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 | |
5fbf680b MW |
1072 | /* two_valued_wta_dispatch_2 is a version of SCM_WTA_DISPATCH_2 for |
1073 | two-valued functions. It is called from primitive generics that take | |
1074 | two arguments and return two values, when the core procedure is | |
1075 | unable to handle the given argument types. If there are GOOPS | |
1076 | methods for this primitive generic, it dispatches to GOOPS and, if | |
1077 | successful, expects two values to be returned, which are placed in | |
1078 | *rp1 and *rp2. If there are no GOOPS methods, it throws a | |
1079 | wrong-type-arg exception. | |
1080 | ||
1081 | FIXME: This obviously belongs somewhere else, but until we decide on | |
1082 | the right API, it is here as a static function, because it is needed | |
1083 | by the *_divide functions below. | |
1084 | */ | |
1085 | static void | |
1086 | two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos, | |
1087 | const char *subr, SCM *rp1, SCM *rp2) | |
1088 | { | |
1089 | if (SCM_UNPACK (gf)) | |
1090 | scm_i_extract_values_2 (scm_call_generic_2 (gf, a1, a2), rp1, rp2); | |
1091 | else | |
1092 | scm_wrong_type_arg (subr, pos, (pos == SCM_ARG1) ? a1 : a2); | |
1093 | } | |
1094 | ||
ff62c168 | 1095 | static SCM scm_i_inexact_euclidean_quotient (double x, double y); |
03ddd15b | 1096 | static SCM scm_i_exact_rational_euclidean_quotient (SCM x, SCM y); |
ff62c168 MW |
1097 | |
1098 | SCM_PRIMITIVE_GENERIC (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, | |
1099 | (SCM x, SCM y), | |
1100 | "Return the integer @var{q} such that\n" | |
1101 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1102 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1103 | "@lisp\n" | |
1104 | "(euclidean-quotient 123 10) @result{} 12\n" | |
1105 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
1106 | "(euclidean-quotient -123 10) @result{} -13\n" | |
1107 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
1108 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
1109 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
1110 | "@end lisp") | |
1111 | #define FUNC_NAME s_scm_euclidean_quotient | |
1112 | { | |
1113 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1114 | { | |
4a46bc2a | 1115 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
1116 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
1117 | { | |
1118 | scm_t_inum yy = SCM_I_INUM (y); | |
1119 | if (SCM_UNLIKELY (yy == 0)) | |
1120 | scm_num_overflow (s_scm_euclidean_quotient); | |
1121 | else | |
1122 | { | |
ff62c168 MW |
1123 | scm_t_inum qq = xx / yy; |
1124 | if (xx < qq * yy) | |
1125 | { | |
1126 | if (yy > 0) | |
1127 | qq--; | |
1128 | else | |
1129 | qq++; | |
1130 | } | |
4a46bc2a MW |
1131 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
1132 | return SCM_I_MAKINUM (qq); | |
1133 | else | |
1134 | return scm_i_inum2big (qq); | |
ff62c168 MW |
1135 | } |
1136 | } | |
1137 | else if (SCM_BIGP (y)) | |
1138 | { | |
4a46bc2a | 1139 | if (xx >= 0) |
ff62c168 MW |
1140 | return SCM_INUM0; |
1141 | else | |
4a46bc2a MW |
1142 | { |
1143 | scm_t_inum qq = - mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1144 | scm_remember_upto_here_1 (y); | |
1145 | return SCM_I_MAKINUM (qq); | |
1146 | } | |
ff62c168 MW |
1147 | } |
1148 | else if (SCM_REALP (y)) | |
4a46bc2a | 1149 | return scm_i_inexact_euclidean_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 1150 | else if (SCM_FRACTIONP (y)) |
03ddd15b | 1151 | return scm_i_exact_rational_euclidean_quotient (x, y); |
ff62c168 MW |
1152 | else |
1153 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1154 | s_scm_euclidean_quotient); | |
1155 | } | |
1156 | else if (SCM_BIGP (x)) | |
1157 | { | |
1158 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1159 | { | |
1160 | scm_t_inum yy = SCM_I_INUM (y); | |
1161 | if (SCM_UNLIKELY (yy == 0)) | |
1162 | scm_num_overflow (s_scm_euclidean_quotient); | |
4a46bc2a MW |
1163 | else if (SCM_UNLIKELY (yy == 1)) |
1164 | return x; | |
ff62c168 MW |
1165 | else |
1166 | { | |
1167 | SCM q = scm_i_mkbig (); | |
1168 | if (yy > 0) | |
1169 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1170 | else | |
1171 | { | |
1172 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1173 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1174 | } | |
1175 | scm_remember_upto_here_1 (x); | |
1176 | return scm_i_normbig (q); | |
1177 | } | |
1178 | } | |
1179 | else if (SCM_BIGP (y)) | |
1180 | { | |
1181 | SCM q = scm_i_mkbig (); | |
1182 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1183 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1184 | SCM_I_BIG_MPZ (x), | |
1185 | SCM_I_BIG_MPZ (y)); | |
1186 | else | |
1187 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1188 | SCM_I_BIG_MPZ (x), | |
1189 | SCM_I_BIG_MPZ (y)); | |
1190 | scm_remember_upto_here_2 (x, y); | |
1191 | return scm_i_normbig (q); | |
1192 | } | |
1193 | else if (SCM_REALP (y)) | |
1194 | return scm_i_inexact_euclidean_quotient | |
1195 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1196 | else if (SCM_FRACTIONP (y)) | |
03ddd15b | 1197 | return scm_i_exact_rational_euclidean_quotient (x, y); |
ff62c168 MW |
1198 | else |
1199 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1200 | s_scm_euclidean_quotient); | |
1201 | } | |
1202 | else if (SCM_REALP (x)) | |
1203 | { | |
1204 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1205 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1206 | return scm_i_inexact_euclidean_quotient | |
1207 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1208 | else | |
1209 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, | |
1210 | s_scm_euclidean_quotient); | |
1211 | } | |
1212 | else if (SCM_FRACTIONP (x)) | |
1213 | { | |
1214 | if (SCM_REALP (y)) | |
1215 | return scm_i_inexact_euclidean_quotient | |
1216 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
03ddd15b MW |
1217 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
1218 | return scm_i_exact_rational_euclidean_quotient (x, y); | |
ff62c168 | 1219 | else |
03ddd15b MW |
1220 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG2, |
1221 | s_scm_euclidean_quotient); | |
ff62c168 MW |
1222 | } |
1223 | else | |
1224 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_quotient, x, y, SCM_ARG1, | |
1225 | s_scm_euclidean_quotient); | |
1226 | } | |
1227 | #undef FUNC_NAME | |
1228 | ||
1229 | static SCM | |
1230 | scm_i_inexact_euclidean_quotient (double x, double y) | |
1231 | { | |
1232 | if (SCM_LIKELY (y > 0)) | |
1233 | return scm_from_double (floor (x / y)); | |
1234 | else if (SCM_LIKELY (y < 0)) | |
1235 | return scm_from_double (ceil (x / y)); | |
1236 | else if (y == 0) | |
1237 | scm_num_overflow (s_scm_euclidean_quotient); /* or return a NaN? */ | |
1238 | else | |
1239 | return scm_nan (); | |
1240 | } | |
1241 | ||
ff62c168 | 1242 | static SCM |
03ddd15b | 1243 | scm_i_exact_rational_euclidean_quotient (SCM x, SCM y) |
ff62c168 | 1244 | { |
03ddd15b MW |
1245 | return scm_euclidean_quotient |
1246 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1247 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
1248 | } |
1249 | ||
1250 | static SCM scm_i_inexact_euclidean_remainder (double x, double y); | |
03ddd15b | 1251 | static SCM scm_i_exact_rational_euclidean_remainder (SCM x, SCM y); |
ff62c168 MW |
1252 | |
1253 | SCM_PRIMITIVE_GENERIC (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, | |
1254 | (SCM x, SCM y), | |
1255 | "Return the real number @var{r} such that\n" | |
1256 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
1257 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1258 | "for some integer @var{q}.\n" | |
1259 | "@lisp\n" | |
1260 | "(euclidean-remainder 123 10) @result{} 3\n" | |
1261 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
1262 | "(euclidean-remainder -123 10) @result{} 7\n" | |
1263 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
1264 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
1265 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
1266 | "@end lisp") | |
1267 | #define FUNC_NAME s_scm_euclidean_remainder | |
1268 | { | |
1269 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1270 | { | |
4a46bc2a | 1271 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
1272 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
1273 | { | |
1274 | scm_t_inum yy = SCM_I_INUM (y); | |
1275 | if (SCM_UNLIKELY (yy == 0)) | |
1276 | scm_num_overflow (s_scm_euclidean_remainder); | |
1277 | else | |
1278 | { | |
4a46bc2a | 1279 | scm_t_inum rr = xx % yy; |
ff62c168 MW |
1280 | if (rr >= 0) |
1281 | return SCM_I_MAKINUM (rr); | |
1282 | else if (yy > 0) | |
1283 | return SCM_I_MAKINUM (rr + yy); | |
1284 | else | |
1285 | return SCM_I_MAKINUM (rr - yy); | |
1286 | } | |
1287 | } | |
1288 | else if (SCM_BIGP (y)) | |
1289 | { | |
ff62c168 MW |
1290 | if (xx >= 0) |
1291 | return x; | |
1292 | else if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1293 | { | |
1294 | SCM r = scm_i_mkbig (); | |
1295 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1296 | scm_remember_upto_here_1 (y); | |
1297 | return scm_i_normbig (r); | |
1298 | } | |
1299 | else | |
1300 | { | |
1301 | SCM r = scm_i_mkbig (); | |
1302 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1303 | scm_remember_upto_here_1 (y); | |
1304 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1305 | return scm_i_normbig (r); | |
1306 | } | |
1307 | } | |
1308 | else if (SCM_REALP (y)) | |
4a46bc2a | 1309 | return scm_i_inexact_euclidean_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 1310 | else if (SCM_FRACTIONP (y)) |
03ddd15b | 1311 | return scm_i_exact_rational_euclidean_remainder (x, y); |
ff62c168 MW |
1312 | else |
1313 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1314 | s_scm_euclidean_remainder); | |
1315 | } | |
1316 | else if (SCM_BIGP (x)) | |
1317 | { | |
1318 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1319 | { | |
1320 | scm_t_inum yy = SCM_I_INUM (y); | |
1321 | if (SCM_UNLIKELY (yy == 0)) | |
1322 | scm_num_overflow (s_scm_euclidean_remainder); | |
1323 | else | |
1324 | { | |
1325 | scm_t_inum rr; | |
1326 | if (yy < 0) | |
1327 | yy = -yy; | |
1328 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1329 | scm_remember_upto_here_1 (x); | |
1330 | return SCM_I_MAKINUM (rr); | |
1331 | } | |
1332 | } | |
1333 | else if (SCM_BIGP (y)) | |
1334 | { | |
1335 | SCM r = scm_i_mkbig (); | |
1336 | mpz_mod (SCM_I_BIG_MPZ (r), | |
1337 | SCM_I_BIG_MPZ (x), | |
1338 | SCM_I_BIG_MPZ (y)); | |
1339 | scm_remember_upto_here_2 (x, y); | |
1340 | return scm_i_normbig (r); | |
1341 | } | |
1342 | else if (SCM_REALP (y)) | |
1343 | return scm_i_inexact_euclidean_remainder | |
1344 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1345 | else if (SCM_FRACTIONP (y)) | |
03ddd15b | 1346 | return scm_i_exact_rational_euclidean_remainder (x, y); |
ff62c168 MW |
1347 | else |
1348 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1349 | s_scm_euclidean_remainder); | |
1350 | } | |
1351 | else if (SCM_REALP (x)) | |
1352 | { | |
1353 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1354 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1355 | return scm_i_inexact_euclidean_remainder | |
1356 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1357 | else | |
1358 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, | |
1359 | s_scm_euclidean_remainder); | |
1360 | } | |
1361 | else if (SCM_FRACTIONP (x)) | |
1362 | { | |
1363 | if (SCM_REALP (y)) | |
1364 | return scm_i_inexact_euclidean_remainder | |
1365 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
03ddd15b MW |
1366 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
1367 | return scm_i_exact_rational_euclidean_remainder (x, y); | |
ff62c168 | 1368 | else |
03ddd15b MW |
1369 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG2, |
1370 | s_scm_euclidean_remainder); | |
ff62c168 MW |
1371 | } |
1372 | else | |
1373 | SCM_WTA_DISPATCH_2 (g_scm_euclidean_remainder, x, y, SCM_ARG1, | |
1374 | s_scm_euclidean_remainder); | |
1375 | } | |
1376 | #undef FUNC_NAME | |
1377 | ||
1378 | static SCM | |
1379 | scm_i_inexact_euclidean_remainder (double x, double y) | |
1380 | { | |
1381 | double q; | |
1382 | ||
1383 | /* Although it would be more efficient to use fmod here, we can't | |
1384 | because it would in some cases produce results inconsistent with | |
1385 | scm_i_inexact_euclidean_quotient, such that x != q * y + r (not | |
1386 | even close). In particular, when x is very close to a multiple of | |
1387 | y, then r might be either 0.0 or abs(y)-epsilon, but those two | |
1388 | cases must correspond to different choices of q. If r = 0.0 then q | |
1389 | must be x/y, and if r = abs(y) then q must be (x-r)/y. If quotient | |
1390 | chooses one and remainder chooses the other, it would be bad. This | |
1391 | problem was observed with x = 130.0 and y = 10/7. */ | |
1392 | if (SCM_LIKELY (y > 0)) | |
1393 | q = floor (x / y); | |
1394 | else if (SCM_LIKELY (y < 0)) | |
1395 | q = ceil (x / y); | |
1396 | else if (y == 0) | |
1397 | scm_num_overflow (s_scm_euclidean_remainder); /* or return a NaN? */ | |
1398 | else | |
1399 | return scm_nan (); | |
1400 | return scm_from_double (x - q * y); | |
1401 | } | |
1402 | ||
ff62c168 | 1403 | static SCM |
03ddd15b | 1404 | scm_i_exact_rational_euclidean_remainder (SCM x, SCM y) |
ff62c168 | 1405 | { |
03ddd15b MW |
1406 | SCM xd = scm_denominator (x); |
1407 | SCM yd = scm_denominator (y); | |
1408 | SCM r1 = scm_euclidean_remainder (scm_product (scm_numerator (x), yd), | |
1409 | scm_product (scm_numerator (y), xd)); | |
1410 | return scm_divide (r1, scm_product (xd, yd)); | |
ff62c168 MW |
1411 | } |
1412 | ||
1413 | ||
5fbf680b MW |
1414 | static void scm_i_inexact_euclidean_divide (double x, double y, |
1415 | SCM *qp, SCM *rp); | |
03ddd15b MW |
1416 | static void scm_i_exact_rational_euclidean_divide (SCM x, SCM y, |
1417 | SCM *qp, SCM *rp); | |
ff62c168 | 1418 | |
5fbf680b | 1419 | SCM_PRIMITIVE_GENERIC (scm_i_euclidean_divide, "euclidean/", 2, 0, 0, |
ff62c168 MW |
1420 | (SCM x, SCM y), |
1421 | "Return the integer @var{q} and the real number @var{r}\n" | |
1422 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1423 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
1424 | "@lisp\n" | |
1425 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
1426 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
1427 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
1428 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
1429 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1430 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1431 | "@end lisp") | |
5fbf680b MW |
1432 | #define FUNC_NAME s_scm_i_euclidean_divide |
1433 | { | |
1434 | SCM q, r; | |
1435 | ||
1436 | scm_euclidean_divide(x, y, &q, &r); | |
1437 | return scm_values (scm_list_2 (q, r)); | |
1438 | } | |
1439 | #undef FUNC_NAME | |
1440 | ||
1441 | #define s_scm_euclidean_divide s_scm_i_euclidean_divide | |
1442 | #define g_scm_euclidean_divide g_scm_i_euclidean_divide | |
1443 | ||
1444 | void | |
1445 | scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 MW |
1446 | { |
1447 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1448 | { | |
4a46bc2a | 1449 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
1450 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
1451 | { | |
1452 | scm_t_inum yy = SCM_I_INUM (y); | |
1453 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 1454 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1455 | else |
1456 | { | |
ff62c168 | 1457 | scm_t_inum qq = xx / yy; |
4a46bc2a | 1458 | scm_t_inum rr = xx % yy; |
ff62c168 MW |
1459 | if (rr < 0) |
1460 | { | |
1461 | if (yy > 0) | |
1462 | { rr += yy; qq--; } | |
1463 | else | |
1464 | { rr -= yy; qq++; } | |
1465 | } | |
4a46bc2a | 1466 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 1467 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 1468 | else |
5fbf680b MW |
1469 | *qp = scm_i_inum2big (qq); |
1470 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 1471 | } |
5fbf680b | 1472 | return; |
ff62c168 MW |
1473 | } |
1474 | else if (SCM_BIGP (y)) | |
1475 | { | |
ff62c168 | 1476 | if (xx >= 0) |
5fbf680b MW |
1477 | { |
1478 | *qp = SCM_INUM0; | |
1479 | *rp = x; | |
1480 | } | |
ff62c168 MW |
1481 | else if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) |
1482 | { | |
1483 | SCM r = scm_i_mkbig (); | |
1484 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1485 | scm_remember_upto_here_1 (y); | |
5fbf680b MW |
1486 | *qp = SCM_I_MAKINUM (-1); |
1487 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
1488 | } |
1489 | else | |
1490 | { | |
1491 | SCM r = scm_i_mkbig (); | |
1492 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1493 | scm_remember_upto_here_1 (y); | |
1494 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
5fbf680b MW |
1495 | *qp = SCM_INUM1; |
1496 | *rp = scm_i_normbig (r); | |
ff62c168 | 1497 | } |
5fbf680b | 1498 | return; |
ff62c168 MW |
1499 | } |
1500 | else if (SCM_REALP (y)) | |
5fbf680b | 1501 | return scm_i_inexact_euclidean_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 1502 | else if (SCM_FRACTIONP (y)) |
03ddd15b | 1503 | return scm_i_exact_rational_euclidean_divide (x, y, qp, rp); |
ff62c168 | 1504 | else |
5fbf680b MW |
1505 | return two_valued_wta_dispatch_2 |
1506 | (g_scm_euclidean_divide, x, y, SCM_ARG2, | |
1507 | s_scm_euclidean_divide, qp, rp); | |
ff62c168 MW |
1508 | } |
1509 | else if (SCM_BIGP (x)) | |
1510 | { | |
1511 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1512 | { | |
1513 | scm_t_inum yy = SCM_I_INUM (y); | |
1514 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 1515 | scm_num_overflow (s_scm_euclidean_divide); |
ff62c168 MW |
1516 | else |
1517 | { | |
1518 | SCM q = scm_i_mkbig (); | |
4a46bc2a | 1519 | scm_t_inum rr; |
ff62c168 | 1520 | if (yy > 0) |
4a46bc2a MW |
1521 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
1522 | SCM_I_BIG_MPZ (x), yy); | |
ff62c168 MW |
1523 | else |
1524 | { | |
4a46bc2a MW |
1525 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
1526 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 MW |
1527 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
1528 | } | |
1529 | scm_remember_upto_here_1 (x); | |
5fbf680b MW |
1530 | *qp = scm_i_normbig (q); |
1531 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 1532 | } |
5fbf680b | 1533 | return; |
ff62c168 MW |
1534 | } |
1535 | else if (SCM_BIGP (y)) | |
1536 | { | |
1537 | SCM q = scm_i_mkbig (); | |
1538 | SCM r = scm_i_mkbig (); | |
1539 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1540 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1541 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1542 | else | |
1543 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1544 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1545 | scm_remember_upto_here_2 (x, y); | |
5fbf680b MW |
1546 | *qp = scm_i_normbig (q); |
1547 | *rp = scm_i_normbig (r); | |
1548 | return; | |
ff62c168 MW |
1549 | } |
1550 | else if (SCM_REALP (y)) | |
ac6ce16b | 1551 | return scm_i_inexact_euclidean_divide |
5fbf680b | 1552 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 1553 | else if (SCM_FRACTIONP (y)) |
03ddd15b | 1554 | return scm_i_exact_rational_euclidean_divide (x, y, qp, rp); |
ff62c168 | 1555 | else |
5fbf680b MW |
1556 | return two_valued_wta_dispatch_2 |
1557 | (g_scm_euclidean_divide, x, y, SCM_ARG2, | |
1558 | s_scm_euclidean_divide, qp, rp); | |
ff62c168 MW |
1559 | } |
1560 | else if (SCM_REALP (x)) | |
1561 | { | |
1562 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1563 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
ac6ce16b | 1564 | return scm_i_inexact_euclidean_divide |
5fbf680b | 1565 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
ff62c168 | 1566 | else |
5fbf680b MW |
1567 | return two_valued_wta_dispatch_2 |
1568 | (g_scm_euclidean_divide, x, y, SCM_ARG2, | |
1569 | s_scm_euclidean_divide, qp, rp); | |
ff62c168 MW |
1570 | } |
1571 | else if (SCM_FRACTIONP (x)) | |
1572 | { | |
1573 | if (SCM_REALP (y)) | |
ac6ce16b | 1574 | return scm_i_inexact_euclidean_divide |
5fbf680b | 1575 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b MW |
1576 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
1577 | return scm_i_exact_rational_euclidean_divide (x, y, qp, rp); | |
ff62c168 | 1578 | else |
03ddd15b MW |
1579 | return two_valued_wta_dispatch_2 |
1580 | (g_scm_euclidean_divide, x, y, SCM_ARG2, | |
1581 | s_scm_euclidean_divide, qp, rp); | |
ff62c168 MW |
1582 | } |
1583 | else | |
5fbf680b MW |
1584 | return two_valued_wta_dispatch_2 (g_scm_euclidean_divide, x, y, SCM_ARG1, |
1585 | s_scm_euclidean_divide, qp, rp); | |
ff62c168 | 1586 | } |
ff62c168 | 1587 | |
5fbf680b MW |
1588 | static void |
1589 | scm_i_inexact_euclidean_divide (double x, double y, SCM *qp, SCM *rp) | |
ff62c168 MW |
1590 | { |
1591 | double q, r; | |
1592 | ||
1593 | if (SCM_LIKELY (y > 0)) | |
1594 | q = floor (x / y); | |
1595 | else if (SCM_LIKELY (y < 0)) | |
1596 | q = ceil (x / y); | |
1597 | else if (y == 0) | |
ac6ce16b | 1598 | scm_num_overflow (s_scm_euclidean_divide); /* or return a NaN? */ |
ff62c168 MW |
1599 | else |
1600 | q = guile_NaN; | |
1601 | r = x - q * y; | |
5fbf680b MW |
1602 | *qp = scm_from_double (q); |
1603 | *rp = scm_from_double (r); | |
ff62c168 MW |
1604 | } |
1605 | ||
5fbf680b | 1606 | static void |
03ddd15b | 1607 | scm_i_exact_rational_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 1608 | { |
03ddd15b MW |
1609 | SCM r1; |
1610 | SCM xd = scm_denominator (x); | |
1611 | SCM yd = scm_denominator (y); | |
1612 | ||
1613 | scm_euclidean_divide (scm_product (scm_numerator (x), yd), | |
1614 | scm_product (scm_numerator (y), xd), | |
1615 | qp, &r1); | |
1616 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
ff62c168 MW |
1617 | } |
1618 | ||
1619 | static SCM scm_i_inexact_centered_quotient (double x, double y); | |
1620 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
03ddd15b | 1621 | static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y); |
ff62c168 MW |
1622 | |
1623 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, | |
1624 | (SCM x, SCM y), | |
1625 | "Return the integer @var{q} such that\n" | |
1626 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
1627 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
1628 | "@lisp\n" | |
1629 | "(centered-quotient 123 10) @result{} 12\n" | |
1630 | "(centered-quotient 123 -10) @result{} -12\n" | |
1631 | "(centered-quotient -123 10) @result{} -12\n" | |
1632 | "(centered-quotient -123 -10) @result{} 12\n" | |
1633 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
1634 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
1635 | "@end lisp") | |
1636 | #define FUNC_NAME s_scm_centered_quotient | |
1637 | { | |
1638 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1639 | { | |
4a46bc2a | 1640 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
1641 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
1642 | { | |
1643 | scm_t_inum yy = SCM_I_INUM (y); | |
1644 | if (SCM_UNLIKELY (yy == 0)) | |
1645 | scm_num_overflow (s_scm_centered_quotient); | |
1646 | else | |
1647 | { | |
ff62c168 | 1648 | scm_t_inum qq = xx / yy; |
4a46bc2a | 1649 | scm_t_inum rr = xx % yy; |
ff62c168 MW |
1650 | if (SCM_LIKELY (xx > 0)) |
1651 | { | |
1652 | if (SCM_LIKELY (yy > 0)) | |
1653 | { | |
1654 | if (rr >= (yy + 1) / 2) | |
1655 | qq++; | |
1656 | } | |
1657 | else | |
1658 | { | |
1659 | if (rr >= (1 - yy) / 2) | |
1660 | qq--; | |
1661 | } | |
1662 | } | |
1663 | else | |
1664 | { | |
1665 | if (SCM_LIKELY (yy > 0)) | |
1666 | { | |
1667 | if (rr < -yy / 2) | |
1668 | qq--; | |
1669 | } | |
1670 | else | |
1671 | { | |
1672 | if (rr < yy / 2) | |
1673 | qq++; | |
1674 | } | |
1675 | } | |
4a46bc2a MW |
1676 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
1677 | return SCM_I_MAKINUM (qq); | |
1678 | else | |
1679 | return scm_i_inum2big (qq); | |
ff62c168 MW |
1680 | } |
1681 | } | |
1682 | else if (SCM_BIGP (y)) | |
1683 | { | |
1684 | /* Pass a denormalized bignum version of x (even though it | |
1685 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
4a46bc2a | 1686 | return scm_i_bigint_centered_quotient (scm_i_long2big (xx), y); |
ff62c168 MW |
1687 | } |
1688 | else if (SCM_REALP (y)) | |
4a46bc2a | 1689 | return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 1690 | else if (SCM_FRACTIONP (y)) |
03ddd15b | 1691 | return scm_i_exact_rational_centered_quotient (x, y); |
ff62c168 MW |
1692 | else |
1693 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1694 | s_scm_centered_quotient); | |
1695 | } | |
1696 | else if (SCM_BIGP (x)) | |
1697 | { | |
1698 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1699 | { | |
1700 | scm_t_inum yy = SCM_I_INUM (y); | |
1701 | if (SCM_UNLIKELY (yy == 0)) | |
1702 | scm_num_overflow (s_scm_centered_quotient); | |
4a46bc2a MW |
1703 | else if (SCM_UNLIKELY (yy == 1)) |
1704 | return x; | |
ff62c168 MW |
1705 | else |
1706 | { | |
1707 | SCM q = scm_i_mkbig (); | |
1708 | scm_t_inum rr; | |
1709 | /* Arrange for rr to initially be non-positive, | |
1710 | because that simplifies the test to see | |
1711 | if it is within the needed bounds. */ | |
1712 | if (yy > 0) | |
1713 | { | |
1714 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
1715 | SCM_I_BIG_MPZ (x), yy); | |
1716 | scm_remember_upto_here_1 (x); | |
1717 | if (rr < -yy / 2) | |
1718 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
1719 | SCM_I_BIG_MPZ (q), 1); | |
1720 | } | |
1721 | else | |
1722 | { | |
1723 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
1724 | SCM_I_BIG_MPZ (x), -yy); | |
1725 | scm_remember_upto_here_1 (x); | |
1726 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1727 | if (rr < yy / 2) | |
1728 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
1729 | SCM_I_BIG_MPZ (q), 1); | |
1730 | } | |
1731 | return scm_i_normbig (q); | |
1732 | } | |
1733 | } | |
1734 | else if (SCM_BIGP (y)) | |
1735 | return scm_i_bigint_centered_quotient (x, y); | |
1736 | else if (SCM_REALP (y)) | |
1737 | return scm_i_inexact_centered_quotient | |
1738 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1739 | else if (SCM_FRACTIONP (y)) | |
03ddd15b | 1740 | return scm_i_exact_rational_centered_quotient (x, y); |
ff62c168 MW |
1741 | else |
1742 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1743 | s_scm_centered_quotient); | |
1744 | } | |
1745 | else if (SCM_REALP (x)) | |
1746 | { | |
1747 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1748 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1749 | return scm_i_inexact_centered_quotient | |
1750 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1751 | else | |
1752 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
1753 | s_scm_centered_quotient); | |
1754 | } | |
1755 | else if (SCM_FRACTIONP (x)) | |
1756 | { | |
1757 | if (SCM_REALP (y)) | |
1758 | return scm_i_inexact_centered_quotient | |
1759 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
03ddd15b MW |
1760 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
1761 | return scm_i_exact_rational_centered_quotient (x, y); | |
ff62c168 | 1762 | else |
03ddd15b MW |
1763 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, |
1764 | s_scm_centered_quotient); | |
ff62c168 MW |
1765 | } |
1766 | else | |
1767 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
1768 | s_scm_centered_quotient); | |
1769 | } | |
1770 | #undef FUNC_NAME | |
1771 | ||
1772 | static SCM | |
1773 | scm_i_inexact_centered_quotient (double x, double y) | |
1774 | { | |
1775 | if (SCM_LIKELY (y > 0)) | |
1776 | return scm_from_double (floor (x/y + 0.5)); | |
1777 | else if (SCM_LIKELY (y < 0)) | |
1778 | return scm_from_double (ceil (x/y - 0.5)); | |
1779 | else if (y == 0) | |
1780 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
1781 | else | |
1782 | return scm_nan (); | |
1783 | } | |
1784 | ||
1785 | /* Assumes that both x and y are bigints, though | |
1786 | x might be able to fit into a fixnum. */ | |
1787 | static SCM | |
1788 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
1789 | { | |
1790 | SCM q, r, min_r; | |
1791 | ||
1792 | /* Note that x might be small enough to fit into a | |
1793 | fixnum, so we must not let it escape into the wild */ | |
1794 | q = scm_i_mkbig (); | |
1795 | r = scm_i_mkbig (); | |
1796 | ||
1797 | /* min_r will eventually become -abs(y)/2 */ | |
1798 | min_r = scm_i_mkbig (); | |
1799 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
1800 | SCM_I_BIG_MPZ (y), 1); | |
1801 | ||
1802 | /* Arrange for rr to initially be non-positive, | |
1803 | because that simplifies the test to see | |
1804 | if it is within the needed bounds. */ | |
1805 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
1806 | { | |
1807 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1808 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1809 | scm_remember_upto_here_2 (x, y); | |
1810 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
1811 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1812 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
1813 | SCM_I_BIG_MPZ (q), 1); | |
1814 | } | |
1815 | else | |
1816 | { | |
1817 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1818 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1819 | scm_remember_upto_here_2 (x, y); | |
1820 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
1821 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
1822 | SCM_I_BIG_MPZ (q), 1); | |
1823 | } | |
1824 | scm_remember_upto_here_2 (r, min_r); | |
1825 | return scm_i_normbig (q); | |
1826 | } | |
1827 | ||
ff62c168 | 1828 | static SCM |
03ddd15b | 1829 | scm_i_exact_rational_centered_quotient (SCM x, SCM y) |
ff62c168 | 1830 | { |
03ddd15b MW |
1831 | return scm_centered_quotient |
1832 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1833 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
1834 | } |
1835 | ||
1836 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
1837 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
03ddd15b | 1838 | static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y); |
ff62c168 MW |
1839 | |
1840 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
1841 | (SCM x, SCM y), | |
1842 | "Return the real number @var{r} such that\n" | |
1843 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
1844 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1845 | "for some integer @var{q}.\n" | |
1846 | "@lisp\n" | |
1847 | "(centered-remainder 123 10) @result{} 3\n" | |
1848 | "(centered-remainder 123 -10) @result{} 3\n" | |
1849 | "(centered-remainder -123 10) @result{} -3\n" | |
1850 | "(centered-remainder -123 -10) @result{} -3\n" | |
1851 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
1852 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
1853 | "@end lisp") | |
1854 | #define FUNC_NAME s_scm_centered_remainder | |
1855 | { | |
1856 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1857 | { | |
4a46bc2a | 1858 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
1859 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
1860 | { | |
1861 | scm_t_inum yy = SCM_I_INUM (y); | |
1862 | if (SCM_UNLIKELY (yy == 0)) | |
1863 | scm_num_overflow (s_scm_centered_remainder); | |
1864 | else | |
1865 | { | |
ff62c168 MW |
1866 | scm_t_inum rr = xx % yy; |
1867 | if (SCM_LIKELY (xx > 0)) | |
1868 | { | |
1869 | if (SCM_LIKELY (yy > 0)) | |
1870 | { | |
1871 | if (rr >= (yy + 1) / 2) | |
1872 | rr -= yy; | |
1873 | } | |
1874 | else | |
1875 | { | |
1876 | if (rr >= (1 - yy) / 2) | |
1877 | rr += yy; | |
1878 | } | |
1879 | } | |
1880 | else | |
1881 | { | |
1882 | if (SCM_LIKELY (yy > 0)) | |
1883 | { | |
1884 | if (rr < -yy / 2) | |
1885 | rr += yy; | |
1886 | } | |
1887 | else | |
1888 | { | |
1889 | if (rr < yy / 2) | |
1890 | rr -= yy; | |
1891 | } | |
1892 | } | |
1893 | return SCM_I_MAKINUM (rr); | |
1894 | } | |
1895 | } | |
1896 | else if (SCM_BIGP (y)) | |
1897 | { | |
1898 | /* Pass a denormalized bignum version of x (even though it | |
1899 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
4a46bc2a | 1900 | return scm_i_bigint_centered_remainder (scm_i_long2big (xx), y); |
ff62c168 MW |
1901 | } |
1902 | else if (SCM_REALP (y)) | |
4a46bc2a | 1903 | return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 1904 | else if (SCM_FRACTIONP (y)) |
03ddd15b | 1905 | return scm_i_exact_rational_centered_remainder (x, y); |
ff62c168 MW |
1906 | else |
1907 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1908 | s_scm_centered_remainder); | |
1909 | } | |
1910 | else if (SCM_BIGP (x)) | |
1911 | { | |
1912 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1913 | { | |
1914 | scm_t_inum yy = SCM_I_INUM (y); | |
1915 | if (SCM_UNLIKELY (yy == 0)) | |
1916 | scm_num_overflow (s_scm_centered_remainder); | |
1917 | else | |
1918 | { | |
1919 | scm_t_inum rr; | |
1920 | /* Arrange for rr to initially be non-positive, | |
1921 | because that simplifies the test to see | |
1922 | if it is within the needed bounds. */ | |
1923 | if (yy > 0) | |
1924 | { | |
1925 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1926 | scm_remember_upto_here_1 (x); | |
1927 | if (rr < -yy / 2) | |
1928 | rr += yy; | |
1929 | } | |
1930 | else | |
1931 | { | |
1932 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1933 | scm_remember_upto_here_1 (x); | |
1934 | if (rr < yy / 2) | |
1935 | rr -= yy; | |
1936 | } | |
1937 | return SCM_I_MAKINUM (rr); | |
1938 | } | |
1939 | } | |
1940 | else if (SCM_BIGP (y)) | |
1941 | return scm_i_bigint_centered_remainder (x, y); | |
1942 | else if (SCM_REALP (y)) | |
1943 | return scm_i_inexact_centered_remainder | |
1944 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1945 | else if (SCM_FRACTIONP (y)) | |
03ddd15b | 1946 | return scm_i_exact_rational_centered_remainder (x, y); |
ff62c168 MW |
1947 | else |
1948 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1949 | s_scm_centered_remainder); | |
1950 | } | |
1951 | else if (SCM_REALP (x)) | |
1952 | { | |
1953 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1954 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1955 | return scm_i_inexact_centered_remainder | |
1956 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1957 | else | |
1958 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
1959 | s_scm_centered_remainder); | |
1960 | } | |
1961 | else if (SCM_FRACTIONP (x)) | |
1962 | { | |
1963 | if (SCM_REALP (y)) | |
1964 | return scm_i_inexact_centered_remainder | |
1965 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
03ddd15b MW |
1966 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
1967 | return scm_i_exact_rational_centered_remainder (x, y); | |
ff62c168 | 1968 | else |
03ddd15b MW |
1969 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, |
1970 | s_scm_centered_remainder); | |
ff62c168 MW |
1971 | } |
1972 | else | |
1973 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
1974 | s_scm_centered_remainder); | |
1975 | } | |
1976 | #undef FUNC_NAME | |
1977 | ||
1978 | static SCM | |
1979 | scm_i_inexact_centered_remainder (double x, double y) | |
1980 | { | |
1981 | double q; | |
1982 | ||
1983 | /* Although it would be more efficient to use fmod here, we can't | |
1984 | because it would in some cases produce results inconsistent with | |
1985 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
1986 | close). In particular, when x-y/2 is very close to a multiple of | |
1987 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
1988 | two cases must correspond to different choices of q. If quotient | |
1989 | chooses one and remainder chooses the other, it would be bad. */ | |
1990 | if (SCM_LIKELY (y > 0)) | |
1991 | q = floor (x/y + 0.5); | |
1992 | else if (SCM_LIKELY (y < 0)) | |
1993 | q = ceil (x/y - 0.5); | |
1994 | else if (y == 0) | |
1995 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
1996 | else | |
1997 | return scm_nan (); | |
1998 | return scm_from_double (x - q * y); | |
1999 | } | |
2000 | ||
2001 | /* Assumes that both x and y are bigints, though | |
2002 | x might be able to fit into a fixnum. */ | |
2003 | static SCM | |
2004 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
2005 | { | |
2006 | SCM r, min_r; | |
2007 | ||
2008 | /* Note that x might be small enough to fit into a | |
2009 | fixnum, so we must not let it escape into the wild */ | |
2010 | r = scm_i_mkbig (); | |
2011 | ||
2012 | /* min_r will eventually become -abs(y)/2 */ | |
2013 | min_r = scm_i_mkbig (); | |
2014 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2015 | SCM_I_BIG_MPZ (y), 1); | |
2016 | ||
2017 | /* Arrange for rr to initially be non-positive, | |
2018 | because that simplifies the test to see | |
2019 | if it is within the needed bounds. */ | |
2020 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2021 | { | |
2022 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
2023 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2024 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2025 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2026 | mpz_add (SCM_I_BIG_MPZ (r), | |
2027 | SCM_I_BIG_MPZ (r), | |
2028 | SCM_I_BIG_MPZ (y)); | |
2029 | } | |
2030 | else | |
2031 | { | |
2032 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
2033 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2034 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2035 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2036 | SCM_I_BIG_MPZ (r), | |
2037 | SCM_I_BIG_MPZ (y)); | |
2038 | } | |
2039 | scm_remember_upto_here_2 (x, y); | |
2040 | return scm_i_normbig (r); | |
2041 | } | |
2042 | ||
ff62c168 | 2043 | static SCM |
03ddd15b | 2044 | scm_i_exact_rational_centered_remainder (SCM x, SCM y) |
ff62c168 | 2045 | { |
03ddd15b MW |
2046 | SCM xd = scm_denominator (x); |
2047 | SCM yd = scm_denominator (y); | |
2048 | SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd), | |
2049 | scm_product (scm_numerator (y), xd)); | |
2050 | return scm_divide (r1, scm_product (xd, yd)); | |
ff62c168 MW |
2051 | } |
2052 | ||
2053 | ||
5fbf680b MW |
2054 | static void scm_i_inexact_centered_divide (double x, double y, |
2055 | SCM *qp, SCM *rp); | |
2056 | static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
03ddd15b MW |
2057 | static void scm_i_exact_rational_centered_divide (SCM x, SCM y, |
2058 | SCM *qp, SCM *rp); | |
ff62c168 | 2059 | |
5fbf680b | 2060 | SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0, |
ff62c168 MW |
2061 | (SCM x, SCM y), |
2062 | "Return the integer @var{q} and the real number @var{r}\n" | |
2063 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2064 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2065 | "@lisp\n" | |
2066 | "(centered/ 123 10) @result{} 12 and 3\n" | |
2067 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
2068 | "(centered/ -123 10) @result{} -12 and -3\n" | |
2069 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
2070 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2071 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
2072 | "@end lisp") | |
5fbf680b MW |
2073 | #define FUNC_NAME s_scm_i_centered_divide |
2074 | { | |
2075 | SCM q, r; | |
2076 | ||
2077 | scm_centered_divide(x, y, &q, &r); | |
2078 | return scm_values (scm_list_2 (q, r)); | |
2079 | } | |
2080 | #undef FUNC_NAME | |
2081 | ||
2082 | #define s_scm_centered_divide s_scm_i_centered_divide | |
2083 | #define g_scm_centered_divide g_scm_i_centered_divide | |
2084 | ||
2085 | void | |
2086 | scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 MW |
2087 | { |
2088 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2089 | { | |
4a46bc2a | 2090 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
2091 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
2092 | { | |
2093 | scm_t_inum yy = SCM_I_INUM (y); | |
2094 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 2095 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2096 | else |
2097 | { | |
ff62c168 | 2098 | scm_t_inum qq = xx / yy; |
4a46bc2a | 2099 | scm_t_inum rr = xx % yy; |
ff62c168 MW |
2100 | if (SCM_LIKELY (xx > 0)) |
2101 | { | |
2102 | if (SCM_LIKELY (yy > 0)) | |
2103 | { | |
2104 | if (rr >= (yy + 1) / 2) | |
2105 | { qq++; rr -= yy; } | |
2106 | } | |
2107 | else | |
2108 | { | |
2109 | if (rr >= (1 - yy) / 2) | |
2110 | { qq--; rr += yy; } | |
2111 | } | |
2112 | } | |
2113 | else | |
2114 | { | |
2115 | if (SCM_LIKELY (yy > 0)) | |
2116 | { | |
2117 | if (rr < -yy / 2) | |
2118 | { qq--; rr += yy; } | |
2119 | } | |
2120 | else | |
2121 | { | |
2122 | if (rr < yy / 2) | |
2123 | { qq++; rr -= yy; } | |
2124 | } | |
2125 | } | |
4a46bc2a | 2126 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 2127 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 2128 | else |
5fbf680b MW |
2129 | *qp = scm_i_inum2big (qq); |
2130 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 2131 | } |
5fbf680b | 2132 | return; |
ff62c168 MW |
2133 | } |
2134 | else if (SCM_BIGP (y)) | |
2135 | { | |
2136 | /* Pass a denormalized bignum version of x (even though it | |
ac6ce16b | 2137 | can fit in a fixnum) to scm_i_bigint_centered_divide */ |
5fbf680b | 2138 | return scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp); |
ff62c168 MW |
2139 | } |
2140 | else if (SCM_REALP (y)) | |
5fbf680b | 2141 | return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 2142 | else if (SCM_FRACTIONP (y)) |
03ddd15b | 2143 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); |
ff62c168 | 2144 | else |
5fbf680b MW |
2145 | return two_valued_wta_dispatch_2 |
2146 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
2147 | s_scm_centered_divide, qp, rp); | |
ff62c168 MW |
2148 | } |
2149 | else if (SCM_BIGP (x)) | |
2150 | { | |
2151 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2152 | { | |
2153 | scm_t_inum yy = SCM_I_INUM (y); | |
2154 | if (SCM_UNLIKELY (yy == 0)) | |
ac6ce16b | 2155 | scm_num_overflow (s_scm_centered_divide); |
ff62c168 MW |
2156 | else |
2157 | { | |
2158 | SCM q = scm_i_mkbig (); | |
2159 | scm_t_inum rr; | |
2160 | /* Arrange for rr to initially be non-positive, | |
2161 | because that simplifies the test to see | |
2162 | if it is within the needed bounds. */ | |
2163 | if (yy > 0) | |
2164 | { | |
2165 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2166 | SCM_I_BIG_MPZ (x), yy); | |
2167 | scm_remember_upto_here_1 (x); | |
2168 | if (rr < -yy / 2) | |
2169 | { | |
2170 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2171 | SCM_I_BIG_MPZ (q), 1); | |
2172 | rr += yy; | |
2173 | } | |
2174 | } | |
2175 | else | |
2176 | { | |
2177 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2178 | SCM_I_BIG_MPZ (x), -yy); | |
2179 | scm_remember_upto_here_1 (x); | |
2180 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2181 | if (rr < yy / 2) | |
2182 | { | |
2183 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2184 | SCM_I_BIG_MPZ (q), 1); | |
2185 | rr -= yy; | |
2186 | } | |
2187 | } | |
5fbf680b MW |
2188 | *qp = scm_i_normbig (q); |
2189 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 2190 | } |
5fbf680b | 2191 | return; |
ff62c168 MW |
2192 | } |
2193 | else if (SCM_BIGP (y)) | |
5fbf680b | 2194 | return scm_i_bigint_centered_divide (x, y, qp, rp); |
ff62c168 | 2195 | else if (SCM_REALP (y)) |
ac6ce16b | 2196 | return scm_i_inexact_centered_divide |
5fbf680b | 2197 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 2198 | else if (SCM_FRACTIONP (y)) |
03ddd15b | 2199 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); |
ff62c168 | 2200 | else |
5fbf680b MW |
2201 | return two_valued_wta_dispatch_2 |
2202 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
2203 | s_scm_centered_divide, qp, rp); | |
ff62c168 MW |
2204 | } |
2205 | else if (SCM_REALP (x)) | |
2206 | { | |
2207 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2208 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
ac6ce16b | 2209 | return scm_i_inexact_centered_divide |
5fbf680b | 2210 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
03ddd15b | 2211 | else |
5fbf680b MW |
2212 | return two_valued_wta_dispatch_2 |
2213 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
2214 | s_scm_centered_divide, qp, rp); | |
ff62c168 MW |
2215 | } |
2216 | else if (SCM_FRACTIONP (x)) | |
2217 | { | |
2218 | if (SCM_REALP (y)) | |
ac6ce16b | 2219 | return scm_i_inexact_centered_divide |
5fbf680b | 2220 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b MW |
2221 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
2222 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
ff62c168 | 2223 | else |
03ddd15b MW |
2224 | return two_valued_wta_dispatch_2 |
2225 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
2226 | s_scm_centered_divide, qp, rp); | |
ff62c168 MW |
2227 | } |
2228 | else | |
5fbf680b MW |
2229 | return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1, |
2230 | s_scm_centered_divide, qp, rp); | |
ff62c168 | 2231 | } |
ff62c168 | 2232 | |
5fbf680b MW |
2233 | static void |
2234 | scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp) | |
ff62c168 MW |
2235 | { |
2236 | double q, r; | |
2237 | ||
2238 | if (SCM_LIKELY (y > 0)) | |
2239 | q = floor (x/y + 0.5); | |
2240 | else if (SCM_LIKELY (y < 0)) | |
2241 | q = ceil (x/y - 0.5); | |
2242 | else if (y == 0) | |
ac6ce16b | 2243 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ |
ff62c168 MW |
2244 | else |
2245 | q = guile_NaN; | |
2246 | r = x - q * y; | |
5fbf680b MW |
2247 | *qp = scm_from_double (q); |
2248 | *rp = scm_from_double (r); | |
ff62c168 MW |
2249 | } |
2250 | ||
2251 | /* Assumes that both x and y are bigints, though | |
2252 | x might be able to fit into a fixnum. */ | |
5fbf680b MW |
2253 | static void |
2254 | scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 MW |
2255 | { |
2256 | SCM q, r, min_r; | |
2257 | ||
2258 | /* Note that x might be small enough to fit into a | |
2259 | fixnum, so we must not let it escape into the wild */ | |
2260 | q = scm_i_mkbig (); | |
2261 | r = scm_i_mkbig (); | |
2262 | ||
2263 | /* min_r will eventually become -abs(y/2) */ | |
2264 | min_r = scm_i_mkbig (); | |
2265 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2266 | SCM_I_BIG_MPZ (y), 1); | |
2267 | ||
2268 | /* Arrange for rr to initially be non-positive, | |
2269 | because that simplifies the test to see | |
2270 | if it is within the needed bounds. */ | |
2271 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2272 | { | |
2273 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2274 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2275 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2276 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2277 | { | |
2278 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2279 | SCM_I_BIG_MPZ (q), 1); | |
2280 | mpz_add (SCM_I_BIG_MPZ (r), | |
2281 | SCM_I_BIG_MPZ (r), | |
2282 | SCM_I_BIG_MPZ (y)); | |
2283 | } | |
2284 | } | |
2285 | else | |
2286 | { | |
2287 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2288 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2289 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2290 | { | |
2291 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2292 | SCM_I_BIG_MPZ (q), 1); | |
2293 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2294 | SCM_I_BIG_MPZ (r), | |
2295 | SCM_I_BIG_MPZ (y)); | |
2296 | } | |
2297 | } | |
2298 | scm_remember_upto_here_2 (x, y); | |
5fbf680b MW |
2299 | *qp = scm_i_normbig (q); |
2300 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
2301 | } |
2302 | ||
5fbf680b | 2303 | static void |
03ddd15b | 2304 | scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 2305 | { |
03ddd15b MW |
2306 | SCM r1; |
2307 | SCM xd = scm_denominator (x); | |
2308 | SCM yd = scm_denominator (y); | |
2309 | ||
2310 | scm_centered_divide (scm_product (scm_numerator (x), yd), | |
2311 | scm_product (scm_numerator (y), xd), | |
2312 | qp, &r1); | |
2313 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
ff62c168 MW |
2314 | } |
2315 | ||
2316 | ||
78d3deb1 AW |
2317 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
2318 | (SCM x, SCM y, SCM rest), | |
2319 | "Return the greatest common divisor of all parameter values.\n" | |
2320 | "If called without arguments, 0 is returned.") | |
2321 | #define FUNC_NAME s_scm_i_gcd | |
2322 | { | |
2323 | while (!scm_is_null (rest)) | |
2324 | { x = scm_gcd (x, y); | |
2325 | y = scm_car (rest); | |
2326 | rest = scm_cdr (rest); | |
2327 | } | |
2328 | return scm_gcd (x, y); | |
2329 | } | |
2330 | #undef FUNC_NAME | |
2331 | ||
2332 | #define s_gcd s_scm_i_gcd | |
2333 | #define g_gcd g_scm_i_gcd | |
2334 | ||
0f2d19dd | 2335 | SCM |
6e8d25a6 | 2336 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 2337 | { |
ca46fb90 | 2338 | if (SCM_UNBNDP (y)) |
1dd79792 | 2339 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 2340 | |
e11e83f3 | 2341 | if (SCM_I_INUMP (x)) |
ca46fb90 | 2342 | { |
e11e83f3 | 2343 | if (SCM_I_INUMP (y)) |
ca46fb90 | 2344 | { |
e25f3727 AW |
2345 | scm_t_inum xx = SCM_I_INUM (x); |
2346 | scm_t_inum yy = SCM_I_INUM (y); | |
2347 | scm_t_inum u = xx < 0 ? -xx : xx; | |
2348 | scm_t_inum v = yy < 0 ? -yy : yy; | |
2349 | scm_t_inum result; | |
0aacf84e MD |
2350 | if (xx == 0) |
2351 | result = v; | |
2352 | else if (yy == 0) | |
2353 | result = u; | |
2354 | else | |
2355 | { | |
e25f3727 AW |
2356 | scm_t_inum k = 1; |
2357 | scm_t_inum t; | |
0aacf84e MD |
2358 | /* Determine a common factor 2^k */ |
2359 | while (!(1 & (u | v))) | |
2360 | { | |
2361 | k <<= 1; | |
2362 | u >>= 1; | |
2363 | v >>= 1; | |
2364 | } | |
2365 | /* Now, any factor 2^n can be eliminated */ | |
2366 | if (u & 1) | |
2367 | t = -v; | |
2368 | else | |
2369 | { | |
2370 | t = u; | |
2371 | b3: | |
2372 | t = SCM_SRS (t, 1); | |
2373 | } | |
2374 | if (!(1 & t)) | |
2375 | goto b3; | |
2376 | if (t > 0) | |
2377 | u = t; | |
2378 | else | |
2379 | v = -t; | |
2380 | t = u - v; | |
2381 | if (t != 0) | |
2382 | goto b3; | |
2383 | result = u * k; | |
2384 | } | |
2385 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 2386 | ? SCM_I_MAKINUM (result) |
e25f3727 | 2387 | : scm_i_inum2big (result)); |
ca46fb90 RB |
2388 | } |
2389 | else if (SCM_BIGP (y)) | |
2390 | { | |
0bff4dce KR |
2391 | SCM_SWAP (x, y); |
2392 | goto big_inum; | |
ca46fb90 RB |
2393 | } |
2394 | else | |
2395 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 2396 | } |
ca46fb90 RB |
2397 | else if (SCM_BIGP (x)) |
2398 | { | |
e11e83f3 | 2399 | if (SCM_I_INUMP (y)) |
ca46fb90 | 2400 | { |
e25f3727 AW |
2401 | scm_t_bits result; |
2402 | scm_t_inum yy; | |
0bff4dce | 2403 | big_inum: |
e11e83f3 | 2404 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
2405 | if (yy == 0) |
2406 | return scm_abs (x); | |
0aacf84e MD |
2407 | if (yy < 0) |
2408 | yy = -yy; | |
ca46fb90 RB |
2409 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
2410 | scm_remember_upto_here_1 (x); | |
0aacf84e | 2411 | return (SCM_POSFIXABLE (result) |
d956fa6f | 2412 | ? SCM_I_MAKINUM (result) |
e25f3727 | 2413 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
2414 | } |
2415 | else if (SCM_BIGP (y)) | |
2416 | { | |
2417 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
2418 | mpz_gcd (SCM_I_BIG_MPZ (result), |
2419 | SCM_I_BIG_MPZ (x), | |
2420 | SCM_I_BIG_MPZ (y)); | |
2421 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
2422 | return scm_i_normbig (result); |
2423 | } | |
2424 | else | |
2425 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 2426 | } |
ca46fb90 | 2427 | else |
09fb7599 | 2428 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
2429 | } |
2430 | ||
78d3deb1 AW |
2431 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
2432 | (SCM x, SCM y, SCM rest), | |
2433 | "Return the least common multiple of the arguments.\n" | |
2434 | "If called without arguments, 1 is returned.") | |
2435 | #define FUNC_NAME s_scm_i_lcm | |
2436 | { | |
2437 | while (!scm_is_null (rest)) | |
2438 | { x = scm_lcm (x, y); | |
2439 | y = scm_car (rest); | |
2440 | rest = scm_cdr (rest); | |
2441 | } | |
2442 | return scm_lcm (x, y); | |
2443 | } | |
2444 | #undef FUNC_NAME | |
2445 | ||
2446 | #define s_lcm s_scm_i_lcm | |
2447 | #define g_lcm g_scm_i_lcm | |
2448 | ||
0f2d19dd | 2449 | SCM |
6e8d25a6 | 2450 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 2451 | { |
ca46fb90 RB |
2452 | if (SCM_UNBNDP (n2)) |
2453 | { | |
2454 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
2455 | return SCM_I_MAKINUM (1L); |
2456 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 2457 | } |
09fb7599 | 2458 | |
e11e83f3 | 2459 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 2460 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 2461 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 2462 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 2463 | |
e11e83f3 | 2464 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 2465 | { |
e11e83f3 | 2466 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
2467 | { |
2468 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 2469 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
2470 | return d; |
2471 | else | |
2472 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
2473 | } | |
2474 | else | |
2475 | { | |
2476 | /* inum n1, big n2 */ | |
2477 | inumbig: | |
2478 | { | |
2479 | SCM result = scm_i_mkbig (); | |
e25f3727 | 2480 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
2481 | if (nn1 == 0) return SCM_INUM0; |
2482 | if (nn1 < 0) nn1 = - nn1; | |
2483 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
2484 | scm_remember_upto_here_1 (n2); | |
2485 | return result; | |
2486 | } | |
2487 | } | |
2488 | } | |
2489 | else | |
2490 | { | |
2491 | /* big n1 */ | |
e11e83f3 | 2492 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
2493 | { |
2494 | SCM_SWAP (n1, n2); | |
2495 | goto inumbig; | |
2496 | } | |
2497 | else | |
2498 | { | |
2499 | SCM result = scm_i_mkbig (); | |
2500 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
2501 | SCM_I_BIG_MPZ (n1), | |
2502 | SCM_I_BIG_MPZ (n2)); | |
2503 | scm_remember_upto_here_2(n1, n2); | |
2504 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
2505 | return result; | |
2506 | } | |
f872b822 | 2507 | } |
0f2d19dd JB |
2508 | } |
2509 | ||
8a525303 GB |
2510 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
2511 | ||
2512 | Logand: | |
2513 | X Y Result Method: | |
2514 | (len) | |
2515 | + + + x (map digit:logand X Y) | |
2516 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
2517 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
2518 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
2519 | ||
2520 | Logior: | |
2521 | X Y Result Method: | |
2522 | ||
2523 | + + + (map digit:logior X Y) | |
2524 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
2525 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
2526 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
2527 | ||
2528 | Logxor: | |
2529 | X Y Result Method: | |
2530 | ||
2531 | + + + (map digit:logxor X Y) | |
2532 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
2533 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
2534 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
2535 | ||
2536 | Logtest: | |
2537 | X Y Result | |
2538 | ||
2539 | + + (any digit:logand X Y) | |
2540 | + - (any digit:logand X (lognot (+ -1 Y))) | |
2541 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
2542 | - - #t | |
2543 | ||
2544 | */ | |
2545 | ||
78d3deb1 AW |
2546 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
2547 | (SCM x, SCM y, SCM rest), | |
2548 | "Return the bitwise AND of the integer arguments.\n\n" | |
2549 | "@lisp\n" | |
2550 | "(logand) @result{} -1\n" | |
2551 | "(logand 7) @result{} 7\n" | |
2552 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
2553 | "@end lisp") | |
2554 | #define FUNC_NAME s_scm_i_logand | |
2555 | { | |
2556 | while (!scm_is_null (rest)) | |
2557 | { x = scm_logand (x, y); | |
2558 | y = scm_car (rest); | |
2559 | rest = scm_cdr (rest); | |
2560 | } | |
2561 | return scm_logand (x, y); | |
2562 | } | |
2563 | #undef FUNC_NAME | |
2564 | ||
2565 | #define s_scm_logand s_scm_i_logand | |
2566 | ||
2567 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 2568 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 2569 | { |
e25f3727 | 2570 | scm_t_inum nn1; |
9a00c9fc | 2571 | |
0aacf84e MD |
2572 | if (SCM_UNBNDP (n2)) |
2573 | { | |
2574 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 2575 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
2576 | else if (!SCM_NUMBERP (n1)) |
2577 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
2578 | else if (SCM_NUMBERP (n1)) | |
2579 | return n1; | |
2580 | else | |
2581 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2582 | } |
09fb7599 | 2583 | |
e11e83f3 | 2584 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2585 | { |
e11e83f3 MV |
2586 | nn1 = SCM_I_INUM (n1); |
2587 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2588 | { |
e25f3727 | 2589 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 2590 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
2591 | } |
2592 | else if SCM_BIGP (n2) | |
2593 | { | |
2594 | intbig: | |
2595 | if (n1 == 0) | |
2596 | return SCM_INUM0; | |
2597 | { | |
2598 | SCM result_z = scm_i_mkbig (); | |
2599 | mpz_t nn1_z; | |
2600 | mpz_init_set_si (nn1_z, nn1); | |
2601 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2602 | scm_remember_upto_here_1 (n2); | |
2603 | mpz_clear (nn1_z); | |
2604 | return scm_i_normbig (result_z); | |
2605 | } | |
2606 | } | |
2607 | else | |
2608 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2609 | } | |
2610 | else if (SCM_BIGP (n1)) | |
2611 | { | |
e11e83f3 | 2612 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2613 | { |
2614 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2615 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2616 | goto intbig; |
2617 | } | |
2618 | else if (SCM_BIGP (n2)) | |
2619 | { | |
2620 | SCM result_z = scm_i_mkbig (); | |
2621 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
2622 | SCM_I_BIG_MPZ (n1), | |
2623 | SCM_I_BIG_MPZ (n2)); | |
2624 | scm_remember_upto_here_2 (n1, n2); | |
2625 | return scm_i_normbig (result_z); | |
2626 | } | |
2627 | else | |
2628 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2629 | } |
0aacf84e | 2630 | else |
09fb7599 | 2631 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2632 | } |
1bbd0b84 | 2633 | #undef FUNC_NAME |
0f2d19dd | 2634 | |
09fb7599 | 2635 | |
78d3deb1 AW |
2636 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
2637 | (SCM x, SCM y, SCM rest), | |
2638 | "Return the bitwise OR of the integer arguments.\n\n" | |
2639 | "@lisp\n" | |
2640 | "(logior) @result{} 0\n" | |
2641 | "(logior 7) @result{} 7\n" | |
2642 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
2643 | "@end lisp") | |
2644 | #define FUNC_NAME s_scm_i_logior | |
2645 | { | |
2646 | while (!scm_is_null (rest)) | |
2647 | { x = scm_logior (x, y); | |
2648 | y = scm_car (rest); | |
2649 | rest = scm_cdr (rest); | |
2650 | } | |
2651 | return scm_logior (x, y); | |
2652 | } | |
2653 | #undef FUNC_NAME | |
2654 | ||
2655 | #define s_scm_logior s_scm_i_logior | |
2656 | ||
2657 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 2658 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 2659 | { |
e25f3727 | 2660 | scm_t_inum nn1; |
9a00c9fc | 2661 | |
0aacf84e MD |
2662 | if (SCM_UNBNDP (n2)) |
2663 | { | |
2664 | if (SCM_UNBNDP (n1)) | |
2665 | return SCM_INUM0; | |
2666 | else if (SCM_NUMBERP (n1)) | |
2667 | return n1; | |
2668 | else | |
2669 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2670 | } |
09fb7599 | 2671 | |
e11e83f3 | 2672 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2673 | { |
e11e83f3 MV |
2674 | nn1 = SCM_I_INUM (n1); |
2675 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2676 | { |
e11e83f3 | 2677 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 2678 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
2679 | } |
2680 | else if (SCM_BIGP (n2)) | |
2681 | { | |
2682 | intbig: | |
2683 | if (nn1 == 0) | |
2684 | return n2; | |
2685 | { | |
2686 | SCM result_z = scm_i_mkbig (); | |
2687 | mpz_t nn1_z; | |
2688 | mpz_init_set_si (nn1_z, nn1); | |
2689 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2690 | scm_remember_upto_here_1 (n2); | |
2691 | mpz_clear (nn1_z); | |
9806de0d | 2692 | return scm_i_normbig (result_z); |
0aacf84e MD |
2693 | } |
2694 | } | |
2695 | else | |
2696 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2697 | } | |
2698 | else if (SCM_BIGP (n1)) | |
2699 | { | |
e11e83f3 | 2700 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2701 | { |
2702 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2703 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2704 | goto intbig; |
2705 | } | |
2706 | else if (SCM_BIGP (n2)) | |
2707 | { | |
2708 | SCM result_z = scm_i_mkbig (); | |
2709 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
2710 | SCM_I_BIG_MPZ (n1), | |
2711 | SCM_I_BIG_MPZ (n2)); | |
2712 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 2713 | return scm_i_normbig (result_z); |
0aacf84e MD |
2714 | } |
2715 | else | |
2716 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2717 | } |
0aacf84e | 2718 | else |
09fb7599 | 2719 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2720 | } |
1bbd0b84 | 2721 | #undef FUNC_NAME |
0f2d19dd | 2722 | |
09fb7599 | 2723 | |
78d3deb1 AW |
2724 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
2725 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
2726 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
2727 | "set in the result if it is set in an odd number of arguments.\n" | |
2728 | "@lisp\n" | |
2729 | "(logxor) @result{} 0\n" | |
2730 | "(logxor 7) @result{} 7\n" | |
2731 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
2732 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 2733 | "@end lisp") |
78d3deb1 AW |
2734 | #define FUNC_NAME s_scm_i_logxor |
2735 | { | |
2736 | while (!scm_is_null (rest)) | |
2737 | { x = scm_logxor (x, y); | |
2738 | y = scm_car (rest); | |
2739 | rest = scm_cdr (rest); | |
2740 | } | |
2741 | return scm_logxor (x, y); | |
2742 | } | |
2743 | #undef FUNC_NAME | |
2744 | ||
2745 | #define s_scm_logxor s_scm_i_logxor | |
2746 | ||
2747 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 2748 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 2749 | { |
e25f3727 | 2750 | scm_t_inum nn1; |
9a00c9fc | 2751 | |
0aacf84e MD |
2752 | if (SCM_UNBNDP (n2)) |
2753 | { | |
2754 | if (SCM_UNBNDP (n1)) | |
2755 | return SCM_INUM0; | |
2756 | else if (SCM_NUMBERP (n1)) | |
2757 | return n1; | |
2758 | else | |
2759 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 2760 | } |
09fb7599 | 2761 | |
e11e83f3 | 2762 | if (SCM_I_INUMP (n1)) |
0aacf84e | 2763 | { |
e11e83f3 MV |
2764 | nn1 = SCM_I_INUM (n1); |
2765 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 2766 | { |
e25f3727 | 2767 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 2768 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
2769 | } |
2770 | else if (SCM_BIGP (n2)) | |
2771 | { | |
2772 | intbig: | |
2773 | { | |
2774 | SCM result_z = scm_i_mkbig (); | |
2775 | mpz_t nn1_z; | |
2776 | mpz_init_set_si (nn1_z, nn1); | |
2777 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
2778 | scm_remember_upto_here_1 (n2); | |
2779 | mpz_clear (nn1_z); | |
2780 | return scm_i_normbig (result_z); | |
2781 | } | |
2782 | } | |
2783 | else | |
2784 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
2785 | } | |
2786 | else if (SCM_BIGP (n1)) | |
2787 | { | |
e11e83f3 | 2788 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
2789 | { |
2790 | SCM_SWAP (n1, n2); | |
e11e83f3 | 2791 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
2792 | goto intbig; |
2793 | } | |
2794 | else if (SCM_BIGP (n2)) | |
2795 | { | |
2796 | SCM result_z = scm_i_mkbig (); | |
2797 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
2798 | SCM_I_BIG_MPZ (n1), | |
2799 | SCM_I_BIG_MPZ (n2)); | |
2800 | scm_remember_upto_here_2 (n1, n2); | |
2801 | return scm_i_normbig (result_z); | |
2802 | } | |
2803 | else | |
2804 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 2805 | } |
0aacf84e | 2806 | else |
09fb7599 | 2807 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 2808 | } |
1bbd0b84 | 2809 | #undef FUNC_NAME |
0f2d19dd | 2810 | |
09fb7599 | 2811 | |
a1ec6916 | 2812 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 2813 | (SCM j, SCM k), |
ba6e7231 KR |
2814 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
2815 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
2816 | "without actually calculating the @code{logand}, just testing\n" | |
2817 | "for non-zero.\n" | |
2818 | "\n" | |
1e6808ea | 2819 | "@lisp\n" |
b380b885 MD |
2820 | "(logtest #b0100 #b1011) @result{} #f\n" |
2821 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 2822 | "@end lisp") |
1bbd0b84 | 2823 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 2824 | { |
e25f3727 | 2825 | scm_t_inum nj; |
9a00c9fc | 2826 | |
e11e83f3 | 2827 | if (SCM_I_INUMP (j)) |
0aacf84e | 2828 | { |
e11e83f3 MV |
2829 | nj = SCM_I_INUM (j); |
2830 | if (SCM_I_INUMP (k)) | |
0aacf84e | 2831 | { |
e25f3727 | 2832 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 2833 | return scm_from_bool (nj & nk); |
0aacf84e MD |
2834 | } |
2835 | else if (SCM_BIGP (k)) | |
2836 | { | |
2837 | intbig: | |
2838 | if (nj == 0) | |
2839 | return SCM_BOOL_F; | |
2840 | { | |
2841 | SCM result; | |
2842 | mpz_t nj_z; | |
2843 | mpz_init_set_si (nj_z, nj); | |
2844 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
2845 | scm_remember_upto_here_1 (k); | |
73e4de09 | 2846 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
2847 | mpz_clear (nj_z); |
2848 | return result; | |
2849 | } | |
2850 | } | |
2851 | else | |
2852 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
2853 | } | |
2854 | else if (SCM_BIGP (j)) | |
2855 | { | |
e11e83f3 | 2856 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
2857 | { |
2858 | SCM_SWAP (j, k); | |
e11e83f3 | 2859 | nj = SCM_I_INUM (j); |
0aacf84e MD |
2860 | goto intbig; |
2861 | } | |
2862 | else if (SCM_BIGP (k)) | |
2863 | { | |
2864 | SCM result; | |
2865 | mpz_t result_z; | |
2866 | mpz_init (result_z); | |
2867 | mpz_and (result_z, | |
2868 | SCM_I_BIG_MPZ (j), | |
2869 | SCM_I_BIG_MPZ (k)); | |
2870 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 2871 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
2872 | mpz_clear (result_z); |
2873 | return result; | |
2874 | } | |
2875 | else | |
2876 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
2877 | } | |
2878 | else | |
2879 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 2880 | } |
1bbd0b84 | 2881 | #undef FUNC_NAME |
0f2d19dd | 2882 | |
c1bfcf60 | 2883 | |
a1ec6916 | 2884 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 2885 | (SCM index, SCM j), |
ba6e7231 KR |
2886 | "Test whether bit number @var{index} in @var{j} is set.\n" |
2887 | "@var{index} starts from 0 for the least significant bit.\n" | |
2888 | "\n" | |
1e6808ea | 2889 | "@lisp\n" |
b380b885 MD |
2890 | "(logbit? 0 #b1101) @result{} #t\n" |
2891 | "(logbit? 1 #b1101) @result{} #f\n" | |
2892 | "(logbit? 2 #b1101) @result{} #t\n" | |
2893 | "(logbit? 3 #b1101) @result{} #t\n" | |
2894 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 2895 | "@end lisp") |
1bbd0b84 | 2896 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 2897 | { |
78166ad5 | 2898 | unsigned long int iindex; |
5efd3c7d | 2899 | iindex = scm_to_ulong (index); |
78166ad5 | 2900 | |
e11e83f3 | 2901 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
2902 | { |
2903 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 2904 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 2905 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 2906 | } |
0aacf84e MD |
2907 | else if (SCM_BIGP (j)) |
2908 | { | |
2909 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
2910 | scm_remember_upto_here_1 (j); | |
73e4de09 | 2911 | return scm_from_bool (val); |
0aacf84e MD |
2912 | } |
2913 | else | |
78166ad5 | 2914 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 2915 | } |
1bbd0b84 | 2916 | #undef FUNC_NAME |
0f2d19dd | 2917 | |
78166ad5 | 2918 | |
a1ec6916 | 2919 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 2920 | (SCM n), |
4d814788 | 2921 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
2922 | "argument.\n" |
2923 | "\n" | |
b380b885 MD |
2924 | "@lisp\n" |
2925 | "(number->string (lognot #b10000000) 2)\n" | |
2926 | " @result{} \"-10000001\"\n" | |
2927 | "(number->string (lognot #b0) 2)\n" | |
2928 | " @result{} \"-1\"\n" | |
1e6808ea | 2929 | "@end lisp") |
1bbd0b84 | 2930 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 2931 | { |
e11e83f3 | 2932 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
2933 | /* No overflow here, just need to toggle all the bits making up the inum. |
2934 | Enhancement: No need to strip the tag and add it back, could just xor | |
2935 | a block of 1 bits, if that worked with the various debug versions of | |
2936 | the SCM typedef. */ | |
e11e83f3 | 2937 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
2938 | |
2939 | } else if (SCM_BIGP (n)) { | |
2940 | SCM result = scm_i_mkbig (); | |
2941 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
2942 | scm_remember_upto_here_1 (n); | |
2943 | return result; | |
2944 | ||
2945 | } else { | |
2946 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
2947 | } | |
0f2d19dd | 2948 | } |
1bbd0b84 | 2949 | #undef FUNC_NAME |
0f2d19dd | 2950 | |
518b7508 KR |
2951 | /* returns 0 if IN is not an integer. OUT must already be |
2952 | initialized. */ | |
2953 | static int | |
2954 | coerce_to_big (SCM in, mpz_t out) | |
2955 | { | |
2956 | if (SCM_BIGP (in)) | |
2957 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
2958 | else if (SCM_I_INUMP (in)) |
2959 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
2960 | else |
2961 | return 0; | |
2962 | ||
2963 | return 1; | |
2964 | } | |
2965 | ||
d885e204 | 2966 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
2967 | (SCM n, SCM k, SCM m), |
2968 | "Return @var{n} raised to the integer exponent\n" | |
2969 | "@var{k}, modulo @var{m}.\n" | |
2970 | "\n" | |
2971 | "@lisp\n" | |
2972 | "(modulo-expt 2 3 5)\n" | |
2973 | " @result{} 3\n" | |
2974 | "@end lisp") | |
d885e204 | 2975 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
2976 | { |
2977 | mpz_t n_tmp; | |
2978 | mpz_t k_tmp; | |
2979 | mpz_t m_tmp; | |
2980 | ||
2981 | /* There are two classes of error we might encounter -- | |
2982 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
2983 | and | |
2984 | 2) wrong-type errors, which of course we'll report by calling | |
2985 | SCM_WRONG_TYPE_ARG. | |
2986 | We don't report those errors immediately, however; instead we do | |
2987 | some cleanup first. These variables tell us which error (if | |
2988 | any) we should report after cleaning up. | |
2989 | */ | |
2990 | int report_overflow = 0; | |
2991 | ||
2992 | int position_of_wrong_type = 0; | |
2993 | SCM value_of_wrong_type = SCM_INUM0; | |
2994 | ||
2995 | SCM result = SCM_UNDEFINED; | |
2996 | ||
2997 | mpz_init (n_tmp); | |
2998 | mpz_init (k_tmp); | |
2999 | mpz_init (m_tmp); | |
3000 | ||
bc36d050 | 3001 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
3002 | { |
3003 | report_overflow = 1; | |
3004 | goto cleanup; | |
3005 | } | |
3006 | ||
3007 | if (!coerce_to_big (n, n_tmp)) | |
3008 | { | |
3009 | value_of_wrong_type = n; | |
3010 | position_of_wrong_type = 1; | |
3011 | goto cleanup; | |
3012 | } | |
3013 | ||
3014 | if (!coerce_to_big (k, k_tmp)) | |
3015 | { | |
3016 | value_of_wrong_type = k; | |
3017 | position_of_wrong_type = 2; | |
3018 | goto cleanup; | |
3019 | } | |
3020 | ||
3021 | if (!coerce_to_big (m, m_tmp)) | |
3022 | { | |
3023 | value_of_wrong_type = m; | |
3024 | position_of_wrong_type = 3; | |
3025 | goto cleanup; | |
3026 | } | |
3027 | ||
3028 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
3029 | will get a divide-by-zero exception when an inverse 1/n mod m | |
3030 | doesn't exist (or is not unique). Since exceptions are hard to | |
3031 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
3032 | a simple failure code, which is easy to handle. */ | |
3033 | ||
3034 | if (-1 == mpz_sgn (k_tmp)) | |
3035 | { | |
3036 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
3037 | { | |
3038 | report_overflow = 1; | |
3039 | goto cleanup; | |
3040 | } | |
3041 | mpz_neg (k_tmp, k_tmp); | |
3042 | } | |
3043 | ||
3044 | result = scm_i_mkbig (); | |
3045 | mpz_powm (SCM_I_BIG_MPZ (result), | |
3046 | n_tmp, | |
3047 | k_tmp, | |
3048 | m_tmp); | |
b7b8c575 KR |
3049 | |
3050 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
3051 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
3052 | ||
518b7508 KR |
3053 | cleanup: |
3054 | mpz_clear (m_tmp); | |
3055 | mpz_clear (k_tmp); | |
3056 | mpz_clear (n_tmp); | |
3057 | ||
3058 | if (report_overflow) | |
3059 | scm_num_overflow (FUNC_NAME); | |
3060 | ||
3061 | if (position_of_wrong_type) | |
3062 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
3063 | value_of_wrong_type); | |
3064 | ||
3065 | return scm_i_normbig (result); | |
3066 | } | |
3067 | #undef FUNC_NAME | |
3068 | ||
a1ec6916 | 3069 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 3070 | (SCM n, SCM k), |
ba6e7231 KR |
3071 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
3072 | "exact integer, @var{n} can be any number.\n" | |
3073 | "\n" | |
2519490c MW |
3074 | "Negative @var{k} is supported, and results in\n" |
3075 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
3076 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 3077 | "includes @math{0^0} is 1.\n" |
1e6808ea | 3078 | "\n" |
b380b885 | 3079 | "@lisp\n" |
ba6e7231 KR |
3080 | "(integer-expt 2 5) @result{} 32\n" |
3081 | "(integer-expt -3 3) @result{} -27\n" | |
3082 | "(integer-expt 5 -3) @result{} 1/125\n" | |
3083 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 3084 | "@end lisp") |
1bbd0b84 | 3085 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 3086 | { |
e25f3727 | 3087 | scm_t_inum i2 = 0; |
1c35cb19 RB |
3088 | SCM z_i2 = SCM_BOOL_F; |
3089 | int i2_is_big = 0; | |
d956fa6f | 3090 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 3091 | |
bfe1f03a MW |
3092 | /* Specifically refrain from checking the type of the first argument. |
3093 | This allows us to exponentiate any object that can be multiplied. | |
3094 | If we must raise to a negative power, we must also be able to | |
3095 | take its reciprocal. */ | |
3096 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 3097 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 3098 | |
bfe1f03a MW |
3099 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
3100 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
3101 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
3102 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
3103 | /* The next check is necessary only because R6RS specifies different | |
3104 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
3105 | we simply skip this case and move on. */ | |
3106 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
3107 | { | |
3108 | /* k cannot be 0 at this point, because we | |
3109 | have already checked for that case above */ | |
3110 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
3111 | return n; |
3112 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
3113 | return scm_nan (); | |
3114 | } | |
ca46fb90 | 3115 | |
e11e83f3 MV |
3116 | if (SCM_I_INUMP (k)) |
3117 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
3118 | else if (SCM_BIGP (k)) |
3119 | { | |
3120 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
3121 | scm_remember_upto_here_1 (k); |
3122 | i2_is_big = 1; | |
3123 | } | |
2830fd91 | 3124 | else |
ca46fb90 RB |
3125 | SCM_WRONG_TYPE_ARG (2, k); |
3126 | ||
3127 | if (i2_is_big) | |
f872b822 | 3128 | { |
ca46fb90 RB |
3129 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
3130 | { | |
3131 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
3132 | n = scm_divide (n, SCM_UNDEFINED); | |
3133 | } | |
3134 | while (1) | |
3135 | { | |
3136 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
3137 | { | |
ca46fb90 RB |
3138 | return acc; |
3139 | } | |
3140 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
3141 | { | |
ca46fb90 RB |
3142 | return scm_product (acc, n); |
3143 | } | |
3144 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
3145 | acc = scm_product (acc, n); | |
3146 | n = scm_product (n, n); | |
3147 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
3148 | } | |
f872b822 | 3149 | } |
ca46fb90 | 3150 | else |
f872b822 | 3151 | { |
ca46fb90 RB |
3152 | if (i2 < 0) |
3153 | { | |
3154 | i2 = -i2; | |
3155 | n = scm_divide (n, SCM_UNDEFINED); | |
3156 | } | |
3157 | while (1) | |
3158 | { | |
3159 | if (0 == i2) | |
3160 | return acc; | |
3161 | if (1 == i2) | |
3162 | return scm_product (acc, n); | |
3163 | if (i2 & 1) | |
3164 | acc = scm_product (acc, n); | |
3165 | n = scm_product (n, n); | |
3166 | i2 >>= 1; | |
3167 | } | |
f872b822 | 3168 | } |
0f2d19dd | 3169 | } |
1bbd0b84 | 3170 | #undef FUNC_NAME |
0f2d19dd | 3171 | |
a1ec6916 | 3172 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 3173 | (SCM n, SCM cnt), |
32f19569 KR |
3174 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
3175 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 3176 | "\n" |
e7644cb2 | 3177 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
3178 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
3179 | "infinity. (Note that this is not the same rounding as\n" | |
3180 | "@code{quotient} does.)\n" | |
3181 | "\n" | |
3182 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
3183 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
3184 | "shift dropping bits.\n" | |
1e6808ea | 3185 | "\n" |
b380b885 | 3186 | "@lisp\n" |
1e6808ea MG |
3187 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
3188 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
3189 | "\n" |
3190 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
3191 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 3192 | "@end lisp") |
1bbd0b84 | 3193 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 3194 | { |
3ab9f56e | 3195 | long bits_to_shift; |
5efd3c7d | 3196 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 3197 | |
788aca27 KR |
3198 | if (SCM_I_INUMP (n)) |
3199 | { | |
e25f3727 | 3200 | scm_t_inum nn = SCM_I_INUM (n); |
788aca27 KR |
3201 | |
3202 | if (bits_to_shift > 0) | |
3203 | { | |
3204 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
3205 | overflow a non-zero fixnum. For smaller shifts we check the | |
3206 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
3207 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
3208 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
3209 | bits_to_shift)". */ | |
3210 | ||
3211 | if (nn == 0) | |
3212 | return n; | |
3213 | ||
3214 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 3215 | && ((scm_t_bits) |
788aca27 KR |
3216 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) |
3217 | <= 1)) | |
3218 | { | |
3219 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
3220 | } | |
3221 | else | |
3222 | { | |
e25f3727 | 3223 | SCM result = scm_i_inum2big (nn); |
788aca27 KR |
3224 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
3225 | bits_to_shift); | |
3226 | return result; | |
3227 | } | |
3228 | } | |
3229 | else | |
3230 | { | |
3231 | bits_to_shift = -bits_to_shift; | |
3232 | if (bits_to_shift >= SCM_LONG_BIT) | |
cff5fa33 | 3233 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1)); |
788aca27 KR |
3234 | else |
3235 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
3236 | } | |
3237 | ||
3238 | } | |
3239 | else if (SCM_BIGP (n)) | |
ca46fb90 | 3240 | { |
788aca27 KR |
3241 | SCM result; |
3242 | ||
3243 | if (bits_to_shift == 0) | |
3244 | return n; | |
3245 | ||
3246 | result = scm_i_mkbig (); | |
3247 | if (bits_to_shift >= 0) | |
3248 | { | |
3249 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
3250 | bits_to_shift); | |
3251 | return result; | |
3252 | } | |
ca46fb90 | 3253 | else |
788aca27 KR |
3254 | { |
3255 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
3256 | we have to allocate a bignum even if the result is going to be a | |
3257 | fixnum. */ | |
3258 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
3259 | -bits_to_shift); | |
3260 | return scm_i_normbig (result); | |
3261 | } | |
3262 | ||
ca46fb90 RB |
3263 | } |
3264 | else | |
788aca27 KR |
3265 | { |
3266 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
3267 | } | |
0f2d19dd | 3268 | } |
1bbd0b84 | 3269 | #undef FUNC_NAME |
0f2d19dd | 3270 | |
3c9f20f8 | 3271 | |
a1ec6916 | 3272 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 3273 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
3274 | "Return the integer composed of the @var{start} (inclusive)\n" |
3275 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
3276 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
3277 | "\n" | |
b380b885 MD |
3278 | "@lisp\n" |
3279 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
3280 | " @result{} \"1010\"\n" | |
3281 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
3282 | " @result{} \"10110\"\n" | |
3283 | "@end lisp") | |
1bbd0b84 | 3284 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 3285 | { |
7f848242 | 3286 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
3287 | istart = scm_to_ulong (start); |
3288 | iend = scm_to_ulong (end); | |
c1bfcf60 | 3289 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 3290 | |
7f848242 KR |
3291 | /* how many bits to keep */ |
3292 | bits = iend - istart; | |
3293 | ||
e11e83f3 | 3294 | if (SCM_I_INUMP (n)) |
0aacf84e | 3295 | { |
e25f3727 | 3296 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
3297 | |
3298 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 3299 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 3300 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 3301 | |
0aacf84e MD |
3302 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
3303 | { | |
3304 | /* Since we emulate two's complement encoded numbers, this | |
3305 | * special case requires us to produce a result that has | |
7f848242 | 3306 | * more bits than can be stored in a fixnum. |
0aacf84e | 3307 | */ |
e25f3727 | 3308 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
3309 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
3310 | bits); | |
3311 | return result; | |
0aacf84e | 3312 | } |
ac0c002c | 3313 | |
7f848242 | 3314 | /* mask down to requisite bits */ |
857ae6af | 3315 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 3316 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
3317 | } |
3318 | else if (SCM_BIGP (n)) | |
ac0c002c | 3319 | { |
7f848242 KR |
3320 | SCM result; |
3321 | if (bits == 1) | |
3322 | { | |
d956fa6f | 3323 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
3324 | } |
3325 | else | |
3326 | { | |
3327 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
3328 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
3329 | such bits into a ulong. */ | |
3330 | result = scm_i_mkbig (); | |
3331 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
3332 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
3333 | result = scm_i_normbig (result); | |
3334 | } | |
3335 | scm_remember_upto_here_1 (n); | |
3336 | return result; | |
ac0c002c | 3337 | } |
0aacf84e | 3338 | else |
78166ad5 | 3339 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 3340 | } |
1bbd0b84 | 3341 | #undef FUNC_NAME |
0f2d19dd | 3342 | |
7f848242 | 3343 | |
e4755e5c JB |
3344 | static const char scm_logtab[] = { |
3345 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
3346 | }; | |
1cc91f1b | 3347 | |
a1ec6916 | 3348 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 3349 | (SCM n), |
1e6808ea MG |
3350 | "Return the number of bits in integer @var{n}. If integer is\n" |
3351 | "positive, the 1-bits in its binary representation are counted.\n" | |
3352 | "If negative, the 0-bits in its two's-complement binary\n" | |
3353 | "representation are counted. If 0, 0 is returned.\n" | |
3354 | "\n" | |
b380b885 MD |
3355 | "@lisp\n" |
3356 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
3357 | " @result{} 4\n" |
3358 | "(logcount 0)\n" | |
3359 | " @result{} 0\n" | |
3360 | "(logcount -2)\n" | |
3361 | " @result{} 1\n" | |
3362 | "@end lisp") | |
3363 | #define FUNC_NAME s_scm_logcount | |
3364 | { | |
e11e83f3 | 3365 | if (SCM_I_INUMP (n)) |
f872b822 | 3366 | { |
e25f3727 AW |
3367 | unsigned long c = 0; |
3368 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
3369 | if (nn < 0) |
3370 | nn = -1 - nn; | |
3371 | while (nn) | |
3372 | { | |
3373 | c += scm_logtab[15 & nn]; | |
3374 | nn >>= 4; | |
3375 | } | |
d956fa6f | 3376 | return SCM_I_MAKINUM (c); |
f872b822 | 3377 | } |
ca46fb90 | 3378 | else if (SCM_BIGP (n)) |
f872b822 | 3379 | { |
ca46fb90 | 3380 | unsigned long count; |
713a4259 KR |
3381 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
3382 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 3383 | else |
713a4259 KR |
3384 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
3385 | scm_remember_upto_here_1 (n); | |
d956fa6f | 3386 | return SCM_I_MAKINUM (count); |
f872b822 | 3387 | } |
ca46fb90 RB |
3388 | else |
3389 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 3390 | } |
ca46fb90 | 3391 | #undef FUNC_NAME |
0f2d19dd JB |
3392 | |
3393 | ||
ca46fb90 RB |
3394 | static const char scm_ilentab[] = { |
3395 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
3396 | }; | |
3397 | ||
0f2d19dd | 3398 | |
ca46fb90 RB |
3399 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
3400 | (SCM n), | |
3401 | "Return the number of bits necessary to represent @var{n}.\n" | |
3402 | "\n" | |
3403 | "@lisp\n" | |
3404 | "(integer-length #b10101010)\n" | |
3405 | " @result{} 8\n" | |
3406 | "(integer-length 0)\n" | |
3407 | " @result{} 0\n" | |
3408 | "(integer-length #b1111)\n" | |
3409 | " @result{} 4\n" | |
3410 | "@end lisp") | |
3411 | #define FUNC_NAME s_scm_integer_length | |
3412 | { | |
e11e83f3 | 3413 | if (SCM_I_INUMP (n)) |
0aacf84e | 3414 | { |
e25f3727 | 3415 | unsigned long c = 0; |
0aacf84e | 3416 | unsigned int l = 4; |
e25f3727 | 3417 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
3418 | if (nn < 0) |
3419 | nn = -1 - nn; | |
3420 | while (nn) | |
3421 | { | |
3422 | c += 4; | |
3423 | l = scm_ilentab [15 & nn]; | |
3424 | nn >>= 4; | |
3425 | } | |
d956fa6f | 3426 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
3427 | } |
3428 | else if (SCM_BIGP (n)) | |
3429 | { | |
3430 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
3431 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
3432 | 1 too big, so check for that and adjust. */ | |
3433 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
3434 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
3435 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
3436 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
3437 | size--; | |
3438 | scm_remember_upto_here_1 (n); | |
d956fa6f | 3439 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
3440 | } |
3441 | else | |
ca46fb90 | 3442 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
3443 | } |
3444 | #undef FUNC_NAME | |
0f2d19dd JB |
3445 | |
3446 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
3447 | #define SCM_MAX_DBL_PREC 60 |
3448 | #define SCM_MAX_DBL_RADIX 36 | |
3449 | ||
3450 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
3451 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
3452 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
3453 | ||
3454 | static | |
3455 | void init_dblprec(int *prec, int radix) { | |
3456 | /* determine floating point precision by adding successively | |
3457 | smaller increments to 1.0 until it is considered == 1.0 */ | |
3458 | double f = ((double)1.0)/radix; | |
3459 | double fsum = 1.0 + f; | |
3460 | ||
3461 | *prec = 0; | |
3462 | while (fsum != 1.0) | |
3463 | { | |
3464 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
3465 | fsum = 1.0; | |
3466 | else | |
3467 | { | |
3468 | f /= radix; | |
3469 | fsum = f + 1.0; | |
3470 | } | |
3471 | } | |
3472 | (*prec) -= 1; | |
3473 | } | |
3474 | ||
3475 | static | |
3476 | void init_fx_radix(double *fx_list, int radix) | |
3477 | { | |
3478 | /* initialize a per-radix list of tolerances. When added | |
3479 | to a number < 1.0, we can determine if we should raund | |
3480 | up and quit converting a number to a string. */ | |
3481 | int i; | |
3482 | fx_list[0] = 0.0; | |
3483 | fx_list[1] = 0.5; | |
3484 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
3485 | fx_list[i] = (fx_list[i-1] / radix); | |
3486 | } | |
3487 | ||
3488 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 3489 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 3490 | |
1be6b49c | 3491 | static size_t |
0b799eea | 3492 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 3493 | { |
0b799eea MV |
3494 | int efmt, dpt, d, i, wp; |
3495 | double *fx; | |
3496 | #ifdef DBL_MIN_10_EXP | |
3497 | double f_cpy; | |
3498 | int exp_cpy; | |
3499 | #endif /* DBL_MIN_10_EXP */ | |
3500 | size_t ch = 0; | |
3501 | int exp = 0; | |
3502 | ||
3503 | if(radix < 2 || | |
3504 | radix > SCM_MAX_DBL_RADIX) | |
3505 | { | |
3506 | /* revert to existing behavior */ | |
3507 | radix = 10; | |
3508 | } | |
3509 | ||
3510 | wp = scm_dblprec[radix-2]; | |
3511 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 3512 | |
f872b822 | 3513 | if (f == 0.0) |
abb7e44d MV |
3514 | { |
3515 | #ifdef HAVE_COPYSIGN | |
3516 | double sgn = copysign (1.0, f); | |
3517 | ||
3518 | if (sgn < 0.0) | |
3519 | a[ch++] = '-'; | |
3520 | #endif | |
abb7e44d MV |
3521 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
3522 | } | |
7351e207 | 3523 | |
2e65b52f | 3524 | if (isinf (f)) |
7351e207 MV |
3525 | { |
3526 | if (f < 0) | |
3527 | strcpy (a, "-inf.0"); | |
3528 | else | |
3529 | strcpy (a, "+inf.0"); | |
3530 | return ch+6; | |
3531 | } | |
2e65b52f | 3532 | else if (isnan (f)) |
7351e207 MV |
3533 | { |
3534 | strcpy (a, "+nan.0"); | |
3535 | return ch+6; | |
3536 | } | |
3537 | ||
f872b822 MD |
3538 | if (f < 0.0) |
3539 | { | |
3540 | f = -f; | |
3541 | a[ch++] = '-'; | |
3542 | } | |
7351e207 | 3543 | |
f872b822 MD |
3544 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
3545 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
3546 | /* just do the checking...if it passes, we do the conversion for our |
3547 | radix again below */ | |
3548 | f_cpy = f; | |
3549 | exp_cpy = exp; | |
3550 | ||
3551 | while (f_cpy < 1.0) | |
f872b822 | 3552 | { |
0b799eea MV |
3553 | f_cpy *= 10.0; |
3554 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
3555 | { |
3556 | a[ch++] = '#'; | |
3557 | a[ch++] = '.'; | |
3558 | a[ch++] = '#'; | |
3559 | return ch; | |
3560 | } | |
f872b822 | 3561 | } |
0b799eea | 3562 | while (f_cpy > 10.0) |
f872b822 | 3563 | { |
0b799eea MV |
3564 | f_cpy *= 0.10; |
3565 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
3566 | { |
3567 | a[ch++] = '#'; | |
3568 | a[ch++] = '.'; | |
3569 | a[ch++] = '#'; | |
3570 | return ch; | |
3571 | } | |
f872b822 | 3572 | } |
0b799eea MV |
3573 | #endif |
3574 | ||
f872b822 MD |
3575 | while (f < 1.0) |
3576 | { | |
0b799eea | 3577 | f *= radix; |
f872b822 MD |
3578 | exp--; |
3579 | } | |
0b799eea | 3580 | while (f > radix) |
f872b822 | 3581 | { |
0b799eea | 3582 | f /= radix; |
f872b822 MD |
3583 | exp++; |
3584 | } | |
0b799eea MV |
3585 | |
3586 | if (f + fx[wp] >= radix) | |
f872b822 MD |
3587 | { |
3588 | f = 1.0; | |
3589 | exp++; | |
3590 | } | |
0f2d19dd | 3591 | zero: |
0b799eea MV |
3592 | #ifdef ENGNOT |
3593 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 3594 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
3595 | exp -= dpt++; |
3596 | efmt = 1; | |
f872b822 MD |
3597 | #else |
3598 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 3599 | if (!efmt) |
cda139a7 MD |
3600 | { |
3601 | if (exp < 0) | |
3602 | { | |
3603 | a[ch++] = '0'; | |
3604 | a[ch++] = '.'; | |
3605 | dpt = exp; | |
f872b822 MD |
3606 | while (++dpt) |
3607 | a[ch++] = '0'; | |
cda139a7 MD |
3608 | } |
3609 | else | |
f872b822 | 3610 | dpt = exp + 1; |
cda139a7 | 3611 | } |
0f2d19dd JB |
3612 | else |
3613 | dpt = 1; | |
f872b822 MD |
3614 | #endif |
3615 | ||
3616 | do | |
3617 | { | |
3618 | d = f; | |
3619 | f -= d; | |
0b799eea | 3620 | a[ch++] = number_chars[d]; |
f872b822 MD |
3621 | if (f < fx[wp]) |
3622 | break; | |
3623 | if (f + fx[wp] >= 1.0) | |
3624 | { | |
0b799eea | 3625 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
3626 | break; |
3627 | } | |
0b799eea | 3628 | f *= radix; |
f872b822 MD |
3629 | if (!(--dpt)) |
3630 | a[ch++] = '.'; | |
0f2d19dd | 3631 | } |
f872b822 | 3632 | while (wp--); |
0f2d19dd JB |
3633 | |
3634 | if (dpt > 0) | |
cda139a7 | 3635 | { |
f872b822 | 3636 | #ifndef ENGNOT |
cda139a7 MD |
3637 | if ((dpt > 4) && (exp > 6)) |
3638 | { | |
f872b822 | 3639 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 3640 | for (i = ch++; i > d; i--) |
f872b822 | 3641 | a[i] = a[i - 1]; |
cda139a7 MD |
3642 | a[d] = '.'; |
3643 | efmt = 1; | |
3644 | } | |
3645 | else | |
f872b822 | 3646 | #endif |
cda139a7 | 3647 | { |
f872b822 MD |
3648 | while (--dpt) |
3649 | a[ch++] = '0'; | |
cda139a7 MD |
3650 | a[ch++] = '.'; |
3651 | } | |
3652 | } | |
f872b822 MD |
3653 | if (a[ch - 1] == '.') |
3654 | a[ch++] = '0'; /* trailing zero */ | |
3655 | if (efmt && exp) | |
3656 | { | |
3657 | a[ch++] = 'e'; | |
3658 | if (exp < 0) | |
3659 | { | |
3660 | exp = -exp; | |
3661 | a[ch++] = '-'; | |
3662 | } | |
0b799eea MV |
3663 | for (i = radix; i <= exp; i *= radix); |
3664 | for (i /= radix; i; i /= radix) | |
f872b822 | 3665 | { |
0b799eea | 3666 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
3667 | exp %= i; |
3668 | } | |
0f2d19dd | 3669 | } |
0f2d19dd JB |
3670 | return ch; |
3671 | } | |
3672 | ||
7a1aba42 MV |
3673 | |
3674 | static size_t | |
3675 | icmplx2str (double real, double imag, char *str, int radix) | |
3676 | { | |
3677 | size_t i; | |
c7218482 | 3678 | double sgn; |
7a1aba42 MV |
3679 | |
3680 | i = idbl2str (real, str, radix); | |
c7218482 MW |
3681 | #ifdef HAVE_COPYSIGN |
3682 | sgn = copysign (1.0, imag); | |
3683 | #else | |
3684 | sgn = imag; | |
3685 | #endif | |
3686 | /* Don't output a '+' for negative numbers or for Inf and | |
3687 | NaN. They will provide their own sign. */ | |
3688 | if (sgn >= 0 && DOUBLE_IS_FINITE (imag)) | |
3689 | str[i++] = '+'; | |
3690 | i += idbl2str (imag, &str[i], radix); | |
3691 | str[i++] = 'i'; | |
7a1aba42 MV |
3692 | return i; |
3693 | } | |
3694 | ||
1be6b49c | 3695 | static size_t |
0b799eea | 3696 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 3697 | { |
1be6b49c | 3698 | size_t i; |
3c9a524f | 3699 | if (SCM_REALP (flt)) |
0b799eea | 3700 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 3701 | else |
7a1aba42 MV |
3702 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
3703 | str, radix); | |
0f2d19dd JB |
3704 | return i; |
3705 | } | |
0f2d19dd | 3706 | |
2881e77b | 3707 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
3708 | characters in the result. |
3709 | rad is output base | |
3710 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 3711 | size_t |
2881e77b MV |
3712 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
3713 | { | |
3714 | if (num < 0) | |
3715 | { | |
3716 | *p++ = '-'; | |
3717 | return scm_iuint2str (-num, rad, p) + 1; | |
3718 | } | |
3719 | else | |
3720 | return scm_iuint2str (num, rad, p); | |
3721 | } | |
3722 | ||
3723 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
3724 | characters in the result. | |
3725 | rad is output base | |
3726 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
3727 | size_t | |
3728 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 3729 | { |
1be6b49c ML |
3730 | size_t j = 1; |
3731 | size_t i; | |
2881e77b | 3732 | scm_t_uintmax n = num; |
5c11cc9d | 3733 | |
a6f3af16 AW |
3734 | if (rad < 2 || rad > 36) |
3735 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
3736 | ||
f872b822 | 3737 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
3738 | j++; |
3739 | ||
3740 | i = j; | |
2881e77b | 3741 | n = num; |
f872b822 MD |
3742 | while (i--) |
3743 | { | |
5c11cc9d GH |
3744 | int d = n % rad; |
3745 | ||
f872b822 | 3746 | n /= rad; |
a6f3af16 | 3747 | p[i] = number_chars[d]; |
f872b822 | 3748 | } |
0f2d19dd JB |
3749 | return j; |
3750 | } | |
3751 | ||
a1ec6916 | 3752 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
3753 | (SCM n, SCM radix), |
3754 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
3755 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
3756 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 3757 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 3758 | { |
1bbd0b84 | 3759 | int base; |
98cb6e75 | 3760 | |
0aacf84e | 3761 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 3762 | base = 10; |
0aacf84e | 3763 | else |
5efd3c7d | 3764 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 3765 | |
e11e83f3 | 3766 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
3767 | { |
3768 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 3769 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 3770 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
3771 | } |
3772 | else if (SCM_BIGP (n)) | |
3773 | { | |
3774 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
3775 | scm_remember_upto_here_1 (n); | |
cc95e00a | 3776 | return scm_take_locale_string (str); |
0aacf84e | 3777 | } |
f92e85f7 MV |
3778 | else if (SCM_FRACTIONP (n)) |
3779 | { | |
f92e85f7 | 3780 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 3781 | scm_from_locale_string ("/"), |
f92e85f7 MV |
3782 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
3783 | } | |
0aacf84e MD |
3784 | else if (SCM_INEXACTP (n)) |
3785 | { | |
3786 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 3787 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
3788 | } |
3789 | else | |
bb628794 | 3790 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 3791 | } |
1bbd0b84 | 3792 | #undef FUNC_NAME |
0f2d19dd JB |
3793 | |
3794 | ||
ca46fb90 RB |
3795 | /* These print routines used to be stubbed here so that scm_repl.c |
3796 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 3797 | |
0f2d19dd | 3798 | int |
e81d98ec | 3799 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 3800 | { |
56e55ac7 | 3801 | char num_buf[FLOBUFLEN]; |
0b799eea | 3802 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
3803 | return !0; |
3804 | } | |
3805 | ||
b479fe9a MV |
3806 | void |
3807 | scm_i_print_double (double val, SCM port) | |
3808 | { | |
3809 | char num_buf[FLOBUFLEN]; | |
3810 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
3811 | } | |
3812 | ||
f3ae5d60 | 3813 | int |
e81d98ec | 3814 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 3815 | |
f3ae5d60 | 3816 | { |
56e55ac7 | 3817 | char num_buf[FLOBUFLEN]; |
0b799eea | 3818 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
3819 | return !0; |
3820 | } | |
1cc91f1b | 3821 | |
7a1aba42 MV |
3822 | void |
3823 | scm_i_print_complex (double real, double imag, SCM port) | |
3824 | { | |
3825 | char num_buf[FLOBUFLEN]; | |
3826 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
3827 | } | |
3828 | ||
f92e85f7 MV |
3829 | int |
3830 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
3831 | { | |
3832 | SCM str; | |
f92e85f7 | 3833 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 3834 | scm_display (str, port); |
f92e85f7 MV |
3835 | scm_remember_upto_here_1 (str); |
3836 | return !0; | |
3837 | } | |
3838 | ||
0f2d19dd | 3839 | int |
e81d98ec | 3840 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 3841 | { |
ca46fb90 RB |
3842 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
3843 | scm_remember_upto_here_1 (exp); | |
3844 | scm_lfwrite (str, (size_t) strlen (str), port); | |
3845 | free (str); | |
0f2d19dd JB |
3846 | return !0; |
3847 | } | |
3848 | /*** END nums->strs ***/ | |
3849 | ||
3c9a524f | 3850 | |
0f2d19dd | 3851 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 3852 | |
3c9a524f DH |
3853 | /* The following functions implement the conversion from strings to numbers. |
3854 | * The implementation somehow follows the grammar for numbers as it is given | |
3855 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
3856 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
3857 | * points should be noted about the implementation: | |
bc3d34f5 | 3858 | * |
3c9a524f DH |
3859 | * * Each function keeps a local index variable 'idx' that points at the |
3860 | * current position within the parsed string. The global index is only | |
3861 | * updated if the function could parse the corresponding syntactic unit | |
3862 | * successfully. | |
bc3d34f5 | 3863 | * |
3c9a524f | 3864 | * * Similarly, the functions keep track of indicators of inexactness ('#', |
bc3d34f5 MW |
3865 | * '.' or exponents) using local variables ('hash_seen', 'x'). |
3866 | * | |
3c9a524f DH |
3867 | * * Sequences of digits are parsed into temporary variables holding fixnums. |
3868 | * Only if these fixnums would overflow, the result variables are updated | |
3869 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
3870 | * the temporary variables holding the fixnums are cleared, and the process | |
3871 | * starts over again. If for example fixnums were able to store five decimal | |
3872 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
3873 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
3874 | * only every five digits two bignum operations were performed. | |
bc3d34f5 MW |
3875 | * |
3876 | * Notes on the handling of exactness specifiers: | |
3877 | * | |
3878 | * When parsing non-real complex numbers, we apply exactness specifiers on | |
3879 | * per-component basis, as is done in PLT Scheme. For complex numbers | |
3880 | * written in rectangular form, exactness specifiers are applied to the | |
3881 | * real and imaginary parts before calling scm_make_rectangular. For | |
3882 | * complex numbers written in polar form, exactness specifiers are applied | |
3883 | * to the magnitude and angle before calling scm_make_polar. | |
3884 | * | |
3885 | * There are two kinds of exactness specifiers: forced and implicit. A | |
3886 | * forced exactness specifier is a "#e" or "#i" prefix at the beginning of | |
3887 | * the entire number, and applies to both components of a complex number. | |
3888 | * "#e" causes each component to be made exact, and "#i" causes each | |
3889 | * component to be made inexact. If no forced exactness specifier is | |
3890 | * present, then the exactness of each component is determined | |
3891 | * independently by the presence or absence of a decimal point or hash mark | |
3892 | * within that component. If a decimal point or hash mark is present, the | |
3893 | * component is made inexact, otherwise it is made exact. | |
3894 | * | |
3895 | * After the exactness specifiers have been applied to each component, they | |
3896 | * are passed to either scm_make_rectangular or scm_make_polar to produce | |
3897 | * the final result. Note that this will result in a real number if the | |
3898 | * imaginary part, magnitude, or angle is an exact 0. | |
3899 | * | |
3900 | * For example, (string->number "#i5.0+0i") does the equivalent of: | |
3901 | * | |
3902 | * (make-rectangular (exact->inexact 5) (exact->inexact 0)) | |
3c9a524f DH |
3903 | */ |
3904 | ||
3905 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
3906 | ||
3907 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
3908 | ||
a6f3af16 AW |
3909 | /* Caller is responsible for checking that the return value is in range |
3910 | for the given radix, which should be <= 36. */ | |
3911 | static unsigned int | |
3912 | char_decimal_value (scm_t_uint32 c) | |
3913 | { | |
3914 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
3915 | that's certainly above any valid decimal, so we take advantage of | |
3916 | that to elide some tests. */ | |
3917 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
3918 | ||
3919 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
3920 | hexadecimals. */ | |
3921 | if (d >= 10U) | |
3922 | { | |
3923 | c = uc_tolower (c); | |
3924 | if (c >= (scm_t_uint32) 'a') | |
3925 | d = c - (scm_t_uint32)'a' + 10U; | |
3926 | } | |
3927 | return d; | |
3928 | } | |
3c9a524f | 3929 | |
2a8fecee | 3930 | static SCM |
3f47e526 | 3931 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 3932 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 3933 | { |
3c9a524f DH |
3934 | unsigned int idx = *p_idx; |
3935 | unsigned int hash_seen = 0; | |
3936 | scm_t_bits shift = 1; | |
3937 | scm_t_bits add = 0; | |
3938 | unsigned int digit_value; | |
3939 | SCM result; | |
3940 | char c; | |
3f47e526 | 3941 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
3942 | |
3943 | if (idx == len) | |
3944 | return SCM_BOOL_F; | |
2a8fecee | 3945 | |
3f47e526 | 3946 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 3947 | digit_value = char_decimal_value (c); |
3c9a524f DH |
3948 | if (digit_value >= radix) |
3949 | return SCM_BOOL_F; | |
3950 | ||
3951 | idx++; | |
d956fa6f | 3952 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 3953 | while (idx != len) |
f872b822 | 3954 | { |
3f47e526 | 3955 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 3956 | if (c == '#') |
3c9a524f DH |
3957 | { |
3958 | hash_seen = 1; | |
3959 | digit_value = 0; | |
3960 | } | |
a6f3af16 AW |
3961 | else if (hash_seen) |
3962 | break; | |
3c9a524f | 3963 | else |
a6f3af16 AW |
3964 | { |
3965 | digit_value = char_decimal_value (c); | |
3966 | /* This check catches non-decimals in addition to out-of-range | |
3967 | decimals. */ | |
3968 | if (digit_value >= radix) | |
3969 | break; | |
3970 | } | |
3c9a524f DH |
3971 | |
3972 | idx++; | |
3973 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
3974 | { | |
d956fa6f | 3975 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 3976 | if (add > 0) |
d956fa6f | 3977 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
3978 | |
3979 | shift = radix; | |
3980 | add = digit_value; | |
3981 | } | |
3982 | else | |
3983 | { | |
3984 | shift = shift * radix; | |
3985 | add = add * radix + digit_value; | |
3986 | } | |
3987 | }; | |
3988 | ||
3989 | if (shift > 1) | |
d956fa6f | 3990 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 3991 | if (add > 0) |
d956fa6f | 3992 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
3993 | |
3994 | *p_idx = idx; | |
3995 | if (hash_seen) | |
3996 | *p_exactness = INEXACT; | |
3997 | ||
3998 | return result; | |
2a8fecee JB |
3999 | } |
4000 | ||
4001 | ||
3c9a524f DH |
4002 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
4003 | * covers the parts of the rules that start at a potential point. The value | |
4004 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
4005 | * in variable result. The content of *p_exactness indicates, whether a hash |
4006 | * has already been seen in the digits before the point. | |
3c9a524f | 4007 | */ |
1cc91f1b | 4008 | |
3f47e526 | 4009 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
4010 | |
4011 | static SCM | |
3f47e526 | 4012 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 4013 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 4014 | { |
3c9a524f DH |
4015 | unsigned int idx = *p_idx; |
4016 | enum t_exactness x = *p_exactness; | |
3f47e526 | 4017 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
4018 | |
4019 | if (idx == len) | |
79d34f68 | 4020 | return result; |
3c9a524f | 4021 | |
3f47e526 | 4022 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
4023 | { |
4024 | scm_t_bits shift = 1; | |
4025 | scm_t_bits add = 0; | |
4026 | unsigned int digit_value; | |
cff5fa33 | 4027 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
4028 | |
4029 | idx++; | |
4030 | while (idx != len) | |
4031 | { | |
3f47e526 MG |
4032 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
4033 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
4034 | { |
4035 | if (x == INEXACT) | |
4036 | return SCM_BOOL_F; | |
4037 | else | |
4038 | digit_value = DIGIT2UINT (c); | |
4039 | } | |
4040 | else if (c == '#') | |
4041 | { | |
4042 | x = INEXACT; | |
4043 | digit_value = 0; | |
4044 | } | |
4045 | else | |
4046 | break; | |
4047 | ||
4048 | idx++; | |
4049 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
4050 | { | |
d956fa6f MV |
4051 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
4052 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 4053 | if (add > 0) |
d956fa6f | 4054 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
4055 | |
4056 | shift = 10; | |
4057 | add = digit_value; | |
4058 | } | |
4059 | else | |
4060 | { | |
4061 | shift = shift * 10; | |
4062 | add = add * 10 + digit_value; | |
4063 | } | |
4064 | }; | |
4065 | ||
4066 | if (add > 0) | |
4067 | { | |
d956fa6f MV |
4068 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
4069 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
4070 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
4071 | } |
4072 | ||
d8592269 | 4073 | result = scm_divide (result, big_shift); |
79d34f68 | 4074 | |
3c9a524f DH |
4075 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
4076 | x = INEXACT; | |
f872b822 | 4077 | } |
3c9a524f | 4078 | |
3c9a524f | 4079 | if (idx != len) |
f872b822 | 4080 | { |
3c9a524f DH |
4081 | int sign = 1; |
4082 | unsigned int start; | |
3f47e526 | 4083 | scm_t_wchar c; |
3c9a524f DH |
4084 | int exponent; |
4085 | SCM e; | |
4086 | ||
4087 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
4088 | ||
3f47e526 | 4089 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 4090 | { |
3c9a524f DH |
4091 | case 'd': case 'D': |
4092 | case 'e': case 'E': | |
4093 | case 'f': case 'F': | |
4094 | case 'l': case 'L': | |
4095 | case 's': case 'S': | |
4096 | idx++; | |
ee0ddd21 AW |
4097 | if (idx == len) |
4098 | return SCM_BOOL_F; | |
4099 | ||
3c9a524f | 4100 | start = idx; |
3f47e526 | 4101 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4102 | if (c == '-') |
4103 | { | |
4104 | idx++; | |
ee0ddd21 AW |
4105 | if (idx == len) |
4106 | return SCM_BOOL_F; | |
4107 | ||
3c9a524f | 4108 | sign = -1; |
3f47e526 | 4109 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4110 | } |
4111 | else if (c == '+') | |
4112 | { | |
4113 | idx++; | |
ee0ddd21 AW |
4114 | if (idx == len) |
4115 | return SCM_BOOL_F; | |
4116 | ||
3c9a524f | 4117 | sign = 1; |
3f47e526 | 4118 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4119 | } |
4120 | else | |
4121 | sign = 1; | |
4122 | ||
3f47e526 | 4123 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
4124 | return SCM_BOOL_F; |
4125 | ||
4126 | idx++; | |
4127 | exponent = DIGIT2UINT (c); | |
4128 | while (idx != len) | |
f872b822 | 4129 | { |
3f47e526 MG |
4130 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
4131 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
4132 | { |
4133 | idx++; | |
4134 | if (exponent <= SCM_MAXEXP) | |
4135 | exponent = exponent * 10 + DIGIT2UINT (c); | |
4136 | } | |
4137 | else | |
4138 | break; | |
f872b822 | 4139 | } |
3c9a524f DH |
4140 | |
4141 | if (exponent > SCM_MAXEXP) | |
f872b822 | 4142 | { |
3c9a524f | 4143 | size_t exp_len = idx - start; |
3f47e526 | 4144 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
4145 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
4146 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 4147 | } |
3c9a524f | 4148 | |
d956fa6f | 4149 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
4150 | if (sign == 1) |
4151 | result = scm_product (result, e); | |
4152 | else | |
f92e85f7 | 4153 | result = scm_divide2real (result, e); |
3c9a524f DH |
4154 | |
4155 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
4156 | x = INEXACT; | |
4157 | ||
f872b822 | 4158 | break; |
3c9a524f | 4159 | |
f872b822 | 4160 | default: |
3c9a524f | 4161 | break; |
f872b822 | 4162 | } |
0f2d19dd | 4163 | } |
3c9a524f DH |
4164 | |
4165 | *p_idx = idx; | |
4166 | if (x == INEXACT) | |
4167 | *p_exactness = x; | |
4168 | ||
4169 | return result; | |
0f2d19dd | 4170 | } |
0f2d19dd | 4171 | |
3c9a524f DH |
4172 | |
4173 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
4174 | ||
4175 | static SCM | |
3f47e526 | 4176 | mem2ureal (SCM mem, unsigned int *p_idx, |
9d427b2c | 4177 | unsigned int radix, enum t_exactness forced_x) |
0f2d19dd | 4178 | { |
3c9a524f | 4179 | unsigned int idx = *p_idx; |
164d2481 | 4180 | SCM result; |
3f47e526 | 4181 | size_t len = scm_i_string_length (mem); |
3c9a524f | 4182 | |
40f89215 NJ |
4183 | /* Start off believing that the number will be exact. This changes |
4184 | to INEXACT if we see a decimal point or a hash. */ | |
9d427b2c | 4185 | enum t_exactness implicit_x = EXACT; |
40f89215 | 4186 | |
3c9a524f DH |
4187 | if (idx == len) |
4188 | return SCM_BOOL_F; | |
4189 | ||
3f47e526 | 4190 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
4191 | { |
4192 | *p_idx = idx+5; | |
4193 | return scm_inf (); | |
4194 | } | |
4195 | ||
3f47e526 | 4196 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 4197 | { |
d8592269 MV |
4198 | /* Cobble up the fractional part. We might want to set the |
4199 | NaN's mantissa from it. */ | |
7351e207 | 4200 | idx += 4; |
9d427b2c | 4201 | mem2uinteger (mem, &idx, 10, &implicit_x); |
7351e207 MV |
4202 | *p_idx = idx; |
4203 | return scm_nan (); | |
4204 | } | |
4205 | ||
3f47e526 | 4206 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
4207 | { |
4208 | if (radix != 10) | |
4209 | return SCM_BOOL_F; | |
4210 | else if (idx + 1 == len) | |
4211 | return SCM_BOOL_F; | |
3f47e526 | 4212 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
4213 | return SCM_BOOL_F; |
4214 | else | |
cff5fa33 | 4215 | result = mem2decimal_from_point (SCM_INUM0, mem, |
9d427b2c | 4216 | p_idx, &implicit_x); |
f872b822 | 4217 | } |
3c9a524f DH |
4218 | else |
4219 | { | |
3c9a524f | 4220 | SCM uinteger; |
3c9a524f | 4221 | |
9d427b2c | 4222 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 4223 | if (scm_is_false (uinteger)) |
3c9a524f DH |
4224 | return SCM_BOOL_F; |
4225 | ||
4226 | if (idx == len) | |
4227 | result = uinteger; | |
3f47e526 | 4228 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 4229 | { |
3c9a524f DH |
4230 | SCM divisor; |
4231 | ||
4232 | idx++; | |
ee0ddd21 AW |
4233 | if (idx == len) |
4234 | return SCM_BOOL_F; | |
3c9a524f | 4235 | |
9d427b2c | 4236 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 4237 | if (scm_is_false (divisor)) |
3c9a524f DH |
4238 | return SCM_BOOL_F; |
4239 | ||
f92e85f7 | 4240 | /* both are int/big here, I assume */ |
cba42c93 | 4241 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 4242 | } |
3c9a524f DH |
4243 | else if (radix == 10) |
4244 | { | |
9d427b2c | 4245 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
73e4de09 | 4246 | if (scm_is_false (result)) |
3c9a524f DH |
4247 | return SCM_BOOL_F; |
4248 | } | |
4249 | else | |
4250 | result = uinteger; | |
4251 | ||
4252 | *p_idx = idx; | |
f872b822 | 4253 | } |
164d2481 | 4254 | |
9d427b2c MW |
4255 | switch (forced_x) |
4256 | { | |
4257 | case EXACT: | |
4258 | if (SCM_INEXACTP (result)) | |
4259 | return scm_inexact_to_exact (result); | |
4260 | else | |
4261 | return result; | |
4262 | case INEXACT: | |
4263 | if (SCM_INEXACTP (result)) | |
4264 | return result; | |
4265 | else | |
4266 | return scm_exact_to_inexact (result); | |
4267 | case NO_EXACTNESS: | |
4268 | if (implicit_x == INEXACT) | |
4269 | { | |
4270 | if (SCM_INEXACTP (result)) | |
4271 | return result; | |
4272 | else | |
4273 | return scm_exact_to_inexact (result); | |
4274 | } | |
4275 | else | |
4276 | return result; | |
4277 | } | |
164d2481 | 4278 | |
9d427b2c MW |
4279 | /* We should never get here */ |
4280 | scm_syserror ("mem2ureal"); | |
3c9a524f | 4281 | } |
0f2d19dd | 4282 | |
0f2d19dd | 4283 | |
3c9a524f | 4284 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 4285 | |
3c9a524f | 4286 | static SCM |
3f47e526 | 4287 | mem2complex (SCM mem, unsigned int idx, |
9d427b2c | 4288 | unsigned int radix, enum t_exactness forced_x) |
3c9a524f | 4289 | { |
3f47e526 | 4290 | scm_t_wchar c; |
3c9a524f DH |
4291 | int sign = 0; |
4292 | SCM ureal; | |
3f47e526 | 4293 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
4294 | |
4295 | if (idx == len) | |
4296 | return SCM_BOOL_F; | |
4297 | ||
3f47e526 | 4298 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4299 | if (c == '+') |
4300 | { | |
4301 | idx++; | |
4302 | sign = 1; | |
4303 | } | |
4304 | else if (c == '-') | |
4305 | { | |
4306 | idx++; | |
4307 | sign = -1; | |
0f2d19dd | 4308 | } |
0f2d19dd | 4309 | |
3c9a524f DH |
4310 | if (idx == len) |
4311 | return SCM_BOOL_F; | |
4312 | ||
9d427b2c | 4313 | ureal = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 4314 | if (scm_is_false (ureal)) |
f872b822 | 4315 | { |
3c9a524f DH |
4316 | /* input must be either +i or -i */ |
4317 | ||
4318 | if (sign == 0) | |
4319 | return SCM_BOOL_F; | |
4320 | ||
3f47e526 MG |
4321 | if (scm_i_string_ref (mem, idx) == 'i' |
4322 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 4323 | { |
3c9a524f DH |
4324 | idx++; |
4325 | if (idx != len) | |
4326 | return SCM_BOOL_F; | |
4327 | ||
cff5fa33 | 4328 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 4329 | } |
3c9a524f DH |
4330 | else |
4331 | return SCM_BOOL_F; | |
0f2d19dd | 4332 | } |
3c9a524f DH |
4333 | else |
4334 | { | |
73e4de09 | 4335 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 4336 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 4337 | |
3c9a524f DH |
4338 | if (idx == len) |
4339 | return ureal; | |
4340 | ||
3f47e526 | 4341 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 4342 | switch (c) |
f872b822 | 4343 | { |
3c9a524f DH |
4344 | case 'i': case 'I': |
4345 | /* either +<ureal>i or -<ureal>i */ | |
4346 | ||
4347 | idx++; | |
4348 | if (sign == 0) | |
4349 | return SCM_BOOL_F; | |
4350 | if (idx != len) | |
4351 | return SCM_BOOL_F; | |
cff5fa33 | 4352 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
4353 | |
4354 | case '@': | |
4355 | /* polar input: <real>@<real>. */ | |
4356 | ||
4357 | idx++; | |
4358 | if (idx == len) | |
4359 | return SCM_BOOL_F; | |
4360 | else | |
f872b822 | 4361 | { |
3c9a524f DH |
4362 | int sign; |
4363 | SCM angle; | |
4364 | SCM result; | |
4365 | ||
3f47e526 | 4366 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
4367 | if (c == '+') |
4368 | { | |
4369 | idx++; | |
ee0ddd21 AW |
4370 | if (idx == len) |
4371 | return SCM_BOOL_F; | |
3c9a524f DH |
4372 | sign = 1; |
4373 | } | |
4374 | else if (c == '-') | |
4375 | { | |
4376 | idx++; | |
ee0ddd21 AW |
4377 | if (idx == len) |
4378 | return SCM_BOOL_F; | |
3c9a524f DH |
4379 | sign = -1; |
4380 | } | |
4381 | else | |
4382 | sign = 1; | |
4383 | ||
9d427b2c | 4384 | angle = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 4385 | if (scm_is_false (angle)) |
3c9a524f DH |
4386 | return SCM_BOOL_F; |
4387 | if (idx != len) | |
4388 | return SCM_BOOL_F; | |
4389 | ||
73e4de09 | 4390 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
4391 | angle = scm_difference (angle, SCM_UNDEFINED); |
4392 | ||
4393 | result = scm_make_polar (ureal, angle); | |
4394 | return result; | |
f872b822 | 4395 | } |
3c9a524f DH |
4396 | case '+': |
4397 | case '-': | |
4398 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 4399 | |
3c9a524f DH |
4400 | idx++; |
4401 | if (idx == len) | |
4402 | return SCM_BOOL_F; | |
4403 | else | |
4404 | { | |
4405 | int sign = (c == '+') ? 1 : -1; | |
9d427b2c | 4406 | SCM imag = mem2ureal (mem, &idx, radix, forced_x); |
0f2d19dd | 4407 | |
73e4de09 | 4408 | if (scm_is_false (imag)) |
d956fa6f | 4409 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 4410 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 4411 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 4412 | |
3c9a524f DH |
4413 | if (idx == len) |
4414 | return SCM_BOOL_F; | |
3f47e526 MG |
4415 | if (scm_i_string_ref (mem, idx) != 'i' |
4416 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 4417 | return SCM_BOOL_F; |
0f2d19dd | 4418 | |
3c9a524f DH |
4419 | idx++; |
4420 | if (idx != len) | |
4421 | return SCM_BOOL_F; | |
0f2d19dd | 4422 | |
1fe5e088 | 4423 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
4424 | } |
4425 | default: | |
4426 | return SCM_BOOL_F; | |
4427 | } | |
4428 | } | |
0f2d19dd | 4429 | } |
0f2d19dd JB |
4430 | |
4431 | ||
3c9a524f DH |
4432 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
4433 | ||
4434 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 4435 | |
0f2d19dd | 4436 | SCM |
3f47e526 | 4437 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 4438 | { |
3c9a524f DH |
4439 | unsigned int idx = 0; |
4440 | unsigned int radix = NO_RADIX; | |
4441 | enum t_exactness forced_x = NO_EXACTNESS; | |
3f47e526 | 4442 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
4443 | |
4444 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 4445 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 4446 | { |
3f47e526 | 4447 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
4448 | { |
4449 | case 'b': case 'B': | |
4450 | if (radix != NO_RADIX) | |
4451 | return SCM_BOOL_F; | |
4452 | radix = DUAL; | |
4453 | break; | |
4454 | case 'd': case 'D': | |
4455 | if (radix != NO_RADIX) | |
4456 | return SCM_BOOL_F; | |
4457 | radix = DEC; | |
4458 | break; | |
4459 | case 'i': case 'I': | |
4460 | if (forced_x != NO_EXACTNESS) | |
4461 | return SCM_BOOL_F; | |
4462 | forced_x = INEXACT; | |
4463 | break; | |
4464 | case 'e': case 'E': | |
4465 | if (forced_x != NO_EXACTNESS) | |
4466 | return SCM_BOOL_F; | |
4467 | forced_x = EXACT; | |
4468 | break; | |
4469 | case 'o': case 'O': | |
4470 | if (radix != NO_RADIX) | |
4471 | return SCM_BOOL_F; | |
4472 | radix = OCT; | |
4473 | break; | |
4474 | case 'x': case 'X': | |
4475 | if (radix != NO_RADIX) | |
4476 | return SCM_BOOL_F; | |
4477 | radix = HEX; | |
4478 | break; | |
4479 | default: | |
f872b822 | 4480 | return SCM_BOOL_F; |
3c9a524f DH |
4481 | } |
4482 | idx += 2; | |
4483 | } | |
4484 | ||
4485 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
4486 | if (radix == NO_RADIX) | |
9d427b2c | 4487 | radix = default_radix; |
f872b822 | 4488 | |
9d427b2c | 4489 | return mem2complex (mem, idx, radix, forced_x); |
0f2d19dd JB |
4490 | } |
4491 | ||
3f47e526 MG |
4492 | SCM |
4493 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
4494 | unsigned int default_radix) | |
4495 | { | |
4496 | SCM str = scm_from_locale_stringn (mem, len); | |
4497 | ||
4498 | return scm_i_string_to_number (str, default_radix); | |
4499 | } | |
4500 | ||
0f2d19dd | 4501 | |
a1ec6916 | 4502 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 4503 | (SCM string, SCM radix), |
1e6808ea | 4504 | "Return a number of the maximally precise representation\n" |
942e5b91 | 4505 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
4506 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
4507 | "is a default radix that may be overridden by an explicit radix\n" | |
4508 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
4509 | "supplied, then the default radix is 10. If string is not a\n" | |
4510 | "syntactically valid notation for a number, then\n" | |
4511 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 4512 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
4513 | { |
4514 | SCM answer; | |
5efd3c7d | 4515 | unsigned int base; |
a6d9e5ab | 4516 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
4517 | |
4518 | if (SCM_UNBNDP (radix)) | |
4519 | base = 10; | |
4520 | else | |
4521 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
4522 | ||
3f47e526 | 4523 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
4524 | scm_remember_upto_here_1 (string); |
4525 | return answer; | |
0f2d19dd | 4526 | } |
1bbd0b84 | 4527 | #undef FUNC_NAME |
3c9a524f DH |
4528 | |
4529 | ||
0f2d19dd JB |
4530 | /*** END strs->nums ***/ |
4531 | ||
5986c47d | 4532 | |
8507ec80 MV |
4533 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
4534 | (SCM x), | |
4535 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
4536 | "otherwise.") | |
4537 | #define FUNC_NAME s_scm_number_p | |
4538 | { | |
4539 | return scm_from_bool (SCM_NUMBERP (x)); | |
4540 | } | |
4541 | #undef FUNC_NAME | |
4542 | ||
4543 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 4544 | (SCM x), |
942e5b91 | 4545 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 4546 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
4547 | "values form subsets of the set of complex numbers, i. e. the\n" |
4548 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
4549 | "rational or integer number.") | |
8507ec80 | 4550 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 4551 | { |
8507ec80 MV |
4552 | /* all numbers are complex. */ |
4553 | return scm_number_p (x); | |
0f2d19dd | 4554 | } |
1bbd0b84 | 4555 | #undef FUNC_NAME |
0f2d19dd | 4556 | |
f92e85f7 MV |
4557 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
4558 | (SCM x), | |
4559 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
4560 | "otherwise. Note that the set of integer values forms a subset of\n" | |
4561 | "the set of real numbers, i. e. the predicate will also be\n" | |
4562 | "fulfilled if @var{x} is an integer number.") | |
4563 | #define FUNC_NAME s_scm_real_p | |
4564 | { | |
c960e556 MW |
4565 | return scm_from_bool |
4566 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
4567 | } |
4568 | #undef FUNC_NAME | |
4569 | ||
4570 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 4571 | (SCM x), |
942e5b91 | 4572 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 4573 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 4574 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
4575 | "fulfilled if @var{x} is an integer number.") |
4576 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 4577 | { |
c960e556 | 4578 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
4579 | return SCM_BOOL_T; |
4580 | else if (SCM_REALP (x)) | |
c960e556 MW |
4581 | /* due to their limited precision, finite floating point numbers are |
4582 | rational as well. (finite means neither infinity nor a NaN) */ | |
4583 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 4584 | else |
bb628794 | 4585 | return SCM_BOOL_F; |
0f2d19dd | 4586 | } |
1bbd0b84 | 4587 | #undef FUNC_NAME |
0f2d19dd | 4588 | |
a1ec6916 | 4589 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 4590 | (SCM x), |
942e5b91 MG |
4591 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
4592 | "else.") | |
1bbd0b84 | 4593 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 4594 | { |
c960e556 | 4595 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 4596 | return SCM_BOOL_T; |
c960e556 MW |
4597 | else if (SCM_REALP (x)) |
4598 | { | |
4599 | double val = SCM_REAL_VALUE (x); | |
4600 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
4601 | } | |
4602 | else | |
8e43ed5d | 4603 | return SCM_BOOL_F; |
0f2d19dd | 4604 | } |
1bbd0b84 | 4605 | #undef FUNC_NAME |
0f2d19dd JB |
4606 | |
4607 | ||
8a1f4f98 AW |
4608 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
4609 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
4610 | (SCM x, SCM y, SCM rest), | |
4611 | "Return @code{#t} if all parameters are numerically equal.") | |
4612 | #define FUNC_NAME s_scm_i_num_eq_p | |
4613 | { | |
4614 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4615 | return SCM_BOOL_T; | |
4616 | while (!scm_is_null (rest)) | |
4617 | { | |
4618 | if (scm_is_false (scm_num_eq_p (x, y))) | |
4619 | return SCM_BOOL_F; | |
4620 | x = y; | |
4621 | y = scm_car (rest); | |
4622 | rest = scm_cdr (rest); | |
4623 | } | |
4624 | return scm_num_eq_p (x, y); | |
4625 | } | |
4626 | #undef FUNC_NAME | |
0f2d19dd | 4627 | SCM |
6e8d25a6 | 4628 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 4629 | { |
d8b95e27 | 4630 | again: |
e11e83f3 | 4631 | if (SCM_I_INUMP (x)) |
0aacf84e | 4632 | { |
e25f3727 | 4633 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 4634 | if (SCM_I_INUMP (y)) |
0aacf84e | 4635 | { |
e25f3727 | 4636 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 4637 | return scm_from_bool (xx == yy); |
0aacf84e MD |
4638 | } |
4639 | else if (SCM_BIGP (y)) | |
4640 | return SCM_BOOL_F; | |
4641 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
4642 | { |
4643 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
4644 | to a double and compare. | |
4645 | ||
4646 | But on a 64-bit system an inum is bigger than a double and | |
4647 | casting it to a double (call that dxx) will round. dxx is at | |
4648 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
4649 | an integer and fits a long. So we cast yy to a long and | |
4650 | compare with plain xx. | |
4651 | ||
4652 | An alternative (for any size system actually) would be to check | |
4653 | yy is an integer (with floor) and is in range of an inum | |
4654 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
4655 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
4656 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
4657 | |
4658 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
4659 | return scm_from_bool ((double) xx == yy |
4660 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4661 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 4662 | } |
0aacf84e | 4663 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 4664 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4665 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
4666 | else if (SCM_FRACTIONP (y)) |
4667 | return SCM_BOOL_F; | |
0aacf84e | 4668 | else |
8a1f4f98 | 4669 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 4670 | } |
0aacf84e MD |
4671 | else if (SCM_BIGP (x)) |
4672 | { | |
e11e83f3 | 4673 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4674 | return SCM_BOOL_F; |
4675 | else if (SCM_BIGP (y)) | |
4676 | { | |
4677 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4678 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 4679 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4680 | } |
4681 | else if (SCM_REALP (y)) | |
4682 | { | |
4683 | int cmp; | |
2e65b52f | 4684 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
4685 | return SCM_BOOL_F; |
4686 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
4687 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4688 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4689 | } |
4690 | else if (SCM_COMPLEXP (y)) | |
4691 | { | |
4692 | int cmp; | |
4693 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
4694 | return SCM_BOOL_F; | |
2e65b52f | 4695 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
4696 | return SCM_BOOL_F; |
4697 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
4698 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4699 | return scm_from_bool (0 == cmp); |
0aacf84e | 4700 | } |
f92e85f7 MV |
4701 | else if (SCM_FRACTIONP (y)) |
4702 | return SCM_BOOL_F; | |
0aacf84e | 4703 | else |
8a1f4f98 | 4704 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 4705 | } |
0aacf84e MD |
4706 | else if (SCM_REALP (x)) |
4707 | { | |
e8c5b1f2 | 4708 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 4709 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
4710 | { |
4711 | /* see comments with inum/real above */ | |
e25f3727 | 4712 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
4713 | return scm_from_bool (xx == (double) yy |
4714 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4715 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 4716 | } |
0aacf84e MD |
4717 | else if (SCM_BIGP (y)) |
4718 | { | |
4719 | int cmp; | |
2e65b52f | 4720 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
4721 | return SCM_BOOL_F; |
4722 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
4723 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4724 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4725 | } |
4726 | else if (SCM_REALP (y)) | |
73e4de09 | 4727 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 4728 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 4729 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4730 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 4731 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
4732 | { |
4733 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4734 | if (isnan (xx)) |
d8b95e27 | 4735 | return SCM_BOOL_F; |
2e65b52f | 4736 | if (isinf (xx)) |
73e4de09 | 4737 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
4738 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4739 | goto again; | |
4740 | } | |
0aacf84e | 4741 | else |
8a1f4f98 | 4742 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 4743 | } |
0aacf84e MD |
4744 | else if (SCM_COMPLEXP (x)) |
4745 | { | |
e11e83f3 MV |
4746 | if (SCM_I_INUMP (y)) |
4747 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
4748 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
4749 | else if (SCM_BIGP (y)) | |
4750 | { | |
4751 | int cmp; | |
4752 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
4753 | return SCM_BOOL_F; | |
2e65b52f | 4754 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
4755 | return SCM_BOOL_F; |
4756 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
4757 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4758 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
4759 | } |
4760 | else if (SCM_REALP (y)) | |
73e4de09 | 4761 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
4762 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
4763 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 4764 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 4765 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 4766 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
4767 | { |
4768 | double xx; | |
4769 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
4770 | return SCM_BOOL_F; | |
4771 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 4772 | if (isnan (xx)) |
d8b95e27 | 4773 | return SCM_BOOL_F; |
2e65b52f | 4774 | if (isinf (xx)) |
73e4de09 | 4775 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
4776 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4777 | goto again; | |
4778 | } | |
f92e85f7 | 4779 | else |
8a1f4f98 | 4780 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
4781 | } |
4782 | else if (SCM_FRACTIONP (x)) | |
4783 | { | |
e11e83f3 | 4784 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
4785 | return SCM_BOOL_F; |
4786 | else if (SCM_BIGP (y)) | |
4787 | return SCM_BOOL_F; | |
4788 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
4789 | { |
4790 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 4791 | if (isnan (yy)) |
d8b95e27 | 4792 | return SCM_BOOL_F; |
2e65b52f | 4793 | if (isinf (yy)) |
73e4de09 | 4794 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
4795 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4796 | goto again; | |
4797 | } | |
f92e85f7 | 4798 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
4799 | { |
4800 | double yy; | |
4801 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
4802 | return SCM_BOOL_F; | |
4803 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 4804 | if (isnan (yy)) |
d8b95e27 | 4805 | return SCM_BOOL_F; |
2e65b52f | 4806 | if (isinf (yy)) |
73e4de09 | 4807 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
4808 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4809 | goto again; | |
4810 | } | |
f92e85f7 MV |
4811 | else if (SCM_FRACTIONP (y)) |
4812 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 4813 | else |
8a1f4f98 | 4814 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 4815 | } |
0aacf84e | 4816 | else |
8a1f4f98 | 4817 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
4818 | } |
4819 | ||
4820 | ||
a5f0b599 KR |
4821 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
4822 | done are good for inums, but for bignums an answer can almost always be | |
4823 | had by just examining a few high bits of the operands, as done by GMP in | |
4824 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
4825 | of the float exponent to take into account. */ | |
4826 | ||
8c93b597 | 4827 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
4828 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
4829 | (SCM x, SCM y, SCM rest), | |
4830 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4831 | "increasing.") | |
4832 | #define FUNC_NAME s_scm_i_num_less_p | |
4833 | { | |
4834 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4835 | return SCM_BOOL_T; | |
4836 | while (!scm_is_null (rest)) | |
4837 | { | |
4838 | if (scm_is_false (scm_less_p (x, y))) | |
4839 | return SCM_BOOL_F; | |
4840 | x = y; | |
4841 | y = scm_car (rest); | |
4842 | rest = scm_cdr (rest); | |
4843 | } | |
4844 | return scm_less_p (x, y); | |
4845 | } | |
4846 | #undef FUNC_NAME | |
0f2d19dd | 4847 | SCM |
6e8d25a6 | 4848 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 4849 | { |
a5f0b599 | 4850 | again: |
e11e83f3 | 4851 | if (SCM_I_INUMP (x)) |
0aacf84e | 4852 | { |
e25f3727 | 4853 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 4854 | if (SCM_I_INUMP (y)) |
0aacf84e | 4855 | { |
e25f3727 | 4856 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 4857 | return scm_from_bool (xx < yy); |
0aacf84e MD |
4858 | } |
4859 | else if (SCM_BIGP (y)) | |
4860 | { | |
4861 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4862 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4863 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
4864 | } |
4865 | else if (SCM_REALP (y)) | |
73e4de09 | 4866 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 4867 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4868 | { |
4869 | /* "x < a/b" becomes "x*b < a" */ | |
4870 | int_frac: | |
4871 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
4872 | y = SCM_FRACTION_NUMERATOR (y); | |
4873 | goto again; | |
4874 | } | |
0aacf84e | 4875 | else |
8a1f4f98 | 4876 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 4877 | } |
0aacf84e MD |
4878 | else if (SCM_BIGP (x)) |
4879 | { | |
e11e83f3 | 4880 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4881 | { |
4882 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4883 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4884 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
4885 | } |
4886 | else if (SCM_BIGP (y)) | |
4887 | { | |
4888 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
4889 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 4890 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
4891 | } |
4892 | else if (SCM_REALP (y)) | |
4893 | { | |
4894 | int cmp; | |
2e65b52f | 4895 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
4896 | return SCM_BOOL_F; |
4897 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
4898 | scm_remember_upto_here_1 (x); | |
73e4de09 | 4899 | return scm_from_bool (cmp < 0); |
0aacf84e | 4900 | } |
f92e85f7 | 4901 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 4902 | goto int_frac; |
0aacf84e | 4903 | else |
8a1f4f98 | 4904 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 4905 | } |
0aacf84e MD |
4906 | else if (SCM_REALP (x)) |
4907 | { | |
e11e83f3 MV |
4908 | if (SCM_I_INUMP (y)) |
4909 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
4910 | else if (SCM_BIGP (y)) |
4911 | { | |
4912 | int cmp; | |
2e65b52f | 4913 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
4914 | return SCM_BOOL_F; |
4915 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
4916 | scm_remember_upto_here_1 (y); | |
73e4de09 | 4917 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
4918 | } |
4919 | else if (SCM_REALP (y)) | |
73e4de09 | 4920 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 4921 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4922 | { |
4923 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 4924 | if (isnan (xx)) |
a5f0b599 | 4925 | return SCM_BOOL_F; |
2e65b52f | 4926 | if (isinf (xx)) |
73e4de09 | 4927 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
4928 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
4929 | goto again; | |
4930 | } | |
f92e85f7 | 4931 | else |
8a1f4f98 | 4932 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
4933 | } |
4934 | else if (SCM_FRACTIONP (x)) | |
4935 | { | |
e11e83f3 | 4936 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
4937 | { |
4938 | /* "a/b < y" becomes "a < y*b" */ | |
4939 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
4940 | x = SCM_FRACTION_NUMERATOR (x); | |
4941 | goto again; | |
4942 | } | |
f92e85f7 | 4943 | else if (SCM_REALP (y)) |
a5f0b599 KR |
4944 | { |
4945 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 4946 | if (isnan (yy)) |
a5f0b599 | 4947 | return SCM_BOOL_F; |
2e65b52f | 4948 | if (isinf (yy)) |
73e4de09 | 4949 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
4950 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
4951 | goto again; | |
4952 | } | |
f92e85f7 | 4953 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
4954 | { |
4955 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
4956 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
4957 | SCM_FRACTION_DENOMINATOR (y)); | |
4958 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
4959 | SCM_FRACTION_DENOMINATOR (x)); | |
4960 | x = new_x; | |
4961 | y = new_y; | |
4962 | goto again; | |
4963 | } | |
0aacf84e | 4964 | else |
8a1f4f98 | 4965 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 4966 | } |
0aacf84e | 4967 | else |
8a1f4f98 | 4968 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
4969 | } |
4970 | ||
4971 | ||
8a1f4f98 AW |
4972 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
4973 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
4974 | (SCM x, SCM y, SCM rest), | |
4975 | "Return @code{#t} if the list of parameters is monotonically\n" | |
4976 | "decreasing.") | |
4977 | #define FUNC_NAME s_scm_i_num_gr_p | |
4978 | { | |
4979 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
4980 | return SCM_BOOL_T; | |
4981 | while (!scm_is_null (rest)) | |
4982 | { | |
4983 | if (scm_is_false (scm_gr_p (x, y))) | |
4984 | return SCM_BOOL_F; | |
4985 | x = y; | |
4986 | y = scm_car (rest); | |
4987 | rest = scm_cdr (rest); | |
4988 | } | |
4989 | return scm_gr_p (x, y); | |
4990 | } | |
4991 | #undef FUNC_NAME | |
4992 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
4993 | SCM |
4994 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 4995 | { |
c76b1eaf | 4996 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 4997 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 4998 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 4999 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
5000 | else |
5001 | return scm_less_p (y, x); | |
0f2d19dd | 5002 | } |
1bbd0b84 | 5003 | #undef FUNC_NAME |
0f2d19dd JB |
5004 | |
5005 | ||
8a1f4f98 AW |
5006 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
5007 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
5008 | (SCM x, SCM y, SCM rest), | |
5009 | "Return @code{#t} if the list of parameters is monotonically\n" | |
5010 | "non-decreasing.") | |
5011 | #define FUNC_NAME s_scm_i_num_leq_p | |
5012 | { | |
5013 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
5014 | return SCM_BOOL_T; | |
5015 | while (!scm_is_null (rest)) | |
5016 | { | |
5017 | if (scm_is_false (scm_leq_p (x, y))) | |
5018 | return SCM_BOOL_F; | |
5019 | x = y; | |
5020 | y = scm_car (rest); | |
5021 | rest = scm_cdr (rest); | |
5022 | } | |
5023 | return scm_leq_p (x, y); | |
5024 | } | |
5025 | #undef FUNC_NAME | |
5026 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
5027 | SCM |
5028 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 5029 | { |
c76b1eaf | 5030 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 5031 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 5032 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 5033 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 5034 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 5035 | return SCM_BOOL_F; |
c76b1eaf | 5036 | else |
73e4de09 | 5037 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 5038 | } |
1bbd0b84 | 5039 | #undef FUNC_NAME |
0f2d19dd JB |
5040 | |
5041 | ||
8a1f4f98 AW |
5042 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
5043 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
5044 | (SCM x, SCM y, SCM rest), | |
5045 | "Return @code{#t} if the list of parameters is monotonically\n" | |
5046 | "non-increasing.") | |
5047 | #define FUNC_NAME s_scm_i_num_geq_p | |
5048 | { | |
5049 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
5050 | return SCM_BOOL_T; | |
5051 | while (!scm_is_null (rest)) | |
5052 | { | |
5053 | if (scm_is_false (scm_geq_p (x, y))) | |
5054 | return SCM_BOOL_F; | |
5055 | x = y; | |
5056 | y = scm_car (rest); | |
5057 | rest = scm_cdr (rest); | |
5058 | } | |
5059 | return scm_geq_p (x, y); | |
5060 | } | |
5061 | #undef FUNC_NAME | |
5062 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
5063 | SCM |
5064 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 5065 | { |
c76b1eaf | 5066 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 5067 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 5068 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 5069 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 5070 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 5071 | return SCM_BOOL_F; |
c76b1eaf | 5072 | else |
73e4de09 | 5073 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 5074 | } |
1bbd0b84 | 5075 | #undef FUNC_NAME |
0f2d19dd JB |
5076 | |
5077 | ||
2519490c MW |
5078 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
5079 | (SCM z), | |
5080 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
5081 | "zero.") | |
5082 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 5083 | { |
e11e83f3 | 5084 | if (SCM_I_INUMP (z)) |
bc36d050 | 5085 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 5086 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5087 | return SCM_BOOL_F; |
0aacf84e | 5088 | else if (SCM_REALP (z)) |
73e4de09 | 5089 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 5090 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 5091 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 5092 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
5093 | else if (SCM_FRACTIONP (z)) |
5094 | return SCM_BOOL_F; | |
0aacf84e | 5095 | else |
2519490c | 5096 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 5097 | } |
2519490c | 5098 | #undef FUNC_NAME |
0f2d19dd JB |
5099 | |
5100 | ||
2519490c MW |
5101 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
5102 | (SCM x), | |
5103 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
5104 | "zero.") | |
5105 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 5106 | { |
e11e83f3 MV |
5107 | if (SCM_I_INUMP (x)) |
5108 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
5109 | else if (SCM_BIGP (x)) |
5110 | { | |
5111 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5112 | scm_remember_upto_here_1 (x); | |
73e4de09 | 5113 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
5114 | } |
5115 | else if (SCM_REALP (x)) | |
73e4de09 | 5116 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
5117 | else if (SCM_FRACTIONP (x)) |
5118 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 5119 | else |
2519490c | 5120 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 5121 | } |
2519490c | 5122 | #undef FUNC_NAME |
0f2d19dd JB |
5123 | |
5124 | ||
2519490c MW |
5125 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
5126 | (SCM x), | |
5127 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
5128 | "zero.") | |
5129 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 5130 | { |
e11e83f3 MV |
5131 | if (SCM_I_INUMP (x)) |
5132 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
5133 | else if (SCM_BIGP (x)) |
5134 | { | |
5135 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5136 | scm_remember_upto_here_1 (x); | |
73e4de09 | 5137 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
5138 | } |
5139 | else if (SCM_REALP (x)) | |
73e4de09 | 5140 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
5141 | else if (SCM_FRACTIONP (x)) |
5142 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 5143 | else |
2519490c | 5144 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 5145 | } |
2519490c | 5146 | #undef FUNC_NAME |
0f2d19dd JB |
5147 | |
5148 | ||
2a06f791 KR |
5149 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
5150 | required by r5rs. On that basis, for exact/inexact combinations the | |
5151 | exact is converted to inexact to compare and possibly return. This is | |
5152 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
5153 | its test, such trouble is not required for min and max. */ | |
5154 | ||
78d3deb1 AW |
5155 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
5156 | (SCM x, SCM y, SCM rest), | |
5157 | "Return the maximum of all parameter values.") | |
5158 | #define FUNC_NAME s_scm_i_max | |
5159 | { | |
5160 | while (!scm_is_null (rest)) | |
5161 | { x = scm_max (x, y); | |
5162 | y = scm_car (rest); | |
5163 | rest = scm_cdr (rest); | |
5164 | } | |
5165 | return scm_max (x, y); | |
5166 | } | |
5167 | #undef FUNC_NAME | |
5168 | ||
5169 | #define s_max s_scm_i_max | |
5170 | #define g_max g_scm_i_max | |
5171 | ||
0f2d19dd | 5172 | SCM |
6e8d25a6 | 5173 | scm_max (SCM x, SCM y) |
0f2d19dd | 5174 | { |
0aacf84e MD |
5175 | if (SCM_UNBNDP (y)) |
5176 | { | |
5177 | if (SCM_UNBNDP (x)) | |
5178 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 5179 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
5180 | return x; |
5181 | else | |
5182 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 5183 | } |
f4c627b3 | 5184 | |
e11e83f3 | 5185 | if (SCM_I_INUMP (x)) |
0aacf84e | 5186 | { |
e25f3727 | 5187 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 5188 | if (SCM_I_INUMP (y)) |
0aacf84e | 5189 | { |
e25f3727 | 5190 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
5191 | return (xx < yy) ? y : x; |
5192 | } | |
5193 | else if (SCM_BIGP (y)) | |
5194 | { | |
5195 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5196 | scm_remember_upto_here_1 (y); | |
5197 | return (sgn < 0) ? x : y; | |
5198 | } | |
5199 | else if (SCM_REALP (y)) | |
5200 | { | |
2e274311 MW |
5201 | double xxd = xx; |
5202 | double yyd = SCM_REAL_VALUE (y); | |
5203 | ||
5204 | if (xxd > yyd) | |
5205 | return scm_from_double (xxd); | |
5206 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
5207 | else if (SCM_LIKELY (!(xxd == yyd))) | |
5208 | return y; | |
5209 | /* Handle signed zeroes properly */ | |
5210 | else if (xx == 0) | |
5211 | return flo0; | |
5212 | else | |
5213 | return y; | |
0aacf84e | 5214 | } |
f92e85f7 MV |
5215 | else if (SCM_FRACTIONP (y)) |
5216 | { | |
e4bc5d6c | 5217 | use_less: |
73e4de09 | 5218 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 5219 | } |
0aacf84e MD |
5220 | else |
5221 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 5222 | } |
0aacf84e MD |
5223 | else if (SCM_BIGP (x)) |
5224 | { | |
e11e83f3 | 5225 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5226 | { |
5227 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5228 | scm_remember_upto_here_1 (x); | |
5229 | return (sgn < 0) ? y : x; | |
5230 | } | |
5231 | else if (SCM_BIGP (y)) | |
5232 | { | |
5233 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
5234 | scm_remember_upto_here_2 (x, y); | |
5235 | return (cmp > 0) ? x : y; | |
5236 | } | |
5237 | else if (SCM_REALP (y)) | |
5238 | { | |
2a06f791 KR |
5239 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
5240 | double xx, yy; | |
5241 | big_real: | |
5242 | xx = scm_i_big2dbl (x); | |
5243 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 5244 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 5245 | } |
f92e85f7 MV |
5246 | else if (SCM_FRACTIONP (y)) |
5247 | { | |
e4bc5d6c | 5248 | goto use_less; |
f92e85f7 | 5249 | } |
0aacf84e MD |
5250 | else |
5251 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 5252 | } |
0aacf84e MD |
5253 | else if (SCM_REALP (x)) |
5254 | { | |
e11e83f3 | 5255 | if (SCM_I_INUMP (y)) |
0aacf84e | 5256 | { |
2e274311 MW |
5257 | scm_t_inum yy = SCM_I_INUM (y); |
5258 | double xxd = SCM_REAL_VALUE (x); | |
5259 | double yyd = yy; | |
5260 | ||
5261 | if (yyd > xxd) | |
5262 | return scm_from_double (yyd); | |
5263 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
5264 | else if (SCM_LIKELY (!(xxd == yyd))) | |
5265 | return x; | |
5266 | /* Handle signed zeroes properly */ | |
5267 | else if (yy == 0) | |
5268 | return flo0; | |
5269 | else | |
5270 | return x; | |
0aacf84e MD |
5271 | } |
5272 | else if (SCM_BIGP (y)) | |
5273 | { | |
b6f8f763 | 5274 | SCM_SWAP (x, y); |
2a06f791 | 5275 | goto big_real; |
0aacf84e MD |
5276 | } |
5277 | else if (SCM_REALP (y)) | |
5278 | { | |
0aacf84e | 5279 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
5280 | double yy = SCM_REAL_VALUE (y); |
5281 | ||
5282 | /* For purposes of max: +inf.0 > nan > everything else, per R6RS */ | |
5283 | if (xx > yy) | |
5284 | return x; | |
5285 | else if (SCM_LIKELY (xx < yy)) | |
5286 | return y; | |
5287 | /* If neither (xx > yy) nor (xx < yy), then | |
5288 | either they're equal or one is a NaN */ | |
5289 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 5290 | return DOUBLE_IS_POSITIVE_INFINITY (yy) ? y : x; |
2e274311 | 5291 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 5292 | return DOUBLE_IS_POSITIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
5293 | /* xx == yy, but handle signed zeroes properly */ |
5294 | else if (double_is_non_negative_zero (yy)) | |
5295 | return y; | |
5296 | else | |
5297 | return x; | |
0aacf84e | 5298 | } |
f92e85f7 MV |
5299 | else if (SCM_FRACTIONP (y)) |
5300 | { | |
5301 | double yy = scm_i_fraction2double (y); | |
5302 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 5303 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
5304 | } |
5305 | else | |
5306 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
5307 | } | |
5308 | else if (SCM_FRACTIONP (x)) | |
5309 | { | |
e11e83f3 | 5310 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5311 | { |
e4bc5d6c | 5312 | goto use_less; |
f92e85f7 MV |
5313 | } |
5314 | else if (SCM_BIGP (y)) | |
5315 | { | |
e4bc5d6c | 5316 | goto use_less; |
f92e85f7 MV |
5317 | } |
5318 | else if (SCM_REALP (y)) | |
5319 | { | |
5320 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
5321 | /* if y==NaN then ">" is false, so we return the NaN y */ |
5322 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
5323 | } |
5324 | else if (SCM_FRACTIONP (y)) | |
5325 | { | |
e4bc5d6c | 5326 | goto use_less; |
f92e85f7 | 5327 | } |
0aacf84e MD |
5328 | else |
5329 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 5330 | } |
0aacf84e | 5331 | else |
f4c627b3 | 5332 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
5333 | } |
5334 | ||
5335 | ||
78d3deb1 AW |
5336 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
5337 | (SCM x, SCM y, SCM rest), | |
5338 | "Return the minimum of all parameter values.") | |
5339 | #define FUNC_NAME s_scm_i_min | |
5340 | { | |
5341 | while (!scm_is_null (rest)) | |
5342 | { x = scm_min (x, y); | |
5343 | y = scm_car (rest); | |
5344 | rest = scm_cdr (rest); | |
5345 | } | |
5346 | return scm_min (x, y); | |
5347 | } | |
5348 | #undef FUNC_NAME | |
5349 | ||
5350 | #define s_min s_scm_i_min | |
5351 | #define g_min g_scm_i_min | |
5352 | ||
0f2d19dd | 5353 | SCM |
6e8d25a6 | 5354 | scm_min (SCM x, SCM y) |
0f2d19dd | 5355 | { |
0aacf84e MD |
5356 | if (SCM_UNBNDP (y)) |
5357 | { | |
5358 | if (SCM_UNBNDP (x)) | |
5359 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 5360 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
5361 | return x; |
5362 | else | |
5363 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 5364 | } |
f4c627b3 | 5365 | |
e11e83f3 | 5366 | if (SCM_I_INUMP (x)) |
0aacf84e | 5367 | { |
e25f3727 | 5368 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 5369 | if (SCM_I_INUMP (y)) |
0aacf84e | 5370 | { |
e25f3727 | 5371 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
5372 | return (xx < yy) ? x : y; |
5373 | } | |
5374 | else if (SCM_BIGP (y)) | |
5375 | { | |
5376 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5377 | scm_remember_upto_here_1 (y); | |
5378 | return (sgn < 0) ? y : x; | |
5379 | } | |
5380 | else if (SCM_REALP (y)) | |
5381 | { | |
5382 | double z = xx; | |
5383 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 5384 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 5385 | } |
f92e85f7 MV |
5386 | else if (SCM_FRACTIONP (y)) |
5387 | { | |
e4bc5d6c | 5388 | use_less: |
73e4de09 | 5389 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 5390 | } |
0aacf84e MD |
5391 | else |
5392 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 5393 | } |
0aacf84e MD |
5394 | else if (SCM_BIGP (x)) |
5395 | { | |
e11e83f3 | 5396 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5397 | { |
5398 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5399 | scm_remember_upto_here_1 (x); | |
5400 | return (sgn < 0) ? x : y; | |
5401 | } | |
5402 | else if (SCM_BIGP (y)) | |
5403 | { | |
5404 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
5405 | scm_remember_upto_here_2 (x, y); | |
5406 | return (cmp > 0) ? y : x; | |
5407 | } | |
5408 | else if (SCM_REALP (y)) | |
5409 | { | |
2a06f791 KR |
5410 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
5411 | double xx, yy; | |
5412 | big_real: | |
5413 | xx = scm_i_big2dbl (x); | |
5414 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 5415 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 5416 | } |
f92e85f7 MV |
5417 | else if (SCM_FRACTIONP (y)) |
5418 | { | |
e4bc5d6c | 5419 | goto use_less; |
f92e85f7 | 5420 | } |
0aacf84e MD |
5421 | else |
5422 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 5423 | } |
0aacf84e MD |
5424 | else if (SCM_REALP (x)) |
5425 | { | |
e11e83f3 | 5426 | if (SCM_I_INUMP (y)) |
0aacf84e | 5427 | { |
e11e83f3 | 5428 | double z = SCM_I_INUM (y); |
0aacf84e | 5429 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 5430 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
5431 | } |
5432 | else if (SCM_BIGP (y)) | |
5433 | { | |
b6f8f763 | 5434 | SCM_SWAP (x, y); |
2a06f791 | 5435 | goto big_real; |
0aacf84e MD |
5436 | } |
5437 | else if (SCM_REALP (y)) | |
5438 | { | |
0aacf84e | 5439 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
5440 | double yy = SCM_REAL_VALUE (y); |
5441 | ||
5442 | /* For purposes of min: -inf.0 < nan < everything else, per R6RS */ | |
5443 | if (xx < yy) | |
5444 | return x; | |
5445 | else if (SCM_LIKELY (xx > yy)) | |
5446 | return y; | |
5447 | /* If neither (xx < yy) nor (xx > yy), then | |
5448 | either they're equal or one is a NaN */ | |
5449 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 5450 | return DOUBLE_IS_NEGATIVE_INFINITY (yy) ? y : x; |
2e274311 | 5451 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 5452 | return DOUBLE_IS_NEGATIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
5453 | /* xx == yy, but handle signed zeroes properly */ |
5454 | else if (double_is_non_negative_zero (xx)) | |
5455 | return y; | |
5456 | else | |
5457 | return x; | |
0aacf84e | 5458 | } |
f92e85f7 MV |
5459 | else if (SCM_FRACTIONP (y)) |
5460 | { | |
5461 | double yy = scm_i_fraction2double (y); | |
5462 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 5463 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 5464 | } |
0aacf84e MD |
5465 | else |
5466 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 5467 | } |
f92e85f7 MV |
5468 | else if (SCM_FRACTIONP (x)) |
5469 | { | |
e11e83f3 | 5470 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5471 | { |
e4bc5d6c | 5472 | goto use_less; |
f92e85f7 MV |
5473 | } |
5474 | else if (SCM_BIGP (y)) | |
5475 | { | |
e4bc5d6c | 5476 | goto use_less; |
f92e85f7 MV |
5477 | } |
5478 | else if (SCM_REALP (y)) | |
5479 | { | |
5480 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
5481 | /* if y==NaN then "<" is false, so we return the NaN y */ |
5482 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
5483 | } |
5484 | else if (SCM_FRACTIONP (y)) | |
5485 | { | |
e4bc5d6c | 5486 | goto use_less; |
f92e85f7 MV |
5487 | } |
5488 | else | |
78d3deb1 | 5489 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 5490 | } |
0aacf84e | 5491 | else |
f4c627b3 | 5492 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
5493 | } |
5494 | ||
5495 | ||
8ccd24f7 AW |
5496 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
5497 | (SCM x, SCM y, SCM rest), | |
5498 | "Return the sum of all parameter values. Return 0 if called without\n" | |
5499 | "any parameters." ) | |
5500 | #define FUNC_NAME s_scm_i_sum | |
5501 | { | |
5502 | while (!scm_is_null (rest)) | |
5503 | { x = scm_sum (x, y); | |
5504 | y = scm_car (rest); | |
5505 | rest = scm_cdr (rest); | |
5506 | } | |
5507 | return scm_sum (x, y); | |
5508 | } | |
5509 | #undef FUNC_NAME | |
5510 | ||
5511 | #define s_sum s_scm_i_sum | |
5512 | #define g_sum g_scm_i_sum | |
5513 | ||
0f2d19dd | 5514 | SCM |
6e8d25a6 | 5515 | scm_sum (SCM x, SCM y) |
0f2d19dd | 5516 | { |
9cc37597 | 5517 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
5518 | { |
5519 | if (SCM_NUMBERP (x)) return x; | |
5520 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 5521 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 5522 | } |
c209c88e | 5523 | |
9cc37597 | 5524 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 5525 | { |
9cc37597 | 5526 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 5527 | { |
e25f3727 AW |
5528 | scm_t_inum xx = SCM_I_INUM (x); |
5529 | scm_t_inum yy = SCM_I_INUM (y); | |
5530 | scm_t_inum z = xx + yy; | |
5531 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
5532 | } |
5533 | else if (SCM_BIGP (y)) | |
5534 | { | |
5535 | SCM_SWAP (x, y); | |
5536 | goto add_big_inum; | |
5537 | } | |
5538 | else if (SCM_REALP (y)) | |
5539 | { | |
e25f3727 | 5540 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 5541 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
5542 | } |
5543 | else if (SCM_COMPLEXP (y)) | |
5544 | { | |
e25f3727 | 5545 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 5546 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
5547 | SCM_COMPLEX_IMAG (y)); |
5548 | } | |
f92e85f7 | 5549 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5550 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
5551 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
5552 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
5553 | else |
5554 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
5555 | } else if (SCM_BIGP (x)) |
5556 | { | |
e11e83f3 | 5557 | if (SCM_I_INUMP (y)) |
0aacf84e | 5558 | { |
e25f3727 | 5559 | scm_t_inum inum; |
0aacf84e MD |
5560 | int bigsgn; |
5561 | add_big_inum: | |
e11e83f3 | 5562 | inum = SCM_I_INUM (y); |
0aacf84e MD |
5563 | if (inum == 0) |
5564 | return x; | |
5565 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5566 | if (inum < 0) | |
5567 | { | |
5568 | SCM result = scm_i_mkbig (); | |
5569 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
5570 | scm_remember_upto_here_1 (x); | |
5571 | /* we know the result will have to be a bignum */ | |
5572 | if (bigsgn == -1) | |
5573 | return result; | |
5574 | return scm_i_normbig (result); | |
5575 | } | |
5576 | else | |
5577 | { | |
5578 | SCM result = scm_i_mkbig (); | |
5579 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
5580 | scm_remember_upto_here_1 (x); | |
5581 | /* we know the result will have to be a bignum */ | |
5582 | if (bigsgn == 1) | |
5583 | return result; | |
5584 | return scm_i_normbig (result); | |
5585 | } | |
5586 | } | |
5587 | else if (SCM_BIGP (y)) | |
5588 | { | |
5589 | SCM result = scm_i_mkbig (); | |
5590 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5591 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5592 | mpz_add (SCM_I_BIG_MPZ (result), | |
5593 | SCM_I_BIG_MPZ (x), | |
5594 | SCM_I_BIG_MPZ (y)); | |
5595 | scm_remember_upto_here_2 (x, y); | |
5596 | /* we know the result will have to be a bignum */ | |
5597 | if (sgn_x == sgn_y) | |
5598 | return result; | |
5599 | return scm_i_normbig (result); | |
5600 | } | |
5601 | else if (SCM_REALP (y)) | |
5602 | { | |
5603 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
5604 | scm_remember_upto_here_1 (x); | |
55f26379 | 5605 | return scm_from_double (result); |
0aacf84e MD |
5606 | } |
5607 | else if (SCM_COMPLEXP (y)) | |
5608 | { | |
5609 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
5610 | + SCM_COMPLEX_REAL (y)); | |
5611 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5612 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 5613 | } |
f92e85f7 | 5614 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5615 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
5616 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
5617 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
5618 | else |
5619 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 5620 | } |
0aacf84e MD |
5621 | else if (SCM_REALP (x)) |
5622 | { | |
e11e83f3 | 5623 | if (SCM_I_INUMP (y)) |
55f26379 | 5624 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
5625 | else if (SCM_BIGP (y)) |
5626 | { | |
5627 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
5628 | scm_remember_upto_here_1 (y); | |
55f26379 | 5629 | return scm_from_double (result); |
0aacf84e MD |
5630 | } |
5631 | else if (SCM_REALP (y)) | |
55f26379 | 5632 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 5633 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5634 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 5635 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5636 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5637 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
5638 | else |
5639 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 5640 | } |
0aacf84e MD |
5641 | else if (SCM_COMPLEXP (x)) |
5642 | { | |
e11e83f3 | 5643 | if (SCM_I_INUMP (y)) |
8507ec80 | 5644 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
5645 | SCM_COMPLEX_IMAG (x)); |
5646 | else if (SCM_BIGP (y)) | |
5647 | { | |
5648 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
5649 | + SCM_COMPLEX_REAL (x)); | |
5650 | scm_remember_upto_here_1 (y); | |
8507ec80 | 5651 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
5652 | } |
5653 | else if (SCM_REALP (y)) | |
8507ec80 | 5654 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
5655 | SCM_COMPLEX_IMAG (x)); |
5656 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 5657 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 5658 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5659 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 5660 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
5661 | SCM_COMPLEX_IMAG (x)); |
5662 | else | |
5663 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
5664 | } | |
5665 | else if (SCM_FRACTIONP (x)) | |
5666 | { | |
e11e83f3 | 5667 | if (SCM_I_INUMP (y)) |
cba42c93 | 5668 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5669 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
5670 | SCM_FRACTION_DENOMINATOR (x)); | |
5671 | else if (SCM_BIGP (y)) | |
cba42c93 | 5672 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5673 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
5674 | SCM_FRACTION_DENOMINATOR (x)); | |
5675 | else if (SCM_REALP (y)) | |
55f26379 | 5676 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 5677 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5678 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
5679 | SCM_COMPLEX_IMAG (y)); |
5680 | else if (SCM_FRACTIONP (y)) | |
5681 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 5682 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5683 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
5684 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
5685 | else |
5686 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 5687 | } |
0aacf84e | 5688 | else |
98cb6e75 | 5689 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
5690 | } |
5691 | ||
5692 | ||
40882e3d KR |
5693 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
5694 | (SCM x), | |
5695 | "Return @math{@var{x}+1}.") | |
5696 | #define FUNC_NAME s_scm_oneplus | |
5697 | { | |
cff5fa33 | 5698 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
5699 | } |
5700 | #undef FUNC_NAME | |
5701 | ||
5702 | ||
78d3deb1 AW |
5703 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
5704 | (SCM x, SCM y, SCM rest), | |
5705 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
5706 | "the sum of all but the first argument are subtracted from the first\n" | |
5707 | "argument.") | |
5708 | #define FUNC_NAME s_scm_i_difference | |
5709 | { | |
5710 | while (!scm_is_null (rest)) | |
5711 | { x = scm_difference (x, y); | |
5712 | y = scm_car (rest); | |
5713 | rest = scm_cdr (rest); | |
5714 | } | |
5715 | return scm_difference (x, y); | |
5716 | } | |
5717 | #undef FUNC_NAME | |
5718 | ||
5719 | #define s_difference s_scm_i_difference | |
5720 | #define g_difference g_scm_i_difference | |
5721 | ||
0f2d19dd | 5722 | SCM |
6e8d25a6 | 5723 | scm_difference (SCM x, SCM y) |
78d3deb1 | 5724 | #define FUNC_NAME s_difference |
0f2d19dd | 5725 | { |
9cc37597 | 5726 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
5727 | { |
5728 | if (SCM_UNBNDP (x)) | |
5729 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
5730 | else | |
e11e83f3 | 5731 | if (SCM_I_INUMP (x)) |
ca46fb90 | 5732 | { |
e25f3727 | 5733 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 5734 | if (SCM_FIXABLE (xx)) |
d956fa6f | 5735 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 5736 | else |
e25f3727 | 5737 | return scm_i_inum2big (xx); |
ca46fb90 RB |
5738 | } |
5739 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
5740 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
5741 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
5742 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
5743 | else if (SCM_REALP (x)) | |
55f26379 | 5744 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 5745 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 5746 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 5747 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 5748 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 5749 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 5750 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
5751 | else |
5752 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 5753 | } |
ca46fb90 | 5754 | |
9cc37597 | 5755 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 5756 | { |
9cc37597 | 5757 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 5758 | { |
e25f3727 AW |
5759 | scm_t_inum xx = SCM_I_INUM (x); |
5760 | scm_t_inum yy = SCM_I_INUM (y); | |
5761 | scm_t_inum z = xx - yy; | |
0aacf84e | 5762 | if (SCM_FIXABLE (z)) |
d956fa6f | 5763 | return SCM_I_MAKINUM (z); |
0aacf84e | 5764 | else |
e25f3727 | 5765 | return scm_i_inum2big (z); |
0aacf84e MD |
5766 | } |
5767 | else if (SCM_BIGP (y)) | |
5768 | { | |
5769 | /* inum-x - big-y */ | |
e25f3727 | 5770 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 5771 | |
0aacf84e | 5772 | if (xx == 0) |
b5c40589 MW |
5773 | { |
5774 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
5775 | bignum, but negating that gives a fixnum. */ | |
5776 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
5777 | } | |
0aacf84e MD |
5778 | else |
5779 | { | |
5780 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5781 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 5782 | |
0aacf84e MD |
5783 | if (xx >= 0) |
5784 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
5785 | else | |
5786 | { | |
5787 | /* x - y == -(y + -x) */ | |
5788 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
5789 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
5790 | } | |
5791 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 5792 | |
0aacf84e MD |
5793 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
5794 | /* we know the result will have to be a bignum */ | |
5795 | return result; | |
5796 | else | |
5797 | return scm_i_normbig (result); | |
5798 | } | |
5799 | } | |
5800 | else if (SCM_REALP (y)) | |
5801 | { | |
e25f3727 | 5802 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
5803 | |
5804 | /* | |
5805 | * We need to handle x == exact 0 | |
5806 | * specially because R6RS states that: | |
5807 | * (- 0.0) ==> -0.0 and | |
5808 | * (- 0.0 0.0) ==> 0.0 | |
5809 | * and the scheme compiler changes | |
5810 | * (- 0.0) into (- 0 0.0) | |
5811 | * So we need to treat (- 0 0.0) like (- 0.0). | |
5812 | * At the C level, (-x) is different than (0.0 - x). | |
5813 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
5814 | */ | |
5815 | if (xx == 0) | |
5816 | return scm_from_double (- SCM_REAL_VALUE (y)); | |
5817 | else | |
5818 | return scm_from_double (xx - SCM_REAL_VALUE (y)); | |
0aacf84e MD |
5819 | } |
5820 | else if (SCM_COMPLEXP (y)) | |
5821 | { | |
e25f3727 | 5822 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
5823 | |
5824 | /* We need to handle x == exact 0 specially. | |
5825 | See the comment above (for SCM_REALP (y)) */ | |
5826 | if (xx == 0) | |
5827 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
5828 | - SCM_COMPLEX_IMAG (y)); | |
5829 | else | |
5830 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
5831 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 5832 | } |
f92e85f7 MV |
5833 | else if (SCM_FRACTIONP (y)) |
5834 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 5835 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5836 | SCM_FRACTION_NUMERATOR (y)), |
5837 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
5838 | else |
5839 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 5840 | } |
0aacf84e MD |
5841 | else if (SCM_BIGP (x)) |
5842 | { | |
e11e83f3 | 5843 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
5844 | { |
5845 | /* big-x - inum-y */ | |
e25f3727 | 5846 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 5847 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 5848 | |
0aacf84e MD |
5849 | scm_remember_upto_here_1 (x); |
5850 | if (sgn_x == 0) | |
c71b0706 | 5851 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 5852 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
5853 | else |
5854 | { | |
5855 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 5856 | |
708f22c6 KR |
5857 | if (yy >= 0) |
5858 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
5859 | else | |
5860 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 5861 | scm_remember_upto_here_1 (x); |
ca46fb90 | 5862 | |
0aacf84e MD |
5863 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
5864 | /* we know the result will have to be a bignum */ | |
5865 | return result; | |
5866 | else | |
5867 | return scm_i_normbig (result); | |
5868 | } | |
5869 | } | |
5870 | else if (SCM_BIGP (y)) | |
5871 | { | |
5872 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
5873 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
5874 | SCM result = scm_i_mkbig (); | |
5875 | mpz_sub (SCM_I_BIG_MPZ (result), | |
5876 | SCM_I_BIG_MPZ (x), | |
5877 | SCM_I_BIG_MPZ (y)); | |
5878 | scm_remember_upto_here_2 (x, y); | |
5879 | /* we know the result will have to be a bignum */ | |
5880 | if ((sgn_x == 1) && (sgn_y == -1)) | |
5881 | return result; | |
5882 | if ((sgn_x == -1) && (sgn_y == 1)) | |
5883 | return result; | |
5884 | return scm_i_normbig (result); | |
5885 | } | |
5886 | else if (SCM_REALP (y)) | |
5887 | { | |
5888 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
5889 | scm_remember_upto_here_1 (x); | |
55f26379 | 5890 | return scm_from_double (result); |
0aacf84e MD |
5891 | } |
5892 | else if (SCM_COMPLEXP (y)) | |
5893 | { | |
5894 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
5895 | - SCM_COMPLEX_REAL (y)); | |
5896 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5897 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 5898 | } |
f92e85f7 | 5899 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 5900 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5901 | SCM_FRACTION_NUMERATOR (y)), |
5902 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 5903 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 5904 | } |
0aacf84e MD |
5905 | else if (SCM_REALP (x)) |
5906 | { | |
e11e83f3 | 5907 | if (SCM_I_INUMP (y)) |
55f26379 | 5908 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
5909 | else if (SCM_BIGP (y)) |
5910 | { | |
5911 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
5912 | scm_remember_upto_here_1 (x); | |
55f26379 | 5913 | return scm_from_double (result); |
0aacf84e MD |
5914 | } |
5915 | else if (SCM_REALP (y)) | |
55f26379 | 5916 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 5917 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5918 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 5919 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5920 | else if (SCM_FRACTIONP (y)) |
55f26379 | 5921 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
5922 | else |
5923 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 5924 | } |
0aacf84e MD |
5925 | else if (SCM_COMPLEXP (x)) |
5926 | { | |
e11e83f3 | 5927 | if (SCM_I_INUMP (y)) |
8507ec80 | 5928 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
5929 | SCM_COMPLEX_IMAG (x)); |
5930 | else if (SCM_BIGP (y)) | |
5931 | { | |
5932 | double real_part = (SCM_COMPLEX_REAL (x) | |
5933 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
5934 | scm_remember_upto_here_1 (x); | |
8507ec80 | 5935 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
5936 | } |
5937 | else if (SCM_REALP (y)) | |
8507ec80 | 5938 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
5939 | SCM_COMPLEX_IMAG (x)); |
5940 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 5941 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 5942 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 5943 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 5944 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
5945 | SCM_COMPLEX_IMAG (x)); |
5946 | else | |
5947 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
5948 | } | |
5949 | else if (SCM_FRACTIONP (x)) | |
5950 | { | |
e11e83f3 | 5951 | if (SCM_I_INUMP (y)) |
f92e85f7 | 5952 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 5953 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5954 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
5955 | SCM_FRACTION_DENOMINATOR (x)); | |
5956 | else if (SCM_BIGP (y)) | |
cba42c93 | 5957 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
5958 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
5959 | SCM_FRACTION_DENOMINATOR (x)); | |
5960 | else if (SCM_REALP (y)) | |
55f26379 | 5961 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 5962 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 5963 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
5964 | -SCM_COMPLEX_IMAG (y)); |
5965 | else if (SCM_FRACTIONP (y)) | |
5966 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 5967 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
5968 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
5969 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
5970 | else |
5971 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 5972 | } |
0aacf84e | 5973 | else |
98cb6e75 | 5974 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 5975 | } |
c05e97b7 | 5976 | #undef FUNC_NAME |
0f2d19dd | 5977 | |
ca46fb90 | 5978 | |
40882e3d KR |
5979 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
5980 | (SCM x), | |
5981 | "Return @math{@var{x}-1}.") | |
5982 | #define FUNC_NAME s_scm_oneminus | |
5983 | { | |
cff5fa33 | 5984 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
5985 | } |
5986 | #undef FUNC_NAME | |
5987 | ||
5988 | ||
78d3deb1 AW |
5989 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
5990 | (SCM x, SCM y, SCM rest), | |
5991 | "Return the product of all arguments. If called without arguments,\n" | |
5992 | "1 is returned.") | |
5993 | #define FUNC_NAME s_scm_i_product | |
5994 | { | |
5995 | while (!scm_is_null (rest)) | |
5996 | { x = scm_product (x, y); | |
5997 | y = scm_car (rest); | |
5998 | rest = scm_cdr (rest); | |
5999 | } | |
6000 | return scm_product (x, y); | |
6001 | } | |
6002 | #undef FUNC_NAME | |
6003 | ||
6004 | #define s_product s_scm_i_product | |
6005 | #define g_product g_scm_i_product | |
6006 | ||
0f2d19dd | 6007 | SCM |
6e8d25a6 | 6008 | scm_product (SCM x, SCM y) |
0f2d19dd | 6009 | { |
9cc37597 | 6010 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
6011 | { |
6012 | if (SCM_UNBNDP (x)) | |
d956fa6f | 6013 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
6014 | else if (SCM_NUMBERP (x)) |
6015 | return x; | |
6016 | else | |
6017 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 6018 | } |
ca46fb90 | 6019 | |
9cc37597 | 6020 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 6021 | { |
e25f3727 | 6022 | scm_t_inum xx; |
f4c627b3 | 6023 | |
5e791807 | 6024 | xinum: |
e11e83f3 | 6025 | xx = SCM_I_INUM (x); |
f4c627b3 | 6026 | |
0aacf84e MD |
6027 | switch (xx) |
6028 | { | |
5e791807 MW |
6029 | case 1: |
6030 | /* exact1 is the universal multiplicative identity */ | |
6031 | return y; | |
6032 | break; | |
6033 | case 0: | |
6034 | /* exact0 times a fixnum is exact0: optimize this case */ | |
6035 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
6036 | return SCM_INUM0; | |
6037 | /* if the other argument is inexact, the result is inexact, | |
6038 | and we must do the multiplication in order to handle | |
6039 | infinities and NaNs properly. */ | |
6040 | else if (SCM_REALP (y)) | |
6041 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
6042 | else if (SCM_COMPLEXP (y)) | |
6043 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
6044 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
6045 | /* we've already handled inexact numbers, | |
6046 | so y must be exact, and we return exact0 */ | |
6047 | else if (SCM_NUMP (y)) | |
6048 | return SCM_INUM0; | |
6049 | else | |
6050 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
6051 | break; | |
6052 | case -1: | |
b5c40589 | 6053 | /* |
5e791807 MW |
6054 | * This case is important for more than just optimization. |
6055 | * It handles the case of negating | |
b5c40589 MW |
6056 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
6057 | * which is a bignum that must be changed back into a fixnum. | |
6058 | * Failure to do so will cause the following to return #f: | |
6059 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
6060 | */ | |
b5c40589 MW |
6061 | return scm_difference(y, SCM_UNDEFINED); |
6062 | break; | |
0aacf84e | 6063 | } |
f4c627b3 | 6064 | |
9cc37597 | 6065 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 6066 | { |
e25f3727 AW |
6067 | scm_t_inum yy = SCM_I_INUM (y); |
6068 | scm_t_inum kk = xx * yy; | |
d956fa6f | 6069 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 6070 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
6071 | return k; |
6072 | else | |
6073 | { | |
e25f3727 | 6074 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
6075 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
6076 | return scm_i_normbig (result); | |
6077 | } | |
6078 | } | |
6079 | else if (SCM_BIGP (y)) | |
6080 | { | |
6081 | SCM result = scm_i_mkbig (); | |
6082 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
6083 | scm_remember_upto_here_1 (y); | |
6084 | return result; | |
6085 | } | |
6086 | else if (SCM_REALP (y)) | |
55f26379 | 6087 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 6088 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 6089 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 6090 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 6091 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 6092 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 6093 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
6094 | else |
6095 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6096 | } |
0aacf84e MD |
6097 | else if (SCM_BIGP (x)) |
6098 | { | |
e11e83f3 | 6099 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6100 | { |
6101 | SCM_SWAP (x, y); | |
5e791807 | 6102 | goto xinum; |
0aacf84e MD |
6103 | } |
6104 | else if (SCM_BIGP (y)) | |
6105 | { | |
6106 | SCM result = scm_i_mkbig (); | |
6107 | mpz_mul (SCM_I_BIG_MPZ (result), | |
6108 | SCM_I_BIG_MPZ (x), | |
6109 | SCM_I_BIG_MPZ (y)); | |
6110 | scm_remember_upto_here_2 (x, y); | |
6111 | return result; | |
6112 | } | |
6113 | else if (SCM_REALP (y)) | |
6114 | { | |
6115 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
6116 | scm_remember_upto_here_1 (x); | |
55f26379 | 6117 | return scm_from_double (result); |
0aacf84e MD |
6118 | } |
6119 | else if (SCM_COMPLEXP (y)) | |
6120 | { | |
6121 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
6122 | scm_remember_upto_here_1 (x); | |
8507ec80 | 6123 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
6124 | z * SCM_COMPLEX_IMAG (y)); |
6125 | } | |
f92e85f7 | 6126 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 6127 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 6128 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
6129 | else |
6130 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6131 | } |
0aacf84e MD |
6132 | else if (SCM_REALP (x)) |
6133 | { | |
e11e83f3 | 6134 | if (SCM_I_INUMP (y)) |
5e791807 MW |
6135 | { |
6136 | SCM_SWAP (x, y); | |
6137 | goto xinum; | |
6138 | } | |
0aacf84e MD |
6139 | else if (SCM_BIGP (y)) |
6140 | { | |
6141 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
6142 | scm_remember_upto_here_1 (y); | |
55f26379 | 6143 | return scm_from_double (result); |
0aacf84e MD |
6144 | } |
6145 | else if (SCM_REALP (y)) | |
55f26379 | 6146 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 6147 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 6148 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 6149 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 6150 | else if (SCM_FRACTIONP (y)) |
55f26379 | 6151 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
6152 | else |
6153 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6154 | } |
0aacf84e MD |
6155 | else if (SCM_COMPLEXP (x)) |
6156 | { | |
e11e83f3 | 6157 | if (SCM_I_INUMP (y)) |
5e791807 MW |
6158 | { |
6159 | SCM_SWAP (x, y); | |
6160 | goto xinum; | |
6161 | } | |
0aacf84e MD |
6162 | else if (SCM_BIGP (y)) |
6163 | { | |
6164 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6165 | scm_remember_upto_here_1 (y); | |
8507ec80 | 6166 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 6167 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
6168 | } |
6169 | else if (SCM_REALP (y)) | |
8507ec80 | 6170 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
6171 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
6172 | else if (SCM_COMPLEXP (y)) | |
6173 | { | |
8507ec80 | 6174 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
6175 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
6176 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
6177 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
6178 | } | |
f92e85f7 MV |
6179 | else if (SCM_FRACTIONP (y)) |
6180 | { | |
6181 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 6182 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
6183 | yy * SCM_COMPLEX_IMAG (x)); |
6184 | } | |
6185 | else | |
6186 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
6187 | } | |
6188 | else if (SCM_FRACTIONP (x)) | |
6189 | { | |
e11e83f3 | 6190 | if (SCM_I_INUMP (y)) |
cba42c93 | 6191 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
6192 | SCM_FRACTION_DENOMINATOR (x)); |
6193 | else if (SCM_BIGP (y)) | |
cba42c93 | 6194 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
6195 | SCM_FRACTION_DENOMINATOR (x)); |
6196 | else if (SCM_REALP (y)) | |
55f26379 | 6197 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
6198 | else if (SCM_COMPLEXP (y)) |
6199 | { | |
6200 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 6201 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
6202 | xx * SCM_COMPLEX_IMAG (y)); |
6203 | } | |
6204 | else if (SCM_FRACTIONP (y)) | |
6205 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 6206 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6207 | SCM_FRACTION_NUMERATOR (y)), |
6208 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
6209 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
6210 | else |
6211 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 6212 | } |
0aacf84e | 6213 | else |
f4c627b3 | 6214 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
6215 | } |
6216 | ||
7351e207 MV |
6217 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
6218 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
6219 | #define ALLOW_DIVIDE_BY_ZERO | |
6220 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
6221 | #endif | |
0f2d19dd | 6222 | |
ba74ef4e MV |
6223 | /* The code below for complex division is adapted from the GNU |
6224 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
6225 | this copyright: */ | |
6226 | ||
6227 | /**************************************************************** | |
6228 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
6229 | ||
6230 | Permission to use, copy, modify, and distribute this software | |
6231 | and its documentation for any purpose and without fee is hereby | |
6232 | granted, provided that the above copyright notice appear in all | |
6233 | copies and that both that the copyright notice and this | |
6234 | permission notice and warranty disclaimer appear in supporting | |
6235 | documentation, and that the names of AT&T Bell Laboratories or | |
6236 | Bellcore or any of their entities not be used in advertising or | |
6237 | publicity pertaining to distribution of the software without | |
6238 | specific, written prior permission. | |
6239 | ||
6240 | AT&T and Bellcore disclaim all warranties with regard to this | |
6241 | software, including all implied warranties of merchantability | |
6242 | and fitness. In no event shall AT&T or Bellcore be liable for | |
6243 | any special, indirect or consequential damages or any damages | |
6244 | whatsoever resulting from loss of use, data or profits, whether | |
6245 | in an action of contract, negligence or other tortious action, | |
6246 | arising out of or in connection with the use or performance of | |
6247 | this software. | |
6248 | ****************************************************************/ | |
6249 | ||
78d3deb1 AW |
6250 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
6251 | (SCM x, SCM y, SCM rest), | |
6252 | "Divide the first argument by the product of the remaining\n" | |
6253 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
6254 | "returned.") | |
6255 | #define FUNC_NAME s_scm_i_divide | |
6256 | { | |
6257 | while (!scm_is_null (rest)) | |
6258 | { x = scm_divide (x, y); | |
6259 | y = scm_car (rest); | |
6260 | rest = scm_cdr (rest); | |
6261 | } | |
6262 | return scm_divide (x, y); | |
6263 | } | |
6264 | #undef FUNC_NAME | |
6265 | ||
6266 | #define s_divide s_scm_i_divide | |
6267 | #define g_divide g_scm_i_divide | |
6268 | ||
f92e85f7 | 6269 | static SCM |
78d3deb1 AW |
6270 | do_divide (SCM x, SCM y, int inexact) |
6271 | #define FUNC_NAME s_divide | |
0f2d19dd | 6272 | { |
f8de44c1 DH |
6273 | double a; |
6274 | ||
9cc37597 | 6275 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
6276 | { |
6277 | if (SCM_UNBNDP (x)) | |
6278 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 6279 | else if (SCM_I_INUMP (x)) |
0aacf84e | 6280 | { |
e25f3727 | 6281 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
6282 | if (xx == 1 || xx == -1) |
6283 | return x; | |
7351e207 | 6284 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6285 | else if (xx == 0) |
6286 | scm_num_overflow (s_divide); | |
7351e207 | 6287 | #endif |
0aacf84e | 6288 | else |
f92e85f7 MV |
6289 | { |
6290 | if (inexact) | |
55f26379 | 6291 | return scm_from_double (1.0 / (double) xx); |
cff5fa33 | 6292 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 6293 | } |
0aacf84e MD |
6294 | } |
6295 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
6296 | { |
6297 | if (inexact) | |
55f26379 | 6298 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cff5fa33 | 6299 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 6300 | } |
0aacf84e MD |
6301 | else if (SCM_REALP (x)) |
6302 | { | |
6303 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 6304 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6305 | if (xx == 0.0) |
6306 | scm_num_overflow (s_divide); | |
6307 | else | |
7351e207 | 6308 | #endif |
55f26379 | 6309 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
6310 | } |
6311 | else if (SCM_COMPLEXP (x)) | |
6312 | { | |
6313 | double r = SCM_COMPLEX_REAL (x); | |
6314 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 6315 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
6316 | { |
6317 | double t = r / i; | |
6318 | double d = i * (1.0 + t * t); | |
8507ec80 | 6319 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
6320 | } |
6321 | else | |
6322 | { | |
6323 | double t = i / r; | |
6324 | double d = r * (1.0 + t * t); | |
8507ec80 | 6325 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
6326 | } |
6327 | } | |
f92e85f7 | 6328 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 6329 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 6330 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
6331 | else |
6332 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 6333 | } |
f8de44c1 | 6334 | |
9cc37597 | 6335 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 6336 | { |
e25f3727 | 6337 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 6338 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 6339 | { |
e25f3727 | 6340 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6341 | if (yy == 0) |
6342 | { | |
7351e207 | 6343 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 6344 | scm_num_overflow (s_divide); |
7351e207 | 6345 | #else |
55f26379 | 6346 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 6347 | #endif |
0aacf84e MD |
6348 | } |
6349 | else if (xx % yy != 0) | |
f92e85f7 MV |
6350 | { |
6351 | if (inexact) | |
55f26379 | 6352 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 6353 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6354 | } |
0aacf84e MD |
6355 | else |
6356 | { | |
e25f3727 | 6357 | scm_t_inum z = xx / yy; |
0aacf84e | 6358 | if (SCM_FIXABLE (z)) |
d956fa6f | 6359 | return SCM_I_MAKINUM (z); |
0aacf84e | 6360 | else |
e25f3727 | 6361 | return scm_i_inum2big (z); |
0aacf84e | 6362 | } |
f872b822 | 6363 | } |
0aacf84e | 6364 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
6365 | { |
6366 | if (inexact) | |
55f26379 | 6367 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 6368 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6369 | } |
0aacf84e MD |
6370 | else if (SCM_REALP (y)) |
6371 | { | |
6372 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6373 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6374 | if (yy == 0.0) |
6375 | scm_num_overflow (s_divide); | |
6376 | else | |
7351e207 | 6377 | #endif |
55f26379 | 6378 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 6379 | } |
0aacf84e MD |
6380 | else if (SCM_COMPLEXP (y)) |
6381 | { | |
6382 | a = xx; | |
6383 | complex_div: /* y _must_ be a complex number */ | |
6384 | { | |
6385 | double r = SCM_COMPLEX_REAL (y); | |
6386 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 6387 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
6388 | { |
6389 | double t = r / i; | |
6390 | double d = i * (1.0 + t * t); | |
8507ec80 | 6391 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
6392 | } |
6393 | else | |
6394 | { | |
6395 | double t = i / r; | |
6396 | double d = r * (1.0 + t * t); | |
8507ec80 | 6397 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
6398 | } |
6399 | } | |
6400 | } | |
f92e85f7 MV |
6401 | else if (SCM_FRACTIONP (y)) |
6402 | /* a / b/c = ac / b */ | |
cba42c93 | 6403 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 6404 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
6405 | else |
6406 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 6407 | } |
0aacf84e MD |
6408 | else if (SCM_BIGP (x)) |
6409 | { | |
e11e83f3 | 6410 | if (SCM_I_INUMP (y)) |
0aacf84e | 6411 | { |
e25f3727 | 6412 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6413 | if (yy == 0) |
6414 | { | |
7351e207 | 6415 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 6416 | scm_num_overflow (s_divide); |
7351e207 | 6417 | #else |
0aacf84e MD |
6418 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
6419 | scm_remember_upto_here_1 (x); | |
6420 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 6421 | #endif |
0aacf84e MD |
6422 | } |
6423 | else if (yy == 1) | |
6424 | return x; | |
6425 | else | |
6426 | { | |
6427 | /* FIXME: HMM, what are the relative performance issues here? | |
6428 | We need to test. Is it faster on average to test | |
6429 | divisible_p, then perform whichever operation, or is it | |
6430 | faster to perform the integer div opportunistically and | |
6431 | switch to real if there's a remainder? For now we take the | |
6432 | middle ground: test, then if divisible, use the faster div | |
6433 | func. */ | |
6434 | ||
e25f3727 | 6435 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
6436 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
6437 | ||
6438 | if (divisible_p) | |
6439 | { | |
6440 | SCM result = scm_i_mkbig (); | |
6441 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
6442 | scm_remember_upto_here_1 (x); | |
6443 | if (yy < 0) | |
6444 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
6445 | return scm_i_normbig (result); | |
6446 | } | |
6447 | else | |
f92e85f7 MV |
6448 | { |
6449 | if (inexact) | |
55f26379 | 6450 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 6451 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 6452 | } |
0aacf84e MD |
6453 | } |
6454 | } | |
6455 | else if (SCM_BIGP (y)) | |
6456 | { | |
a4955a04 MW |
6457 | /* big_x / big_y */ |
6458 | if (inexact) | |
0aacf84e | 6459 | { |
a4955a04 MW |
6460 | /* It's easily possible for the ratio x/y to fit a double |
6461 | but one or both x and y be too big to fit a double, | |
6462 | hence the use of mpq_get_d rather than converting and | |
6463 | dividing. */ | |
6464 | mpq_t q; | |
6465 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
6466 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
6467 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
6468 | } |
6469 | else | |
6470 | { | |
a4955a04 MW |
6471 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
6472 | SCM_I_BIG_MPZ (y)); | |
6473 | if (divisible_p) | |
6474 | { | |
6475 | SCM result = scm_i_mkbig (); | |
6476 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
6477 | SCM_I_BIG_MPZ (x), | |
6478 | SCM_I_BIG_MPZ (y)); | |
6479 | scm_remember_upto_here_2 (x, y); | |
6480 | return scm_i_normbig (result); | |
6481 | } | |
6482 | else | |
6483 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
6484 | } |
6485 | } | |
6486 | else if (SCM_REALP (y)) | |
6487 | { | |
6488 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6489 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6490 | if (yy == 0.0) |
6491 | scm_num_overflow (s_divide); | |
6492 | else | |
7351e207 | 6493 | #endif |
55f26379 | 6494 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
6495 | } |
6496 | else if (SCM_COMPLEXP (y)) | |
6497 | { | |
6498 | a = scm_i_big2dbl (x); | |
6499 | goto complex_div; | |
6500 | } | |
f92e85f7 | 6501 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 6502 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 6503 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
6504 | else |
6505 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 6506 | } |
0aacf84e MD |
6507 | else if (SCM_REALP (x)) |
6508 | { | |
6509 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 6510 | if (SCM_I_INUMP (y)) |
0aacf84e | 6511 | { |
e25f3727 | 6512 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 6513 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6514 | if (yy == 0) |
6515 | scm_num_overflow (s_divide); | |
6516 | else | |
7351e207 | 6517 | #endif |
55f26379 | 6518 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
6519 | } |
6520 | else if (SCM_BIGP (y)) | |
6521 | { | |
6522 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6523 | scm_remember_upto_here_1 (y); | |
55f26379 | 6524 | return scm_from_double (rx / dby); |
0aacf84e MD |
6525 | } |
6526 | else if (SCM_REALP (y)) | |
6527 | { | |
6528 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6529 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6530 | if (yy == 0.0) |
6531 | scm_num_overflow (s_divide); | |
6532 | else | |
7351e207 | 6533 | #endif |
55f26379 | 6534 | return scm_from_double (rx / yy); |
0aacf84e MD |
6535 | } |
6536 | else if (SCM_COMPLEXP (y)) | |
6537 | { | |
6538 | a = rx; | |
6539 | goto complex_div; | |
6540 | } | |
f92e85f7 | 6541 | else if (SCM_FRACTIONP (y)) |
55f26379 | 6542 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
6543 | else |
6544 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 6545 | } |
0aacf84e MD |
6546 | else if (SCM_COMPLEXP (x)) |
6547 | { | |
6548 | double rx = SCM_COMPLEX_REAL (x); | |
6549 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 6550 | if (SCM_I_INUMP (y)) |
0aacf84e | 6551 | { |
e25f3727 | 6552 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 6553 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
6554 | if (yy == 0) |
6555 | scm_num_overflow (s_divide); | |
6556 | else | |
7351e207 | 6557 | #endif |
0aacf84e MD |
6558 | { |
6559 | double d = yy; | |
8507ec80 | 6560 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
6561 | } |
6562 | } | |
6563 | else if (SCM_BIGP (y)) | |
6564 | { | |
6565 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
6566 | scm_remember_upto_here_1 (y); | |
8507ec80 | 6567 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
6568 | } |
6569 | else if (SCM_REALP (y)) | |
6570 | { | |
6571 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 6572 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
6573 | if (yy == 0.0) |
6574 | scm_num_overflow (s_divide); | |
6575 | else | |
7351e207 | 6576 | #endif |
8507ec80 | 6577 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
6578 | } |
6579 | else if (SCM_COMPLEXP (y)) | |
6580 | { | |
6581 | double ry = SCM_COMPLEX_REAL (y); | |
6582 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 6583 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
6584 | { |
6585 | double t = ry / iy; | |
6586 | double d = iy * (1.0 + t * t); | |
8507ec80 | 6587 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
6588 | } |
6589 | else | |
6590 | { | |
6591 | double t = iy / ry; | |
6592 | double d = ry * (1.0 + t * t); | |
8507ec80 | 6593 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
6594 | } |
6595 | } | |
f92e85f7 MV |
6596 | else if (SCM_FRACTIONP (y)) |
6597 | { | |
6598 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 6599 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 6600 | } |
0aacf84e MD |
6601 | else |
6602 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 6603 | } |
f92e85f7 MV |
6604 | else if (SCM_FRACTIONP (x)) |
6605 | { | |
e11e83f3 | 6606 | if (SCM_I_INUMP (y)) |
f92e85f7 | 6607 | { |
e25f3727 | 6608 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
6609 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
6610 | if (yy == 0) | |
6611 | scm_num_overflow (s_divide); | |
6612 | else | |
6613 | #endif | |
cba42c93 | 6614 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6615 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
6616 | } | |
6617 | else if (SCM_BIGP (y)) | |
6618 | { | |
cba42c93 | 6619 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
6620 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
6621 | } | |
6622 | else if (SCM_REALP (y)) | |
6623 | { | |
6624 | double yy = SCM_REAL_VALUE (y); | |
6625 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6626 | if (yy == 0.0) | |
6627 | scm_num_overflow (s_divide); | |
6628 | else | |
6629 | #endif | |
55f26379 | 6630 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
6631 | } |
6632 | else if (SCM_COMPLEXP (y)) | |
6633 | { | |
6634 | a = scm_i_fraction2double (x); | |
6635 | goto complex_div; | |
6636 | } | |
6637 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 6638 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
6639 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
6640 | else | |
6641 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
6642 | } | |
0aacf84e | 6643 | else |
f8de44c1 | 6644 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 6645 | } |
f92e85f7 MV |
6646 | |
6647 | SCM | |
6648 | scm_divide (SCM x, SCM y) | |
6649 | { | |
78d3deb1 | 6650 | return do_divide (x, y, 0); |
f92e85f7 MV |
6651 | } |
6652 | ||
6653 | static SCM scm_divide2real (SCM x, SCM y) | |
6654 | { | |
78d3deb1 | 6655 | return do_divide (x, y, 1); |
f92e85f7 | 6656 | } |
c05e97b7 | 6657 | #undef FUNC_NAME |
0f2d19dd | 6658 | |
fa605590 | 6659 | |
0f2d19dd | 6660 | double |
3101f40f | 6661 | scm_c_truncate (double x) |
0f2d19dd | 6662 | { |
fa605590 KR |
6663 | #if HAVE_TRUNC |
6664 | return trunc (x); | |
6665 | #else | |
f872b822 MD |
6666 | if (x < 0.0) |
6667 | return -floor (-x); | |
6668 | return floor (x); | |
fa605590 | 6669 | #endif |
0f2d19dd | 6670 | } |
0f2d19dd | 6671 | |
3101f40f MV |
6672 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
6673 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
6674 | Then half-way cases are identified and adjusted down if the | |
6675 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
6676 | |
6677 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
6678 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
6679 | ||
6680 | An odd "result" value is identified with result/2 != floor(result/2). | |
6681 | This is done with plus_half, since that value is ready for use sooner in | |
6682 | a pipelined cpu, and we're already requiring plus_half == result. | |
6683 | ||
6684 | Note however that we need to be careful when x is big and already an | |
6685 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
6686 | us to return such a value, incorrectly. For instance if the hardware is | |
6687 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
6688 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
6689 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
6690 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
6691 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
6692 | ||
6693 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
6694 | x is already an integer. If it is then clearly that's the desired result | |
6695 | already. And if it's not then the exponent must be small enough to allow | |
6696 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
6697 | ||
0f2d19dd | 6698 | double |
3101f40f | 6699 | scm_c_round (double x) |
0f2d19dd | 6700 | { |
6187f48b KR |
6701 | double plus_half, result; |
6702 | ||
6703 | if (x == floor (x)) | |
6704 | return x; | |
6705 | ||
6706 | plus_half = x + 0.5; | |
6707 | result = floor (plus_half); | |
3101f40f | 6708 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
6709 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
6710 | ? result - 1 | |
6711 | : result); | |
0f2d19dd JB |
6712 | } |
6713 | ||
f92e85f7 MV |
6714 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
6715 | (SCM x), | |
6716 | "Round the number @var{x} towards zero.") | |
6717 | #define FUNC_NAME s_scm_truncate_number | |
6718 | { | |
73e4de09 | 6719 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
6720 | return scm_floor (x); |
6721 | else | |
6722 | return scm_ceiling (x); | |
6723 | } | |
6724 | #undef FUNC_NAME | |
6725 | ||
f92e85f7 MV |
6726 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, |
6727 | (SCM x), | |
6728 | "Round the number @var{x} towards the nearest integer. " | |
6729 | "When it is exactly halfway between two integers, " | |
6730 | "round towards the even one.") | |
6731 | #define FUNC_NAME s_scm_round_number | |
6732 | { | |
e11e83f3 | 6733 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
6734 | return x; |
6735 | else if (SCM_REALP (x)) | |
3101f40f | 6736 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 6737 | else |
bae30667 KR |
6738 | { |
6739 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
6740 | single quotient+remainder division then examining to see which way | |
6741 | the rounding should go. */ | |
6742 | SCM plus_half = scm_sum (x, exactly_one_half); | |
6743 | SCM result = scm_floor (plus_half); | |
3101f40f | 6744 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
6745 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
6746 | && scm_is_true (scm_odd_p (result))) | |
cff5fa33 | 6747 | return scm_difference (result, SCM_INUM1); |
bae30667 KR |
6748 | else |
6749 | return result; | |
6750 | } | |
f92e85f7 MV |
6751 | } |
6752 | #undef FUNC_NAME | |
6753 | ||
6754 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
6755 | (SCM x), | |
6756 | "Round the number @var{x} towards minus infinity.") | |
6757 | #define FUNC_NAME s_scm_floor | |
6758 | { | |
e11e83f3 | 6759 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
6760 | return x; |
6761 | else if (SCM_REALP (x)) | |
55f26379 | 6762 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
6763 | else if (SCM_FRACTIONP (x)) |
6764 | { | |
6765 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
6766 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 6767 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
6768 | { |
6769 | /* For positive x, rounding towards zero is correct. */ | |
6770 | return q; | |
6771 | } | |
6772 | else | |
6773 | { | |
6774 | /* For negative x, we need to return q-1 unless x is an | |
6775 | integer. But fractions are never integer, per our | |
6776 | assumptions. */ | |
cff5fa33 | 6777 | return scm_difference (q, SCM_INUM1); |
f92e85f7 MV |
6778 | } |
6779 | } | |
6780 | else | |
6781 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
6782 | } | |
6783 | #undef FUNC_NAME | |
6784 | ||
6785 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
6786 | (SCM x), | |
6787 | "Round the number @var{x} towards infinity.") | |
6788 | #define FUNC_NAME s_scm_ceiling | |
6789 | { | |
e11e83f3 | 6790 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
6791 | return x; |
6792 | else if (SCM_REALP (x)) | |
55f26379 | 6793 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
6794 | else if (SCM_FRACTIONP (x)) |
6795 | { | |
6796 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
6797 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 6798 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
6799 | { |
6800 | /* For negative x, rounding towards zero is correct. */ | |
6801 | return q; | |
6802 | } | |
6803 | else | |
6804 | { | |
6805 | /* For positive x, we need to return q+1 unless x is an | |
6806 | integer. But fractions are never integer, per our | |
6807 | assumptions. */ | |
cff5fa33 | 6808 | return scm_sum (q, SCM_INUM1); |
f92e85f7 MV |
6809 | } |
6810 | } | |
6811 | else | |
6812 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
6813 | } | |
6814 | #undef FUNC_NAME | |
0f2d19dd | 6815 | |
2519490c MW |
6816 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
6817 | (SCM x, SCM y), | |
6818 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 6819 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 6820 | { |
01c7284a MW |
6821 | if (scm_is_integer (y)) |
6822 | { | |
6823 | if (scm_is_true (scm_exact_p (y))) | |
6824 | return scm_integer_expt (x, y); | |
6825 | else | |
6826 | { | |
6827 | /* Here we handle the case where the exponent is an inexact | |
6828 | integer. We make the exponent exact in order to use | |
6829 | scm_integer_expt, and thus avoid the spurious imaginary | |
6830 | parts that may result from round-off errors in the general | |
6831 | e^(y log x) method below (for example when squaring a large | |
6832 | negative number). In this case, we must return an inexact | |
6833 | result for correctness. We also make the base inexact so | |
6834 | that scm_integer_expt will use fast inexact arithmetic | |
6835 | internally. Note that making the base inexact is not | |
6836 | sufficient to guarantee an inexact result, because | |
6837 | scm_integer_expt will return an exact 1 when the exponent | |
6838 | is 0, even if the base is inexact. */ | |
6839 | return scm_exact_to_inexact | |
6840 | (scm_integer_expt (scm_exact_to_inexact (x), | |
6841 | scm_inexact_to_exact (y))); | |
6842 | } | |
6843 | } | |
6fc4d012 AW |
6844 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
6845 | { | |
6846 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
6847 | } | |
2519490c | 6848 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 6849 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c MW |
6850 | else if (scm_is_complex (x)) |
6851 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); | |
6852 | else | |
6853 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); | |
0f2d19dd | 6854 | } |
1bbd0b84 | 6855 | #undef FUNC_NAME |
0f2d19dd | 6856 | |
7f41099e MW |
6857 | /* sin/cos/tan/asin/acos/atan |
6858 | sinh/cosh/tanh/asinh/acosh/atanh | |
6859 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
6860 | Written by Jerry D. Hedden, (C) FSF. | |
6861 | See the file `COPYING' for terms applying to this program. */ | |
6862 | ||
ad79736c AW |
6863 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
6864 | (SCM z), | |
6865 | "Compute the sine of @var{z}.") | |
6866 | #define FUNC_NAME s_scm_sin | |
6867 | { | |
8deddc94 MW |
6868 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6869 | return z; /* sin(exact0) = exact0 */ | |
6870 | else if (scm_is_real (z)) | |
ad79736c AW |
6871 | return scm_from_double (sin (scm_to_double (z))); |
6872 | else if (SCM_COMPLEXP (z)) | |
6873 | { double x, y; | |
6874 | x = SCM_COMPLEX_REAL (z); | |
6875 | y = SCM_COMPLEX_IMAG (z); | |
6876 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
6877 | cos (x) * sinh (y)); | |
6878 | } | |
6879 | else | |
6880 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
6881 | } | |
6882 | #undef FUNC_NAME | |
0f2d19dd | 6883 | |
ad79736c AW |
6884 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
6885 | (SCM z), | |
6886 | "Compute the cosine of @var{z}.") | |
6887 | #define FUNC_NAME s_scm_cos | |
6888 | { | |
8deddc94 MW |
6889 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6890 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
6891 | else if (scm_is_real (z)) | |
ad79736c AW |
6892 | return scm_from_double (cos (scm_to_double (z))); |
6893 | else if (SCM_COMPLEXP (z)) | |
6894 | { double x, y; | |
6895 | x = SCM_COMPLEX_REAL (z); | |
6896 | y = SCM_COMPLEX_IMAG (z); | |
6897 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
6898 | -sin (x) * sinh (y)); | |
6899 | } | |
6900 | else | |
6901 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
6902 | } | |
6903 | #undef FUNC_NAME | |
6904 | ||
6905 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
6906 | (SCM z), | |
6907 | "Compute the tangent of @var{z}.") | |
6908 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 6909 | { |
8deddc94 MW |
6910 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6911 | return z; /* tan(exact0) = exact0 */ | |
6912 | else if (scm_is_real (z)) | |
ad79736c AW |
6913 | return scm_from_double (tan (scm_to_double (z))); |
6914 | else if (SCM_COMPLEXP (z)) | |
6915 | { double x, y, w; | |
6916 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
6917 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
6918 | w = cos (x) + cosh (y); | |
6919 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6920 | if (w == 0.0) | |
6921 | scm_num_overflow (s_scm_tan); | |
6922 | #endif | |
6923 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
6924 | } | |
6925 | else | |
6926 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
6927 | } | |
6928 | #undef FUNC_NAME | |
6929 | ||
6930 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
6931 | (SCM z), | |
6932 | "Compute the hyperbolic sine of @var{z}.") | |
6933 | #define FUNC_NAME s_scm_sinh | |
6934 | { | |
8deddc94 MW |
6935 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6936 | return z; /* sinh(exact0) = exact0 */ | |
6937 | else if (scm_is_real (z)) | |
ad79736c AW |
6938 | return scm_from_double (sinh (scm_to_double (z))); |
6939 | else if (SCM_COMPLEXP (z)) | |
6940 | { double x, y; | |
6941 | x = SCM_COMPLEX_REAL (z); | |
6942 | y = SCM_COMPLEX_IMAG (z); | |
6943 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
6944 | cosh (x) * sin (y)); | |
6945 | } | |
6946 | else | |
6947 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
6948 | } | |
6949 | #undef FUNC_NAME | |
6950 | ||
6951 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
6952 | (SCM z), | |
6953 | "Compute the hyperbolic cosine of @var{z}.") | |
6954 | #define FUNC_NAME s_scm_cosh | |
6955 | { | |
8deddc94 MW |
6956 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6957 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
6958 | else if (scm_is_real (z)) | |
ad79736c AW |
6959 | return scm_from_double (cosh (scm_to_double (z))); |
6960 | else if (SCM_COMPLEXP (z)) | |
6961 | { double x, y; | |
6962 | x = SCM_COMPLEX_REAL (z); | |
6963 | y = SCM_COMPLEX_IMAG (z); | |
6964 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
6965 | sinh (x) * sin (y)); | |
6966 | } | |
6967 | else | |
6968 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
6969 | } | |
6970 | #undef FUNC_NAME | |
6971 | ||
6972 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
6973 | (SCM z), | |
6974 | "Compute the hyperbolic tangent of @var{z}.") | |
6975 | #define FUNC_NAME s_scm_tanh | |
6976 | { | |
8deddc94 MW |
6977 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
6978 | return z; /* tanh(exact0) = exact0 */ | |
6979 | else if (scm_is_real (z)) | |
ad79736c AW |
6980 | return scm_from_double (tanh (scm_to_double (z))); |
6981 | else if (SCM_COMPLEXP (z)) | |
6982 | { double x, y, w; | |
6983 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
6984 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
6985 | w = cosh (x) + cos (y); | |
6986 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
6987 | if (w == 0.0) | |
6988 | scm_num_overflow (s_scm_tanh); | |
6989 | #endif | |
6990 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
6991 | } | |
6992 | else | |
6993 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
6994 | } | |
6995 | #undef FUNC_NAME | |
6996 | ||
6997 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
6998 | (SCM z), | |
6999 | "Compute the arc sine of @var{z}.") | |
7000 | #define FUNC_NAME s_scm_asin | |
7001 | { | |
8deddc94 MW |
7002 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
7003 | return z; /* asin(exact0) = exact0 */ | |
7004 | else if (scm_is_real (z)) | |
ad79736c AW |
7005 | { |
7006 | double w = scm_to_double (z); | |
7007 | if (w >= -1.0 && w <= 1.0) | |
7008 | return scm_from_double (asin (w)); | |
7009 | else | |
7010 | return scm_product (scm_c_make_rectangular (0, -1), | |
7011 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
7012 | } | |
7013 | else if (SCM_COMPLEXP (z)) | |
7014 | { double x, y; | |
7015 | x = SCM_COMPLEX_REAL (z); | |
7016 | y = SCM_COMPLEX_IMAG (z); | |
7017 | return scm_product (scm_c_make_rectangular (0, -1), | |
7018 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
7019 | } | |
7020 | else | |
7021 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
7022 | } | |
7023 | #undef FUNC_NAME | |
7024 | ||
7025 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
7026 | (SCM z), | |
7027 | "Compute the arc cosine of @var{z}.") | |
7028 | #define FUNC_NAME s_scm_acos | |
7029 | { | |
8deddc94 MW |
7030 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
7031 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
7032 | else if (scm_is_real (z)) | |
ad79736c AW |
7033 | { |
7034 | double w = scm_to_double (z); | |
7035 | if (w >= -1.0 && w <= 1.0) | |
7036 | return scm_from_double (acos (w)); | |
7037 | else | |
7038 | return scm_sum (scm_from_double (acos (0.0)), | |
7039 | scm_product (scm_c_make_rectangular (0, 1), | |
7040 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
7041 | } | |
7042 | else if (SCM_COMPLEXP (z)) | |
7043 | { double x, y; | |
7044 | x = SCM_COMPLEX_REAL (z); | |
7045 | y = SCM_COMPLEX_IMAG (z); | |
7046 | return scm_sum (scm_from_double (acos (0.0)), | |
7047 | scm_product (scm_c_make_rectangular (0, 1), | |
7048 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
7049 | } | |
7050 | else | |
7051 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
7052 | } | |
7053 | #undef FUNC_NAME | |
7054 | ||
7055 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
7056 | (SCM z, SCM y), | |
7057 | "With one argument, compute the arc tangent of @var{z}.\n" | |
7058 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
7059 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
7060 | #define FUNC_NAME s_scm_atan | |
7061 | { | |
7062 | if (SCM_UNBNDP (y)) | |
7063 | { | |
8deddc94 MW |
7064 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
7065 | return z; /* atan(exact0) = exact0 */ | |
7066 | else if (scm_is_real (z)) | |
ad79736c AW |
7067 | return scm_from_double (atan (scm_to_double (z))); |
7068 | else if (SCM_COMPLEXP (z)) | |
7069 | { | |
7070 | double v, w; | |
7071 | v = SCM_COMPLEX_REAL (z); | |
7072 | w = SCM_COMPLEX_IMAG (z); | |
7073 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
7074 | scm_c_make_rectangular (v, w + 1.0))), | |
7075 | scm_c_make_rectangular (0, 2)); | |
7076 | } | |
7077 | else | |
18104cac | 7078 | SCM_WTA_DISPATCH_1 (g_scm_atan, z, SCM_ARG1, s_scm_atan); |
ad79736c AW |
7079 | } |
7080 | else if (scm_is_real (z)) | |
7081 | { | |
7082 | if (scm_is_real (y)) | |
7083 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
7084 | else | |
7085 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
7086 | } | |
7087 | else | |
7088 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
7089 | } | |
7090 | #undef FUNC_NAME | |
7091 | ||
7092 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
7093 | (SCM z), | |
7094 | "Compute the inverse hyperbolic sine of @var{z}.") | |
7095 | #define FUNC_NAME s_scm_sys_asinh | |
7096 | { | |
8deddc94 MW |
7097 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
7098 | return z; /* asinh(exact0) = exact0 */ | |
7099 | else if (scm_is_real (z)) | |
ad79736c AW |
7100 | return scm_from_double (asinh (scm_to_double (z))); |
7101 | else if (scm_is_number (z)) | |
7102 | return scm_log (scm_sum (z, | |
7103 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 7104 | SCM_INUM1)))); |
ad79736c AW |
7105 | else |
7106 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
7107 | } | |
7108 | #undef FUNC_NAME | |
7109 | ||
7110 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
7111 | (SCM z), | |
7112 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
7113 | #define FUNC_NAME s_scm_sys_acosh | |
7114 | { | |
8deddc94 MW |
7115 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
7116 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
7117 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
7118 | return scm_from_double (acosh (scm_to_double (z))); |
7119 | else if (scm_is_number (z)) | |
7120 | return scm_log (scm_sum (z, | |
7121 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 7122 | SCM_INUM1)))); |
ad79736c AW |
7123 | else |
7124 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
7125 | } | |
7126 | #undef FUNC_NAME | |
7127 | ||
7128 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
7129 | (SCM z), | |
7130 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
7131 | #define FUNC_NAME s_scm_sys_atanh | |
7132 | { | |
8deddc94 MW |
7133 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
7134 | return z; /* atanh(exact0) = exact0 */ | |
7135 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
7136 | return scm_from_double (atanh (scm_to_double (z))); |
7137 | else if (scm_is_number (z)) | |
cff5fa33 MW |
7138 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
7139 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
7140 | SCM_I_MAKINUM (2)); |
7141 | else | |
7142 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 7143 | } |
1bbd0b84 | 7144 | #undef FUNC_NAME |
0f2d19dd | 7145 | |
8507ec80 MV |
7146 | SCM |
7147 | scm_c_make_rectangular (double re, double im) | |
7148 | { | |
c7218482 | 7149 | SCM z; |
03604fcf | 7150 | |
c7218482 MW |
7151 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
7152 | "complex")); | |
7153 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); | |
7154 | SCM_COMPLEX_REAL (z) = re; | |
7155 | SCM_COMPLEX_IMAG (z) = im; | |
7156 | return z; | |
8507ec80 | 7157 | } |
0f2d19dd | 7158 | |
a1ec6916 | 7159 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
7160 | (SCM real_part, SCM imaginary_part), |
7161 | "Return a complex number constructed of the given @var{real-part} " | |
7162 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 7163 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 7164 | { |
ad79736c AW |
7165 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
7166 | SCM_ARG1, FUNC_NAME, "real"); | |
7167 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
7168 | SCM_ARG2, FUNC_NAME, "real"); | |
c7218482 MW |
7169 | |
7170 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ | |
7171 | if (scm_is_eq (imaginary_part, SCM_INUM0)) | |
7172 | return real_part; | |
7173 | else | |
7174 | return scm_c_make_rectangular (scm_to_double (real_part), | |
7175 | scm_to_double (imaginary_part)); | |
0f2d19dd | 7176 | } |
1bbd0b84 | 7177 | #undef FUNC_NAME |
0f2d19dd | 7178 | |
8507ec80 MV |
7179 | SCM |
7180 | scm_c_make_polar (double mag, double ang) | |
7181 | { | |
7182 | double s, c; | |
5e647d08 LC |
7183 | |
7184 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
7185 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
7186 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
7187 | details. */ | |
7188 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
7189 | sincos (ang, &s, &c); |
7190 | #else | |
7191 | s = sin (ang); | |
7192 | c = cos (ang); | |
7193 | #endif | |
9d427b2c MW |
7194 | |
7195 | /* If s and c are NaNs, this indicates that the angle is a NaN, | |
7196 | infinite, or perhaps simply too large to determine its value | |
7197 | mod 2*pi. However, we know something that the floating-point | |
7198 | implementation doesn't know: We know that s and c are finite. | |
7199 | Therefore, if the magnitude is zero, return a complex zero. | |
7200 | ||
7201 | The reason we check for the NaNs instead of using this case | |
7202 | whenever mag == 0.0 is because when the angle is known, we'd | |
7203 | like to return the correct kind of non-real complex zero: | |
7204 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending | |
7205 | on which quadrant the angle is in. | |
7206 | */ | |
7207 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) | |
7208 | return scm_c_make_rectangular (0.0, 0.0); | |
7209 | else | |
7210 | return scm_c_make_rectangular (mag * c, mag * s); | |
8507ec80 | 7211 | } |
0f2d19dd | 7212 | |
a1ec6916 | 7213 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
c7218482 MW |
7214 | (SCM mag, SCM ang), |
7215 | "Return the complex number @var{mag} * e^(i * @var{ang}).") | |
1bbd0b84 | 7216 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 7217 | { |
c7218482 MW |
7218 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
7219 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); | |
7220 | ||
7221 | /* If mag is exact0, return exact0 */ | |
7222 | if (scm_is_eq (mag, SCM_INUM0)) | |
7223 | return SCM_INUM0; | |
7224 | /* Return a real if ang is exact0 */ | |
7225 | else if (scm_is_eq (ang, SCM_INUM0)) | |
7226 | return mag; | |
7227 | else | |
7228 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); | |
0f2d19dd | 7229 | } |
1bbd0b84 | 7230 | #undef FUNC_NAME |
0f2d19dd JB |
7231 | |
7232 | ||
2519490c MW |
7233 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
7234 | (SCM z), | |
7235 | "Return the real part of the number @var{z}.") | |
7236 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 7237 | { |
2519490c | 7238 | if (SCM_COMPLEXP (z)) |
55f26379 | 7239 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 7240 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 7241 | return z; |
0aacf84e | 7242 | else |
2519490c | 7243 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 7244 | } |
2519490c | 7245 | #undef FUNC_NAME |
0f2d19dd JB |
7246 | |
7247 | ||
2519490c MW |
7248 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
7249 | (SCM z), | |
7250 | "Return the imaginary part of the number @var{z}.") | |
7251 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 7252 | { |
2519490c MW |
7253 | if (SCM_COMPLEXP (z)) |
7254 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
c7218482 | 7255 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 7256 | return SCM_INUM0; |
0aacf84e | 7257 | else |
2519490c | 7258 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 7259 | } |
2519490c | 7260 | #undef FUNC_NAME |
0f2d19dd | 7261 | |
2519490c MW |
7262 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
7263 | (SCM z), | |
7264 | "Return the numerator of the number @var{z}.") | |
7265 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 7266 | { |
2519490c | 7267 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
7268 | return z; |
7269 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 7270 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
7271 | else if (SCM_REALP (z)) |
7272 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
7273 | else | |
2519490c | 7274 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 7275 | } |
2519490c | 7276 | #undef FUNC_NAME |
f92e85f7 MV |
7277 | |
7278 | ||
2519490c MW |
7279 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
7280 | (SCM z), | |
7281 | "Return the denominator of the number @var{z}.") | |
7282 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 7283 | { |
2519490c | 7284 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 7285 | return SCM_INUM1; |
f92e85f7 | 7286 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 7287 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
7288 | else if (SCM_REALP (z)) |
7289 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
7290 | else | |
2519490c | 7291 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
f92e85f7 | 7292 | } |
2519490c | 7293 | #undef FUNC_NAME |
0f2d19dd | 7294 | |
2519490c MW |
7295 | |
7296 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
7297 | (SCM z), | |
7298 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
7299 | "@code{abs} for real arguments, but also allows complex numbers.") | |
7300 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 7301 | { |
e11e83f3 | 7302 | if (SCM_I_INUMP (z)) |
0aacf84e | 7303 | { |
e25f3727 | 7304 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
7305 | if (zz >= 0) |
7306 | return z; | |
7307 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 7308 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 7309 | else |
e25f3727 | 7310 | return scm_i_inum2big (-zz); |
5986c47d | 7311 | } |
0aacf84e MD |
7312 | else if (SCM_BIGP (z)) |
7313 | { | |
7314 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
7315 | scm_remember_upto_here_1 (z); | |
7316 | if (sgn < 0) | |
7317 | return scm_i_clonebig (z, 0); | |
7318 | else | |
7319 | return z; | |
5986c47d | 7320 | } |
0aacf84e | 7321 | else if (SCM_REALP (z)) |
55f26379 | 7322 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 7323 | else if (SCM_COMPLEXP (z)) |
55f26379 | 7324 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
7325 | else if (SCM_FRACTIONP (z)) |
7326 | { | |
73e4de09 | 7327 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 7328 | return z; |
cba42c93 | 7329 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
7330 | SCM_FRACTION_DENOMINATOR (z)); |
7331 | } | |
0aacf84e | 7332 | else |
2519490c | 7333 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
0f2d19dd | 7334 | } |
2519490c | 7335 | #undef FUNC_NAME |
0f2d19dd JB |
7336 | |
7337 | ||
2519490c MW |
7338 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
7339 | (SCM z), | |
7340 | "Return the angle of the complex number @var{z}.") | |
7341 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 7342 | { |
c8ae173e | 7343 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 7344 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
7345 | But if atan2 follows the floating point rounding mode, then the value |
7346 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 7347 | if (SCM_I_INUMP (z)) |
0aacf84e | 7348 | { |
e11e83f3 | 7349 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 7350 | return flo0; |
0aacf84e | 7351 | else |
55f26379 | 7352 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 7353 | } |
0aacf84e MD |
7354 | else if (SCM_BIGP (z)) |
7355 | { | |
7356 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
7357 | scm_remember_upto_here_1 (z); | |
7358 | if (sgn < 0) | |
55f26379 | 7359 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 7360 | else |
e7efe8e7 | 7361 | return flo0; |
0f2d19dd | 7362 | } |
0aacf84e | 7363 | else if (SCM_REALP (z)) |
c8ae173e KR |
7364 | { |
7365 | if (SCM_REAL_VALUE (z) >= 0) | |
e7efe8e7 | 7366 | return flo0; |
c8ae173e | 7367 | else |
55f26379 | 7368 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 7369 | } |
0aacf84e | 7370 | else if (SCM_COMPLEXP (z)) |
55f26379 | 7371 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
7372 | else if (SCM_FRACTIONP (z)) |
7373 | { | |
73e4de09 | 7374 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 7375 | return flo0; |
55f26379 | 7376 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 7377 | } |
0aacf84e | 7378 | else |
2519490c | 7379 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 7380 | } |
2519490c | 7381 | #undef FUNC_NAME |
0f2d19dd JB |
7382 | |
7383 | ||
2519490c MW |
7384 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
7385 | (SCM z), | |
7386 | "Convert the number @var{z} to its inexact representation.\n") | |
7387 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 7388 | { |
e11e83f3 | 7389 | if (SCM_I_INUMP (z)) |
55f26379 | 7390 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 7391 | else if (SCM_BIGP (z)) |
55f26379 | 7392 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 7393 | else if (SCM_FRACTIONP (z)) |
55f26379 | 7394 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
7395 | else if (SCM_INEXACTP (z)) |
7396 | return z; | |
7397 | else | |
2519490c | 7398 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
3c9a524f | 7399 | } |
2519490c | 7400 | #undef FUNC_NAME |
3c9a524f DH |
7401 | |
7402 | ||
2519490c MW |
7403 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
7404 | (SCM z), | |
7405 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 7406 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 7407 | { |
c7218482 | 7408 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f872b822 | 7409 | return z; |
c7218482 | 7410 | else |
0aacf84e | 7411 | { |
c7218482 MW |
7412 | double val; |
7413 | ||
7414 | if (SCM_REALP (z)) | |
7415 | val = SCM_REAL_VALUE (z); | |
7416 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) | |
7417 | val = SCM_COMPLEX_REAL (z); | |
7418 | else | |
7419 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); | |
7420 | ||
7421 | if (!SCM_LIKELY (DOUBLE_IS_FINITE (val))) | |
f92e85f7 | 7422 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 7423 | else |
f92e85f7 MV |
7424 | { |
7425 | mpq_t frac; | |
7426 | SCM q; | |
7427 | ||
7428 | mpq_init (frac); | |
c7218482 | 7429 | mpq_set_d (frac, val); |
cba42c93 | 7430 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
c7218482 | 7431 | scm_i_mpz2num (mpq_denref (frac))); |
f92e85f7 | 7432 | |
cba42c93 | 7433 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
7434 | for frac... |
7435 | */ | |
7436 | mpq_clear (frac); | |
7437 | return q; | |
7438 | } | |
c2ff8ab0 | 7439 | } |
0f2d19dd | 7440 | } |
1bbd0b84 | 7441 | #undef FUNC_NAME |
0f2d19dd | 7442 | |
f92e85f7 | 7443 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
7444 | (SCM x, SCM eps), |
7445 | "Returns the @emph{simplest} rational number differing\n" | |
7446 | "from @var{x} by no more than @var{eps}.\n" | |
7447 | "\n" | |
7448 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
7449 | "exact result when both its arguments are exact. Thus, you might need\n" | |
7450 | "to use @code{inexact->exact} on the arguments.\n" | |
7451 | "\n" | |
7452 | "@lisp\n" | |
7453 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
7454 | "@result{} 6/5\n" | |
7455 | "@end lisp") | |
f92e85f7 MV |
7456 | #define FUNC_NAME s_scm_rationalize |
7457 | { | |
605f6980 MW |
7458 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
7459 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
7460 | eps = scm_abs (eps); | |
7461 | if (scm_is_false (scm_positive_p (eps))) | |
7462 | { | |
7463 | /* eps is either zero or a NaN */ | |
7464 | if (scm_is_true (scm_nan_p (eps))) | |
7465 | return scm_nan (); | |
7466 | else if (SCM_INEXACTP (eps)) | |
7467 | return scm_exact_to_inexact (x); | |
7468 | else | |
7469 | return x; | |
7470 | } | |
7471 | else if (scm_is_false (scm_finite_p (eps))) | |
7472 | { | |
7473 | if (scm_is_true (scm_finite_p (x))) | |
7474 | return flo0; | |
7475 | else | |
7476 | return scm_nan (); | |
7477 | } | |
7478 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 7479 | return x; |
605f6980 MW |
7480 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
7481 | scm_ceiling (scm_difference (x, eps))))) | |
7482 | { | |
7483 | /* There's an integer within range; we want the one closest to zero */ | |
7484 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
7485 | { | |
7486 | /* zero is within range */ | |
7487 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
7488 | return flo0; | |
7489 | else | |
7490 | return SCM_INUM0; | |
7491 | } | |
7492 | else if (scm_is_true (scm_positive_p (x))) | |
7493 | return scm_ceiling (scm_difference (x, eps)); | |
7494 | else | |
7495 | return scm_floor (scm_sum (x, eps)); | |
7496 | } | |
7497 | else | |
f92e85f7 MV |
7498 | { |
7499 | /* Use continued fractions to find closest ratio. All | |
7500 | arithmetic is done with exact numbers. | |
7501 | */ | |
7502 | ||
7503 | SCM ex = scm_inexact_to_exact (x); | |
7504 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
7505 | SCM tt = SCM_INUM1; |
7506 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
7507 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
7508 | SCM rx; |
7509 | int i = 0; | |
7510 | ||
f92e85f7 MV |
7511 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
7512 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
7513 | ||
7514 | /* We stop after a million iterations just to be absolutely sure | |
7515 | that we don't go into an infinite loop. The process normally | |
7516 | converges after less than a dozen iterations. | |
7517 | */ | |
7518 | ||
f92e85f7 MV |
7519 | while (++i < 1000000) |
7520 | { | |
7521 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
7522 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
7523 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
7524 | scm_is_false | |
f92e85f7 | 7525 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 7526 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
7527 | { |
7528 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 7529 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
7530 | return scm_exact_to_inexact (res); |
7531 | else | |
7532 | return res; | |
7533 | } | |
f92e85f7 MV |
7534 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
7535 | SCM_UNDEFINED); | |
7536 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
7537 | a2 = a1; | |
7538 | b2 = b1; | |
7539 | a1 = a; | |
7540 | b1 = b; | |
7541 | } | |
7542 | scm_num_overflow (s_scm_rationalize); | |
7543 | } | |
f92e85f7 MV |
7544 | } |
7545 | #undef FUNC_NAME | |
7546 | ||
73e4de09 MV |
7547 | /* conversion functions */ |
7548 | ||
7549 | int | |
7550 | scm_is_integer (SCM val) | |
7551 | { | |
7552 | return scm_is_true (scm_integer_p (val)); | |
7553 | } | |
7554 | ||
7555 | int | |
7556 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
7557 | { | |
e11e83f3 | 7558 | if (SCM_I_INUMP (val)) |
73e4de09 | 7559 | { |
e11e83f3 | 7560 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
7561 | return n >= min && n <= max; |
7562 | } | |
7563 | else if (SCM_BIGP (val)) | |
7564 | { | |
7565 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
7566 | return 0; | |
7567 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
7568 | { |
7569 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
7570 | { | |
7571 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
7572 | return n >= min && n <= max; | |
7573 | } | |
7574 | else | |
7575 | return 0; | |
7576 | } | |
73e4de09 MV |
7577 | else |
7578 | { | |
d956fa6f MV |
7579 | scm_t_intmax n; |
7580 | size_t count; | |
73e4de09 | 7581 | |
d956fa6f MV |
7582 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
7583 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
7584 | return 0; | |
7585 | ||
7586 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
7587 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 7588 | |
d956fa6f | 7589 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 7590 | { |
d956fa6f MV |
7591 | if (n < 0) |
7592 | return 0; | |
73e4de09 | 7593 | } |
73e4de09 MV |
7594 | else |
7595 | { | |
d956fa6f MV |
7596 | n = -n; |
7597 | if (n >= 0) | |
7598 | return 0; | |
73e4de09 | 7599 | } |
d956fa6f MV |
7600 | |
7601 | return n >= min && n <= max; | |
73e4de09 MV |
7602 | } |
7603 | } | |
73e4de09 MV |
7604 | else |
7605 | return 0; | |
7606 | } | |
7607 | ||
7608 | int | |
7609 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
7610 | { | |
e11e83f3 | 7611 | if (SCM_I_INUMP (val)) |
73e4de09 | 7612 | { |
e11e83f3 | 7613 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
7614 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
7615 | } | |
7616 | else if (SCM_BIGP (val)) | |
7617 | { | |
7618 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
7619 | return 0; | |
7620 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
7621 | { |
7622 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
7623 | { | |
7624 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
7625 | return n >= min && n <= max; | |
7626 | } | |
7627 | else | |
7628 | return 0; | |
7629 | } | |
73e4de09 MV |
7630 | else |
7631 | { | |
d956fa6f MV |
7632 | scm_t_uintmax n; |
7633 | size_t count; | |
73e4de09 | 7634 | |
d956fa6f MV |
7635 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
7636 | return 0; | |
73e4de09 | 7637 | |
d956fa6f MV |
7638 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
7639 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 7640 | return 0; |
d956fa6f MV |
7641 | |
7642 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
7643 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 7644 | |
d956fa6f | 7645 | return n >= min && n <= max; |
73e4de09 MV |
7646 | } |
7647 | } | |
73e4de09 MV |
7648 | else |
7649 | return 0; | |
7650 | } | |
7651 | ||
1713d319 MV |
7652 | static void |
7653 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
7654 | { | |
7655 | scm_error (scm_out_of_range_key, | |
7656 | NULL, | |
7657 | "Value out of range ~S to ~S: ~S", | |
7658 | scm_list_3 (min, max, bad_val), | |
7659 | scm_list_1 (bad_val)); | |
7660 | } | |
7661 | ||
bfd7932e MV |
7662 | #define TYPE scm_t_intmax |
7663 | #define TYPE_MIN min | |
7664 | #define TYPE_MAX max | |
7665 | #define SIZEOF_TYPE 0 | |
7666 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
7667 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
7668 | #include "libguile/conv-integer.i.c" | |
7669 | ||
7670 | #define TYPE scm_t_uintmax | |
7671 | #define TYPE_MIN min | |
7672 | #define TYPE_MAX max | |
7673 | #define SIZEOF_TYPE 0 | |
7674 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
7675 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
7676 | #include "libguile/conv-uinteger.i.c" | |
7677 | ||
7678 | #define TYPE scm_t_int8 | |
7679 | #define TYPE_MIN SCM_T_INT8_MIN | |
7680 | #define TYPE_MAX SCM_T_INT8_MAX | |
7681 | #define SIZEOF_TYPE 1 | |
7682 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
7683 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
7684 | #include "libguile/conv-integer.i.c" | |
7685 | ||
7686 | #define TYPE scm_t_uint8 | |
7687 | #define TYPE_MIN 0 | |
7688 | #define TYPE_MAX SCM_T_UINT8_MAX | |
7689 | #define SIZEOF_TYPE 1 | |
7690 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
7691 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
7692 | #include "libguile/conv-uinteger.i.c" | |
7693 | ||
7694 | #define TYPE scm_t_int16 | |
7695 | #define TYPE_MIN SCM_T_INT16_MIN | |
7696 | #define TYPE_MAX SCM_T_INT16_MAX | |
7697 | #define SIZEOF_TYPE 2 | |
7698 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
7699 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
7700 | #include "libguile/conv-integer.i.c" | |
7701 | ||
7702 | #define TYPE scm_t_uint16 | |
7703 | #define TYPE_MIN 0 | |
7704 | #define TYPE_MAX SCM_T_UINT16_MAX | |
7705 | #define SIZEOF_TYPE 2 | |
7706 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
7707 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
7708 | #include "libguile/conv-uinteger.i.c" | |
7709 | ||
7710 | #define TYPE scm_t_int32 | |
7711 | #define TYPE_MIN SCM_T_INT32_MIN | |
7712 | #define TYPE_MAX SCM_T_INT32_MAX | |
7713 | #define SIZEOF_TYPE 4 | |
7714 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
7715 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
7716 | #include "libguile/conv-integer.i.c" | |
7717 | ||
7718 | #define TYPE scm_t_uint32 | |
7719 | #define TYPE_MIN 0 | |
7720 | #define TYPE_MAX SCM_T_UINT32_MAX | |
7721 | #define SIZEOF_TYPE 4 | |
7722 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
7723 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
7724 | #include "libguile/conv-uinteger.i.c" | |
7725 | ||
904a78f1 MG |
7726 | #define TYPE scm_t_wchar |
7727 | #define TYPE_MIN (scm_t_int32)-1 | |
7728 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
7729 | #define SIZEOF_TYPE 4 | |
7730 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
7731 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
7732 | #include "libguile/conv-integer.i.c" | |
7733 | ||
bfd7932e MV |
7734 | #define TYPE scm_t_int64 |
7735 | #define TYPE_MIN SCM_T_INT64_MIN | |
7736 | #define TYPE_MAX SCM_T_INT64_MAX | |
7737 | #define SIZEOF_TYPE 8 | |
7738 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
7739 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
7740 | #include "libguile/conv-integer.i.c" | |
7741 | ||
7742 | #define TYPE scm_t_uint64 | |
7743 | #define TYPE_MIN 0 | |
7744 | #define TYPE_MAX SCM_T_UINT64_MAX | |
7745 | #define SIZEOF_TYPE 8 | |
7746 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
7747 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
7748 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 7749 | |
cd036260 MV |
7750 | void |
7751 | scm_to_mpz (SCM val, mpz_t rop) | |
7752 | { | |
7753 | if (SCM_I_INUMP (val)) | |
7754 | mpz_set_si (rop, SCM_I_INUM (val)); | |
7755 | else if (SCM_BIGP (val)) | |
7756 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
7757 | else | |
7758 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
7759 | } | |
7760 | ||
7761 | SCM | |
7762 | scm_from_mpz (mpz_t val) | |
7763 | { | |
7764 | return scm_i_mpz2num (val); | |
7765 | } | |
7766 | ||
73e4de09 MV |
7767 | int |
7768 | scm_is_real (SCM val) | |
7769 | { | |
7770 | return scm_is_true (scm_real_p (val)); | |
7771 | } | |
7772 | ||
55f26379 MV |
7773 | int |
7774 | scm_is_rational (SCM val) | |
7775 | { | |
7776 | return scm_is_true (scm_rational_p (val)); | |
7777 | } | |
7778 | ||
73e4de09 MV |
7779 | double |
7780 | scm_to_double (SCM val) | |
7781 | { | |
55f26379 MV |
7782 | if (SCM_I_INUMP (val)) |
7783 | return SCM_I_INUM (val); | |
7784 | else if (SCM_BIGP (val)) | |
7785 | return scm_i_big2dbl (val); | |
7786 | else if (SCM_FRACTIONP (val)) | |
7787 | return scm_i_fraction2double (val); | |
7788 | else if (SCM_REALP (val)) | |
7789 | return SCM_REAL_VALUE (val); | |
7790 | else | |
7a1aba42 | 7791 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
7792 | } |
7793 | ||
7794 | SCM | |
7795 | scm_from_double (double val) | |
7796 | { | |
978c52d1 LC |
7797 | SCM z; |
7798 | ||
7799 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
7800 | ||
7801 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 7802 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 7803 | |
55f26379 | 7804 | return z; |
73e4de09 MV |
7805 | } |
7806 | ||
220058a8 | 7807 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
7808 | |
7809 | float | |
e25f3727 | 7810 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 7811 | { |
220058a8 AW |
7812 | scm_c_issue_deprecation_warning |
7813 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
7814 | ||
55f26379 MV |
7815 | if (SCM_BIGP (num)) |
7816 | { | |
7817 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 7818 | if (!isinf (res)) |
55f26379 MV |
7819 | return res; |
7820 | else | |
7821 | scm_out_of_range (NULL, num); | |
7822 | } | |
7823 | else | |
7824 | return scm_to_double (num); | |
7825 | } | |
7826 | ||
7827 | double | |
e25f3727 | 7828 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 7829 | { |
220058a8 AW |
7830 | scm_c_issue_deprecation_warning |
7831 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
7832 | ||
55f26379 MV |
7833 | if (SCM_BIGP (num)) |
7834 | { | |
7835 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 7836 | if (!isinf (res)) |
55f26379 MV |
7837 | return res; |
7838 | else | |
7839 | scm_out_of_range (NULL, num); | |
7840 | } | |
7841 | else | |
7842 | return scm_to_double (num); | |
7843 | } | |
7844 | ||
7845 | #endif | |
7846 | ||
8507ec80 MV |
7847 | int |
7848 | scm_is_complex (SCM val) | |
7849 | { | |
7850 | return scm_is_true (scm_complex_p (val)); | |
7851 | } | |
7852 | ||
7853 | double | |
7854 | scm_c_real_part (SCM z) | |
7855 | { | |
7856 | if (SCM_COMPLEXP (z)) | |
7857 | return SCM_COMPLEX_REAL (z); | |
7858 | else | |
7859 | { | |
7860 | /* Use the scm_real_part to get proper error checking and | |
7861 | dispatching. | |
7862 | */ | |
7863 | return scm_to_double (scm_real_part (z)); | |
7864 | } | |
7865 | } | |
7866 | ||
7867 | double | |
7868 | scm_c_imag_part (SCM z) | |
7869 | { | |
7870 | if (SCM_COMPLEXP (z)) | |
7871 | return SCM_COMPLEX_IMAG (z); | |
7872 | else | |
7873 | { | |
7874 | /* Use the scm_imag_part to get proper error checking and | |
7875 | dispatching. The result will almost always be 0.0, but not | |
7876 | always. | |
7877 | */ | |
7878 | return scm_to_double (scm_imag_part (z)); | |
7879 | } | |
7880 | } | |
7881 | ||
7882 | double | |
7883 | scm_c_magnitude (SCM z) | |
7884 | { | |
7885 | return scm_to_double (scm_magnitude (z)); | |
7886 | } | |
7887 | ||
7888 | double | |
7889 | scm_c_angle (SCM z) | |
7890 | { | |
7891 | return scm_to_double (scm_angle (z)); | |
7892 | } | |
7893 | ||
7894 | int | |
7895 | scm_is_number (SCM z) | |
7896 | { | |
7897 | return scm_is_true (scm_number_p (z)); | |
7898 | } | |
7899 | ||
8ab3d8a0 KR |
7900 | |
7901 | /* In the following functions we dispatch to the real-arg funcs like log() | |
7902 | when we know the arg is real, instead of just handing everything to | |
7903 | clog() for instance. This is in case clog() doesn't optimize for a | |
7904 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
7905 | well use it to go straight to the applicable C func. */ | |
7906 | ||
2519490c MW |
7907 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
7908 | (SCM z), | |
7909 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
7910 | #define FUNC_NAME s_scm_log |
7911 | { | |
7912 | if (SCM_COMPLEXP (z)) | |
7913 | { | |
4b26c03e | 7914 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
7915 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
7916 | #else | |
7917 | double re = SCM_COMPLEX_REAL (z); | |
7918 | double im = SCM_COMPLEX_IMAG (z); | |
7919 | return scm_c_make_rectangular (log (hypot (re, im)), | |
7920 | atan2 (im, re)); | |
7921 | #endif | |
7922 | } | |
2519490c | 7923 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7924 | { |
7925 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
7926 | although the value itself overflows. */ | |
7927 | double re = scm_to_double (z); | |
7928 | double l = log (fabs (re)); | |
7929 | if (re >= 0.0) | |
7930 | return scm_from_double (l); | |
7931 | else | |
7932 | return scm_c_make_rectangular (l, M_PI); | |
7933 | } | |
2519490c MW |
7934 | else |
7935 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); | |
8ab3d8a0 KR |
7936 | } |
7937 | #undef FUNC_NAME | |
7938 | ||
7939 | ||
2519490c MW |
7940 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
7941 | (SCM z), | |
7942 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
7943 | #define FUNC_NAME s_scm_log10 |
7944 | { | |
7945 | if (SCM_COMPLEXP (z)) | |
7946 | { | |
7947 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
7948 | clog() and a multiply by M_LOG10E, rather than the fallback | |
7949 | log10+hypot+atan2.) */ | |
f328f862 LC |
7950 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
7951 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
7952 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
7953 | #else | |
7954 | double re = SCM_COMPLEX_REAL (z); | |
7955 | double im = SCM_COMPLEX_IMAG (z); | |
7956 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
7957 | M_LOG10E * atan2 (im, re)); | |
7958 | #endif | |
7959 | } | |
2519490c | 7960 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7961 | { |
7962 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
7963 | although the value itself overflows. */ | |
7964 | double re = scm_to_double (z); | |
7965 | double l = log10 (fabs (re)); | |
7966 | if (re >= 0.0) | |
7967 | return scm_from_double (l); | |
7968 | else | |
7969 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
7970 | } | |
2519490c MW |
7971 | else |
7972 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); | |
8ab3d8a0 KR |
7973 | } |
7974 | #undef FUNC_NAME | |
7975 | ||
7976 | ||
2519490c MW |
7977 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
7978 | (SCM z), | |
7979 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
7980 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
7981 | #define FUNC_NAME s_scm_exp |
7982 | { | |
7983 | if (SCM_COMPLEXP (z)) | |
7984 | { | |
4b26c03e | 7985 | #if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
7986 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
7987 | #else | |
7988 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
7989 | SCM_COMPLEX_IMAG (z)); | |
7990 | #endif | |
7991 | } | |
2519490c | 7992 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
7993 | { |
7994 | /* When z is a negative bignum the conversion to double overflows, | |
7995 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
7996 | return scm_from_double (exp (scm_to_double (z))); | |
7997 | } | |
2519490c MW |
7998 | else |
7999 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); | |
8ab3d8a0 KR |
8000 | } |
8001 | #undef FUNC_NAME | |
8002 | ||
8003 | ||
2519490c MW |
8004 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
8005 | (SCM z), | |
8006 | "Return the square root of @var{z}. Of the two possible roots\n" | |
ffb62a43 | 8007 | "(positive and negative), the one with positive real part\n" |
2519490c MW |
8008 | "is returned, or if that's zero then a positive imaginary part.\n" |
8009 | "Thus,\n" | |
8010 | "\n" | |
8011 | "@example\n" | |
8012 | "(sqrt 9.0) @result{} 3.0\n" | |
8013 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
8014 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
8015 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
8016 | "@end example") | |
8ab3d8a0 KR |
8017 | #define FUNC_NAME s_scm_sqrt |
8018 | { | |
2519490c | 8019 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 8020 | { |
f328f862 LC |
8021 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
8022 | && defined SCM_COMPLEX_VALUE | |
2519490c | 8023 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 8024 | #else |
2519490c MW |
8025 | double re = SCM_COMPLEX_REAL (z); |
8026 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
8027 | return scm_c_make_polar (sqrt (hypot (re, im)), |
8028 | 0.5 * atan2 (im, re)); | |
8029 | #endif | |
8030 | } | |
2519490c | 8031 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 8032 | { |
2519490c | 8033 | double xx = scm_to_double (z); |
8ab3d8a0 KR |
8034 | if (xx < 0) |
8035 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
8036 | else | |
8037 | return scm_from_double (sqrt (xx)); | |
8038 | } | |
2519490c MW |
8039 | else |
8040 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); | |
8ab3d8a0 KR |
8041 | } |
8042 | #undef FUNC_NAME | |
8043 | ||
8044 | ||
8045 | ||
0f2d19dd JB |
8046 | void |
8047 | scm_init_numbers () | |
0f2d19dd | 8048 | { |
0b799eea MV |
8049 | int i; |
8050 | ||
713a4259 KR |
8051 | mpz_init_set_si (z_negative_one, -1); |
8052 | ||
a261c0e9 DH |
8053 | /* It may be possible to tune the performance of some algorithms by using |
8054 | * the following constants to avoid the creation of bignums. Please, before | |
8055 | * using these values, remember the two rules of program optimization: | |
8056 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 8057 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 8058 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 8059 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 8060 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 8061 | |
f3ae5d60 MD |
8062 | scm_add_feature ("complex"); |
8063 | scm_add_feature ("inexact"); | |
e7efe8e7 | 8064 | flo0 = scm_from_double (0.0); |
0b799eea MV |
8065 | |
8066 | /* determine floating point precision */ | |
55f26379 | 8067 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
8068 | { |
8069 | init_dblprec(&scm_dblprec[i-2],i); | |
8070 | init_fx_radix(fx_per_radix[i-2],i); | |
8071 | } | |
f872b822 | 8072 | #ifdef DBL_DIG |
0b799eea | 8073 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 8074 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 8075 | #endif |
1be6b49c | 8076 | |
cff5fa33 | 8077 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 8078 | #include "libguile/numbers.x" |
0f2d19dd | 8079 | } |
89e00824 ML |
8080 | |
8081 | /* | |
8082 | Local Variables: | |
8083 | c-file-style: "gnu" | |
8084 | End: | |
8085 | */ |