | "\n" | |
1e6808ea | 2868 | "@lisp\n" |
b380b885 MD |
2869 | "(logbit? 0 #b1101) @result{} #t\n" |
2870 | "(logbit? 1 #b1101) @result{} #f\n" | |
2871 | "(logbit? 2 #b1101) @result{} #t\n" | |
2872 | "(logbit? 3 #b1101) @result{} #t\n" | |
2873 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 2874 | "@end lisp") |
1bbd0b84 | 2875 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 2876 | { |
78166ad5 | 2877 | unsigned long int iindex; |
5efd3c7d | 2878 | iindex = scm_to_ulong (index); |
78166ad5 | 2879 | |
e11e83f3 | 2880 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
2881 | { |
2882 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 2883 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 2884 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 2885 | } |
0aacf84e MD |
2886 | else if (SCM_BIGP (j)) |
2887 | { | |
2888 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
2889 | scm_remember_upto_here_1 (j); | |
73e4de09 | 2890 | return scm_from_bool (val); |
0aacf84e MD |
2891 | } |
2892 | else | |
78166ad5 | 2893 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 2894 | } |
1bbd0b84 | 2895 | #undef FUNC_NAME |
0f2d19dd | 2896 | |
78166ad5 | 2897 | |
a1ec6916 | 2898 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 2899 | (SCM n), |
4d814788 | 2900 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
2901 | "argument.\n" |
2902 | "\n" | |
b380b885 MD |
2903 | "@lisp\n" |
2904 | "(number->string (lognot #b10000000) 2)\n" | |
2905 | " @result{} \"-10000001\"\n" | |
2906 | "(number->string (lognot #b0) 2)\n" | |
2907 | " @result{} \"-1\"\n" | |
1e6808ea | 2908 | "@end lisp") |
1bbd0b84 | 2909 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 2910 | { |
e11e83f3 | 2911 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
2912 | /* No overflow here, just need to toggle all the bits making up the inum. |
2913 | Enhancement: No need to strip the tag and add it back, could just xor | |
2914 | a block of 1 bits, if that worked with the various debug versions of | |
2915 | the SCM typedef. */ | |
e11e83f3 | 2916 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
2917 | |
2918 | } else if (SCM_BIGP (n)) { | |
2919 | SCM result = scm_i_mkbig (); | |
2920 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
2921 | scm_remember_upto_here_1 (n); | |
2922 | return result; | |
2923 | ||
2924 | } else { | |
2925 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
2926 | } | |
0f2d19dd | 2927 | } |
1bbd0b84 | 2928 | #undef FUNC_NAME |
0f2d19dd | 2929 | |
518b7508 KR |
2930 | /* returns 0 if IN is not an integer. OUT must already be |
2931 | initialized. */ | |
2932 | static int | |
2933 | coerce_to_big (SCM in, mpz_t out) | |
2934 | { | |
2935 | if (SCM_BIGP (in)) | |
2936 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
2937 | else if (SCM_I_INUMP (in)) |
2938 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
2939 | else |
2940 | return 0; | |
2941 | ||
2942 | return 1; | |
2943 | } | |
2944 | ||
d885e204 | 2945 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
2946 | (SCM n, SCM k, SCM m), |
2947 | "Return @var{n} raised to the integer exponent\n" | |
2948 | "@var{k}, modulo @var{m}.\n" | |
2949 | "\n" | |
2950 | "@lisp\n" | |
2951 | "(modulo-expt 2 3 5)\n" | |
2952 | " @result{} 3\n" | |
2953 | "@end lisp") | |
d885e204 | 2954 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
2955 | { |
2956 | mpz_t n_tmp; | |
2957 | mpz_t k_tmp; | |
2958 | mpz_t m_tmp; | |
2959 | ||
2960 | /* There are two classes of error we might encounter -- | |
2961 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
2962 | and | |
2963 | 2) wrong-type errors, which of course we'll report by calling | |
2964 | SCM_WRONG_TYPE_ARG. | |
2965 | We don't report those errors immediately, however; instead we do | |
2966 | some cleanup first. These variables tell us which error (if | |
2967 | any) we should report after cleaning up. | |
2968 | */ | |
2969 | int report_overflow = 0; | |
2970 | ||
2971 | int position_of_wrong_type = 0; | |
2972 | SCM value_of_wrong_type = SCM_INUM0; | |
2973 | ||
2974 | SCM result = SCM_UNDEFINED; | |
2975 | ||
2976 | mpz_init (n_tmp); | |
2977 | mpz_init (k_tmp); | |
2978 | mpz_init (m_tmp); | |
2979 | ||
bc36d050 | 2980 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
2981 | { |
2982 | report_overflow = 1; | |
2983 | goto cleanup; | |
2984 | } | |
2985 | ||
2986 | if (!coerce_to_big (n, n_tmp)) | |
2987 | { | |
2988 | value_of_wrong_type = n; | |
2989 | position_of_wrong_type = 1; | |
2990 | goto cleanup; | |
2991 | } | |
2992 | ||
2993 | if (!coerce_to_big (k, k_tmp)) | |
2994 | { | |
2995 | value_of_wrong_type = k; | |
2996 | position_of_wrong_type = 2; | |
2997 | goto cleanup; | |
2998 | } | |
2999 | ||
3000 | if (!coerce_to_big (m, m_tmp)) | |
3001 | { | |
3002 | value_of_wrong_type = m; | |
3003 | position_of_wrong_type = 3; | |
3004 | goto cleanup; | |
3005 | } | |
3006 | ||
3007 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
3008 | will get a divide-by-zero exception when an inverse 1/n mod m | |
3009 | doesn't exist (or is not unique). Since exceptions are hard to | |
3010 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
3011 | a simple failure code, which is easy to handle. */ | |
3012 | ||
3013 | if (-1 == mpz_sgn (k_tmp)) | |
3014 | { | |
3015 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
3016 | { | |
3017 | report_overflow = 1; | |
3018 | goto cleanup; | |
3019 | } | |
3020 | mpz_neg (k_tmp, k_tmp); | |
3021 | } | |
3022 | ||
3023 | result = scm_i_mkbig (); | |
3024 | mpz_powm (SCM_I_BIG_MPZ (result), | |
3025 | n_tmp, | |
3026 | k_tmp, | |
3027 | m_tmp); | |
b7b8c575 KR |
3028 | |
3029 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
3030 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
3031 | ||
518b7508 KR |
3032 | cleanup: |
3033 | mpz_clear (m_tmp); | |
3034 | mpz_clear (k_tmp); | |
3035 | mpz_clear (n_tmp); | |
3036 | ||
3037 | if (report_overflow) | |
3038 | scm_num_overflow (FUNC_NAME); | |
3039 | ||
3040 | if (position_of_wrong_type) | |
3041 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
3042 | value_of_wrong_type); | |
3043 | ||
3044 | return scm_i_normbig (result); | |
3045 | } | |
3046 | #undef FUNC_NAME | |
3047 | ||
a1ec6916 | 3048 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 3049 | (SCM n, SCM k), |
ba6e7231 KR |
3050 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
3051 | "exact integer, @var{n} can be any number.\n" | |
3052 | "\n" | |
2519490c MW |
3053 | "Negative @var{k} is supported, and results in\n" |
3054 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
3055 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 3056 | "includes @math{0^0} is 1.\n" |
1e6808ea | 3057 | "\n" |
b380b885 | 3058 | "@lisp\n" |
ba6e7231 KR |
3059 | "(integer-expt 2 5) @result{} 32\n" |
3060 | "(integer-expt -3 3) @result{} -27\n" | |
3061 | "(integer-expt 5 -3) @result{} 1/125\n" | |
3062 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 3063 | "@end lisp") |
1bbd0b84 | 3064 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 3065 | { |
e25f3727 | 3066 | scm_t_inum i2 = 0; |
1c35cb19 RB |
3067 | SCM z_i2 = SCM_BOOL_F; |
3068 | int i2_is_big = 0; | |
d956fa6f | 3069 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 3070 | |
bfe1f03a MW |
3071 | /* Specifically refrain from checking the type of the first argument. |
3072 | This allows us to exponentiate any object that can be multiplied. | |
3073 | If we must raise to a negative power, we must also be able to | |
3074 | take its reciprocal. */ | |
3075 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 3076 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 3077 | |
bfe1f03a MW |
3078 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
3079 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
3080 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
3081 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
3082 | /* The next check is necessary only because R6RS specifies different | |
3083 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
3084 | we simply skip this case and move on. */ | |
3085 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
3086 | { | |
3087 | /* k cannot be 0 at this point, because we | |
3088 | have already checked for that case above */ | |
3089 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
3090 | return n; |
3091 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
3092 | return scm_nan (); | |
3093 | } | |
ca46fb90 | 3094 | |
e11e83f3 MV |
3095 | if (SCM_I_INUMP (k)) |
3096 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
3097 | else if (SCM_BIGP (k)) |
3098 | { | |
3099 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
3100 | scm_remember_upto_here_1 (k); |
3101 | i2_is_big = 1; | |
3102 | } | |
2830fd91 | 3103 | else |
ca46fb90 RB |
3104 | SCM_WRONG_TYPE_ARG (2, k); |
3105 | ||
3106 | if (i2_is_big) | |
f872b822 | 3107 | { |
ca46fb90 RB |
3108 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
3109 | { | |
3110 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
3111 | n = scm_divide (n, SCM_UNDEFINED); | |
3112 | } | |
3113 | while (1) | |
3114 | { | |
3115 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
3116 | { | |
ca46fb90 RB |
3117 | return acc; |
3118 | } | |
3119 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
3120 | { | |
ca46fb90 RB |
3121 | return scm_product (acc, n); |
3122 | } | |
3123 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
3124 | acc = scm_product (acc, n); | |
3125 | n = scm_product (n, n); | |
3126 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
3127 | } | |
f872b822 | 3128 | } |
ca46fb90 | 3129 | else |
f872b822 | 3130 | { |
ca46fb90 RB |
3131 | if (i2 < 0) |
3132 | { | |
3133 | i2 = -i2; | |
3134 | n = scm_divide (n, SCM_UNDEFINED); | |
3135 | } | |
3136 | while (1) | |
3137 | { | |
3138 | if (0 == i2) | |
3139 | return acc; | |
3140 | if (1 == i2) | |
3141 | return scm_product (acc, n); | |
3142 | if (i2 & 1) | |
3143 | acc = scm_product (acc, n); | |
3144 | n = scm_product (n, n); | |
3145 | i2 >>= 1; | |
3146 | } | |
f872b822 | 3147 | } |
0f2d19dd | 3148 | } |
1bbd0b84 | 3149 | #undef FUNC_NAME |
0f2d19dd | 3150 | |
a1ec6916 | 3151 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 3152 | (SCM n, SCM cnt), |
32f19569 KR |
3153 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
3154 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 3155 | "\n" |
e7644cb2 | 3156 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
3157 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
3158 | "infinity. (Note that this is not the same rounding as\n" | |
3159 | "@code{quotient} does.)\n" | |
3160 | "\n" | |
3161 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
3162 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
3163 | "shift dropping bits.\n" | |
1e6808ea | 3164 | "\n" |
b380b885 | 3165 | "@lisp\n" |
1e6808ea MG |
3166 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
3167 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
3168 | "\n" |
3169 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
3170 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 3171 | "@end lisp") |
1bbd0b84 | 3172 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 3173 | { |
3ab9f56e | 3174 | long bits_to_shift; |
5efd3c7d | 3175 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 3176 | |
788aca27 KR |
3177 | if (SCM_I_INUMP (n)) |
3178 | { | |
e25f3727 | 3179 | scm_t_inum nn = SCM_I_INUM (n); |
788aca27 KR |
3180 | |
3181 | if (bits_to_shift > 0) | |
3182 | { | |
3183 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
3184 | overflow a non-zero fixnum. For smaller shifts we check the | |
3185 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
3186 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
3187 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
3188 | bits_to_shift)". */ | |
3189 | ||
3190 | if (nn == 0) | |
3191 | return n; | |
3192 | ||
3193 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 3194 | && ((scm_t_bits) |
788aca27 KR |
3195 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) |
3196 | <= 1)) | |
3197 | { | |
3198 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
3199 | } | |
3200 | else | |
3201 | { | |
e25f3727 | 3202 | SCM result = scm_i_inum2big (nn); |
788aca27 KR |
3203 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
3204 | bits_to_shift); | |
3205 | return result; | |
3206 | } | |
3207 | } | |
3208 | else | |
3209 | { | |
3210 | bits_to_shift = -bits_to_shift; | |
3211 | if (bits_to_shift >= SCM_LONG_BIT) | |
cff5fa33 | 3212 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1)); |
788aca27 KR |
3213 | else |
3214 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
3215 | } | |
3216 | ||
3217 | } | |
3218 | else if (SCM_BIGP (n)) | |
ca46fb90 | 3219 | { |
788aca27 KR |
3220 | SCM result; |
3221 | ||
3222 | if (bits_to_shift == 0) | |
3223 | return n; | |
3224 | ||
3225 | result = scm_i_mkbig (); | |
3226 | if (bits_to_shift >= 0) | |
3227 | { | |
3228 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
3229 | bits_to_shift); | |
3230 | return result; | |
3231 | } | |
ca46fb90 | 3232 | else |
788aca27 KR |
3233 | { |
3234 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
3235 | we have to allocate a bignum even if the result is going to be a | |
3236 | fixnum. */ | |
3237 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
3238 | -bits_to_shift); | |
3239 | return scm_i_normbig (result); | |
3240 | } | |
3241 | ||
ca46fb90 RB |
3242 | } |
3243 | else | |
788aca27 KR |
3244 | { |
3245 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
3246 | } | |
0f2d19dd | 3247 | } |
1bbd0b84 | 3248 | #undef FUNC_NAME |
0f2d19dd | 3249 | |
3c9f20f8 | 3250 | |
a1ec6916 | 3251 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 3252 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
3253 | "Return the integer composed of the @var{start} (inclusive)\n" |
3254 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
3255 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
3256 | "\n" | |
b380b885 MD |
3257 | "@lisp\n" |
3258 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
3259 | " @result{} \"1010\"\n" | |
3260 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
3261 | " @result{} \"10110\"\n" | |
3262 | "@end lisp") | |
1bbd0b84 | 3263 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 3264 | { |
7f848242 | 3265 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
3266 | istart = scm_to_ulong (start); |
3267 | iend = scm_to_ulong (end); | |
c1bfcf60 | 3268 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 3269 | |
7f848242 KR |
3270 | /* how many bits to keep */ |
3271 | bits = iend - istart; | |
3272 | ||
e11e83f3 | 3273 | if (SCM_I_INUMP (n)) |
0aacf84e | 3274 | { |
e25f3727 | 3275 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
3276 | |
3277 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 3278 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 3279 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 3280 | |
0aacf84e MD |
3281 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
3282 | { | |
3283 | /* Since we emulate two's complement encoded numbers, this | |
3284 | * special case requires us to produce a result that has | |
7f848242 | 3285 | * more bits than can be stored in a fixnum. |
0aacf84e | 3286 | */ |
e25f3727 | 3287 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
3288 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
3289 | bits); | |
3290 | return result; | |
0aacf84e | 3291 | } |
ac0c002c | 3292 | |
7f848242 | 3293 | /* mask down to requisite bits */ |
857ae6af | 3294 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 3295 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
3296 | } |
3297 | else if (SCM_BIGP (n)) | |
ac0c002c | 3298 | { |
7f848242 KR |
3299 | SCM result; |
3300 | if (bits == 1) | |
3301 | { | |
d956fa6f | 3302 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
3303 | } |
3304 | else | |
3305 | { | |
3306 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
3307 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
3308 | such bits into a ulong. */ | |
3309 | result = scm_i_mkbig (); | |
3310 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
3311 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
3312 | result = scm_i_normbig (result); | |
3313 | } | |
3314 | scm_remember_upto_here_1 (n); | |
3315 | return result; | |
ac0c002c | 3316 | } |
0aacf84e | 3317 | else |
78166ad5 | 3318 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 3319 | } |
1bbd0b84 | 3320 | #undef FUNC_NAME |
0f2d19dd | 3321 | |
7f848242 | 3322 | |
e4755e5c JB |
3323 | static const char scm_logtab[] = { |
3324 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
3325 | }; | |
1cc91f1b | 3326 | |
a1ec6916 | 3327 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 3328 | (SCM n), |
1e6808ea MG |
3329 | "Return the number of bits in integer @var{n}. If integer is\n" |
3330 | "positive, the 1-bits in its binary representation are counted.\n" | |
3331 | "If negative, the 0-bits in its two's-complement binary\n" | |
3332 | "representation are counted. If 0, 0 is returned.\n" | |
3333 | "\n" | |
b380b885 MD |
3334 | "@lisp\n" |
3335 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
3336 | " @result{} 4\n" |
3337 | "(logcount 0)\n" | |
3338 | " @result{} 0\n" | |
3339 | "(logcount -2)\n" | |
3340 | " @result{} 1\n" | |
3341 | "@end lisp") | |
3342 | #define FUNC_NAME s_scm_logcount | |
3343 | { | |
e11e83f3 | 3344 | if (SCM_I_INUMP (n)) |
f872b822 | 3345 | { |
e25f3727 AW |
3346 | unsigned long c = 0; |
3347 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
3348 | if (nn < 0) |
3349 | nn = -1 - nn; | |
3350 | while (nn) | |
3351 | { | |
3352 | c += scm_logtab[15 & nn]; | |
3353 | nn >>= 4; | |
3354 | } | |
d956fa6f | 3355 | return SCM_I_MAKINUM (c); |
f872b822 | 3356 | } |
ca46fb90 | 3357 | else if (SCM_BIGP (n)) |
f872b822 | 3358 | { |
ca46fb90 | 3359 | unsigned long count; |
713a4259 KR |
3360 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
3361 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 3362 | else |
713a4259 KR |
3363 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
3364 | scm_remember_upto_here_1 (n); | |
d956fa6f | 3365 | return SCM_I_MAKINUM (count); |
f872b822 | 3366 | } |
ca46fb90 RB |
3367 | else |
3368 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 3369 | } |
ca46fb90 | 3370 | #undef FUNC_NAME |
0f2d19dd JB |
3371 | |
3372 | ||
ca46fb90 RB |
3373 | static const char scm_ilentab[] = { |
3374 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
3375 | }; | |
3376 | ||
0f2d19dd | 3377 | |
ca46fb90 RB |
3378 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
3379 | (SCM n), | |
3380 | "Return the number of bits necessary to represent @var{n}.\n" | |
3381 | "\n" | |
3382 | "@lisp\n" | |
3383 | "(integer-length #b10101010)\n" | |
3384 | " @result{} 8\n" | |
3385 | "(integer-length 0)\n" | |
3386 | " @result{} 0\n" | |
3387 | "(integer-length #b1111)\n" | |
3388 | " @result{} 4\n" | |
3389 | "@end lisp") | |
3390 | #define FUNC_NAME s_scm_integer_length | |
3391 | { | |
e11e83f3 | 3392 | if (SCM_I_INUMP (n)) |
0aacf84e | 3393 | { |
e25f3727 | 3394 | unsigned long c = 0; |
0aacf84e | 3395 | unsigned int l = 4; |
e25f3727 | 3396 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
3397 | if (nn < 0) |
3398 | nn = -1 - nn; | |
3399 | while (nn) | |
3400 | { | |
3401 | c += 4; | |
3402 | l = scm_ilentab [15 & nn]; | |
3403 | nn >>= 4; | |
3404 | } | |
d956fa6f | 3405 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
3406 | } |
3407 | else if (SCM_BIGP (n)) | |
3408 | { | |
3409 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
3410 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
3411 | 1 too big, so check for that and adjust. */ | |
3412 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
3413 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
3414 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
3415 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
3416 | size--; | |
3417 | scm_remember_upto_here_1 (n); | |
d956fa6f | 3418 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
3419 | } |
3420 | else | |
ca46fb90 | 3421 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
3422 | } |
3423 | #undef FUNC_NAME | |
0f2d19dd JB |
3424 | |
3425 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
3426 | #define SCM_MAX_DBL_PREC 60 |
3427 | #define SCM_MAX_DBL_RADIX 36 | |
3428 | ||
3429 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
3430 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
3431 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
3432 | ||
3433 | static | |
3434 | void init_dblprec(int *prec, int radix) { | |
3435 | /* determine floating point precision by adding successively | |
3436 | smaller increments to 1.0 until it is considered == 1.0 */ | |
3437 | double f = ((double)1.0)/radix; | |
3438 | double fsum = 1.0 + f; | |
3439 | ||
3440 | *prec = 0; | |
3441 | while (fsum != 1.0) | |
3442 | { | |
3443 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
3444 | fsum = 1.0; | |
3445 | else | |
3446 | { | |
3447 | f /= radix; | |
3448 | fsum = f + 1.0; | |
3449 | } | |
3450 | } | |
3451 | (*prec) -= 1; | |
3452 | } | |
3453 | ||
3454 | static | |
3455 | void init_fx_radix(double *fx_list, int radix) | |
3456 | { | |
3457 | /* initialize a per-radix list of tolerances. When added | |
3458 | to a number < 1.0, we can determine if we should raund | |
3459 | up and quit converting a number to a string. */ | |
3460 | int i; | |
3461 | fx_list[0] = 0.0; | |
3462 | fx_list[1] = 0.5; | |
3463 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
3464 | fx_list[i] = (fx_list[i-1] / radix); | |
3465 | } | |
3466 | ||
3467 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 3468 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 3469 | |
1be6b49c | 3470 | static size_t |
0b799eea | 3471 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 3472 | { |
0b799eea MV |
3473 | int efmt, dpt, d, i, wp; |
3474 | double *fx; | |
3475 | #ifdef DBL_MIN_10_EXP | |
3476 | double f_cpy; | |
3477 | int exp_cpy; | |
3478 | #endif /* DBL_MIN_10_EXP */ | |
3479 | size_t ch = 0; | |
3480 | int exp = 0; | |
3481 | ||
3482 | if(radix < 2 || | |
3483 | radix > SCM_MAX_DBL_RADIX) | |
3484 | { | |
3485 | /* revert to existing behavior */ | |
3486 | radix = 10; | |
3487 | } | |
3488 | ||
3489 | wp = scm_dblprec[radix-2]; | |
3490 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 3491 | |
f872b822 | 3492 | if (f == 0.0) |
abb7e44d MV |
3493 | { |
3494 | #ifdef HAVE_COPYSIGN | |
3495 | double sgn = copysign (1.0, f); | |
3496 | ||
3497 | if (sgn < 0.0) | |
3498 | a[ch++] = '-'; | |
3499 | #endif | |
abb7e44d MV |
3500 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
3501 | } | |
7351e207 | 3502 | |
2e65b52f | 3503 | if (isinf (f)) |
7351e207 MV |
3504 | { |
3505 | if (f < 0) | |
3506 | strcpy (a, "-inf.0"); | |
3507 | else | |
3508 | strcpy (a, "+inf.0"); | |
3509 | return ch+6; | |
3510 | } | |
2e65b52f | 3511 | else if (isnan (f)) |
7351e207 MV |
3512 | { |
3513 | strcpy (a, "+nan.0"); | |
3514 | return ch+6; | |
3515 | } | |
3516 | ||
f872b822 MD |
3517 | if (f < 0.0) |
3518 | { | |
3519 | f = -f; | |
3520 | a[ch++] = '-'; | |
3521 | } | |
7351e207 | 3522 | |
f872b822 MD |
3523 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
3524 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
3525 | /* just do the checking...if it passes, we do the conversion for our |
3526 | radix again below */ | |
3527 | f_cpy = f; | |
3528 | exp_cpy = exp; | |
3529 | ||
3530 | while (f_cpy < 1.0) | |
f872b822 | 3531 | { |
0b799eea MV |
3532 | f_cpy *= 10.0; |
3533 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
3534 | { |
3535 | a[ch++] = '#'; | |
3536 | a[ch++] = '.'; | |
3537 | a[ch++] = '#'; | |
3538 | return ch; | |
3539 | } | |
f872b822 | 3540 | } |
0b799eea | 3541 | while (f_cpy > 10.0) |
f872b822 | 3542 | { |
0b799eea MV |
3543 | f_cpy *= 0.10; |
3544 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
3545 | { |
3546 | a[ch++] = '#'; | |
3547 | a[ch++] = '.'; | |
3548 | a[ch++] = '#'; | |
3549 | return ch; | |
3550 | } | |
f872b822 | 3551 | } |
0b799eea MV |
3552 | #endif |
3553 | ||
f872b822 MD |
3554 | while (f < 1.0) |
3555 | { | |
0b799eea | 3556 | f *= radix; |
f872b822 MD |
3557 | exp--; |
3558 | } | |
0b799eea | 3559 | while (f > radix) |
f872b822 | 3560 | { |
0b799eea | 3561 | f /= radix; |
f872b822 MD |
3562 | exp++; |
3563 | } | |
0b799eea MV |
3564 | |
3565 | if (f + fx[wp] >= radix) | |
f872b822 MD |
3566 | { |
3567 | f = 1.0; | |
3568 | exp++; | |
3569 | } | |
0f2d19dd | 3570 | zero: |
0b799eea MV |
3571 | #ifdef ENGNOT |
3572 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 3573 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
3574 | exp -= dpt++; |
3575 | efmt = 1; | |
f872b822 MD |
3576 | #else |
3577 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 3578 | if (!efmt) |
cda139a7 MD |
3579 | { |
3580 | if (exp < 0) | |
3581 | { | |
3582 | a[ch++] = '0'; | |
3583 | a[ch++] = '.'; | |
3584 | dpt = exp; | |
f872b822 MD |
3585 | while (++dpt) |
3586 | a[ch++] = '0'; | |
cda139a7 MD |
3587 | } |
3588 | else | |
f872b822 | 3589 | dpt = exp + 1; |
cda139a7 | 3590 | } |
0f2d19dd JB |
3591 | else |
3592 | dpt = 1; | |
f872b822 MD |
3593 | #endif |
3594 | ||
3595 | do | |
3596 | { | |
3597 | d = f; | |
3598 | f -= d; | |
0b799eea | 3599 | a[ch++] = number_chars[d]; |
f872b822 MD |
3600 | if (f < fx[wp]) |
3601 | break; | |
3602 | if (f + fx[wp] >= 1.0) | |
3603 | { | |
0b799eea | 3604 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
3605 | break; |
3606 | } | |
0b799eea | 3607 | f *= radix; |
f872b822 MD |
3608 | if (!(--dpt)) |
3609 | a[ch++] = '.'; | |
0f2d19dd | 3610 | } |
f872b822 | 3611 | while (wp--); |
0f2d19dd JB |
3612 | |
3613 | if (dpt > 0) | |
cda139a7 | 3614 | { |
f872b822 | 3615 | #ifndef ENGNOT |
cda139a7 MD |
3616 | if ((dpt > 4) && (exp > 6)) |
3617 | { | |
f872b822 | 3618 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 3619 | for (i = ch++; i > d; i--) |
f872b822 | 3620 | a[i] = a[i - 1]; |
cda139a7 MD |
3621 | a[d] = '.'; |
3622 | efmt = 1; | |
3623 | } | |
3624 | else | |
f872b822 | 3625 | #endif |
cda139a7 | 3626 | { |
f872b822 MD |
3627 | while (--dpt) |
3628 | a[ch++] = '0'; | |
cda139a7 MD |
3629 | a[ch++] = '.'; |
3630 | } | |
3631 | } | |
f872b822 MD |
3632 | if (a[ch - 1] == '.') |
3633 | a[ch++] = '0'; /* trailing zero */ | |
3634 | if (efmt && exp) | |
3635 | { | |
3636 | a[ch++] = 'e'; | |
3637 | if (exp < 0) | |
3638 | { | |
3639 | exp = -exp; | |
3640 | a[ch++] = '-'; | |
3641 | } | |
0b799eea MV |
3642 | for (i = radix; i <= exp; i *= radix); |
3643 | for (i /= radix; i; i /= radix) | |
f872b822 | 3644 | { |
0b799eea | 3645 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
3646 | exp %= i; |
3647 | } | |
0f2d19dd | 3648 | } |
0f2d19dd JB |
3649 | return ch; |
3650 | } | |
3651 | ||
7a1aba42 MV |
3652 | |
3653 | static size_t | |
3654 | icmplx2str (double real, double imag, char *str, int radix) | |
3655 | { | |
3656 | size_t i; | |
c7218482 | 3657 | double sgn; |
7a1aba42 MV |
3658 | |
3659 | i = idbl2str (real, str, radix); | |
c7218482 MW |
3660 | #ifdef HAVE_COPYSIGN |
3661 | sgn = copysign (1.0, imag); | |
3662 | #else | |
3663 | sgn = imag; | |
3664 | #endif | |
3665 | /* Don't output a '+' for negative numbers or for Inf and | |
3666 | NaN. They will provide their own sign. */ | |
3667 | if (sgn >= 0 && DOUBLE_IS_FINITE (imag)) | |
3668 | str[i++] = '+'; | |
3669 | i += idbl2str (imag, &str[i], radix); | |
3670 | str[i++] = 'i'; | |
7a1aba42 MV |
3671 | return i; |
3672 | } | |
3673 | ||
1be6b49c | 3674 | static size_t |
0b799eea | 3675 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 3676 | { |
1be6b49c | 3677 | size_t i; |
3c9a524f | 3678 | if (SCM_REALP (flt)) |
0b799eea | 3679 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 3680 | else |
7a1aba42 MV |
3681 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
3682 | str, radix); | |
0f2d19dd JB |
3683 | return i; |
3684 | } | |
0f2d19dd | 3685 | |
2881e77b | 3686 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
3687 | characters in the result. |
3688 | rad is output base | |
3689 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 3690 | size_t |
2881e77b MV |
3691 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
3692 | { | |
3693 | if (num < 0) | |
3694 | { | |
3695 | *p++ = '-'; | |
3696 | return scm_iuint2str (-num, rad, p) + 1; | |
3697 | } | |
3698 | else | |
3699 | return scm_iuint2str (num, rad, p); | |
3700 | } | |
3701 | ||
3702 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
3703 | characters in the result. | |
3704 | rad is output base | |
3705 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
3706 | size_t | |
3707 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 3708 | { |
1be6b49c ML |
3709 | size_t j = 1; |
3710 | size_t i; | |
2881e77b | 3711 | scm_t_uintmax n = num; |
5c11cc9d | 3712 | |
a6f3af16 AW |
3713 | if (rad < 2 || rad > 36) |
3714 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
3715 | ||
f872b822 | 3716 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
3717 | j++; |
3718 | ||
3719 | i = j; | |
2881e77b | 3720 | n = num; |
f872b822 MD |
3721 | while (i--) |
3722 | { | |
5c11cc9d GH |
3723 | int d = n % rad; |
3724 | ||
f872b822 | 3725 | n /= rad; |
a6f3af16 | 3726 | p[i] = number_chars[d]; |
f872b822 | 3727 | } |
0f2d19dd JB |
3728 | return j; |
3729 | } | |
3730 | ||
a1ec6916 | 3731 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
3732 | (SCM n, SCM radix), |
3733 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
3734 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
3735 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 3736 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 3737 | { |
1bbd0b84 | 3738 | int base; |
98cb6e75 | 3739 | |
0aacf84e | 3740 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 3741 | base = 10; |
0aacf84e | 3742 | else |
5efd3c7d | 3743 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 3744 | |
e11e83f3 | 3745 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
3746 | { |
3747 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 3748 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 3749 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
3750 | } |
3751 | else if (SCM_BIGP (n)) | |
3752 | { | |
3753 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
3754 | scm_remember_upto_here_1 (n); | |
cc95e00a | 3755 | return scm_take_locale_string (str); |
0aacf84e | 3756 | } |
f92e85f7 MV |
3757 | else if (SCM_FRACTIONP (n)) |
3758 | { | |
f92e85f7 | 3759 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 3760 | scm_from_locale_string ("/"), |
f92e85f7 MV |
3761 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
3762 | } | |
0aacf84e MD |
3763 | else if (SCM_INEXACTP (n)) |
3764 | { | |
3765 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 3766 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
3767 | } |
3768 | else | |
bb628794 | 3769 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 3770 | } |
1bbd0b84 | 3771 | #undef FUNC_NAME |
0f2d19dd JB |
3772 | |
3773 | ||
ca46fb90 RB |
3774 | /* These print routines used to be stubbed here so that scm_repl.c |
3775 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 3776 | |
0f2d19dd | 3777 | int |
e81d98ec | 3778 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 3779 | { |
56e55ac7 | 3780 | char num_buf[FLOBUFLEN]; |
0b799eea | 3781 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
3782 | return !0; |
3783 | } | |
3784 | ||
b479fe9a MV |
3785 | void |
3786 | scm_i_print_double (double val, SCM port) | |
3787 | { | |
3788 | char num_buf[FLOBUFLEN]; | |
3789 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
3790 | } | |
3791 | ||
f3ae5d60 | 3792 | int |
e81d98ec | 3793 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 3794 | |
f3ae5d60 | 3795 | { |
56e55ac7 | 3796 | char num_buf[FLOBUFLEN]; |
0b799eea | 3797 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
3798 | return !0; |
3799 | } | |
1cc91f1b | 3800 | |
7a1aba42 MV |
3801 | void |
3802 | scm_i_print_complex (double real, double imag, SCM port) | |
3803 | { | |
3804 | char num_buf[FLOBUFLEN]; | |
3805 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
3806 | } | |
3807 | ||
f92e85f7 MV |
3808 | int |
3809 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
3810 | { | |
3811 | SCM str; | |
f92e85f7 | 3812 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 3813 | scm_display (str, port); |
f92e85f7 MV |
3814 | scm_remember_upto_here_1 (str); |
3815 | return !0; | |
3816 | } | |
3817 | ||
0f2d19dd | 3818 | int |
e81d98ec | 3819 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 3820 | { |
ca46fb90 RB |
3821 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
3822 | scm_remember_upto_here_1 (exp); | |
3823 | scm_lfwrite (str, (size_t) strlen (str), port); | |
3824 | free (str); | |
0f2d19dd JB |
3825 | return !0; |
3826 | } | |
3827 | /*** END nums->strs ***/ | |
3828 | ||
3c9a524f | 3829 | |
0f2d19dd | 3830 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 3831 | |
3c9a524f DH |
3832 | /* The following functions implement the conversion from strings to numbers. |
3833 | * The implementation somehow follows the grammar for numbers as it is given | |
3834 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
3835 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
3836 | * points should be noted about the implementation: | |
3837 | * * Each function keeps a local index variable 'idx' that points at the | |
3838 | * current position within the parsed string. The global index is only | |
3839 | * updated if the function could parse the corresponding syntactic unit | |
3840 | * successfully. | |
3841 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
3842 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
3843 | * global exactness information is only updated after each part has been | |
3844 | * successfully parsed. | |
3845 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
3846 | * Only if these fixnums would overflow, the result variables are updated | |
3847 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
3848 | * the temporary variables holding the fixnums are cleared, and the process | |
3849 | * starts over again. If for example fixnums were able to store five decimal | |
3850 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
3851 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
3852 | * only every five digits two bignum operations were performed. | |
3853 | */ | |
3854 | ||
3855 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
3856 | ||
3857 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
3858 | ||
a6f3af16 AW |
3859 | /* Caller is responsible for checking that the return value is in range |
3860 | for the given radix, which should be <= 36. */ | |
3861 | static unsigned int | |
3862 | char_decimal_value (scm_t_uint32 c) | |
3863 | { | |
3864 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
3865 | that's certainly above any valid decimal, so we take advantage of | |
3866 | that to elide some tests. */ | |
3867 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
3868 | ||
3869 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
3870 | hexadecimals. */ | |
3871 | if (d >= 10U) | |
3872 | { | |
3873 | c = uc_tolower (c); | |
3874 | if (c >= (scm_t_uint32) 'a') | |
3875 | d = c - (scm_t_uint32)'a' + 10U; | |
3876 | } | |
3877 | return d; | |
3878 | } | |
3c9a524f | 3879 | |
2a8fecee | 3880 | static SCM |
3f47e526 | 3881 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 3882 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 3883 | { |
3c9a524f DH |
3884 | unsigned int idx = *p_idx; |
3885 | unsigned int hash_seen = 0; | |
3886 | scm_t_bits shift = 1; | |
3887 | scm_t_bits add = 0; | |
3888 | unsigned int digit_value; | |
3889 | SCM result; | |
3890 | char c; | |
3f47e526 | 3891 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
3892 | |
3893 | if (idx == len) | |
3894 | return SCM_BOOL_F; | |
2a8fecee | 3895 | |
3f47e526 | 3896 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 3897 | digit_value = char_decimal_value (c); |
3c9a524f DH |
3898 | if (digit_value >= radix) |
3899 | return SCM_BOOL_F; | |
3900 | ||
3901 | idx++; | |
d956fa6f | 3902 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 3903 | while (idx != len) |
f872b822 | 3904 | { |
3f47e526 | 3905 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 3906 | if (c == '#') |
3c9a524f DH |
3907 | { |
3908 | hash_seen = 1; | |
3909 | digit_value = 0; | |
3910 | } | |
a6f3af16 AW |
3911 | else if (hash_seen) |
3912 | break; | |
3c9a524f | 3913 | else |
a6f3af16 AW |
3914 | { |
3915 | digit_value = char_decimal_value (c); | |
3916 | /* This check catches non-decimals in addition to out-of-range | |
3917 | decimals. */ | |
3918 | if (digit_value >= radix) | |
3919 | break; | |
3920 | } | |
3c9a524f DH |
3921 | |
3922 | idx++; | |
3923 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
3924 | { | |
d956fa6f | 3925 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 3926 | if (add > 0) |
d956fa6f | 3927 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
3928 | |
3929 | shift = radix; | |
3930 | add = digit_value; | |
3931 | } | |
3932 | else | |
3933 | { | |
3934 | shift = shift * radix; | |
3935 | add = add * radix + digit_value; | |
3936 | } | |
3937 | }; | |
3938 | ||
3939 | if (shift > 1) | |
d956fa6f | 3940 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 3941 | if (add > 0) |
d956fa6f | 3942 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
3943 | |
3944 | *p_idx = idx; | |
3945 | if (hash_seen) | |
3946 | *p_exactness = INEXACT; | |
3947 | ||
3948 | return result; | |
2a8fecee JB |
3949 | } |
3950 | ||
3951 | ||
3c9a524f DH |
3952 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
3953 | * covers the parts of the rules that start at a potential point. The value | |
3954 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
3955 | * in variable result. The content of *p_exactness indicates, whether a hash |
3956 | * has already been seen in the digits before the point. | |
3c9a524f | 3957 | */ |
1cc91f1b | 3958 | |
3f47e526 | 3959 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
3960 | |
3961 | static SCM | |
3f47e526 | 3962 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 3963 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 3964 | { |
3c9a524f DH |
3965 | unsigned int idx = *p_idx; |
3966 | enum t_exactness x = *p_exactness; | |
3f47e526 | 3967 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
3968 | |
3969 | if (idx == len) | |
79d34f68 | 3970 | return result; |
3c9a524f | 3971 | |
3f47e526 | 3972 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
3973 | { |
3974 | scm_t_bits shift = 1; | |
3975 | scm_t_bits add = 0; | |
3976 | unsigned int digit_value; | |
cff5fa33 | 3977 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
3978 | |
3979 | idx++; | |
3980 | while (idx != len) | |
3981 | { | |
3f47e526 MG |
3982 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
3983 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
3984 | { |
3985 | if (x == INEXACT) | |
3986 | return SCM_BOOL_F; | |
3987 | else | |
3988 | digit_value = DIGIT2UINT (c); | |
3989 | } | |
3990 | else if (c == '#') | |
3991 | { | |
3992 | x = INEXACT; | |
3993 | digit_value = 0; | |
3994 | } | |
3995 | else | |
3996 | break; | |
3997 | ||
3998 | idx++; | |
3999 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
4000 | { | |
d956fa6f MV |
4001 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
4002 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 4003 | if (add > 0) |
d956fa6f | 4004 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
4005 | |
4006 | shift = 10; | |
4007 | add = digit_value; | |
4008 | } | |
4009 | else | |
4010 | { | |
4011 | shift = shift * 10; | |
4012 | add = add * 10 + digit_value; | |
4013 | } | |
4014 | }; | |
4015 | ||
4016 | if (add > 0) | |
4017 | { | |
d956fa6f MV |
4018 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
4019 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
4020 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
4021 | } |
4022 | ||
d8592269 | 4023 | result = scm_divide (result, big_shift); |
79d34f68 | 4024 | |
3c9a524f DH |
4025 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
4026 | x = INEXACT; | |
f872b822 | 4027 | } |
3c9a524f | 4028 | |
3c9a524f | 4029 | if (idx != len) |
f872b822 | 4030 | { |
3c9a524f DH |
4031 | int sign = 1; |
4032 | unsigned int start; | |
3f47e526 | 4033 | scm_t_wchar c; |
3c9a524f DH |
4034 | int exponent; |
4035 | SCM e; | |
4036 | ||
4037 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
4038 | ||
3f47e526 | 4039 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 4040 | { |
3c9a524f DH |
4041 | case 'd': case 'D': |
4042 | case 'e': case 'E': | |
4043 | case 'f': case 'F': | |
4044 | case 'l': case 'L': | |
4045 | case 's': case 'S': | |
4046 | idx++; | |
ee0ddd21 AW |
4047 | if (idx == len) |
4048 | return SCM_BOOL_F; | |
4049 | ||
3c9a524f | 4050 | start = idx; |
3f47e526 | 4051 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4052 | if (c == '-') |
4053 | { | |
4054 | idx++; | |
ee0ddd21 AW |
4055 | if (idx == len) |
4056 | return SCM_BOOL_F; | |
4057 | ||
3c9a524f | 4058 | sign = -1; |
3f47e526 | 4059 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4060 | } |
4061 | else if (c == '+') | |
4062 | { | |
4063 | idx++; | |
ee0ddd21 AW |
4064 | if (idx == len) |
4065 | return SCM_BOOL_F; | |
4066 | ||
3c9a524f | 4067 | sign = 1; |
3f47e526 | 4068 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4069 | } |
4070 | else | |
4071 | sign = 1; | |
4072 | ||
3f47e526 | 4073 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
4074 | return SCM_BOOL_F; |
4075 | ||
4076 | idx++; | |
4077 | exponent = DIGIT2UINT (c); | |
4078 | while (idx != len) | |
f872b822 | 4079 | { |
3f47e526 MG |
4080 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
4081 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
4082 | { |
4083 | idx++; | |
4084 | if (exponent <= SCM_MAXEXP) | |
4085 | exponent = exponent * 10 + DIGIT2UINT (c); | |
4086 | } | |
4087 | else | |
4088 | break; | |
f872b822 | 4089 | } |
3c9a524f DH |
4090 | |
4091 | if (exponent > SCM_MAXEXP) | |
f872b822 | 4092 | { |
3c9a524f | 4093 | size_t exp_len = idx - start; |
3f47e526 | 4094 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
4095 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
4096 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 4097 | } |
3c9a524f | 4098 | |
d956fa6f | 4099 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
4100 | if (sign == 1) |
4101 | result = scm_product (result, e); | |
4102 | else | |
f92e85f7 | 4103 | result = scm_divide2real (result, e); |
3c9a524f DH |
4104 | |
4105 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
4106 | x = INEXACT; | |
4107 | ||
f872b822 | 4108 | break; |
3c9a524f | 4109 | |
f872b822 | 4110 | default: |
3c9a524f | 4111 | break; |
f872b822 | 4112 | } |
0f2d19dd | 4113 | } |
3c9a524f DH |
4114 | |
4115 | *p_idx = idx; | |
4116 | if (x == INEXACT) | |
4117 | *p_exactness = x; | |
4118 | ||
4119 | return result; | |
0f2d19dd | 4120 | } |
0f2d19dd | 4121 | |
3c9a524f DH |
4122 | |
4123 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
4124 | ||
4125 | static SCM | |
3f47e526 | 4126 | mem2ureal (SCM mem, unsigned int *p_idx, |
9d427b2c | 4127 | unsigned int radix, enum t_exactness forced_x) |
0f2d19dd | 4128 | { |
3c9a524f | 4129 | unsigned int idx = *p_idx; |
164d2481 | 4130 | SCM result; |
3f47e526 | 4131 | size_t len = scm_i_string_length (mem); |
3c9a524f | 4132 | |
40f89215 NJ |
4133 | /* Start off believing that the number will be exact. This changes |
4134 | to INEXACT if we see a decimal point or a hash. */ | |
9d427b2c | 4135 | enum t_exactness implicit_x = EXACT; |
40f89215 | 4136 | |
3c9a524f DH |
4137 | if (idx == len) |
4138 | return SCM_BOOL_F; | |
4139 | ||
3f47e526 | 4140 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
4141 | { |
4142 | *p_idx = idx+5; | |
4143 | return scm_inf (); | |
4144 | } | |
4145 | ||
3f47e526 | 4146 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 4147 | { |
d8592269 MV |
4148 | /* Cobble up the fractional part. We might want to set the |
4149 | NaN's mantissa from it. */ | |
7351e207 | 4150 | idx += 4; |
9d427b2c | 4151 | mem2uinteger (mem, &idx, 10, &implicit_x); |
7351e207 MV |
4152 | *p_idx = idx; |
4153 | return scm_nan (); | |
4154 | } | |
4155 | ||
3f47e526 | 4156 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
4157 | { |
4158 | if (radix != 10) | |
4159 | return SCM_BOOL_F; | |
4160 | else if (idx + 1 == len) | |
4161 | return SCM_BOOL_F; | |
3f47e526 | 4162 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
4163 | return SCM_BOOL_F; |
4164 | else | |
cff5fa33 | 4165 | result = mem2decimal_from_point (SCM_INUM0, mem, |
9d427b2c | 4166 | p_idx, &implicit_x); |
f872b822 | 4167 | } |
3c9a524f DH |
4168 | else |
4169 | { | |
3c9a524f | 4170 | SCM uinteger; |
3c9a524f | 4171 | |
9d427b2c | 4172 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 4173 | if (scm_is_false (uinteger)) |
3c9a524f DH |
4174 | return SCM_BOOL_F; |
4175 | ||
4176 | if (idx == len) | |
4177 | result = uinteger; | |
3f47e526 | 4178 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 4179 | { |
3c9a524f DH |
4180 | SCM divisor; |
4181 | ||
4182 | idx++; | |
ee0ddd21 AW |
4183 | if (idx == len) |
4184 | return SCM_BOOL_F; | |
3c9a524f | 4185 | |
9d427b2c | 4186 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 4187 | if (scm_is_false (divisor)) |
3c9a524f DH |
4188 | return SCM_BOOL_F; |
4189 | ||
f92e85f7 | 4190 | /* both are int/big here, I assume */ |
cba42c93 | 4191 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 4192 | } |
3c9a524f DH |
4193 | else if (radix == 10) |
4194 | { | |
9d427b2c | 4195 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
73e4de09 | 4196 | if (scm_is_false (result)) |
3c9a524f DH |
4197 | return SCM_BOOL_F; |
4198 | } | |
4199 | else | |
4200 | result = uinteger; | |
4201 | ||
4202 | *p_idx = idx; | |
f872b822 | 4203 | } |
164d2481 | 4204 | |
9d427b2c MW |
4205 | switch (forced_x) |
4206 | { | |
4207 | case EXACT: | |
4208 | if (SCM_INEXACTP (result)) | |
4209 | return scm_inexact_to_exact (result); | |
4210 | else | |
4211 | return result; | |
4212 | case INEXACT: | |
4213 | if (SCM_INEXACTP (result)) | |
4214 | return result; | |
4215 | else | |
4216 | return scm_exact_to_inexact (result); | |
4217 | case NO_EXACTNESS: | |
4218 | if (implicit_x == INEXACT) | |
4219 | { | |
4220 | if (SCM_INEXACTP (result)) | |
4221 | return result; | |
4222 | else | |
4223 | return scm_exact_to_inexact (result); | |
4224 | } | |
4225 | else | |
4226 | return result; | |
4227 | } | |
164d2481 | 4228 | |
9d427b2c MW |
4229 | /* We should never get here */ |
4230 | scm_syserror ("mem2ureal"); | |
3c9a524f | 4231 | } |
0f2d19dd | 4232 | |
0f2d19dd | 4233 | |
3c9a524f | 4234 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 4235 | |
3c9a524f | 4236 | static SCM |
3f47e526 | 4237 | mem2complex (SCM mem, unsigned int idx, |
9d427b2c | 4238 | unsigned int radix, enum t_exactness forced_x) |
3c9a524f | 4239 | { |
3f47e526 | 4240 | scm_t_wchar c; |
3c9a524f DH |
4241 | int sign = 0; |
4242 | SCM ureal; | |
3f47e526 | 4243 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
4244 | |
4245 | if (idx == len) | |
4246 | return SCM_BOOL_F; | |
4247 | ||
3f47e526 | 4248 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4249 | if (c == '+') |
4250 | { | |
4251 | idx++; | |
4252 | sign = 1; | |
4253 | } | |
4254 | else if (c == '-') | |
4255 | { | |
4256 | idx++; | |
4257 | sign = -1; | |
0f2d19dd | 4258 | } |
0f2d19dd | 4259 | |
3c9a524f DH |
4260 | if (idx == len) |
4261 | return SCM_BOOL_F; | |
4262 | ||
9d427b2c | 4263 | ureal = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 4264 | if (scm_is_false (ureal)) |
f872b822 | 4265 | { |
3c9a524f DH |
4266 | /* input must be either +i or -i */ |
4267 | ||
4268 | if (sign == 0) | |
4269 | return SCM_BOOL_F; | |
4270 | ||
3f47e526 MG |
4271 | if (scm_i_string_ref (mem, idx) == 'i' |
4272 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 4273 | { |
3c9a524f DH |
4274 | idx++; |
4275 | if (idx != len) | |
4276 | return SCM_BOOL_F; | |
4277 | ||
cff5fa33 | 4278 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 4279 | } |
3c9a524f DH |
4280 | else |
4281 | return SCM_BOOL_F; | |
0f2d19dd | 4282 | } |
3c9a524f DH |
4283 | else |
4284 | { | |
73e4de09 | 4285 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 4286 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 4287 | |
3c9a524f DH |
4288 | if (idx == len) |
4289 | return ureal; | |
4290 | ||
3f47e526 | 4291 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 4292 | switch (c) |
f872b822 | 4293 | { |
3c9a524f DH |
4294 | case 'i': case 'I': |
4295 | /* either +<ureal>i or -<ureal>i */ | |
4296 | ||
4297 | idx++; | |
4298 | if (sign == 0) | |
4299 | return SCM_BOOL_F; | |
4300 | if (idx != len) | |
4301 | return SCM_BOOL_F; | |
cff5fa33 | 4302 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
4303 | |
4304 | case '@': | |
4305 | /* polar input: <real>@<real>. */ | |
4306 | ||
4307 | idx++; | |
4308 | if (idx == len) | |
4309 | return SCM_BOOL_F; | |
4310 | else | |
f872b822 | 4311 | { |
3c9a524f DH |
4312 | int sign; |
4313 | SCM angle; | |
4314 | SCM result; | |
4315 | ||
3f47e526 | 4316 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4317 | if (c == '+') |
4318 | { | |
4319 | idx++; | |
ee0ddd21 AW |
4320 | if (idx == len) |
4321 | return SCM_BOOL_F; | |
3c9a524f DH |
4322 | sign = 1; |
4323 | } | |
4324 | else if (c == '-') | |
4325 | { | |
4326 | idx++; | |
ee0ddd21 AW |
4327 | if (idx == len) |
4328 | return SCM_BOOL_F; | |
3c9a524f DH |
4329 | sign = -1; |
4330 | } | |
4331 | else | |
4332 | sign = 1; | |
4333 | ||
9d427b2c | 4334 | angle = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 4335 | if (scm_is_false (angle)) |
3c9a524f DH |
4336 | return SCM_BOOL_F; |
4337 | if (idx != len) | |
4338 | return SCM_BOOL_F; | |
4339 | ||
73e4de09 | 4340 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
4341 | angle = scm_difference (angle, SCM_UNDEFINED); |
4342 | ||
4343 | result = scm_make_polar (ureal, angle); | |
4344 | return result; | |
f872b822 | 4345 | } |
3c9a524f DH |
4346 | case '+': |
4347 | case '-': | |
4348 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 4349 | |
3c9a524f DH |
4350 | idx++; |
4351 | if (idx == len) | |
4352 | return SCM_BOOL_F; | |
4353 | else | |
4354 | { | |
4355 | int sign = (c == '+') ? 1 : -1; | |
9d427b2c | 4356 | SCM imag = mem2ureal (mem, &idx, radix, forced_x); |
0f2d19dd | 4357 | |
73e4de09 | 4358 | if (scm_is_false (imag)) |
d956fa6f | 4359 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 4360 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 4361 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 4362 | |
3c9a524f DH |
4363 | if (idx == len) |
4364 | return SCM_BOOL_F; | |
3f47e526 MG |
4365 | if (scm_i_string_ref (mem, idx) != 'i' |
4366 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 4367 | return SCM_BOOL_F; |
0f2d19dd | 4368 | |
3c9a524f DH |
4369 | idx++; |
4370 | if (idx != len) | |
4371 | return SCM_BOOL_F; | |
0f2d19dd | 4372 | |
1fe5e088 | 4373 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
4374 | } |
4375 | default: | |
4376 | return SCM_BOOL_F; | |
4377 | } | |
4378 | } | |
0f2d19dd | 4379 | } |
0f2d19dd JB |
4380 | |
4381 | ||
3c9a524f DH |
4382 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
4383 | ||
4384 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 4385 | |
0f2d19dd | 4386 | SCM |
3f47e526 | 4387 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 4388 | { |
3c9a524f DH |
4389 | unsigned int idx = 0; |
4390 | unsigned int radix = NO_RADIX; | |
4391 | enum t_exactness forced_x = NO_EXACTNESS; | |
3f47e526 | 4392 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
4393 | |
4394 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 4395 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 4396 | { |
3f47e526 | 4397 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
4398 | { |
4399 | case 'b': case 'B': | |
4400 | if (radix != NO_RADIX) | |
4401 | return SCM_BOOL_F; | |
4402 | radix = DUAL; | |
4403 | break; | |
4404 | case 'd': case 'D': | |
4405 | if (radix != NO_RADIX) | |
4406 | return SCM_BOOL_F; | |
4407 | radix = DEC; | |
4408 | break; | |
4409 | case 'i': case 'I': | |
4410 | if (forced_x != NO_EXACTNESS) | |
4411 | return SCM_BOOL_F; | |
4412 | forced_x = INEXACT; | |
4413 | break; | |
4414 | case 'e': case 'E': | |
4415 | if (forced_x != NO_EXACTNESS) | |
4416 | return SCM_BOOL_F; | |
4417 | forced_x = EXACT; | |
4418 | break; | |
4419 | case 'o': case 'O': | |
4420 | if (radix != NO_RADIX) | |
4421 | return SCM_BOOL_F; | |
4422 | radix = OCT; | |
4423 | break; | |
4424 | case 'x': case 'X': | |
4425 | if (radix != NO_RADIX) | |
4426 | return SCM_BOOL_F; | |
4427 | radix = HEX; | |
4428 | break; | |
4429 | default: | |
f872b822 | 4430 | return SCM_BOOL_F; |
3c9a524f DH |
4431 | } |
4432 | idx += 2; | |
4433 | } | |
4434 | ||
4435 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
4436 | if (radix == NO_RADIX) | |
9d427b2c | 4437 | radix = default_radix; |
f872b822 | 4438 | |
9d427b2c | 4439 | return mem2complex (mem, idx, radix, forced_x); |
0f2d19dd JB |
4440 | } |
4441 | ||
3f47e526 MG |
4442 | SCM |
4443 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
4444 | unsigned int default_radix) | |
4445 | { | |
4446 | SCM str = scm_from_locale_stringn (mem, len); | |
4447 | ||
4448 | return scm_i_string_to_number (str, default_radix); | |
4449 | } | |
4450 | ||
0f2d19dd | 4451 | |
a1ec6916 | 4452 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 4453 | (SCM string, SCM radix), |
1e6808ea | 4454 | "Return a number of the maximally precise representation\n" |
942e5b91 | 4455 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
4456 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
4457 | "is a default radix that may be overridden by an explicit radix\n" | |
4458 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
4459 | "supplied, then the default radix is 10. If string is not a\n" | |
4460 | "syntactically valid notation for a number, then\n" | |
4461 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 4462 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
4463 | { |
4464 | SCM answer; | |
5efd3c7d | 4465 | unsigned int base; |
a6d9e5ab | 4466 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
4467 | |
4468 | if (SCM_UNBNDP (radix)) | |
4469 | base = 10; | |
4470 | else | |
4471 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
4472 | ||
3f47e526 | 4473 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
4474 | scm_remember_upto_here_1 (string); |
4475 | return answer; | |
0f2d19dd | 4476 | } |
1bbd0b84 | 4477 | #undef FUNC_NAME |
3c9a524f DH |
4478 | |
4479 | ||
0f2d19dd JB |
4480 | /*** END strs->nums ***/ |
4481 | ||
5986c47d | 4482 | |
8507ec80 MV |
4483 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
4484 | (SCM x), | |
4485 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
4486 | "otherwise.") | |
4487 | #define FUNC_NAME s_scm_number_p | |
4488 | { | |
4489 | return scm_from_bool (SCM_NUMBERP (x)); | |
4490 | } | |
4491 | #undef FUNC_NAME | |
4492 | ||
4493 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 4494 | (SCM x), |
942e5b91 | 4495 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 4496 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
4497 | "values form subsets of the set of complex numbers, i. e. the\n" |
4498 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
4499 | "rational or integer number.") | |
8507ec80 | 4500 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 4501 | { |
8507ec80 MV |
4502 | /* all numbers are complex. */ |
4503 | return scm_number_p (x); | |
0f2d19dd | 4504 | } |
1bbd0b84 | 4505 | #undef FUNC_NAME |
0f2d19dd | 4506 | |
f92e85f7 MV |
4507 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
4508 | (SCM x), | |
4509 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
4510 | "otherwise. Note that the set of integer values forms a subset of\n" | |
4511 | "the set of real numbers, i. e. the predicate will also be\n" | |
4512 | "fulfilled if @var{x} is an integer number.") | |
4513 | #define FUNC_NAME s_scm_real_p | |
4514 | { | |
c960e556 MW |
4515 | return scm_from_bool |
4516 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
4517 | } |
4518 | #undef FUNC_NAME | |
4519 | ||
4520 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 4521 | (SCM x), |
942e5b91 | 4522 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 4523 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 4524 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
4525 | "fulfilled if @var{x} is an integer number.") |
4526 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 4527 | { |
c960e556 | 4528 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
4529 | return SCM_BOOL_T; |
4530 | else if (SCM_REALP (x)) | |
c960e556 MW |
4531 | /* due to their limited precision, finite floating point numbers are |
4532 | rational as well. (finite means neither infinity nor a NaN) */ | |
4533 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 4534 | else |
bb628794 | 4535 | return SCM_BOOL_F; |
0f2d19dd | 4536 | } |
1bbd0b84 | 4537 | #undef FUNC_NAME |
0f2d19dd | 4538 | |
a1ec6916 | 4539 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 4540 | (SCM x), |
942e5b91 MG |
4541 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
4542 | "else.") | |
1bbd0b84 | 4543 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 4544 | { |
c960e556 | 4545 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 4546 | return SCM_BOOL_T; |
c960e556 MW |
4547 | else if (SCM_REALP (x)) |
4548 | { | |
4549 | double val = SCM_REAL_VALUE (x); | |
4550 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
4551 | } | |
4552 | else | |
8e43ed5d | 4553 | return SCM_BOOL_F; |
0f2d19dd | 4554 | } |
1bbd0b84 | 4555 | #undef FUNC_NAME |
0f2d19dd JB |
4556 | |
4557 | ||
8a1f4f98 AW |
4558 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
4559 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
4560 | (SCM x, SCM y, SCM rest), | |
4561 | "Return @code{#t} if all parameters are numerically equal.") | |
4562 | #define FUNC_NAME s_scm_i_num_eq_p | |
4563 | { | |
4564 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4565 | return SCM_BOOL_T; | |
4566 | while (!scm_is_null (rest)) | |
4567 | { | |
4568 | if (scm_is_false (scm_num_eq_p (x, y))) | |
4569 | return SCM_BOOL_F; | |
4570 | x = y; | |
4571 | y = scm_car (rest); | |
4572 | rest = scm_cdr (rest); | |
4573 | } | |
4574 | return scm_num_eq_p (x, y); | |
4575 | } | |
4576 | #undef FUNC_NAME | |
0f2d19dd | 4577 | SCM |
6e8d25a6 | 4578 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 4579 | { |
d8b95e27 | 4580 | again: |
e11e83f3 | 4581 | if (SCM_I_INUMP (x)) |
0aacf84e | 4582 | { |
e25f3727 | 4583 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 4584 | if (SCM_I_INUMP (y)) |
0aacf84e | 4585 | { |
e25f3727 | 4586 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 4587 | return scm_from_bool (xx == yy); |
0aacf84e MD |
4588 | } |
4589 | else if (SCM_BIGP (y)) | |
4590 | return SCM_BOOL_F; | |
4591 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
4592 | { |
4593 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
4594 | to a double and compare. | |
4595 | ||
4596 | But on a 64-bit system an inum is bigger than a double and | |
4597 | casting it to a double (call that dxx) will round. dxx is at | |
4598 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
4599 | an integer and fits a long. So we cast yy to a long and | |
4600 | compare with plain xx. | |
4601 | ||
4602 | An alternative (for any size system actually) would be to check | |
4603 | yy is an integer (with floor) and is in range of an inum | |
4604 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
4605 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
4606 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
4607 | |
4608 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
4609 | return scm_from_bool ((double) xx == yy |
4610 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4611 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 4612 | } |
0aacf84e | 4613 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 4614 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4615 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
4616 | else if (SCM_FRACTIONP (y)) |
4617 | return SCM_BOOL_F; | |
0aacf84e | 4618 | else |
8a1f4f98 | 4619 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 4620 | } |
0aacf84e MD |
4621 | else if (SCM_BIGP (x)) |
4622 | { | |
e11e83f3 | 4623 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4624 | return SCM_BOOL_F; |
4625 | else if (SCM_BIGP (y)) | |
4626 | { | |
4627 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4628 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 4629 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4630 | } |
4631 | else if (SCM_REALP (y)) | |
4632 | { | |
4633 | int cmp; | |
2e65b52f | 4634 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
4635 | return SCM_BOOL_F; |
4636 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
4637 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4638 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4639 | } |
4640 | else if (SCM_COMPLEXP (y)) | |
4641 | { | |
4642 | int cmp; | |
4643 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
4644 | return SCM_BOOL_F; | |
2e65b52f | 4645 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
4646 | return SCM_BOOL_F; |
4647 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
4648 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4649 | return scm_from_bool (0 == cmp); |
0aacf84e | 4650 | } |
f92e85f7 MV |
4651 | else if (SCM_FRACTIONP (y)) |
4652 | return SCM_BOOL_F; | |
0aacf84e | 4653 | else |
8a1f4f98 | 4654 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 4655 | } |
0aacf84e MD |
4656 | else if (SCM_REALP (x)) |
4657 | { | |
e8c5b1f2 | 4658 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 4659 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
4660 | { |
4661 | /* see comments with inum/real above */ | |
e25f3727 | 4662 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
4663 | return scm_from_bool (xx == (double) yy |
4664 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4665 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 4666 | } |
0aacf84e MD |
4667 | else if (SCM_BIGP (y)) |
4668 | { | |
4669 | int cmp; | |
2e65b52f | 4670 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
4671 | return SCM_BOOL_F; |
4672 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
4673 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4674 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4675 | } |
4676 | else if (SCM_REALP (y)) | |
73e4de09 | 4677 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 4678 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 4679 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4680 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 4681 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
4682 | { |
4683 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4684 | if (isnan (xx)) |
d8b95e27 | 4685 | return SCM_BOOL_F; |
2e65b52f | 4686 | if (isinf (xx)) |
73e4de09 | 4687 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
4688 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4689 | goto again; | |
4690 | } | |
0aacf84e | 4691 | else |
8a1f4f98 | 4692 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 4693 | } |
0aacf84e MD |
4694 | else if (SCM_COMPLEXP (x)) |
4695 | { | |
e11e83f3 MV |
4696 | if (SCM_I_INUMP (y)) |
4697 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
4698 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
4699 | else if (SCM_BIGP (y)) | |
4700 | { | |
4701 | int cmp; | |
4702 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
4703 | return SCM_BOOL_F; | |
2e65b52f | 4704 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
4705 | return SCM_BOOL_F; |
4706 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
4707 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4708 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4709 | } |
4710 | else if (SCM_REALP (y)) | |
73e4de09 | 4711 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
4712 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
4713 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 4714 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4715 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 4716 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
4717 | { |
4718 | double xx; | |
4719 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
4720 | return SCM_BOOL_F; | |
4721 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 4722 | if (isnan (xx)) |
d8b95e27 | 4723 | return SCM_BOOL_F; |
2e65b52f | 4724 | if (isinf (xx)) |
73e4de09 | 4725 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
4726 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4727 | goto again; | |
4728 | } | |
f92e85f7 | 4729 | else |
8a1f4f98 | 4730 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
4731 | } |
4732 | else if (SCM_FRACTIONP (x)) | |
4733 | { | |
e11e83f3 | 4734 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
4735 | return SCM_BOOL_F; |
4736 | else if (SCM_BIGP (y)) | |
4737 | return SCM_BOOL_F; | |
4738 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
4739 | { |
4740 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 4741 | if (isnan (yy)) |
d8b95e27 | 4742 | return SCM_BOOL_F; |
2e65b52f | 4743 | if (isinf (yy)) |
73e4de09 | 4744 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
4745 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4746 | goto again; | |
4747 | } | |
f92e85f7 | 4748 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
4749 | { |
4750 | double yy; | |
4751 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
4752 | return SCM_BOOL_F; | |
4753 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 4754 | if (isnan (yy)) |
d8b95e27 | 4755 | return SCM_BOOL_F; |
2e65b52f | 4756 | if (isinf (yy)) |
73e4de09 | 4757 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
4758 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4759 | goto again; | |
4760 | } | |
f92e85f7 MV |
4761 | else if (SCM_FRACTIONP (y)) |
4762 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 4763 | else |
8a1f4f98 | 4764 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 4765 | } |
0aacf84e | 4766 | else |
8a1f4f98 | 4767 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
4768 | } |
4769 | ||
4770 | ||
a5f0b599 KR |
4771 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
4772 | done are good for inums, but for bignums an answer can almost always be | |
4773 | had by just examining a few high bits of the operands, as done by GMP in | |
4774 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
4775 | of the float exponent to take into account. */ | |
4776 | ||
8c93b597 | 4777 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
4778 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
4779 | (SCM x, SCM y, SCM rest), | |
4780 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4781 | "increasing.") | |
4782 | #define FUNC_NAME s_scm_i_num_less_p | |
4783 | { | |
4784 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4785 | return SCM_BOOL_T; | |
4786 | while (!scm_is_null (rest)) | |
4787 | { | |
4788 | if (scm_is_false (scm_less_p (x, y))) | |
4789 | return SCM_BOOL_F; | |
4790 | x = y; | |
4791 | y = scm_car (rest); | |
4792 | rest = scm_cdr (rest); | |
4793 | } | |
4794 | return scm_less_p (x, y); | |
4795 | } | |
4796 | #undef FUNC_NAME | |
0f2d19dd | 4797 | SCM |
6e8d25a6 | 4798 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 4799 | { |
a5f0b599 | 4800 | again: |
e11e83f3 | 4801 | if (SCM_I_INUMP (x)) |
0aacf84e | 4802 | { |
e25f3727 | 4803 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 4804 | if (SCM_I_INUMP (y)) |
0aacf84e | 4805 | { |
e25f3727 | 4806 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 4807 | return scm_from_bool (xx < yy); |
0aacf84e MD |
4808 | } |
4809 | else if (SCM_BIGP (y)) | |
4810 | { | |
4811 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4812 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4813 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
4814 | } |
4815 | else if (SCM_REALP (y)) | |
73e4de09 | 4816 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 4817 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4818 | { |
4819 | /* "x < a/b" becomes "x*b < a" */ | |
4820 | int_frac: | |
4821 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
4822 | y = SCM_FRACTION_NUMERATOR (y); | |
4823 | goto again; | |
4824 | } | |
0aacf84e | 4825 | else |
8a1f4f98 | 4826 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 4827 | } |
0aacf84e MD |
4828 | else if (SCM_BIGP (x)) |
4829 | { | |
e11e83f3 | 4830 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4831 | { |
4832 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4833 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4834 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
4835 | } |
4836 | else if (SCM_BIGP (y)) | |
4837 | { | |
4838 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4839 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 4840 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
4841 | } |
4842 | else if (SCM_REALP (y)) | |
4843 | { | |
4844 | int cmp; | |
2e65b52f | 4845 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
4846 | return SCM_BOOL_F; |
4847 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
4848 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4849 | return scm_from_bool (cmp < 0); |
0aacf84e | 4850 | } |
f92e85f7 | 4851 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 4852 | goto int_frac; |
0aacf84e | 4853 | else |
8a1f4f98 | 4854 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 4855 | } |
0aacf84e MD |
4856 | else if (SCM_REALP (x)) |
4857 | { | |
e11e83f3 MV |
4858 | if (SCM_I_INUMP (y)) |
4859 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
4860 | else if (SCM_BIGP (y)) |
4861 | { | |
4862 | int cmp; | |
2e65b52f | 4863 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
4864 | return SCM_BOOL_F; |
4865 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
4866 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4867 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
4868 | } |
4869 | else if (SCM_REALP (y)) | |
73e4de09 | 4870 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 4871 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4872 | { |
4873 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4874 | if (isnan (xx)) |
a5f0b599 | 4875 | return SCM_BOOL_F; |
2e65b52f | 4876 | if (isinf (xx)) |
73e4de09 | 4877 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
4878 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4879 | goto again; | |
4880 | } | |
f92e85f7 | 4881 | else |
8a1f4f98 | 4882 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
4883 | } |
4884 | else if (SCM_FRACTIONP (x)) | |
4885 | { | |
e11e83f3 | 4886 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
4887 | { |
4888 | /* "a/b < y" becomes "a < y*b" */ | |
4889 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
4890 | x = SCM_FRACTION_NUMERATOR (x); | |
4891 | goto again; | |
4892 | } | |
f92e85f7 | 4893 | else if (SCM_REALP (y)) |
a5f0b599 KR |
4894 | { |
4895 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 4896 | if (isnan (yy)) |
a5f0b599 | 4897 | return SCM_BOOL_F; |
2e65b52f | 4898 | if (isinf (yy)) |
73e4de09 | 4899 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
4900 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4901 | goto again; | |
4902 | } | |
f92e85f7 | 4903 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4904 | { |
4905 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
4906 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
4907 | SCM_FRACTION_DENOMINATOR (y)); | |
4908 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
4909 | SCM_FRACTION_DENOMINATOR (x)); | |
4910 | x = new_x; | |
4911 | y = new_y; | |
4912 | goto again; | |
4913 | } | |
0aacf84e | 4914 | else |
8a1f4f98 | 4915 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 4916 | } |
0aacf84e | 4917 | else |
8a1f4f98 | 4918 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
4919 | } |
4920 | ||
4921 | ||
8a1f4f98 AW |
4922 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
4923 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
4924 | (SCM x, SCM y, SCM rest), | |
4925 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4926 | "decreasing.") | |
4927 | #define FUNC_NAME s_scm_i_num_gr_p | |
4928 | { | |
4929 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4930 | return SCM_BOOL_T; | |
4931 | while (!scm_is_null (rest)) | |
4932 | { | |
4933 | if (scm_is_false (scm_gr_p (x, y))) | |
4934 | return SCM_BOOL_F; | |
4935 | x = y; | |
4936 | y = scm_car (rest); | |
4937 | rest = scm_cdr (rest); | |
4938 | } | |
4939 | return scm_gr_p (x, y); | |
4940 | } | |
4941 | #undef FUNC_NAME | |
4942 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
4943 | SCM |
4944 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 4945 | { |
c76b1eaf | 4946 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 4947 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 4948 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 4949 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
4950 | else |
4951 | return scm_less_p (y, x); | |
0f2d19dd | 4952 | } |
1bbd0b84 | 4953 | #undef FUNC_NAME |
0f2d19dd JB |
4954 | |
4955 | ||
8a1f4f98 AW |
4956 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
4957 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
4958 | (SCM x, SCM y, SCM rest), | |
4959 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4960 | "non-decreasing.") | |
4961 | #define FUNC_NAME s_scm_i_num_leq_p | |
4962 | { | |
4963 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4964 | return SCM_BOOL_T; | |
4965 | while (!scm_is_null (rest)) | |
4966 | { | |
4967 | if (scm_is_false (scm_leq_p (x, y))) | |
4968 | return SCM_BOOL_F; | |
4969 | x = y; | |
4970 | y = scm_car (rest); | |
4971 | rest = scm_cdr (rest); | |
4972 | } | |
4973 | return scm_leq_p (x, y); | |
4974 | } | |
4975 | #undef FUNC_NAME | |
4976 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
4977 | SCM |
4978 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 4979 | { |
c76b1eaf | 4980 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 4981 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 4982 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 4983 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 4984 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 4985 | return SCM_BOOL_F; |
c76b1eaf | 4986 | else |
73e4de09 | 4987 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 4988 | } |
1bbd0b84 | 4989 | #undef FUNC_NAME |
0f2d19dd JB |
4990 | |
4991 | ||
8a1f4f98 AW |
4992 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
4993 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
4994 | (SCM x, SCM y, SCM rest), | |
4995 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4996 | "non-increasing.") | |
4997 | #define FUNC_NAME s_scm_i_num_geq_p | |
4998 | { | |
4999 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
5000 | return SCM_BOOL_T; | |
5001 | while (!scm_is_null (rest)) | |
5002 | { | |
5003 | if (scm_is_false (scm_geq_p (x, y))) | |
5004 | return SCM_BOOL_F; | |
5005 | x = y; | |
5006 | y = scm_car (rest); | |
5007 | rest = scm_cdr (rest); | |
5008 | } | |
5009 | return scm_geq_p (x, y); | |
5010 | } | |
5011 | #undef FUNC_NAME | |
5012 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
5013 | SCM |
5014 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 5015 | { |
c76b1eaf | 5016 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 5017 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 5018 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 5019 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 5020 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 5021 | return SCM_BOOL_F; |
c76b1eaf | 5022 | else |
73e4de09 | 5023 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 5024 | } |
1bbd0b84 | 5025 | #undef FUNC_NAME |
0f2d19dd JB |
5026 | |
5027 | ||
2519490c MW |
5028 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
5029 | (SCM z), | |
5030 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
5031 | "zero.") | |
5032 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 5033 | { |
e11e83f3 | 5034 | if (SCM_I_INUMP (z)) |
bc36d050 | 5035 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 5036 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5037 | return SCM_BOOL_F; |
0aacf84e | 5038 | else if (SCM_REALP (z)) |
73e4de09 | 5039 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 5040 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 5041 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 5042 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
5043 | else if (SCM_FRACTIONP (z)) |
5044 | return SCM_BOOL_F; | |
0aacf84e | 5045 | else |
2519490c | 5046 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 5047 | } |
2519490c | 5048 | #undef FUNC_NAME |
0f2d19dd JB |
5049 | |
5050 | ||
2519490c MW |
5051 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
5052 | (SCM x), | |
5053 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
5054 | "zero.") | |
5055 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 5056 | { |
e11e83f3 MV |
5057 | if (SCM_I_INUMP (x)) |
5058 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
5059 | else if (SCM_BIGP (x)) |
5060 | { | |
5061 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5062 | scm_remember_upto_here_1 (x); | |
73e4de09 | 5063 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
5064 | } |
5065 | else if (SCM_REALP (x)) | |
73e4de09 | 5066 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
5067 | else if (SCM_FRACTIONP (x)) |
5068 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 5069 | else |
2519490c | 5070 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 5071 | } |
2519490c | 5072 | #undef FUNC_NAME |
0f2d19dd JB |
5073 | |
5074 | ||
2519490c MW |
5075 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
5076 | (SCM x), | |
5077 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
5078 | "zero.") | |
5079 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 5080 | { |
e11e83f3 MV |
5081 | if (SCM_I_INUMP (x)) |
5082 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
5083 | else if (SCM_BIGP (x)) |
5084 | { | |
5085 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5086 | scm_remember_upto_here_1 (x); | |
73e4de09 | 5087 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
5088 | } |
5089 | else if (SCM_REALP (x)) | |
73e4de09 | 5090 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
5091 | else if (SCM_FRACTIONP (x)) |
5092 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 5093 | else |
2519490c | 5094 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 5095 | } |
2519490c | 5096 | #undef FUNC_NAME |
0f2d19dd JB |
5097 | |
5098 | ||
2a06f791 KR |
5099 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
5100 | required by r5rs. On that basis, for exact/inexact combinations the | |
5101 | exact is converted to inexact to compare and possibly return. This is | |
5102 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
5103 | its test, such trouble is not required for min and max. */ | |
5104 | ||
78d3deb1 AW |
5105 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
5106 | (SCM x, SCM y, SCM rest), | |
5107 | "Return the maximum of all parameter values.") | |
5108 | #define FUNC_NAME s_scm_i_max | |
5109 | { | |
5110 | while (!scm_is_null (rest)) | |
5111 | { x = scm_max (x, y); | |
5112 | y = scm_car (rest); | |
5113 | rest = scm_cdr (rest); | |
5114 | } | |
5115 | return scm_max (x, y); | |
5116 | } | |
5117 | #undef FUNC_NAME | |
5118 | ||
5119 | #define s_max s_scm_i_max | |
5120 | #define g_max g_scm_i_max | |
5121 | ||
0f2d19dd | 5122 | SCM |
6e8d25a6 | 5123 | scm_max (SCM x, SCM y) |
0f2d19dd | 5124 | { |
0aacf84e MD |
5125 | if (SCM_UNBNDP (y)) |
5126 | { | |
5127 | if (SCM_UNBNDP (x)) | |
5128 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 5129 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
5130 | return x; |
5131 | else | |
5132 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 5133 | } |
f4c627b3 | 5134 | |
e11e83f3 | 5135 | if (SCM_I_INUMP (x)) |
0aacf84e | 5136 | { |
e25f3727 | 5137 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 5138 | if (SCM_I_INUMP (y)) |
0aacf84e | 5139 | { |
e25f3727 | 5140 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
5141 | return (xx < yy) ? y : x; |
5142 | } | |
5143 | else if (SCM_BIGP (y)) | |
5144 | { | |
5145 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5146 | scm_remember_upto_here_1 (y); | |
5147 | return (sgn < 0) ? x : y; | |
5148 | } | |
5149 | else if (SCM_REALP (y)) | |
5150 | { | |
2e274311 MW |
5151 | double xxd = xx; |
5152 | double yyd = SCM_REAL_VALUE (y); | |
5153 | ||
5154 | if (xxd > yyd) | |
5155 | return scm_from_double (xxd); | |
5156 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
5157 | else if (SCM_LIKELY (!(xxd == yyd))) | |
5158 | return y; | |
5159 | /* Handle signed zeroes properly */ | |
5160 | else if (xx == 0) | |
5161 | return flo0; | |
5162 | else | |
5163 | return y; | |
0aacf84e | 5164 | } |
f92e85f7 MV |
5165 | else if (SCM_FRACTIONP (y)) |
5166 | { | |
e4bc5d6c | 5167 | use_less: |
73e4de09 | 5168 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 5169 | } |
0aacf84e MD |
5170 | else |
5171 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 5172 | } |
0aacf84e MD |
5173 | else if (SCM_BIGP (x)) |
5174 | { | |
e11e83f3 | 5175 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5176 | { |
5177 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5178 | scm_remember_upto_here_1 (x); | |
5179 | return (sgn < 0) ? y : x; | |
5180 | } | |
5181 | else if (SCM_BIGP (y)) | |
5182 | { | |
5183 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
5184 | scm_remember_upto_here_2 (x, y); | |
5185 | return (cmp > 0) ? x : y; | |
5186 | } | |
5187 | else if (SCM_REALP (y)) | |
5188 | { | |
2a06f791 KR |
5189 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
5190 | double xx, yy; | |
5191 | big_real: | |
5192 | xx = scm_i_big2dbl (x); | |
5193 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 5194 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 5195 | } |
f92e85f7 MV |
5196 | else if (SCM_FRACTIONP (y)) |
5197 | { | |
e4bc5d6c | 5198 | goto use_less; |
f92e85f7 | 5199 | } |
0aacf84e MD |
5200 | else |
5201 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 5202 | } |
0aacf84e MD |
5203 | else if (SCM_REALP (x)) |
5204 | { | |
e11e83f3 | 5205 | if (SCM_I_INUMP (y)) |
0aacf84e | 5206 | { |
2e274311 MW |
5207 | scm_t_inum yy = SCM_I_INUM (y); |
5208 | double xxd = SCM_REAL_VALUE (x); | |
5209 | double yyd = yy; | |
5210 | ||
5211 | if (yyd > xxd) | |
5212 | return scm_from_double (yyd); | |
5213 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
5214 | else if (SCM_LIKELY (!(xxd == yyd))) | |
5215 | return x; | |
5216 | /* Handle signed zeroes properly */ | |
5217 | else if (yy == 0) | |
5218 | return flo0; | |
5219 | else | |
5220 | return x; | |
0aacf84e MD |
5221 | } |
5222 | else if (SCM_BIGP (y)) | |
5223 | { | |
b6f8f763 | 5224 | SCM_SWAP (x, y); |
2a06f791 | 5225 | goto big_real; |
0aacf84e MD |
5226 | } |
5227 | else if (SCM_REALP (y)) | |
5228 | { | |
0aacf84e | 5229 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
5230 | double yy = SCM_REAL_VALUE (y); |
5231 | ||
5232 | /* For purposes of max: +inf.0 > nan > everything else, per R6RS */ | |
5233 | if (xx > yy) | |
5234 | return x; | |
5235 | else if (SCM_LIKELY (xx < yy)) | |
5236 | return y; | |
5237 | /* If neither (xx > yy) nor (xx < yy), then | |
5238 | either they're equal or one is a NaN */ | |
5239 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 5240 | return DOUBLE_IS_POSITIVE_INFINITY (yy) ? y : x; |
2e274311 | 5241 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 5242 | return DOUBLE_IS_POSITIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
5243 | /* xx == yy, but handle signed zeroes properly */ |
5244 | else if (double_is_non_negative_zero (yy)) | |
5245 | return y; | |
5246 | else | |
5247 | return x; | |
0aacf84e | 5248 | } |
f92e85f7 MV |
5249 | else if (SCM_FRACTIONP (y)) |
5250 | { | |
5251 | double yy = scm_i_fraction2double (y); | |
5252 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 5253 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
5254 | } |
5255 | else | |
5256 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
5257 | } | |
5258 | else if (SCM_FRACTIONP (x)) | |
5259 | { | |
e11e83f3 | 5260 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5261 | { |
e4bc5d6c | 5262 | goto use_less; |
f92e85f7 MV |
5263 | } |
5264 | else if (SCM_BIGP (y)) | |
5265 | { | |
e4bc5d6c | 5266 | goto use_less; |
f92e85f7 MV |
5267 | } |
5268 | else if (SCM_REALP (y)) | |
5269 | { | |
5270 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
5271 | /* if y==NaN then ">" is false, so we return the NaN y */ |
5272 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
5273 | } |
5274 | else if (SCM_FRACTIONP (y)) | |
5275 | { | |
e4bc5d6c | 5276 | goto use_less; |
f92e85f7 | 5277 | } |
0aacf84e MD |
5278 | else |
5279 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 5280 | } |
0aacf84e | 5281 | else |
f4c627b3 | 5282 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
5283 | } |
5284 | ||
5285 | ||
78d3deb1 AW |
5286 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
5287 | (SCM x, SCM y, SCM rest), | |
5288 | "Return the minimum of all parameter values.") | |
5289 | #define FUNC_NAME s_scm_i_min | |
5290 | { | |
5291 | while (!scm_is_null (rest)) | |
5292 | { x = scm_min (x, y); | |
5293 | y = scm_car (rest); | |
5294 | rest = scm_cdr (rest); | |
5295 | } | |
5296 | return scm_min (x, y); | |
5297 | } | |
5298 | #undef FUNC_NAME | |
5299 | ||
5300 | #define s_min s_scm_i_min | |
5301 | #define g_min g_scm_i_min | |
5302 | ||
0f2d19dd | 5303 | SCM |
6e8d25a6 | 5304 | scm_min (SCM x, SCM y) |
0f2d19dd | 5305 | { |
0aacf84e MD |
5306 | if (SCM_UNBNDP (y)) |
5307 | { | |
5308 | if (SCM_UNBNDP (x)) | |
5309 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 5310 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
5311 | return x; |
5312 | else | |
5313 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 5314 | } |
f4c627b3 | 5315 | |
e11e83f3 | 5316 | if (SCM_I_INUMP (x)) |
0aacf84e | 5317 | { |
e25f3727 | 5318 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 5319 | if (SCM_I_INUMP (y)) |
0aacf84e | 5320 | { |
e25f3727 | 5321 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
5322 | return (xx < yy) ? x : y; |
5323 | } | |
5324 | else if (SCM_BIGP (y)) | |
5325 | { | |
5326 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5327 | scm_remember_upto_here_1 (y); | |
5328 | return (sgn < 0) ? y : x; | |
5329 | } | |
5330 | else if (SCM_REALP (y)) | |
5331 | { | |
5332 | double z = xx; | |
5333 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 5334 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 5335 | } |
f92e85f7 MV |
5336 | else if (SCM_FRACTIONP (y)) |
5337 | { | |
e4bc5d6c | 5338 | use_less: |
73e4de09 | 5339 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 5340 | } |
0aacf84e MD |
5341 | else |
5342 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 5343 | } |
0aacf84e MD |
5344 | else if (SCM_BIGP (x)) |
5345 | { | |
e11e83f3 | 5346 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5347 | { |
5348 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5349 | scm_remember_upto_here_1 (x); | |
5350 | return (sgn < 0) ? x : y; | |
5351 | } | |
5352 | else if (SCM_BIGP (y)) | |
5353 | { | |
5354 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
5355 | scm_remember_upto_here_2 (x, y); | |
5356 | return (cmp > 0) ? y : x; | |
5357 | } | |
5358 | else if (SCM_REALP (y)) | |
5359 | { | |
2a06f791 KR |
5360 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
5361 | double xx, yy; | |
5362 | big_real: | |
5363 | xx = scm_i_big2dbl (x); | |
5364 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 5365 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 5366 | } |
f92e85f7 MV |
5367 | else if (SCM_FRACTIONP (y)) |
5368 | { | |
e4bc5d6c | 5369 | goto use_less; |
f92e85f7 | 5370 | } |
0aacf84e MD |
5371 | else |
5372 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 5373 | } |
0aacf84e MD |
5374 | else if (SCM_REALP (x)) |
5375 | { | |
e11e83f3 | 5376 | if (SCM_I_INUMP (y)) |
0aacf84e | 5377 | { |
e11e83f3 | 5378 | double z = SCM_I_INUM (y); |
0aacf84e | 5379 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 5380 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
5381 | } |
5382 | else if (SCM_BIGP (y)) | |
5383 | { | |
b6f8f763 | 5384 | SCM_SWAP (x, y); |
2a06f791 | 5385 | goto big_real; |
0aacf84e MD |
5386 | } |
5387 | else if (SCM_REALP (y)) | |
5388 | { | |
0aacf84e | 5389 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
5390 | double yy = SCM_REAL_VALUE (y); |
5391 | ||
5392 | /* For purposes of min: -inf.0 < nan < everything else, per R6RS */ | |
5393 | if (xx < yy) | |
5394 | return x; | |
5395 | else if (SCM_LIKELY (xx > yy)) | |
5396 | return y; | |
5397 | /* If neither (xx < yy) nor (xx > yy), then | |
5398 | either they're equal or one is a NaN */ | |
5399 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 5400 | return DOUBLE_IS_NEGATIVE_INFINITY (yy) ? y : x; |
2e274311 | 5401 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 5402 | return DOUBLE_IS_NEGATIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
5403 | /* xx == yy, but handle signed zeroes properly */ |
5404 | else if (double_is_non_negative_zero (xx)) | |
5405 | return y; | |
5406 | else | |
5407 | return x; | |
0aacf84e | 5408 | } |
f92e85f7 MV |
5409 | else if (SCM_FRACTIONP (y)) |
5410 | { | |
5411 | double yy = scm_i_fraction2double (y); | |
5412 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 5413 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 5414 | } |
0aacf84e MD |
5415 | else |
5416 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 5417 | } |
f92e85f7 MV |
5418 | else if (SCM_FRACTIONP (x)) |
5419 | { | |
e11e83f3 | 5420 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5421 | { |
e4bc5d6c | 5422 | goto use_less; |
f92e85f7 MV |
5423 | } |
5424 | else if (SCM_BIGP (y)) | |
5425 | { | |
e4bc5d6c | 5426 | goto use_less; |
f92e85f7 MV |
5427 | } |
5428 | else if (SCM_REALP (y)) | |
5429 | { | |
5430 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
5431 | /* if y==NaN then "<" is false, so we return the NaN y */ |
5432 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
5433 | } |
5434 | else if (SCM_FRACTIONP (y)) | |
5435 | { | |
e4bc5d6c | 5436 | goto use_less; |
f92e85f7 MV |
5437 | } |
5438 | else | |
78d3deb1 | 5439 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 5440 | } |
0aacf84e | 5441 | else |
f4c627b3 | 5442 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
5443 | } |
5444 | ||
5445 | ||
8ccd24f7 AW |
5446 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
5447 | (SCM x, SCM y, SCM rest), | |
5448 | "Return the sum of all parameter values. Return 0 if called without\n" | |
5449 | "any parameters." ) | |
5450 | #define FUNC_NAME s_scm_i_sum | |
5451 | { | |
5452 | while (!scm_is_null (rest)) | |
5453 | { x = scm_sum (x, y); | |
5454 | y = scm_car (rest); | |
5455 | rest = scm_cdr (rest); | |
5456 | } | |
5457 | return scm_sum (x, y); | |
5458 | } | |
5459 | #undef FUNC_NAME | |
5460 | ||
5461 | #define s_sum s_scm_i_sum | |
5462 | #define g_sum g_scm_i_sum | |
5463 | ||
0f2d19dd | 5464 | SCM |
6e8d25a6 | 5465 | scm_sum (SCM x, SCM y) |
0f2d19dd | 5466 | { |
9cc37597 | 5467 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
5468 | { |
5469 | if (SCM_NUMBERP (x)) return x; | |
5470 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 5471 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 5472 | } |
c209c88e | 5473 | |
9cc37597 | 5474 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 5475 | { |
9cc37597 | 5476 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 5477 | { |
e25f3727 AW |
5478 | scm_t_inum xx = SCM_I_INUM (x); |
5479 | scm_t_inum yy = SCM_I_INUM (y); | |
5480 | scm_t_inum z = xx + yy; | |
5481 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
5482 | } |
5483 | else if (SCM_BIGP (y)) | |
5484 | { | |
5485 | SCM_SWAP (x, y); | |
5486 | goto add_big_inum; | |
5487 | } | |
5488 | else if (SCM_REALP (y)) | |
5489 | { | |
e25f3727 | 5490 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 5491 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
5492 | } |
5493 | else if (SCM_COMPLEXP (y)) | |
5494 | { | |
e25f3727 | 5495 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 5496 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
5497 | SCM_COMPLEX_IMAG (y)); |
5498 | } | |
f92e85f7 | 5499 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5500 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
5501 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
5502 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
5503 | else |
5504 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
5505 | } else if (SCM_BIGP (x)) |
5506 | { | |
e11e83f3 | 5507 | if (SCM_I_INUMP (y)) |
0aacf84e | 5508 | { |
e25f3727 | 5509 | scm_t_inum inum; |
0aacf84e MD |
5510 | int bigsgn; |
5511 | add_big_inum: | |
e11e83f3 | 5512 | inum = SCM_I_INUM (y); |
0aacf84e MD |
5513 | if (inum == 0) |
5514 | return x; | |
5515 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5516 | if (inum < 0) | |
5517 | { | |
5518 | SCM result = scm_i_mkbig (); | |
5519 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
5520 | scm_remember_upto_here_1 (x); | |
5521 | /* we know the result will have to be a bignum */ | |
5522 | if (bigsgn == -1) | |
5523 | return result; | |
5524 | return scm_i_normbig (result); | |
5525 | } | |
5526 | else | |
5527 | { | |
5528 | SCM result = scm_i_mkbig (); | |
5529 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
5530 | scm_remember_upto_here_1 (x); | |
5531 | /* we know the result will have to be a bignum */ | |
5532 | if (bigsgn == 1) | |
5533 | return result; | |
5534 | return scm_i_normbig (result); | |
5535 | } | |
5536 | } | |
5537 | else if (SCM_BIGP (y)) | |
5538 | { | |
5539 | SCM result = scm_i_mkbig (); | |
5540 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5541 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5542 | mpz_add (SCM_I_BIG_MPZ (result), | |
5543 | SCM_I_BIG_MPZ (x), | |
5544 | SCM_I_BIG_MPZ (y)); | |
5545 | scm_remember_upto_here_2 (x, y); | |
5546 | /* we know the result will have to be a bignum */ | |
5547 | if (sgn_x == sgn_y) | |
5548 | return result; | |
5549 | return scm_i_normbig (result); | |
5550 | } | |
5551 | else if (SCM_REALP (y)) | |
5552 | { | |
5553 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
5554 | scm_remember_upto_here_1 (x); | |
55f26379 | 5555 | return scm_from_double (result); |
0aacf84e MD |
5556 | } |
5557 | else if (SCM_COMPLEXP (y)) | |
5558 | { | |
5559 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
5560 | + SCM_COMPLEX_REAL (y)); | |
5561 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5562 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 5563 | } |
f92e85f7 | 5564 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5565 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
5566 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
5567 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
5568 | else |
5569 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 5570 | } |
0aacf84e MD |
5571 | else if (SCM_REALP (x)) |
5572 | { | |
e11e83f3 | 5573 | if (SCM_I_INUMP (y)) |
55f26379 | 5574 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
5575 | else if (SCM_BIGP (y)) |
5576 | { | |
5577 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
5578 | scm_remember_upto_here_1 (y); | |
55f26379 | 5579 | return scm_from_double (result); |
0aacf84e MD |
5580 | } |
5581 | else if (SCM_REALP (y)) | |
55f26379 | 5582 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 5583 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5584 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 5585 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5586 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5587 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
5588 | else |
5589 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 5590 | } |
0aacf84e MD |
5591 | else if (SCM_COMPLEXP (x)) |
5592 | { | |
e11e83f3 | 5593 | if (SCM_I_INUMP (y)) |
8507ec80 | 5594 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
5595 | SCM_COMPLEX_IMAG (x)); |
5596 | else if (SCM_BIGP (y)) | |
5597 | { | |
5598 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
5599 | + SCM_COMPLEX_REAL (x)); | |
5600 | scm_remember_upto_here_1 (y); | |
8507ec80 | 5601 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
5602 | } |
5603 | else if (SCM_REALP (y)) | |
8507ec80 | 5604 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
5605 | SCM_COMPLEX_IMAG (x)); |
5606 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 5607 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 5608 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5609 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 5610 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
5611 | SCM_COMPLEX_IMAG (x)); |
5612 | else | |
5613 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
5614 | } | |
5615 | else if (SCM_FRACTIONP (x)) | |
5616 | { | |
e11e83f3 | 5617 | if (SCM_I_INUMP (y)) |
cba42c93 | 5618 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5619 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
5620 | SCM_FRACTION_DENOMINATOR (x)); | |
5621 | else if (SCM_BIGP (y)) | |
cba42c93 | 5622 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5623 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
5624 | SCM_FRACTION_DENOMINATOR (x)); | |
5625 | else if (SCM_REALP (y)) | |
55f26379 | 5626 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 5627 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5628 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
5629 | SCM_COMPLEX_IMAG (y)); |
5630 | else if (SCM_FRACTIONP (y)) | |
5631 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 5632 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5633 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
5634 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
5635 | else |
5636 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 5637 | } |
0aacf84e | 5638 | else |
98cb6e75 | 5639 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
5640 | } |
5641 | ||
5642 | ||
40882e3d KR |
5643 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
5644 | (SCM x), | |
5645 | "Return @math{@var{x}+1}.") | |
5646 | #define FUNC_NAME s_scm_oneplus | |
5647 | { | |
cff5fa33 | 5648 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
5649 | } |
5650 | #undef FUNC_NAME | |
5651 | ||
5652 | ||
78d3deb1 AW |
5653 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
5654 | (SCM x, SCM y, SCM rest), | |
5655 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
5656 | "the sum of all but the first argument are subtracted from the first\n" | |
5657 | "argument.") | |
5658 | #define FUNC_NAME s_scm_i_difference | |
5659 | { | |
5660 | while (!scm_is_null (rest)) | |
5661 | { x = scm_difference (x, y); | |
5662 | y = scm_car (rest); | |
5663 | rest = scm_cdr (rest); | |
5664 | } | |
5665 | return scm_difference (x, y); | |
5666 | } | |
5667 | #undef FUNC_NAME | |
5668 | ||
5669 | #define s_difference s_scm_i_difference | |
5670 | #define g_difference g_scm_i_difference | |
5671 | ||
0f2d19dd | 5672 | SCM |
6e8d25a6 | 5673 | scm_difference (SCM x, SCM y) |
78d3deb1 | 5674 | #define FUNC_NAME s_difference |
0f2d19dd | 5675 | { |
9cc37597 | 5676 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
5677 | { |
5678 | if (SCM_UNBNDP (x)) | |
5679 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
5680 | else | |
e11e83f3 | 5681 | if (SCM_I_INUMP (x)) |
ca46fb90 | 5682 | { |
e25f3727 | 5683 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 5684 | if (SCM_FIXABLE (xx)) |
d956fa6f | 5685 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 5686 | else |
e25f3727 | 5687 | return scm_i_inum2big (xx); |
ca46fb90 RB |
5688 | } |
5689 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
5690 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
5691 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
5692 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
5693 | else if (SCM_REALP (x)) | |
55f26379 | 5694 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 5695 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 5696 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 5697 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 5698 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 5699 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 5700 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
5701 | else |
5702 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 5703 | } |
ca46fb90 | 5704 | |
9cc37597 | 5705 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 5706 | { |
9cc37597 | 5707 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 5708 | { |
e25f3727 AW |
5709 | scm_t_inum xx = SCM_I_INUM (x); |
5710 | scm_t_inum yy = SCM_I_INUM (y); | |
5711 | scm_t_inum z = xx - yy; | |
0aacf84e | 5712 | if (SCM_FIXABLE (z)) |
d956fa6f | 5713 | return SCM_I_MAKINUM (z); |
0aacf84e | 5714 | else |
e25f3727 | 5715 | return scm_i_inum2big (z); |
0aacf84e MD |
5716 | } |
5717 | else if (SCM_BIGP (y)) | |
5718 | { | |
5719 | /* inum-x - big-y */ | |
e25f3727 | 5720 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 5721 | |
0aacf84e | 5722 | if (xx == 0) |
b5c40589 MW |
5723 | { |
5724 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
5725 | bignum, but negating that gives a fixnum. */ | |
5726 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
5727 | } | |
0aacf84e MD |
5728 | else |
5729 | { | |
5730 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5731 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 5732 | |
0aacf84e MD |
5733 | if (xx >= 0) |
5734 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
5735 | else | |
5736 | { | |
5737 | /* x - y == -(y + -x) */ | |
5738 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
5739 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
5740 | } | |
5741 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 5742 | |
0aacf84e MD |
5743 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
5744 | /* we know the result will have to be a bignum */ | |
5745 | return result; | |
5746 | else | |
5747 | return scm_i_normbig (result); | |
5748 | } | |
5749 | } | |
5750 | else if (SCM_REALP (y)) | |
5751 | { | |
e25f3727 | 5752 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
5753 | |
5754 | /* | |
5755 | * We need to handle x == exact 0 | |
5756 | * specially because R6RS states that: | |
5757 | * (- 0.0) ==> -0.0 and | |
5758 | * (- 0.0 0.0) ==> 0.0 | |
5759 | * and the scheme compiler changes | |
5760 | * (- 0.0) into (- 0 0.0) | |
5761 | * So we need to treat (- 0 0.0) like (- 0.0). | |
5762 | * At the C level, (-x) is different than (0.0 - x). | |
5763 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
5764 | */ | |
5765 | if (xx == 0) | |
5766 | return scm_from_double (- SCM_REAL_VALUE (y)); | |
5767 | else | |
5768 | return scm_from_double (xx - SCM_REAL_VALUE (y)); | |
0aacf84e MD |
5769 | } |
5770 | else if (SCM_COMPLEXP (y)) | |
5771 | { | |
e25f3727 | 5772 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
5773 | |
5774 | /* We need to handle x == exact 0 specially. | |
5775 | See the comment above (for SCM_REALP (y)) */ | |
5776 | if (xx == 0) | |
5777 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
5778 | - SCM_COMPLEX_IMAG (y)); | |
5779 | else | |
5780 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
5781 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 5782 | } |
f92e85f7 MV |
5783 | else if (SCM_FRACTIONP (y)) |
5784 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 5785 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5786 | SCM_FRACTION_NUMERATOR (y)), |
5787 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
5788 | else |
5789 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 5790 | } |
0aacf84e MD |
5791 | else if (SCM_BIGP (x)) |
5792 | { | |
e11e83f3 | 5793 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5794 | { |
5795 | /* big-x - inum-y */ | |
e25f3727 | 5796 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 5797 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 5798 | |
0aacf84e MD |
5799 | scm_remember_upto_here_1 (x); |
5800 | if (sgn_x == 0) | |
c71b0706 | 5801 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 5802 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
5803 | else |
5804 | { | |
5805 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 5806 | |
708f22c6 KR |
5807 | if (yy >= 0) |
5808 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
5809 | else | |
5810 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 5811 | scm_remember_upto_here_1 (x); |
ca46fb90 | 5812 | |
0aacf84e MD |
5813 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
5814 | /* we know the result will have to be a bignum */ | |
5815 | return result; | |
5816 | else | |
5817 | return scm_i_normbig (result); | |
5818 | } | |
5819 | } | |
5820 | else if (SCM_BIGP (y)) | |
5821 | { | |
5822 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5823 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5824 | SCM result = scm_i_mkbig (); | |
5825 | mpz_sub (SCM_I_BIG_MPZ (result), | |
5826 | SCM_I_BIG_MPZ (x), | |
5827 | SCM_I_BIG_MPZ (y)); | |
5828 | scm_remember_upto_here_2 (x, y); | |
5829 | /* we know the result will have to be a bignum */ | |
5830 | if ((sgn_x == 1) && (sgn_y == -1)) | |
5831 | return result; | |
5832 | if ((sgn_x == -1) && (sgn_y == 1)) | |
5833 | return result; | |
5834 | return scm_i_normbig (result); | |
5835 | } | |
5836 | else if (SCM_REALP (y)) | |
5837 | { | |
5838 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
5839 | scm_remember_upto_here_1 (x); | |
55f26379 | 5840 | return scm_from_double (result); |
0aacf84e MD |
5841 | } |
5842 | else if (SCM_COMPLEXP (y)) | |
5843 | { | |
5844 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
5845 | - SCM_COMPLEX_REAL (y)); | |
5846 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5847 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 5848 | } |
f92e85f7 | 5849 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5850 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5851 | SCM_FRACTION_NUMERATOR (y)), |
5852 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 5853 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 5854 | } |
0aacf84e MD |
5855 | else if (SCM_REALP (x)) |
5856 | { | |
e11e83f3 | 5857 | if (SCM_I_INUMP (y)) |
55f26379 | 5858 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
5859 | else if (SCM_BIGP (y)) |
5860 | { | |
5861 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
5862 | scm_remember_upto_here_1 (x); | |
55f26379 | 5863 | return scm_from_double (result); |
0aacf84e MD |
5864 | } |
5865 | else if (SCM_REALP (y)) | |
55f26379 | 5866 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 5867 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5868 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 5869 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5870 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5871 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
5872 | else |
5873 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 5874 | } |
0aacf84e MD |
5875 | else if (SCM_COMPLEXP (x)) |
5876 | { | |
e11e83f3 | 5877 | if (SCM_I_INUMP (y)) |
8507ec80 | 5878 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
5879 | SCM_COMPLEX_IMAG (x)); |
5880 | else if (SCM_BIGP (y)) | |
5881 | { | |
5882 | double real_part = (SCM_COMPLEX_REAL (x) | |
5883 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
5884 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5885 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
5886 | } |
5887 | else if (SCM_REALP (y)) | |
8507ec80 | 5888 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
5889 | SCM_COMPLEX_IMAG (x)); |
5890 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 5891 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 5892 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5893 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 5894 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
5895 | SCM_COMPLEX_IMAG (x)); |
5896 | else | |
5897 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
5898 | } | |
5899 | else if (SCM_FRACTIONP (x)) | |
5900 | { | |
e11e83f3 | 5901 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5902 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 5903 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5904 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
5905 | SCM_FRACTION_DENOMINATOR (x)); | |
5906 | else if (SCM_BIGP (y)) | |
cba42c93 | 5907 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5908 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
5909 | SCM_FRACTION_DENOMINATOR (x)); | |
5910 | else if (SCM_REALP (y)) | |
55f26379 | 5911 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 5912 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5913 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
5914 | -SCM_COMPLEX_IMAG (y)); |
5915 | else if (SCM_FRACTIONP (y)) | |
5916 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 5917 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5918 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
5919 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
5920 | else |
5921 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 5922 | } |
0aacf84e | 5923 | else |
98cb6e75 | 5924 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 5925 | } |
c05e97b7 | 5926 | #undef FUNC_NAME |
0f2d19dd | 5927 | |
ca46fb90 | 5928 | |
40882e3d KR |
5929 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
5930 | (SCM x), | |
5931 | "Return @math{@var{x}-1}.") | |
5932 | #define FUNC_NAME s_scm_oneminus | |
5933 | { | |
cff5fa33 | 5934 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
5935 | } |
5936 | #undef FUNC_NAME | |
5937 | ||
5938 | ||
78d3deb1 AW |
5939 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
5940 | (SCM x, SCM y, SCM rest), | |
5941 | "Return the product of all arguments. If called without arguments,\n" | |
5942 | "1 is returned.") | |
5943 | #define FUNC_NAME s_scm_i_product | |
5944 | { | |
5945 | while (!scm_is_null (rest)) | |
5946 | { x = scm_product (x, y); | |
5947 | y = scm_car (rest); | |
5948 | rest = scm_cdr (rest); | |
5949 | } | |
5950 | return scm_product (x, y); | |
5951 | } | |
5952 | #undef FUNC_NAME | |
5953 | ||
5954 | #define s_product s_scm_i_product | |
5955 | #define g_product g_scm_i_product | |
5956 | ||
0f2d19dd | 5957 | SCM |
6e8d25a6 | 5958 | scm_product (SCM x, SCM y) |
0f2d19dd | 5959 | { |
9cc37597 | 5960 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
5961 | { |
5962 | if (SCM_UNBNDP (x)) | |
d956fa6f | 5963 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
5964 | else if (SCM_NUMBERP (x)) |
5965 | return x; | |
5966 | else | |
5967 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 5968 | } |
ca46fb90 | 5969 | |
9cc37597 | 5970 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 5971 | { |
e25f3727 | 5972 | scm_t_inum xx; |
f4c627b3 | 5973 | |
5e791807 | 5974 | xinum: |
e11e83f3 | 5975 | xx = SCM_I_INUM (x); |
f4c627b3 | 5976 | |
0aacf84e MD |
5977 | switch (xx) |
5978 | { | |
5e791807 MW |
5979 | case 1: |
5980 | /* exact1 is the universal multiplicative identity */ | |
5981 | return y; | |
5982 | break; | |
5983 | case 0: | |
5984 | /* exact0 times a fixnum is exact0: optimize this case */ | |
5985 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
5986 | return SCM_INUM0; | |
5987 | /* if the other argument is inexact, the result is inexact, | |
5988 | and we must do the multiplication in order to handle | |
5989 | infinities and NaNs properly. */ | |
5990 | else if (SCM_REALP (y)) | |
5991 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
5992 | else if (SCM_COMPLEXP (y)) | |
5993 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
5994 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
5995 | /* we've already handled inexact numbers, | |
5996 | so y must be exact, and we return exact0 */ | |
5997 | else if (SCM_NUMP (y)) | |
5998 | return SCM_INUM0; | |
5999 | else | |
6000 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
6001 | break; | |
6002 | case -1: | |
b5c40589 | 6003 | /* |
5e791807 MW |
6004 | * This case is important for more than just optimization. |
6005 | * It handles the case of negating | |
b5c40589 MW |
6006 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
6007 | * which is a bignum that must be changed back into a fixnum. | |
6008 | * Failure to do so will cause the following to return #f: | |
6009 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
6010 | */ | |
b5c40589 MW |
6011 | return scm_difference(y, SCM_UNDEFINED); |
6012 | break; | |
0aacf84e | 6013 | } |
f4c627b3 | 6014 | |
9cc37597 | 6015 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 6016 | { |
e25f3727 AW |
6017 | scm_t_inum yy = SCM_I_INUM (y); |
6018 | scm_t_inum kk = xx * yy; | |
d956fa6f | 6019 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 6020 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
6021 | return k; |
6022 | else | |
6023 | { | |
e25f3727 | 6024 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
6025 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
6026 | return scm_i_normbig (result); | |
6027 | } | |
6028 | } | |
6029 | else if (SCM_BIGP (y)) | |
6030 | { | |
6031 | SCM result = scm_i_mkbig (); | |
6032 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
6033 | scm_remember_upto_here_1 (y); | |
6034 | return result; | |
6035 | } | |
6036 | else if (SCM_REALP (y)) | |
55f26379 | 6037 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 6038 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 6039 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 6040 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 6041 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 6042 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 6043 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
6044 | else |
6045 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6046 | } |
0aacf84e MD |
6047 | else if (SCM_BIGP (x)) |
6048 | { | |
e11e83f3 | 6049 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6050 | { |
6051 | SCM_SWAP (x, y); | |
5e791807 | 6052 | goto xinum; |
0aacf84e MD |
6053 | } |
6054 | else if (SCM_BIGP (y)) | |
6055 | { | |
6056 | SCM result = scm_i_mkbig (); | |
6057 | mpz_mul (SCM_I_BIG_MPZ (result), | |
6058 | SCM_I_BIG_MPZ (x), | |
6059 | SCM_I_BIG_MPZ (y)); | |
6060 | scm_remember_upto_here_2 (x, y); | |
6061 | return result; | |
6062 | } | |
6063 | else if (SCM_REALP (y)) | |
6064 | { | |
6065 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
6066 | scm_remember_upto_here_1 (x); | |
55f26379 | 6067 | return scm_from_double (result); |
0aacf84e MD |
6068 | } |
6069 | else if (SCM_COMPLEXP (y)) | |
6070 | { | |
6071 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
6072 | scm_remember_upto_here_1 (x); | |
8507ec80 | 6073 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
6074 | z * SCM_COMPLEX_IMAG (y)); |
6075 | } | |
f92e85f7 | 6076 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 6077 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 6078 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
6079 | else |
6080 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6081 | } |
0aacf84e MD |
6082 | else if (SCM_REALP (x)) |
6083 | { | |
e11e83f3 | 6084 | if (SCM_I_INUMP (y)) |
5e791807 MW |
6085 | { |
6086 | SCM_SWAP (x, y); | |
6087 | goto xinum; | |
6088 | } | |
0aacf84e MD |
6089 | else if (SCM_BIGP (y)) |
6090 | { | |
6091 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
6092 | scm_remember_upto_here_1 (y); | |
55f26379 | 6093 | return scm_from_double (result); |
0aacf84e MD |
6094 | } |
6095 | else if (SCM_REALP (y)) | |
55f26379 | 6096 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 6097 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 6098 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 6099 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 6100 | else if (SCM_FRACTIONP (y)) |
55f26379 | 6101 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
6102 | else |
6103 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6104 | } |
0aacf84e MD |
6105 | else if (SCM_COMPLEXP (x)) |
6106 | { | |
e11e83f3 | 6107 | if (SCM_I_INUMP (y)) |
5e791807 MW |
6108 | { |
6109 | SCM_SWAP (x, y); | |
6110 | goto xinum; | |
6111 | } | |
0aacf84e MD |
6112 | else if (SCM_BIGP (y)) |
6113 | { | |
6114 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6115 | scm_remember_upto_here_1 (y); | |
8507ec80 | 6116 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 6117 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
6118 | } |
6119 | else if (SCM_REALP (y)) | |
8507ec80 | 6120 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
6121 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
6122 | else if (SCM_COMPLEXP (y)) | |
6123 | { | |
8507ec80 | 6124 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
6125 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
6126 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
6127 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
6128 | } | |
f92e85f7 MV |
6129 | else if (SCM_FRACTIONP (y)) |
6130 | { | |
6131 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 6132 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
6133 | yy * SCM_COMPLEX_IMAG (x)); |
6134 | } | |
6135 | else | |
6136 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
6137 | } | |
6138 | else if (SCM_FRACTIONP (x)) | |
6139 | { | |
e11e83f3 | 6140 | if (SCM_I_INUMP (y)) |
cba42c93 | 6141 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
6142 | SCM_FRACTION_DENOMINATOR (x)); |
6143 | else if (SCM_BIGP (y)) | |
cba42c93 | 6144 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
6145 | SCM_FRACTION_DENOMINATOR (x)); |
6146 | else if (SCM_REALP (y)) | |
55f26379 | 6147 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
6148 | else if (SCM_COMPLEXP (y)) |
6149 | { | |
6150 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 6151 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
6152 | xx * SCM_COMPLEX_IMAG (y)); |
6153 | } | |
6154 | else if (SCM_FRACTIONP (y)) | |
6155 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 6156 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6157 | SCM_FRACTION_NUMERATOR (y)), |
6158 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
6159 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
6160 | else |
6161 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6162 | } |
0aacf84e | 6163 | else |
f4c627b3 | 6164 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
6165 | } |
6166 | ||
7351e207 MV |
6167 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
6168 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
6169 | #define ALLOW_DIVIDE_BY_ZERO | |
6170 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
6171 | #endif | |
0f2d19dd | 6172 | |
ba74ef4e MV |
6173 | /* The code below for complex division is adapted from the GNU |
6174 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
6175 | this copyright: */ | |
6176 | ||
6177 | /**************************************************************** | |
6178 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
6179 | ||
6180 | Permission to use, copy, modify, and distribute this software | |
6181 | and its documentation for any purpose and without fee is hereby | |
6182 | granted, provided that the above copyright notice appear in all | |
6183 | copies and that both that the copyright notice and this | |
6184 | permission notice and warranty disclaimer appear in supporting | |
6185 | documentation, and that the names of AT&T Bell Laboratories or | |
6186 | Bellcore or any of their entities not be used in advertising or | |
6187 | publicity pertaining to distribution of the software without | |
6188 | specific, written prior permission. | |
6189 | ||
6190 | AT&T and Bellcore disclaim all warranties with regard to this | |
6191 | software, including all implied warranties of merchantability | |
6192 | and fitness. In no event shall AT&T or Bellcore be liable for | |
6193 | any special, indirect or consequential damages or any damages | |
6194 | whatsoever resulting from loss of use, data or profits, whether | |
6195 | in an action of contract, negligence or other tortious action, | |
6196 | arising out of or in connection with the use or performance of | |
6197 | this software. | |
6198 | ****************************************************************/ | |
6199 | ||
78d3deb1 AW |
6200 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
6201 | (SCM x, SCM y, SCM rest), | |
6202 | "Divide the first argument by the product of the remaining\n" | |
6203 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
6204 | "returned.") | |
6205 | #define FUNC_NAME s_scm_i_divide | |
6206 | { | |
6207 | while (!scm_is_null (rest)) | |
6208 | { x = scm_divide (x, y); | |
6209 | y = scm_car (rest); | |
6210 | rest = scm_cdr (rest); | |
6211 | } | |
6212 | return scm_divide (x, y); | |
6213 | } | |
6214 | #undef FUNC_NAME | |
6215 | ||
6216 | #define s_divide s_scm_i_divide | |
6217 | #define g_divide g_scm_i_divide | |
6218 | ||
f92e85f7 | 6219 | static SCM |
78d3deb1 AW |
6220 | do_divide (SCM x, SCM y, int inexact) |
6221 | #define FUNC_NAME s_divide | |
0f2d19dd | 6222 | { |
f8de44c1 DH |
6223 | double a; |
6224 | ||
9cc37597 | 6225 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
6226 | { |
6227 | if (SCM_UNBNDP (x)) | |
6228 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 6229 | else if (SCM_I_INUMP (x)) |
0aacf84e | 6230 | { |
e25f3727 | 6231 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
6232 | if (xx == 1 || xx == -1) |
6233 | return x; | |
7351e207 | 6234 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6235 | else if (xx == 0) |
6236 | scm_num_overflow (s_divide); | |
7351e207 | 6237 | #endif |
0aacf84e | 6238 | else |
f92e85f7 MV |
6239 | { |
6240 | if (inexact) | |
55f26379 | 6241 | return scm_from_double (1.0 / (double) xx); |
cff5fa33 | 6242 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 6243 | } |
0aacf84e MD |
6244 | } |
6245 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
6246 | { |
6247 | if (inexact) | |
55f26379 | 6248 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cff5fa33 | 6249 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 6250 | } |
0aacf84e MD |
6251 | else if (SCM_REALP (x)) |
6252 | { | |
6253 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 6254 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6255 | if (xx == 0.0) |
6256 | scm_num_overflow (s_divide); | |
6257 | else | |
7351e207 | 6258 | #endif |
55f26379 | 6259 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
6260 | } |
6261 | else if (SCM_COMPLEXP (x)) | |
6262 | { | |
6263 | double r = SCM_COMPLEX_REAL (x); | |
6264 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 6265 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
6266 | { |
6267 | double t = r / i; | |
6268 | double d = i * (1.0 + t * t); | |
8507ec80 | 6269 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
6270 | } |
6271 | else | |
6272 | { | |
6273 | double t = i / r; | |
6274 | double d = r * (1.0 + t * t); | |
8507ec80 | 6275 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
6276 | } |
6277 | } | |
f92e85f7 | 6278 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 6279 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 6280 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
6281 | else |
6282 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 6283 | } |
f8de44c1 | 6284 | |
9cc37597 | 6285 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 6286 | { |
e25f3727 | 6287 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 6288 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 6289 | { |
e25f3727 | 6290 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6291 | if (yy == 0) |
6292 | { | |
7351e207 | 6293 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 6294 | scm_num_overflow (s_divide); |
7351e207 | 6295 | #else |
55f26379 | 6296 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 6297 | #endif |
0aacf84e MD |
6298 | } |
6299 | else if (xx % yy != 0) | |
f92e85f7 MV |
6300 | { |
6301 | if (inexact) | |
55f26379 | 6302 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 6303 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6304 | } |
0aacf84e MD |
6305 | else |
6306 | { | |
e25f3727 | 6307 | scm_t_inum z = xx / yy; |
0aacf84e | 6308 | if (SCM_FIXABLE (z)) |
d956fa6f | 6309 | return SCM_I_MAKINUM (z); |
0aacf84e | 6310 | else |
e25f3727 | 6311 | return scm_i_inum2big (z); |
0aacf84e | 6312 | } |
f872b822 | 6313 | } |
0aacf84e | 6314 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
6315 | { |
6316 | if (inexact) | |
55f26379 | 6317 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 6318 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6319 | } |
0aacf84e MD |
6320 | else if (SCM_REALP (y)) |
6321 | { | |
6322 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6323 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6324 | if (yy == 0.0) |
6325 | scm_num_overflow (s_divide); | |
6326 | else | |
7351e207 | 6327 | #endif |
55f26379 | 6328 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 6329 | } |
0aacf84e MD |
6330 | else if (SCM_COMPLEXP (y)) |
6331 | { | |
6332 | a = xx; | |
6333 | complex_div: /* y _must_ be a complex number */ | |
6334 | { | |
6335 | double r = SCM_COMPLEX_REAL (y); | |
6336 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 6337 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
6338 | { |
6339 | double t = r / i; | |
6340 | double d = i * (1.0 + t * t); | |
8507ec80 | 6341 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
6342 | } |
6343 | else | |
6344 | { | |
6345 | double t = i / r; | |
6346 | double d = r * (1.0 + t * t); | |
8507ec80 | 6347 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
6348 | } |
6349 | } | |
6350 | } | |
f92e85f7 MV |
6351 | else if (SCM_FRACTIONP (y)) |
6352 | /* a / b/c = ac / b */ | |
cba42c93 | 6353 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 6354 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
6355 | else |
6356 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 6357 | } |
0aacf84e MD |
6358 | else if (SCM_BIGP (x)) |
6359 | { | |
e11e83f3 | 6360 | if (SCM_I_INUMP (y)) |
0aacf84e | 6361 | { |
e25f3727 | 6362 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6363 | if (yy == 0) |
6364 | { | |
7351e207 | 6365 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 6366 | scm_num_overflow (s_divide); |
7351e207 | 6367 | #else |
0aacf84e MD |
6368 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
6369 | scm_remember_upto_here_1 (x); | |
6370 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 6371 | #endif |
0aacf84e MD |
6372 | } |
6373 | else if (yy == 1) | |
6374 | return x; | |
6375 | else | |
6376 | { | |
6377 | /* FIXME: HMM, what are the relative performance issues here? | |
6378 | We need to test. Is it faster on average to test | |
6379 | divisible_p, then perform whichever operation, or is it | |
6380 | faster to perform the integer div opportunistically and | |
6381 | switch to real if there's a remainder? For now we take the | |
6382 | middle ground: test, then if divisible, use the faster div | |
6383 | func. */ | |
6384 | ||
e25f3727 | 6385 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
6386 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
6387 | ||
6388 | if (divisible_p) | |
6389 | { | |
6390 | SCM result = scm_i_mkbig (); | |
6391 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
6392 | scm_remember_upto_here_1 (x); | |
6393 | if (yy < 0) | |
6394 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
6395 | return scm_i_normbig (result); | |
6396 | } | |
6397 | else | |
f92e85f7 MV |
6398 | { |
6399 | if (inexact) | |
55f26379 | 6400 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 6401 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6402 | } |
0aacf84e MD |
6403 | } |
6404 | } | |
6405 | else if (SCM_BIGP (y)) | |
6406 | { | |
a4955a04 MW |
6407 | /* big_x / big_y */ |
6408 | if (inexact) | |
0aacf84e | 6409 | { |
a4955a04 MW |
6410 | /* It's easily possible for the ratio x/y to fit a double |
6411 | but one or both x and y be too big to fit a double, | |
6412 | hence the use of mpq_get_d rather than converting and | |
6413 | dividing. */ | |
6414 | mpq_t q; | |
6415 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
6416 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
6417 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
6418 | } |
6419 | else | |
6420 | { | |
a4955a04 MW |
6421 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
6422 | SCM_I_BIG_MPZ (y)); | |
6423 | if (divisible_p) | |
6424 | { | |
6425 | SCM result = scm_i_mkbig (); | |
6426 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
6427 | SCM_I_BIG_MPZ (x), | |
6428 | SCM_I_BIG_MPZ (y)); | |
6429 | scm_remember_upto_here_2 (x, y); | |
6430 | return scm_i_normbig (result); | |
6431 | } | |
6432 | else | |
6433 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
6434 | } |
6435 | } | |
6436 | else if (SCM_REALP (y)) | |
6437 | { | |
6438 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6439 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6440 | if (yy == 0.0) |
6441 | scm_num_overflow (s_divide); | |
6442 | else | |
7351e207 | 6443 | #endif |
55f26379 | 6444 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
6445 | } |
6446 | else if (SCM_COMPLEXP (y)) | |
6447 | { | |
6448 | a = scm_i_big2dbl (x); | |
6449 | goto complex_div; | |
6450 | } | |
f92e85f7 | 6451 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 6452 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 6453 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
6454 | else |
6455 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 6456 | } |
0aacf84e MD |
6457 | else if (SCM_REALP (x)) |
6458 | { | |
6459 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 6460 | if (SCM_I_INUMP (y)) |
0aacf84e | 6461 | { |
e25f3727 | 6462 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 6463 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6464 | if (yy == 0) |
6465 | scm_num_overflow (s_divide); | |
6466 | else | |
7351e207 | 6467 | #endif |
55f26379 | 6468 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
6469 | } |
6470 | else if (SCM_BIGP (y)) | |
6471 | { | |
6472 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6473 | scm_remember_upto_here_1 (y); | |
55f26379 | 6474 | return scm_from_double (rx / dby); |
0aacf84e MD |
6475 | } |
6476 | else if (SCM_REALP (y)) | |
6477 | { | |
6478 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6479 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6480 | if (yy == 0.0) |
6481 | scm_num_overflow (s_divide); | |
6482 | else | |
7351e207 | 6483 | #endif |
55f26379 | 6484 | return scm_from_double (rx / yy); |
0aacf84e MD |
6485 | } |
6486 | else if (SCM_COMPLEXP (y)) | |
6487 | { | |
6488 | a = rx; | |
6489 | goto complex_div; | |
6490 | } | |
f92e85f7 | 6491 | else if (SCM_FRACTIONP (y)) |
55f26379 | 6492 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
6493 | else |
6494 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 6495 | } |
0aacf84e MD |
6496 | else if (SCM_COMPLEXP (x)) |
6497 | { | |
6498 | double rx = SCM_COMPLEX_REAL (x); | |
6499 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 6500 | if (SCM_I_INUMP (y)) |
0aacf84e | 6501 | { |
e25f3727 | 6502 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 6503 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6504 | if (yy == 0) |
6505 | scm_num_overflow (s_divide); | |
6506 | else | |
7351e207 | 6507 | #endif |
0aacf84e MD |
6508 | { |
6509 | double d = yy; | |
8507ec80 | 6510 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
6511 | } |
6512 | } | |
6513 | else if (SCM_BIGP (y)) | |
6514 | { | |
6515 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6516 | scm_remember_upto_here_1 (y); | |
8507ec80 | 6517 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
6518 | } |
6519 | else if (SCM_REALP (y)) | |
6520 | { | |
6521 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6522 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6523 | if (yy == 0.0) |
6524 | scm_num_overflow (s_divide); | |
6525 | else | |
7351e207 | 6526 | #endif |
8507ec80 | 6527 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
6528 | } |
6529 | else if (SCM_COMPLEXP (y)) | |
6530 | { | |
6531 | double ry = SCM_COMPLEX_REAL (y); | |
6532 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 6533 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
6534 | { |
6535 | double t = ry / iy; | |
6536 | double d = iy * (1.0 + t * t); | |
8507ec80 | 6537 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
6538 | } |
6539 | else | |
6540 | { | |
6541 | double t = iy / ry; | |
6542 | double d = ry * (1.0 + t * t); | |
8507ec80 | 6543 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
6544 | } |
6545 | } | |
f92e85f7 MV |
6546 | else if (SCM_FRACTIONP (y)) |
6547 | { | |
6548 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 6549 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 6550 | } |
0aacf84e MD |
6551 | else |
6552 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 6553 | } |
f92e85f7 MV |
6554 | else if (SCM_FRACTIONP (x)) |
6555 | { | |
e11e83f3 | 6556 | if (SCM_I_INUMP (y)) |
f92e85f7 | 6557 | { |
e25f3727 | 6558 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
6559 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
6560 | if (yy == 0) | |
6561 | scm_num_overflow (s_divide); | |
6562 | else | |
6563 | #endif | |
cba42c93 | 6564 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6565 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
6566 | } | |
6567 | else if (SCM_BIGP (y)) | |
6568 | { | |
cba42c93 | 6569 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6570 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
6571 | } | |
6572 | else if (SCM_REALP (y)) | |
6573 | { | |
6574 | double yy = SCM_REAL_VALUE (y); | |
6575 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6576 | if (yy == 0.0) | |
6577 | scm_num_overflow (s_divide); | |
6578 | else | |
6579 | #endif | |
55f26379 | 6580 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
6581 | } |
6582 | else if (SCM_COMPLEXP (y)) | |
6583 | { | |
6584 | a = scm_i_fraction2double (x); | |
6585 | goto complex_div; | |
6586 | } | |
6587 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 6588 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
6589 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
6590 | else | |
6591 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
6592 | } | |
0aacf84e | 6593 | else |
f8de44c1 | 6594 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 6595 | } |
f92e85f7 MV |
6596 | |
6597 | SCM | |
6598 | scm_divide (SCM x, SCM y) | |
6599 | { | |
78d3deb1 | 6600 | return do_divide (x, y, 0); |
f92e85f7 MV |
6601 | } |
6602 | ||
6603 | static SCM scm_divide2real (SCM x, SCM y) | |
6604 | { | |
78d3deb1 | 6605 | return do_divide (x, y, 1); |
f92e85f7 | 6606 | } |
c05e97b7 | 6607 | #undef FUNC_NAME |
0f2d19dd | 6608 | |
fa605590 | 6609 | |
0f2d19dd | 6610 | double |
3101f40f | 6611 | scm_c_truncate (double x) |
0f2d19dd | 6612 | { |
fa605590 KR |
6613 | #if HAVE_TRUNC |
6614 | return trunc (x); | |
6615 | #else | |
f872b822 MD |
6616 | if (x < 0.0) |
6617 | return -floor (-x); | |
6618 | return floor (x); | |
fa605590 | 6619 | #endif |
0f2d19dd | 6620 | } |
0f2d19dd | 6621 | |
3101f40f MV |
6622 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
6623 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
6624 | Then half-way cases are identified and adjusted down if the | |
6625 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
6626 | |
6627 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
6628 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
6629 | ||
6630 | An odd "result" value is identified with result/2 != floor(result/2). | |
6631 | This is done with plus_half, since that value is ready for use sooner in | |
6632 | a pipelined cpu, and we're already requiring plus_half == result. | |
6633 | ||
6634 | Note however that we need to be careful when x is big and already an | |
6635 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
6636 | us to return such a value, incorrectly. For instance if the hardware is | |
6637 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
6638 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
6639 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
6640 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
6641 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
6642 | ||
6643 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
6644 | x is already an integer. If it is then clearly that's the desired result | |
6645 | already. And if it's not then the exponent must be small enough to allow | |
6646 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
6647 | ||
0f2d19dd | 6648 | double |
3101f40f | 6649 | scm_c_round (double x) |
0f2d19dd | 6650 | { |
6187f48b KR |
6651 | double plus_half, result; |
6652 | ||
6653 | if (x == floor (x)) | |
6654 | return x; | |
6655 | ||
6656 | plus_half = x + 0.5; | |
6657 | result = floor (plus_half); | |
3101f40f | 6658 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
6659 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
6660 | ? result - 1 | |
6661 | : result); | |
0f2d19dd JB |
6662 | } |
6663 | ||
f92e85f7 MV |
6664 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
6665 | (SCM x), | |
6666 | "Round the number @var{x} towards zero.") | |
6667 | #define FUNC_NAME s_scm_truncate_number | |
6668 | { | |
73e4de09 | 6669 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
6670 | return scm_floor (x); |
6671 | else | |
6672 | return scm_ceiling (x); | |
6673 | } | |
6674 | #undef FUNC_NAME | |
6675 | ||
f92e85f7 MV |
6676 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, |
6677 | (SCM x), | |
6678 | "Round the number @var{x} towards the nearest integer. " | |
6679 | "When it is exactly halfway between two integers, " | |
6680 | "round towards the even one.") | |
6681 | #define FUNC_NAME s_scm_round_number | |
6682 | { | |
e11e83f3 | 6683 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
6684 | return x; |
6685 | else if (SCM_REALP (x)) | |
3101f40f | 6686 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 6687 | else |
bae30667 KR |
6688 | { |
6689 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
6690 | single quotient+remainder division then examining to see which way | |
6691 | the rounding should go. */ | |
6692 | SCM plus_half = scm_sum (x, exactly_one_half); | |
6693 | SCM result = scm_floor (plus_half); | |
3101f40f | 6694 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
6695 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
6696 | && scm_is_true (scm_odd_p (result))) | |
cff5fa33 | 6697 | return scm_difference (result, SCM_INUM1); |
bae30667 KR |
6698 | else |
6699 | return result; | |
6700 | } | |
f92e85f7 MV |
6701 | } |
6702 | #undef FUNC_NAME | |
6703 | ||
6704 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
6705 | (SCM x), | |
6706 | "Round the number @var{x} towards minus infinity.") | |
6707 | #define FUNC_NAME s_scm_floor | |
6708 | { | |
e11e83f3 | 6709 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
6710 | return x; |
6711 | else if (SCM_REALP (x)) | |
55f26379 | 6712 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
6713 | else if (SCM_FRACTIONP (x)) |
6714 | { | |
6715 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
6716 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 6717 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
6718 | { |
6719 | /* For positive x, rounding towards zero is correct. */ | |
6720 | return q; | |
6721 | } | |
6722 | else | |
6723 | { | |
6724 | /* For negative x, we need to return q-1 unless x is an | |
6725 | integer. But fractions are never integer, per our | |
6726 | assumptions. */ | |
cff5fa33 | 6727 | return scm_difference (q, SCM_INUM1); |
f92e85f7 MV |
6728 | } |
6729 | } | |
6730 | else | |
6731 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
6732 | } | |
6733 | #undef FUNC_NAME | |
6734 | ||
6735 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
6736 | (SCM x), | |
6737 | "Round the number @var{x} towards infinity.") | |
6738 | #define FUNC_NAME s_scm_ceiling | |
6739 | { | |
e11e83f3 | 6740 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
6741 | return x; |
6742 | else if (SCM_REALP (x)) | |
55f26379 | 6743 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
6744 | else if (SCM_FRACTIONP (x)) |
6745 | { | |
6746 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
6747 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 6748 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
6749 | { |
6750 | /* For negative x, rounding towards zero is correct. */ | |
6751 | return q; | |
6752 | } | |
6753 | else | |
6754 | { | |
6755 | /* For positive x, we need to return q+1 unless x is an | |
6756 | integer. But fractions are never integer, per our | |
6757 | assumptions. */ | |
cff5fa33 | 6758 | return scm_sum (q, SCM_INUM1); |
f92e85f7 MV |
6759 | } |
6760 | } | |
6761 | else | |
6762 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
6763 | } | |
6764 | #undef FUNC_NAME | |
0f2d19dd | 6765 | |
2519490c MW |
6766 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
6767 | (SCM x, SCM y), | |
6768 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 6769 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 6770 | { |
01c7284a MW |
6771 | if (scm_is_integer (y)) |
6772 | { | |
6773 | if (scm_is_true (scm_exact_p (y))) | |
6774 | return scm_integer_expt (x, y); | |
6775 | else | |
6776 | { | |
6777 | /* Here we handle the case where the exponent is an inexact | |
6778 | integer. We make the exponent exact in order to use | |
6779 | scm_integer_expt, and thus avoid the spurious imaginary | |
6780 | parts that may result from round-off errors in the general | |
6781 | e^(y log x) method below (for example when squaring a large | |
6782 | negative number). In this case, we must return an inexact | |
6783 | result for correctness. We also make the base inexact so | |
6784 | that scm_integer_expt will use fast inexact arithmetic | |
6785 | internally. Note that making the base inexact is not | |
6786 | sufficient to guarantee an inexact result, because | |
6787 | scm_integer_expt will return an exact 1 when the exponent | |
6788 | is 0, even if the base is inexact. */ | |
6789 | return scm_exact_to_inexact | |
6790 | (scm_integer_expt (scm_exact_to_inexact (x), | |
6791 | scm_inexact_to_exact (y))); | |
6792 | } | |
6793 | } | |
6fc4d012 AW |
6794 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
6795 | { | |
6796 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
6797 | } | |
2519490c | 6798 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 6799 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c MW |
6800 | else if (scm_is_complex (x)) |
6801 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); | |
6802 | else | |
6803 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); | |
0f2d19dd | 6804 | } |
1bbd0b84 | 6805 | #undef FUNC_NAME |
0f2d19dd | 6806 | |
7f41099e MW |
6807 | /* sin/cos/tan/asin/acos/atan |
6808 | sinh/cosh/tanh/asinh/acosh/atanh | |
6809 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
6810 | Written by Jerry D. Hedden, (C) FSF. | |
6811 | See the file `COPYING' for terms applying to this program. */ | |
6812 | ||
ad79736c AW |
6813 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
6814 | (SCM z), | |
6815 | "Compute the sine of @var{z}.") | |
6816 | #define FUNC_NAME s_scm_sin | |
6817 | { | |
8deddc94 MW |
6818 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6819 | return z; /* sin(exact0) = exact0 */ | |
6820 | else if (scm_is_real (z)) | |
ad79736c AW |
6821 | return scm_from_double (sin (scm_to_double (z))); |
6822 | else if (SCM_COMPLEXP (z)) | |
6823 | { double x, y; | |
6824 | x = SCM_COMPLEX_REAL (z); | |
6825 | y = SCM_COMPLEX_IMAG (z); | |
6826 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
6827 | cos (x) * sinh (y)); | |
6828 | } | |
6829 | else | |
6830 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
6831 | } | |
6832 | #undef FUNC_NAME | |
0f2d19dd | 6833 | |
ad79736c AW |
6834 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
6835 | (SCM z), | |
6836 | "Compute the cosine of @var{z}.") | |
6837 | #define FUNC_NAME s_scm_cos | |
6838 | { | |
8deddc94 MW |
6839 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6840 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
6841 | else if (scm_is_real (z)) | |
ad79736c AW |
6842 | return scm_from_double (cos (scm_to_double (z))); |
6843 | else if (SCM_COMPLEXP (z)) | |
6844 | { double x, y; | |
6845 | x = SCM_COMPLEX_REAL (z); | |
6846 | y = SCM_COMPLEX_IMAG (z); | |
6847 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
6848 | -sin (x) * sinh (y)); | |
6849 | } | |
6850 | else | |
6851 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
6852 | } | |
6853 | #undef FUNC_NAME | |
6854 | ||
6855 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
6856 | (SCM z), | |
6857 | "Compute the tangent of @var{z}.") | |
6858 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 6859 | { |
8deddc94 MW |
6860 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6861 | return z; /* tan(exact0) = exact0 */ | |
6862 | else if (scm_is_real (z)) | |
ad79736c AW |
6863 | return scm_from_double (tan (scm_to_double (z))); |
6864 | else if (SCM_COMPLEXP (z)) | |
6865 | { double x, y, w; | |
6866 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
6867 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
6868 | w = cos (x) + cosh (y); | |
6869 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6870 | if (w == 0.0) | |
6871 | scm_num_overflow (s_scm_tan); | |
6872 | #endif | |
6873 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
6874 | } | |
6875 | else | |
6876 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
6877 | } | |
6878 | #undef FUNC_NAME | |
6879 | ||
6880 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
6881 | (SCM z), | |
6882 | "Compute the hyperbolic sine of @var{z}.") | |
6883 | #define FUNC_NAME s_scm_sinh | |
6884 | { | |
8deddc94 MW |
6885 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6886 | return z; /* sinh(exact0) = exact0 */ | |
6887 | else if (scm_is_real (z)) | |
ad79736c AW |
6888 | return scm_from_double (sinh (scm_to_double (z))); |
6889 | else if (SCM_COMPLEXP (z)) | |
6890 | { double x, y; | |
6891 | x = SCM_COMPLEX_REAL (z); | |
6892 | y = SCM_COMPLEX_IMAG (z); | |
6893 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
6894 | cosh (x) * sin (y)); | |
6895 | } | |
6896 | else | |
6897 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
6898 | } | |
6899 | #undef FUNC_NAME | |
6900 | ||
6901 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
6902 | (SCM z), | |
6903 | "Compute the hyperbolic cosine of @var{z}.") | |
6904 | #define FUNC_NAME s_scm_cosh | |
6905 | { | |
8deddc94 MW |
6906 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6907 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
6908 | else if (scm_is_real (z)) | |
ad79736c AW |
6909 | return scm_from_double (cosh (scm_to_double (z))); |
6910 | else if (SCM_COMPLEXP (z)) | |
6911 | { double x, y; | |
6912 | x = SCM_COMPLEX_REAL (z); | |
6913 | y = SCM_COMPLEX_IMAG (z); | |
6914 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
6915 | sinh (x) * sin (y)); | |
6916 | } | |
6917 | else | |
6918 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
6919 | } | |
6920 | #undef FUNC_NAME | |
6921 | ||
6922 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
6923 | (SCM z), | |
6924 | "Compute the hyperbolic tangent of @var{z}.") | |
6925 | #define FUNC_NAME s_scm_tanh | |
6926 | { | |
8deddc94 MW |
6927 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6928 | return z; /* tanh(exact0) = exact0 */ | |
6929 | else if (scm_is_real (z)) | |
ad79736c AW |
6930 | return scm_from_double (tanh (scm_to_double (z))); |
6931 | else if (SCM_COMPLEXP (z)) | |
6932 | { double x, y, w; | |
6933 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
6934 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
6935 | w = cosh (x) + cos (y); | |
6936 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6937 | if (w == 0.0) | |
6938 | scm_num_overflow (s_scm_tanh); | |
6939 | #endif | |
6940 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
6941 | } | |
6942 | else | |
6943 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
6944 | } | |
6945 | #undef FUNC_NAME | |
6946 | ||
6947 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
6948 | (SCM z), | |
6949 | "Compute the arc sine of @var{z}.") | |
6950 | #define FUNC_NAME s_scm_asin | |
6951 | { | |
8deddc94 MW |
6952 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6953 | return z; /* asin(exact0) = exact0 */ | |
6954 | else if (scm_is_real (z)) | |
ad79736c AW |
6955 | { |
6956 | double w = scm_to_double (z); | |
6957 | if (w >= -1.0 && w <= 1.0) | |
6958 | return scm_from_double (asin (w)); | |
6959 | else | |
6960 | return scm_product (scm_c_make_rectangular (0, -1), | |
6961 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
6962 | } | |
6963 | else if (SCM_COMPLEXP (z)) | |
6964 | { double x, y; | |
6965 | x = SCM_COMPLEX_REAL (z); | |
6966 | y = SCM_COMPLEX_IMAG (z); | |
6967 | return scm_product (scm_c_make_rectangular (0, -1), | |
6968 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
6969 | } | |
6970 | else | |
6971 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
6972 | } | |
6973 | #undef FUNC_NAME | |
6974 | ||
6975 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
6976 | (SCM z), | |
6977 | "Compute the arc cosine of @var{z}.") | |
6978 | #define FUNC_NAME s_scm_acos | |
6979 | { | |
8deddc94 MW |
6980 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
6981 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
6982 | else if (scm_is_real (z)) | |
ad79736c AW |
6983 | { |
6984 | double w = scm_to_double (z); | |
6985 | if (w >= -1.0 && w <= 1.0) | |
6986 | return scm_from_double (acos (w)); | |
6987 | else | |
6988 | return scm_sum (scm_from_double (acos (0.0)), | |
6989 | scm_product (scm_c_make_rectangular (0, 1), | |
6990 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
6991 | } | |
6992 | else if (SCM_COMPLEXP (z)) | |
6993 | { double x, y; | |
6994 | x = SCM_COMPLEX_REAL (z); | |
6995 | y = SCM_COMPLEX_IMAG (z); | |
6996 | return scm_sum (scm_from_double (acos (0.0)), | |
6997 | scm_product (scm_c_make_rectangular (0, 1), | |
6998 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
6999 | } | |
7000 | else | |
7001 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
7002 | } | |
7003 | #undef FUNC_NAME | |
7004 | ||
7005 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
7006 | (SCM z, SCM y), | |
7007 | "With one argument, compute the arc tangent of @var{z}.\n" | |
7008 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
7009 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
7010 | #define FUNC_NAME s_scm_atan | |
7011 | { | |
7012 | if (SCM_UNBNDP (y)) | |
7013 | { | |
8deddc94 MW |
7014 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
7015 | return z; /* atan(exact0) = exact0 */ | |
7016 | else if (scm_is_real (z)) | |
ad79736c AW |
7017 | return scm_from_double (atan (scm_to_double (z))); |
7018 | else if (SCM_COMPLEXP (z)) | |
7019 | { | |
7020 | double v, w; | |
7021 | v = SCM_COMPLEX_REAL (z); | |
7022 | w = SCM_COMPLEX_IMAG (z); | |
7023 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
7024 | scm_c_make_rectangular (v, w + 1.0))), | |
7025 | scm_c_make_rectangular (0, 2)); | |
7026 | } | |
7027 | else | |
7028 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
7029 | } | |
7030 | else if (scm_is_real (z)) | |
7031 | { | |
7032 | if (scm_is_real (y)) | |
7033 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
7034 | else | |
7035 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
7036 | } | |
7037 | else | |
7038 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
7039 | } | |
7040 | #undef FUNC_NAME | |
7041 | ||
7042 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
7043 | (SCM z), | |
7044 | "Compute the inverse hyperbolic sine of @var{z}.") | |
7045 | #define FUNC_NAME s_scm_sys_asinh | |
7046 | { | |
8deddc94 MW |
7047 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
7048 | return z; /* asinh(exact0) = exact0 */ | |
7049 | else if (scm_is_real (z)) | |
ad79736c AW |
7050 | return scm_from_double (asinh (scm_to_double (z))); |
7051 | else if (scm_is_number (z)) | |
7052 | return scm_log (scm_sum (z, | |
7053 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 7054 | SCM_INUM1)))); |
ad79736c AW |
7055 | else |
7056 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
7057 | } | |
7058 | #undef FUNC_NAME | |
7059 | ||
7060 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
7061 | (SCM z), | |
7062 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
7063 | #define FUNC_NAME s_scm_sys_acosh | |
7064 | { | |
8deddc94 MW |
7065 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
7066 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
7067 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
7068 | return scm_from_double (acosh (scm_to_double (z))); |
7069 | else if (scm_is_number (z)) | |
7070 | return scm_log (scm_sum (z, | |
7071 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 7072 | SCM_INUM1)))); |
ad79736c AW |
7073 | else |
7074 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
7075 | } | |
7076 | #undef FUNC_NAME | |
7077 | ||
7078 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
7079 | (SCM z), | |
7080 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
7081 | #define FUNC_NAME s_scm_sys_atanh | |
7082 | { | |
8deddc94 MW |
7083 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
7084 | return z; /* atanh(exact0) = exact0 */ | |
7085 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
7086 | return scm_from_double (atanh (scm_to_double (z))); |
7087 | else if (scm_is_number (z)) | |
cff5fa33 MW |
7088 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
7089 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
7090 | SCM_I_MAKINUM (2)); |
7091 | else | |
7092 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 7093 | } |
1bbd0b84 | 7094 | #undef FUNC_NAME |
0f2d19dd | 7095 | |
8507ec80 MV |
7096 | SCM |
7097 | scm_c_make_rectangular (double re, double im) | |
7098 | { | |
c7218482 | 7099 | SCM z; |
03604fcf | 7100 | |
c7218482 MW |
7101 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
7102 | "complex")); | |
7103 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); | |
7104 | SCM_COMPLEX_REAL (z) = re; | |
7105 | SCM_COMPLEX_IMAG (z) = im; | |
7106 | return z; | |
8507ec80 | 7107 | } |
0f2d19dd | 7108 | |
a1ec6916 | 7109 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
7110 | (SCM real_part, SCM imaginary_part), |
7111 | "Return a complex number constructed of the given @var{real-part} " | |
7112 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 7113 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 7114 | { |
ad79736c AW |
7115 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
7116 | SCM_ARG1, FUNC_NAME, "real"); | |
7117 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
7118 | SCM_ARG2, FUNC_NAME, "real"); | |
c7218482 MW |
7119 | |
7120 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ | |
7121 | if (scm_is_eq (imaginary_part, SCM_INUM0)) | |
7122 | return real_part; | |
7123 | else | |
7124 | return scm_c_make_rectangular (scm_to_double (real_part), | |
7125 | scm_to_double (imaginary_part)); | |
0f2d19dd | 7126 | } |
1bbd0b84 | 7127 | #undef FUNC_NAME |
0f2d19dd | 7128 | |
8507ec80 MV |
7129 | SCM |
7130 | scm_c_make_polar (double mag, double ang) | |
7131 | { | |
7132 | double s, c; | |
5e647d08 LC |
7133 | |
7134 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
7135 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
7136 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
7137 | details. */ | |
7138 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
7139 | sincos (ang, &s, &c); |
7140 | #else | |
7141 | s = sin (ang); | |
7142 | c = cos (ang); | |
7143 | #endif | |
9d427b2c MW |
7144 | |
7145 | /* If s and c are NaNs, this indicates that the angle is a NaN, | |
7146 | infinite, or perhaps simply too large to determine its value | |
7147 | mod 2*pi. However, we know something that the floating-point | |
7148 | implementation doesn't know: We know that s and c are finite. | |
7149 | Therefore, if the magnitude is zero, return a complex zero. | |
7150 | ||
7151 | The reason we check for the NaNs instead of using this case | |
7152 | whenever mag == 0.0 is because when the angle is known, we'd | |
7153 | like to return the correct kind of non-real complex zero: | |
7154 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending | |
7155 | on which quadrant the angle is in. | |
7156 | */ | |
7157 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) | |
7158 | return scm_c_make_rectangular (0.0, 0.0); | |
7159 | else | |
7160 | return scm_c_make_rectangular (mag * c, mag * s); | |
8507ec80 | 7161 | } |
0f2d19dd | 7162 | |
a1ec6916 | 7163 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
c7218482 MW |
7164 | (SCM mag, SCM ang), |
7165 | "Return the complex number @var{mag} * e^(i * @var{ang}).") | |
1bbd0b84 | 7166 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 7167 | { |
c7218482 MW |
7168 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
7169 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); | |
7170 | ||
7171 | /* If mag is exact0, return exact0 */ | |
7172 | if (scm_is_eq (mag, SCM_INUM0)) | |
7173 | return SCM_INUM0; | |
7174 | /* Return a real if ang is exact0 */ | |
7175 | else if (scm_is_eq (ang, SCM_INUM0)) | |
7176 | return mag; | |
7177 | else | |
7178 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); | |
0f2d19dd | 7179 | } |
1bbd0b84 | 7180 | #undef FUNC_NAME |
0f2d19dd JB |
7181 | |
7182 | ||
2519490c MW |
7183 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
7184 | (SCM z), | |
7185 | "Return the real part of the number @var{z}.") | |
7186 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 7187 | { |
2519490c | 7188 | if (SCM_COMPLEXP (z)) |
55f26379 | 7189 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 7190 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 7191 | return z; |
0aacf84e | 7192 | else |
2519490c | 7193 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 7194 | } |
2519490c | 7195 | #undef FUNC_NAME |
0f2d19dd JB |
7196 | |
7197 | ||
2519490c MW |
7198 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
7199 | (SCM z), | |
7200 | "Return the imaginary part of the number @var{z}.") | |
7201 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 7202 | { |
2519490c MW |
7203 | if (SCM_COMPLEXP (z)) |
7204 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
c7218482 | 7205 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 7206 | return SCM_INUM0; |
0aacf84e | 7207 | else |
2519490c | 7208 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 7209 | } |
2519490c | 7210 | #undef FUNC_NAME |
0f2d19dd | 7211 | |
2519490c MW |
7212 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
7213 | (SCM z), | |
7214 | "Return the numerator of the number @var{z}.") | |
7215 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 7216 | { |
2519490c | 7217 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
7218 | return z; |
7219 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 7220 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
7221 | else if (SCM_REALP (z)) |
7222 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
7223 | else | |
2519490c | 7224 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 7225 | } |
2519490c | 7226 | #undef FUNC_NAME |
f92e85f7 MV |
7227 | |
7228 | ||
2519490c MW |
7229 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
7230 | (SCM z), | |
7231 | "Return the denominator of the number @var{z}.") | |
7232 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 7233 | { |
2519490c | 7234 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 7235 | return SCM_INUM1; |
f92e85f7 | 7236 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 7237 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
7238 | else if (SCM_REALP (z)) |
7239 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
7240 | else | |
2519490c | 7241 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
f92e85f7 | 7242 | } |
2519490c | 7243 | #undef FUNC_NAME |
0f2d19dd | 7244 | |
2519490c MW |
7245 | |
7246 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
7247 | (SCM z), | |
7248 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
7249 | "@code{abs} for real arguments, but also allows complex numbers.") | |
7250 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 7251 | { |
e11e83f3 | 7252 | if (SCM_I_INUMP (z)) |
0aacf84e | 7253 | { |
e25f3727 | 7254 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
7255 | if (zz >= 0) |
7256 | return z; | |
7257 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 7258 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 7259 | else |
e25f3727 | 7260 | return scm_i_inum2big (-zz); |
5986c47d | 7261 | } |
0aacf84e MD |
7262 | else if (SCM_BIGP (z)) |
7263 | { | |
7264 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
7265 | scm_remember_upto_here_1 (z); | |
7266 | if (sgn < 0) | |
7267 | return scm_i_clonebig (z, 0); | |
7268 | else | |
7269 | return z; | |
5986c47d | 7270 | } |
0aacf84e | 7271 | else if (SCM_REALP (z)) |
55f26379 | 7272 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 7273 | else if (SCM_COMPLEXP (z)) |
55f26379 | 7274 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
7275 | else if (SCM_FRACTIONP (z)) |
7276 | { | |
73e4de09 | 7277 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 7278 | return z; |
cba42c93 | 7279 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
7280 | SCM_FRACTION_DENOMINATOR (z)); |
7281 | } | |
0aacf84e | 7282 | else |
2519490c | 7283 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
0f2d19dd | 7284 | } |
2519490c | 7285 | #undef FUNC_NAME |
0f2d19dd JB |
7286 | |
7287 | ||
2519490c MW |
7288 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
7289 | (SCM z), | |
7290 | "Return the angle of the complex number @var{z}.") | |
7291 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 7292 | { |
c8ae173e | 7293 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 7294 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
7295 | But if atan2 follows the floating point rounding mode, then the value |
7296 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 7297 | if (SCM_I_INUMP (z)) |
0aacf84e | 7298 | { |
e11e83f3 | 7299 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 7300 | return flo0; |
0aacf84e | 7301 | else |
55f26379 | 7302 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 7303 | } |
0aacf84e MD |
7304 | else if (SCM_BIGP (z)) |
7305 | { | |
7306 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
7307 | scm_remember_upto_here_1 (z); | |
7308 | if (sgn < 0) | |
55f26379 | 7309 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 7310 | else |
e7efe8e7 | 7311 | return flo0; |
0f2d19dd | 7312 | } |
0aacf84e | 7313 | else if (SCM_REALP (z)) |
c8ae173e KR |
7314 | { |
7315 | if (SCM_REAL_VALUE (z) >= 0) | |
e7efe8e7 | 7316 | return flo0; |
c8ae173e | 7317 | else |
55f26379 | 7318 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 7319 | } |
0aacf84e | 7320 | else if (SCM_COMPLEXP (z)) |
55f26379 | 7321 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
7322 | else if (SCM_FRACTIONP (z)) |
7323 | { | |
73e4de09 | 7324 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 7325 | return flo0; |
55f26379 | 7326 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 7327 | } |
0aacf84e | 7328 | else |
2519490c | 7329 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 7330 | } |
2519490c | 7331 | #undef FUNC_NAME |
0f2d19dd JB |
7332 | |
7333 | ||
2519490c MW |
7334 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
7335 | (SCM z), | |
7336 | "Convert the number @var{z} to its inexact representation.\n") | |
7337 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 7338 | { |
e11e83f3 | 7339 | if (SCM_I_INUMP (z)) |
55f26379 | 7340 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 7341 | else if (SCM_BIGP (z)) |
55f26379 | 7342 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 7343 | else if (SCM_FRACTIONP (z)) |
55f26379 | 7344 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
7345 | else if (SCM_INEXACTP (z)) |
7346 | return z; | |
7347 | else | |
2519490c | 7348 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
3c9a524f | 7349 | } |
2519490c | 7350 | #undef FUNC_NAME |
3c9a524f DH |
7351 | |
7352 | ||
2519490c MW |
7353 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
7354 | (SCM z), | |
7355 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 7356 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 7357 | { |
c7218482 | 7358 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f872b822 | 7359 | return z; |
c7218482 | 7360 | else |
0aacf84e | 7361 | { |
c7218482 MW |
7362 | double val; |
7363 | ||
7364 | if (SCM_REALP (z)) | |
7365 | val = SCM_REAL_VALUE (z); | |
7366 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) | |
7367 | val = SCM_COMPLEX_REAL (z); | |
7368 | else | |
7369 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); | |
7370 | ||
7371 | if (!SCM_LIKELY (DOUBLE_IS_FINITE (val))) | |
f92e85f7 | 7372 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 7373 | else |
f92e85f7 MV |
7374 | { |
7375 | mpq_t frac; | |
7376 | SCM q; | |
7377 | ||
7378 | mpq_init (frac); | |
c7218482 | 7379 | mpq_set_d (frac, val); |
cba42c93 | 7380 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
c7218482 | 7381 | scm_i_mpz2num (mpq_denref (frac))); |
f92e85f7 | 7382 | |
cba42c93 | 7383 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
7384 | for frac... |
7385 | */ | |
7386 | mpq_clear (frac); | |
7387 | return q; | |
7388 | } | |
c2ff8ab0 | 7389 | } |
0f2d19dd | 7390 | } |
1bbd0b84 | 7391 | #undef FUNC_NAME |
0f2d19dd | 7392 | |
f92e85f7 | 7393 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
7394 | (SCM x, SCM eps), |
7395 | "Returns the @emph{simplest} rational number differing\n" | |
7396 | "from @var{x} by no more than @var{eps}.\n" | |
7397 | "\n" | |
7398 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
7399 | "exact result when both its arguments are exact. Thus, you might need\n" | |
7400 | "to use @code{inexact->exact} on the arguments.\n" | |
7401 | "\n" | |
7402 | "@lisp\n" | |
7403 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
7404 | "@result{} 6/5\n" | |
7405 | "@end lisp") | |
f92e85f7 MV |
7406 | #define FUNC_NAME s_scm_rationalize |
7407 | { | |
605f6980 MW |
7408 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
7409 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
7410 | eps = scm_abs (eps); | |
7411 | if (scm_is_false (scm_positive_p (eps))) | |
7412 | { | |
7413 | /* eps is either zero or a NaN */ | |
7414 | if (scm_is_true (scm_nan_p (eps))) | |
7415 | return scm_nan (); | |
7416 | else if (SCM_INEXACTP (eps)) | |
7417 | return scm_exact_to_inexact (x); | |
7418 | else | |
7419 | return x; | |
7420 | } | |
7421 | else if (scm_is_false (scm_finite_p (eps))) | |
7422 | { | |
7423 | if (scm_is_true (scm_finite_p (x))) | |
7424 | return flo0; | |
7425 | else | |
7426 | return scm_nan (); | |
7427 | } | |
7428 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 7429 | return x; |
605f6980 MW |
7430 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
7431 | scm_ceiling (scm_difference (x, eps))))) | |
7432 | { | |
7433 | /* There's an integer within range; we want the one closest to zero */ | |
7434 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
7435 | { | |
7436 | /* zero is within range */ | |
7437 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
7438 | return flo0; | |
7439 | else | |
7440 | return SCM_INUM0; | |
7441 | } | |
7442 | else if (scm_is_true (scm_positive_p (x))) | |
7443 | return scm_ceiling (scm_difference (x, eps)); | |
7444 | else | |
7445 | return scm_floor (scm_sum (x, eps)); | |
7446 | } | |
7447 | else | |
f92e85f7 MV |
7448 | { |
7449 | /* Use continued fractions to find closest ratio. All | |
7450 | arithmetic is done with exact numbers. | |
7451 | */ | |
7452 | ||
7453 | SCM ex = scm_inexact_to_exact (x); | |
7454 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
7455 | SCM tt = SCM_INUM1; |
7456 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
7457 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
7458 | SCM rx; |
7459 | int i = 0; | |
7460 | ||
f92e85f7 MV |
7461 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
7462 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
7463 | ||
7464 | /* We stop after a million iterations just to be absolutely sure | |
7465 | that we don't go into an infinite loop. The process normally | |
7466 | converges after less than a dozen iterations. | |
7467 | */ | |
7468 | ||
f92e85f7 MV |
7469 | while (++i < 1000000) |
7470 | { | |
7471 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
7472 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
7473 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
7474 | scm_is_false | |
f92e85f7 | 7475 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 7476 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
7477 | { |
7478 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 7479 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
7480 | return scm_exact_to_inexact (res); |
7481 | else | |
7482 | return res; | |
7483 | } | |
f92e85f7 MV |
7484 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
7485 | SCM_UNDEFINED); | |
7486 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
7487 | a2 = a1; | |
7488 | b2 = b1; | |
7489 | a1 = a; | |
7490 | b1 = b; | |
7491 | } | |
7492 | scm_num_overflow (s_scm_rationalize); | |
7493 | } | |
f92e85f7 MV |
7494 | } |
7495 | #undef FUNC_NAME | |
7496 | ||
73e4de09 MV |
7497 | /* conversion functions */ |
7498 | ||
7499 | int | |
7500 | scm_is_integer (SCM val) | |
7501 | { | |
7502 | return scm_is_true (scm_integer_p (val)); | |
7503 | } | |
7504 | ||
7505 | int | |
7506 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
7507 | { | |
e11e83f3 | 7508 | if (SCM_I_INUMP (val)) |
73e4de09 | 7509 | { |
e11e83f3 | 7510 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
7511 | return n >= min && n <= max; |
7512 | } | |
7513 | else if (SCM_BIGP (val)) | |
7514 | { | |
7515 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
7516 | return 0; | |
7517 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
7518 | { |
7519 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
7520 | { | |
7521 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
7522 | return n >= min && n <= max; | |
7523 | } | |
7524 | else | |
7525 | return 0; | |
7526 | } | |
73e4de09 MV |
7527 | else |
7528 | { | |
d956fa6f MV |
7529 | scm_t_intmax n; |
7530 | size_t count; | |
73e4de09 | 7531 | |
d956fa6f MV |
7532 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
7533 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
7534 | return 0; | |
7535 | ||
7536 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
7537 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 7538 | |
d956fa6f | 7539 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 7540 | { |
d956fa6f MV |
7541 | if (n < 0) |
7542 | return 0; | |
73e4de09 | 7543 | } |
73e4de09 MV |
7544 | else |
7545 | { | |
d956fa6f MV |
7546 | n = -n; |
7547 | if (n >= 0) | |
7548 | return 0; | |
73e4de09 | 7549 | } |
d956fa6f MV |
7550 | |
7551 | return n >= min && n <= max; | |
73e4de09 MV |
7552 | } |
7553 | } | |
73e4de09 MV |
7554 | else |
7555 | return 0; | |
7556 | } | |
7557 | ||
7558 | int | |
7559 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
7560 | { | |
e11e83f3 | 7561 | if (SCM_I_INUMP (val)) |
73e4de09 | 7562 | { |
e11e83f3 | 7563 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
7564 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
7565 | } | |
7566 | else if (SCM_BIGP (val)) | |
7567 | { | |
7568 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
7569 | return 0; | |
7570 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
7571 | { |
7572 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
7573 | { | |
7574 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
7575 | return n >= min && n <= max; | |
7576 | } | |
7577 | else | |
7578 | return 0; | |
7579 | } | |
73e4de09 MV |
7580 | else |
7581 | { | |
d956fa6f MV |
7582 | scm_t_uintmax n; |
7583 | size_t count; | |
73e4de09 | 7584 | |
d956fa6f MV |
7585 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
7586 | return 0; | |
73e4de09 | 7587 | |
d956fa6f MV |
7588 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
7589 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 7590 | return 0; |
d956fa6f MV |
7591 | |
7592 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
7593 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 7594 | |
d956fa6f | 7595 | return n >= min && n <= max; |
73e4de09 MV |
7596 | } |
7597 | } | |
73e4de09 MV |
7598 | else |
7599 | return 0; | |
7600 | } | |
7601 | ||
1713d319 MV |
7602 | static void |
7603 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
7604 | { | |
7605 | scm_error (scm_out_of_range_key, | |
7606 | NULL, | |
7607 | "Value out of range ~S to ~S: ~S", | |
7608 | scm_list_3 (min, max, bad_val), | |
7609 | scm_list_1 (bad_val)); | |
7610 | } | |
7611 | ||
bfd7932e MV |
7612 | #define TYPE scm_t_intmax |
7613 | #define TYPE_MIN min | |
7614 | #define TYPE_MAX max | |
7615 | #define SIZEOF_TYPE 0 | |
7616 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
7617 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
7618 | #include "libguile/conv-integer.i.c" | |
7619 | ||
7620 | #define TYPE scm_t_uintmax | |
7621 | #define TYPE_MIN min | |
7622 | #define TYPE_MAX max | |
7623 | #define SIZEOF_TYPE 0 | |
7624 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
7625 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
7626 | #include "libguile/conv-uinteger.i.c" | |
7627 | ||
7628 | #define TYPE scm_t_int8 | |
7629 | #define TYPE_MIN SCM_T_INT8_MIN | |
7630 | #define TYPE_MAX SCM_T_INT8_MAX | |
7631 | #define SIZEOF_TYPE 1 | |
7632 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
7633 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
7634 | #include "libguile/conv-integer.i.c" | |
7635 | ||
7636 | #define TYPE scm_t_uint8 | |
7637 | #define TYPE_MIN 0 | |
7638 | #define TYPE_MAX SCM_T_UINT8_MAX | |
7639 | #define SIZEOF_TYPE 1 | |
7640 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
7641 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
7642 | #include "libguile/conv-uinteger.i.c" | |
7643 | ||
7644 | #define TYPE scm_t_int16 | |
7645 | #define TYPE_MIN SCM_T_INT16_MIN | |
7646 | #define TYPE_MAX SCM_T_INT16_MAX | |
7647 | #define SIZEOF_TYPE 2 | |
7648 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
7649 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
7650 | #include "libguile/conv-integer.i.c" | |
7651 | ||
7652 | #define TYPE scm_t_uint16 | |
7653 | #define TYPE_MIN 0 | |
7654 | #define TYPE_MAX SCM_T_UINT16_MAX | |
7655 | #define SIZEOF_TYPE 2 | |
7656 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
7657 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
7658 | #include "libguile/conv-uinteger.i.c" | |
7659 | ||
7660 | #define TYPE scm_t_int32 | |
7661 | #define TYPE_MIN SCM_T_INT32_MIN | |
7662 | #define TYPE_MAX SCM_T_INT32_MAX | |
7663 | #define SIZEOF_TYPE 4 | |
7664 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
7665 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
7666 | #include "libguile/conv-integer.i.c" | |
7667 | ||
7668 | #define TYPE scm_t_uint32 | |
7669 | #define TYPE_MIN 0 | |
7670 | #define TYPE_MAX SCM_T_UINT32_MAX | |
7671 | #define SIZEOF_TYPE 4 | |
7672 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
7673 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
7674 | #include "libguile/conv-uinteger.i.c" | |
7675 | ||
904a78f1 MG |
7676 | #define TYPE scm_t_wchar |
7677 | #define TYPE_MIN (scm_t_int32)-1 | |
7678 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
7679 | #define SIZEOF_TYPE 4 | |
7680 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
7681 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
7682 | #include "libguile/conv-integer.i.c" | |
7683 | ||
bfd7932e MV |
7684 | #define TYPE scm_t_int64 |
7685 | #define TYPE_MIN SCM_T_INT64_MIN | |
7686 | #define TYPE_MAX SCM_T_INT64_MAX | |
7687 | #define SIZEOF_TYPE 8 | |
7688 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
7689 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
7690 | #include "libguile/conv-integer.i.c" | |
7691 | ||
7692 | #define TYPE scm_t_uint64 | |
7693 | #define TYPE_MIN 0 | |
7694 | #define TYPE_MAX SCM_T_UINT64_MAX | |
7695 | #define SIZEOF_TYPE 8 | |
7696 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
7697 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
7698 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 7699 | |
cd036260 MV |
7700 | void |
7701 | scm_to_mpz (SCM val, mpz_t rop) | |
7702 | { | |
7703 | if (SCM_I_INUMP (val)) | |
7704 | mpz_set_si (rop, SCM_I_INUM (val)); | |
7705 | else if (SCM_BIGP (val)) | |
7706 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
7707 | else | |
7708 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
7709 | } | |
7710 | ||
7711 | SCM | |
7712 | scm_from_mpz (mpz_t val) | |
7713 | { | |
7714 | return scm_i_mpz2num (val); | |
7715 | } | |
7716 | ||
73e4de09 MV |
7717 | int |
7718 | scm_is_real (SCM val) | |
7719 | { | |
7720 | return scm_is_true (scm_real_p (val)); | |
7721 | } | |
7722 | ||
55f26379 MV |
7723 | int |
7724 | scm_is_rational (SCM val) | |
7725 | { | |
7726 | return scm_is_true (scm_rational_p (val)); | |
7727 | } | |
7728 | ||
73e4de09 MV |
7729 | double |
7730 | scm_to_double (SCM val) | |
7731 | { | |
55f26379 MV |
7732 | if (SCM_I_INUMP (val)) |
7733 | return SCM_I_INUM (val); | |
7734 | else if (SCM_BIGP (val)) | |
7735 | return scm_i_big2dbl (val); | |
7736 | else if (SCM_FRACTIONP (val)) | |
7737 | return scm_i_fraction2double (val); | |
7738 | else if (SCM_REALP (val)) | |
7739 | return SCM_REAL_VALUE (val); | |
7740 | else | |
7a1aba42 | 7741 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
7742 | } |
7743 | ||
7744 | SCM | |
7745 | scm_from_double (double val) | |
7746 | { | |
978c52d1 LC |
7747 | SCM z; |
7748 | ||
7749 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
7750 | ||
7751 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 7752 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 7753 | |
55f26379 | 7754 | return z; |
73e4de09 MV |
7755 | } |
7756 | ||
220058a8 | 7757 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
7758 | |
7759 | float | |
e25f3727 | 7760 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 7761 | { |
220058a8 AW |
7762 | scm_c_issue_deprecation_warning |
7763 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
7764 | ||
55f26379 MV |
7765 | if (SCM_BIGP (num)) |
7766 | { | |
7767 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 7768 | if (!isinf (res)) |
55f26379 MV |
7769 | return res; |
7770 | else | |
7771 | scm_out_of_range (NULL, num); | |
7772 | } | |
7773 | else | |
7774 | return scm_to_double (num); | |
7775 | } | |
7776 | ||
7777 | double | |
e25f3727 | 7778 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 7779 | { |
220058a8 AW |
7780 | scm_c_issue_deprecation_warning |
7781 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
7782 | ||
55f26379 MV |
7783 | if (SCM_BIGP (num)) |
7784 | { | |
7785 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 7786 | if (!isinf (res)) |
55f26379 MV |
7787 | return res; |
7788 | else | |
7789 | scm_out_of_range (NULL, num); | |
7790 | } | |
7791 | else | |
7792 | return scm_to_double (num); | |
7793 | } | |
7794 | ||
7795 | #endif | |
7796 | ||
8507ec80 MV |
7797 | int |
7798 | scm_is_complex (SCM val) | |
7799 | { | |
7800 | return scm_is_true (scm_complex_p (val)); | |
7801 | } | |
7802 | ||
7803 | double | |
7804 | scm_c_real_part (SCM z) | |
7805 | { | |
7806 | if (SCM_COMPLEXP (z)) | |
7807 | return SCM_COMPLEX_REAL (z); | |
7808 | else | |
7809 | { | |
7810 | /* Use the scm_real_part to get proper error checking and | |
7811 | dispatching. | |
7812 | */ | |
7813 | return scm_to_double (scm_real_part (z)); | |
7814 | } | |
7815 | } | |
7816 | ||
7817 | double | |
7818 | scm_c_imag_part (SCM z) | |
7819 | { | |
7820 | if (SCM_COMPLEXP (z)) | |
7821 | return SCM_COMPLEX_IMAG (z); | |
7822 | else | |
7823 | { | |
7824 | /* Use the scm_imag_part to get proper error checking and | |
7825 | dispatching. The result will almost always be 0.0, but not | |
7826 | always. | |
7827 | */ | |
7828 | return scm_to_double (scm_imag_part (z)); | |
7829 | } | |
7830 | } | |
7831 | ||
7832 | double | |
7833 | scm_c_magnitude (SCM z) | |
7834 | { | |
7835 | return scm_to_double (scm_magnitude (z)); | |
7836 | } | |
7837 | ||
7838 | double | |
7839 | scm_c_angle (SCM z) | |
7840 | { | |
7841 | return scm_to_double (scm_angle (z)); | |
7842 | } | |
7843 | ||
7844 | int | |
7845 | scm_is_number (SCM z) | |
7846 | { | |
7847 | return scm_is_true (scm_number_p (z)); | |
7848 | } | |
7849 | ||
8ab3d8a0 KR |
7850 | |
7851 | /* In the following functions we dispatch to the real-arg funcs like log() | |
7852 | when we know the arg is real, instead of just handing everything to | |
7853 | clog() for instance. This is in case clog() doesn't optimize for a | |
7854 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
7855 | well use it to go straight to the applicable C func. */ | |
7856 | ||
2519490c MW |
7857 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
7858 | (SCM z), | |
7859 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
7860 | #define FUNC_NAME s_scm_log |
7861 | { | |
7862 | if (SCM_COMPLEXP (z)) | |
7863 | { | |
4b26c03e | 7864 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
7865 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
7866 | #else | |
7867 | double re = SCM_COMPLEX_REAL (z); | |
7868 | double im = SCM_COMPLEX_IMAG (z); | |
7869 | return scm_c_make_rectangular (log (hypot (re, im)), | |
7870 | atan2 (im, re)); | |
7871 | #endif | |
7872 | } | |
2519490c | 7873 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7874 | { |
7875 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
7876 | although the value itself overflows. */ | |
7877 | double re = scm_to_double (z); | |
7878 | double l = log (fabs (re)); | |
7879 | if (re >= 0.0) | |
7880 | return scm_from_double (l); | |
7881 | else | |
7882 | return scm_c_make_rectangular (l, M_PI); | |
7883 | } | |
2519490c MW |
7884 | else |
7885 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); | |
8ab3d8a0 KR |
7886 | } |
7887 | #undef FUNC_NAME | |
7888 | ||
7889 | ||
2519490c MW |
7890 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
7891 | (SCM z), | |
7892 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
7893 | #define FUNC_NAME s_scm_log10 |
7894 | { | |
7895 | if (SCM_COMPLEXP (z)) | |
7896 | { | |
7897 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
7898 | clog() and a multiply by M_LOG10E, rather than the fallback | |
7899 | log10+hypot+atan2.) */ | |
f328f862 LC |
7900 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
7901 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
7902 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
7903 | #else | |
7904 | double re = SCM_COMPLEX_REAL (z); | |
7905 | double im = SCM_COMPLEX_IMAG (z); | |
7906 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
7907 | M_LOG10E * atan2 (im, re)); | |
7908 | #endif | |
7909 | } | |
2519490c | 7910 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7911 | { |
7912 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
7913 | although the value itself overflows. */ | |
7914 | double re = scm_to_double (z); | |
7915 | double l = log10 (fabs (re)); | |
7916 | if (re >= 0.0) | |
7917 | return scm_from_double (l); | |
7918 | else | |
7919 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
7920 | } | |
2519490c MW |
7921 | else |
7922 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); | |
8ab3d8a0 KR |
7923 | } |
7924 | #undef FUNC_NAME | |
7925 | ||
7926 | ||
2519490c MW |
7927 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
7928 | (SCM z), | |
7929 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
7930 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
7931 | #define FUNC_NAME s_scm_exp |
7932 | { | |
7933 | if (SCM_COMPLEXP (z)) | |
7934 | { | |
4b26c03e | 7935 | #if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
7936 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
7937 | #else | |
7938 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
7939 | SCM_COMPLEX_IMAG (z)); | |
7940 | #endif | |
7941 | } | |
2519490c | 7942 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7943 | { |
7944 | /* When z is a negative bignum the conversion to double overflows, | |
7945 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
7946 | return scm_from_double (exp (scm_to_double (z))); | |
7947 | } | |
2519490c MW |
7948 | else |
7949 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); | |
8ab3d8a0 KR |
7950 | } |
7951 | #undef FUNC_NAME | |
7952 | ||
7953 | ||
2519490c MW |
7954 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
7955 | (SCM z), | |
7956 | "Return the square root of @var{z}. Of the two possible roots\n" | |
7957 | "(positive and negative), the one with the a positive real part\n" | |
7958 | "is returned, or if that's zero then a positive imaginary part.\n" | |
7959 | "Thus,\n" | |
7960 | "\n" | |
7961 | "@example\n" | |
7962 | "(sqrt 9.0) @result{} 3.0\n" | |
7963 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
7964 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
7965 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
7966 | "@end example") | |
8ab3d8a0 KR |
7967 | #define FUNC_NAME s_scm_sqrt |
7968 | { | |
2519490c | 7969 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 7970 | { |
f328f862 LC |
7971 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
7972 | && defined SCM_COMPLEX_VALUE | |
2519490c | 7973 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 7974 | #else |
2519490c MW |
7975 | double re = SCM_COMPLEX_REAL (z); |
7976 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
7977 | return scm_c_make_polar (sqrt (hypot (re, im)), |
7978 | 0.5 * atan2 (im, re)); | |
7979 | #endif | |
7980 | } | |
2519490c | 7981 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 7982 | { |
2519490c | 7983 | double xx = scm_to_double (z); |
8ab3d8a0 KR |
7984 | if (xx < 0) |
7985 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
7986 | else | |
7987 | return scm_from_double (sqrt (xx)); | |
7988 | } | |
2519490c MW |
7989 | else |
7990 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); | |
8ab3d8a0 KR |
7991 | } |
7992 | #undef FUNC_NAME | |
7993 | ||
7994 | ||
7995 | ||
0f2d19dd JB |
7996 | void |
7997 | scm_init_numbers () | |
0f2d19dd | 7998 | { |
0b799eea MV |
7999 | int i; |
8000 | ||
713a4259 KR |
8001 | mpz_init_set_si (z_negative_one, -1); |
8002 | ||
a261c0e9 DH |
8003 | /* It may be possible to tune the performance of some algorithms by using |
8004 | * the following constants to avoid the creation of bignums. Please, before | |
8005 | * using these values, remember the two rules of program optimization: | |
8006 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 8007 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 8008 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 8009 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 8010 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 8011 | |
f3ae5d60 MD |
8012 | scm_add_feature ("complex"); |
8013 | scm_add_feature ("inexact"); | |
e7efe8e7 | 8014 | flo0 = scm_from_double (0.0); |
0b799eea MV |
8015 | |
8016 | /* determine floating point precision */ | |
55f26379 | 8017 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
8018 | { |
8019 | init_dblprec(&scm_dblprec[i-2],i); | |
8020 | init_fx_radix(fx_per_radix[i-2],i); | |
8021 | } | |
f872b822 | 8022 | #ifdef DBL_DIG |
0b799eea | 8023 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 8024 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 8025 | #endif |
1be6b49c | 8026 | |
cff5fa33 | 8027 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 8028 | #include "libguile/numbers.x" |
0f2d19dd | 8029 | } |
89e00824 ML |
8030 | |
8031 | /* | |
8032 | Local Variables: | |
8033 | c-file-style: "gnu" | |
8034 | End: | |
8035 | */ |