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; |
a5f6b751 | 114 | static SCM flo_log10e; |
e7efe8e7 | 115 | |
34d19ef6 | 116 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 117 | |
56e55ac7 | 118 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
119 | * printed or scm_string representation of an inexact number. |
120 | */ | |
0b799eea | 121 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 122 | |
b127c712 | 123 | |
ad79736c AW |
124 | #if !defined (HAVE_ASINH) |
125 | static double asinh (double x) { return log (x + sqrt (x * x + 1)); } | |
126 | #endif | |
127 | #if !defined (HAVE_ACOSH) | |
128 | static double acosh (double x) { return log (x + sqrt (x * x - 1)); } | |
129 | #endif | |
130 | #if !defined (HAVE_ATANH) | |
131 | static double atanh (double x) { return 0.5 * log ((1 + x) / (1 - x)); } | |
132 | #endif | |
133 | ||
f8a8200b KR |
134 | /* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses |
135 | an explicit check. In some future gmp (don't know what version number), | |
136 | mpz_cmp_d is supposed to do this itself. */ | |
137 | #if 1 | |
b127c712 | 138 | #define xmpz_cmp_d(z, d) \ |
2e65b52f | 139 | (isinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) |
b127c712 KR |
140 | #else |
141 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
142 | #endif | |
143 | ||
f92e85f7 | 144 | |
4b26c03e | 145 | #if defined (GUILE_I) |
bca69a9f | 146 | #if HAVE_COMPLEX_DOUBLE |
8ab3d8a0 KR |
147 | |
148 | /* For an SCM object Z which is a complex number (ie. satisfies | |
149 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
150 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 151 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 152 | |
7a35784c | 153 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
8ab3d8a0 KR |
154 | |
155 | /* Convert a C "complex double" to an SCM value. */ | |
7a35784c | 156 | static inline SCM |
8ab3d8a0 KR |
157 | scm_from_complex_double (complex double z) |
158 | { | |
159 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
160 | } | |
bca69a9f | 161 | |
8ab3d8a0 | 162 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 163 | #endif /* GUILE_I */ |
8ab3d8a0 | 164 | |
0f2d19dd JB |
165 | \f |
166 | ||
713a4259 | 167 | static mpz_t z_negative_one; |
ac0c002c DH |
168 | |
169 | \f | |
864e7d42 LC |
170 | /* Clear the `mpz_t' embedded in bignum PTR. */ |
171 | static void | |
172 | finalize_bignum (GC_PTR ptr, GC_PTR data) | |
173 | { | |
174 | SCM bignum; | |
175 | ||
176 | bignum = PTR2SCM (ptr); | |
177 | mpz_clear (SCM_I_BIG_MPZ (bignum)); | |
178 | } | |
179 | ||
d017fcdf LC |
180 | /* Return a new uninitialized bignum. */ |
181 | static inline SCM | |
182 | make_bignum (void) | |
183 | { | |
184 | scm_t_bits *p; | |
864e7d42 LC |
185 | GC_finalization_proc prev_finalizer; |
186 | GC_PTR prev_finalizer_data; | |
d017fcdf LC |
187 | |
188 | /* Allocate one word for the type tag and enough room for an `mpz_t'. */ | |
189 | p = scm_gc_malloc_pointerless (sizeof (scm_t_bits) + sizeof (mpz_t), | |
190 | "bignum"); | |
191 | p[0] = scm_tc16_big; | |
192 | ||
864e7d42 LC |
193 | GC_REGISTER_FINALIZER_NO_ORDER (p, finalize_bignum, NULL, |
194 | &prev_finalizer, | |
195 | &prev_finalizer_data); | |
196 | ||
d017fcdf LC |
197 | return SCM_PACK (p); |
198 | } | |
ac0c002c | 199 | |
864e7d42 | 200 | |
189171c5 | 201 | SCM |
ca46fb90 RB |
202 | scm_i_mkbig () |
203 | { | |
204 | /* Return a newly created bignum. */ | |
d017fcdf | 205 | SCM z = make_bignum (); |
ca46fb90 RB |
206 | mpz_init (SCM_I_BIG_MPZ (z)); |
207 | return z; | |
208 | } | |
209 | ||
e25f3727 AW |
210 | static SCM |
211 | scm_i_inum2big (scm_t_inum x) | |
212 | { | |
213 | /* Return a newly created bignum initialized to X. */ | |
214 | SCM z = make_bignum (); | |
215 | #if SIZEOF_VOID_P == SIZEOF_LONG | |
216 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
217 | #else | |
218 | /* Note that in this case, you'll also have to check all mpz_*_ui and | |
219 | mpz_*_si invocations in Guile. */ | |
220 | #error creation of mpz not implemented for this inum size | |
221 | #endif | |
222 | return z; | |
223 | } | |
224 | ||
189171c5 | 225 | SCM |
c71b0706 MV |
226 | scm_i_long2big (long x) |
227 | { | |
228 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 229 | SCM z = make_bignum (); |
c71b0706 MV |
230 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); |
231 | return z; | |
232 | } | |
233 | ||
189171c5 | 234 | SCM |
c71b0706 MV |
235 | scm_i_ulong2big (unsigned long x) |
236 | { | |
237 | /* Return a newly created bignum initialized to X. */ | |
d017fcdf | 238 | SCM z = make_bignum (); |
c71b0706 MV |
239 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); |
240 | return z; | |
241 | } | |
242 | ||
189171c5 | 243 | SCM |
ca46fb90 RB |
244 | scm_i_clonebig (SCM src_big, int same_sign_p) |
245 | { | |
246 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
d017fcdf | 247 | SCM z = make_bignum (); |
ca46fb90 | 248 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); |
0aacf84e MD |
249 | if (!same_sign_p) |
250 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
251 | return z; |
252 | } | |
253 | ||
189171c5 | 254 | int |
ca46fb90 RB |
255 | scm_i_bigcmp (SCM x, SCM y) |
256 | { | |
257 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
258 | /* presume we already know x and y are bignums */ | |
259 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
260 | scm_remember_upto_here_2 (x, y); | |
261 | return result; | |
262 | } | |
263 | ||
189171c5 | 264 | SCM |
ca46fb90 RB |
265 | scm_i_dbl2big (double d) |
266 | { | |
267 | /* results are only defined if d is an integer */ | |
d017fcdf | 268 | SCM z = make_bignum (); |
ca46fb90 RB |
269 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); |
270 | return z; | |
271 | } | |
272 | ||
f92e85f7 MV |
273 | /* Convert a integer in double representation to a SCM number. */ |
274 | ||
189171c5 | 275 | SCM |
f92e85f7 MV |
276 | scm_i_dbl2num (double u) |
277 | { | |
278 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
279 | powers of 2, so there's no rounding when making "double" values | |
280 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
281 | get rounded on a 64-bit machine, hence the "+1". | |
282 | ||
283 | The use of floor() to force to an integer value ensures we get a | |
284 | "numerically closest" value without depending on how a | |
285 | double->long cast or how mpz_set_d will round. For reference, | |
286 | double->long probably follows the hardware rounding mode, | |
287 | mpz_set_d truncates towards zero. */ | |
288 | ||
289 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
290 | representable as a double? */ | |
291 | ||
292 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
293 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
e25f3727 | 294 | return SCM_I_MAKINUM ((scm_t_inum) u); |
f92e85f7 MV |
295 | else |
296 | return scm_i_dbl2big (u); | |
297 | } | |
298 | ||
089c9a59 KR |
299 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
300 | with R5RS exact->inexact. | |
301 | ||
302 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
303 | (ie. truncate towards zero), then adjust to get the closest double by |
304 | examining the next lower bit and adding 1 (to the absolute value) if | |
305 | necessary. | |
306 | ||
307 | Bignums exactly half way between representable doubles are rounded to the | |
308 | next higher absolute value (ie. away from zero). This seems like an | |
309 | adequate interpretation of R5RS "numerically closest", and it's easier | |
310 | and faster than a full "nearest-even" style. | |
311 | ||
312 | The bit test must be done on the absolute value of the mpz_t, which means | |
313 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
314 | negatives as twos complement. | |
315 | ||
316 | In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up | |
317 | following the hardware rounding mode, but applied to the absolute value | |
318 | of the mpz_t operand. This is not what we want so we put the high | |
319 | DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when, | |
320 | mpz_get_d is supposed to always truncate towards zero. | |
321 | ||
322 | ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3 | |
323 | is a slowdown. It'd be faster to pick out the relevant high bits with | |
324 | mpz_getlimbn if we could be bothered coding that, and if the new | |
325 | truncating gmp doesn't come out. */ | |
089c9a59 KR |
326 | |
327 | double | |
ca46fb90 RB |
328 | scm_i_big2dbl (SCM b) |
329 | { | |
089c9a59 KR |
330 | double result; |
331 | size_t bits; | |
332 | ||
333 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
334 | ||
f8a8200b | 335 | #if 1 |
089c9a59 | 336 | { |
f8a8200b | 337 | /* Current GMP, eg. 4.1.3, force truncation towards zero */ |
089c9a59 KR |
338 | mpz_t tmp; |
339 | if (bits > DBL_MANT_DIG) | |
340 | { | |
341 | size_t shift = bits - DBL_MANT_DIG; | |
342 | mpz_init2 (tmp, DBL_MANT_DIG); | |
343 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
344 | result = ldexp (mpz_get_d (tmp), shift); | |
345 | mpz_clear (tmp); | |
346 | } | |
347 | else | |
348 | { | |
349 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
350 | } | |
351 | } | |
352 | #else | |
f8a8200b | 353 | /* Future GMP */ |
089c9a59 KR |
354 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
355 | #endif | |
356 | ||
357 | if (bits > DBL_MANT_DIG) | |
358 | { | |
359 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
360 | /* test bit number "pos" in absolute value */ | |
361 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
362 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
363 | { | |
364 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
365 | } | |
366 | } | |
367 | ||
ca46fb90 RB |
368 | scm_remember_upto_here_1 (b); |
369 | return result; | |
370 | } | |
371 | ||
189171c5 | 372 | SCM |
ca46fb90 RB |
373 | scm_i_normbig (SCM b) |
374 | { | |
375 | /* convert a big back to a fixnum if it'll fit */ | |
376 | /* presume b is a bignum */ | |
377 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
378 | { | |
e25f3727 | 379 | scm_t_inum val = mpz_get_si (SCM_I_BIG_MPZ (b)); |
ca46fb90 | 380 | if (SCM_FIXABLE (val)) |
d956fa6f | 381 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
382 | } |
383 | return b; | |
384 | } | |
f872b822 | 385 | |
f92e85f7 MV |
386 | static SCM_C_INLINE_KEYWORD SCM |
387 | scm_i_mpz2num (mpz_t b) | |
388 | { | |
389 | /* convert a mpz number to a SCM number. */ | |
390 | if (mpz_fits_slong_p (b)) | |
391 | { | |
e25f3727 | 392 | scm_t_inum val = mpz_get_si (b); |
f92e85f7 | 393 | if (SCM_FIXABLE (val)) |
d956fa6f | 394 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
395 | } |
396 | ||
397 | { | |
d017fcdf | 398 | SCM z = make_bignum (); |
f92e85f7 MV |
399 | mpz_init_set (SCM_I_BIG_MPZ (z), b); |
400 | return z; | |
401 | } | |
402 | } | |
403 | ||
404 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
405 | static SCM scm_divide2real (SCM x, SCM y); | |
406 | ||
cba42c93 MV |
407 | static SCM |
408 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 409 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 410 | { |
c60e130c MV |
411 | /* First make sure the arguments are proper. |
412 | */ | |
e11e83f3 | 413 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 414 | { |
bc36d050 | 415 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 416 | scm_num_overflow ("make-ratio"); |
cff5fa33 | 417 | if (scm_is_eq (denominator, SCM_INUM1)) |
f92e85f7 MV |
418 | return numerator; |
419 | } | |
420 | else | |
421 | { | |
422 | if (!(SCM_BIGP(denominator))) | |
423 | SCM_WRONG_TYPE_ARG (2, denominator); | |
424 | } | |
e11e83f3 | 425 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
426 | SCM_WRONG_TYPE_ARG (1, numerator); |
427 | ||
428 | /* Then flip signs so that the denominator is positive. | |
429 | */ | |
73e4de09 | 430 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
431 | { |
432 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
433 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
434 | } | |
435 | ||
436 | /* Now consider for each of the four fixnum/bignum combinations | |
437 | whether the rational number is really an integer. | |
438 | */ | |
e11e83f3 | 439 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 440 | { |
e25f3727 | 441 | scm_t_inum x = SCM_I_INUM (numerator); |
bc36d050 | 442 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 443 | return SCM_INUM0; |
e11e83f3 | 444 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 445 | { |
e25f3727 | 446 | scm_t_inum y; |
e11e83f3 | 447 | y = SCM_I_INUM (denominator); |
f92e85f7 | 448 | if (x == y) |
cff5fa33 | 449 | return SCM_INUM1; |
f92e85f7 | 450 | if ((x % y) == 0) |
d956fa6f | 451 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 452 | } |
dd5130ca KR |
453 | else |
454 | { | |
455 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
456 | of that value for the denominator, as a bignum. Apart from |
457 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
458 | integer. */ | |
459 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
460 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
461 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 462 | return SCM_I_MAKINUM(-1); |
dd5130ca | 463 | } |
f92e85f7 | 464 | } |
c60e130c | 465 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 466 | { |
e11e83f3 | 467 | if (SCM_I_INUMP (denominator)) |
c60e130c | 468 | { |
e25f3727 | 469 | scm_t_inum yy = SCM_I_INUM (denominator); |
c60e130c MV |
470 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
471 | return scm_divide (numerator, denominator); | |
472 | } | |
473 | else | |
f92e85f7 | 474 | { |
bc36d050 | 475 | if (scm_is_eq (numerator, denominator)) |
cff5fa33 | 476 | return SCM_INUM1; |
c60e130c MV |
477 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
478 | SCM_I_BIG_MPZ (denominator))) | |
479 | return scm_divide(numerator, denominator); | |
f92e85f7 | 480 | } |
f92e85f7 | 481 | } |
c60e130c MV |
482 | |
483 | /* No, it's a proper fraction. | |
484 | */ | |
e2bf3b19 HWN |
485 | { |
486 | SCM divisor = scm_gcd (numerator, denominator); | |
cff5fa33 | 487 | if (!(scm_is_eq (divisor, SCM_INUM1))) |
e2bf3b19 HWN |
488 | { |
489 | numerator = scm_divide (numerator, divisor); | |
490 | denominator = scm_divide (denominator, divisor); | |
491 | } | |
492 | ||
493 | return scm_double_cell (scm_tc16_fraction, | |
494 | SCM_UNPACK (numerator), | |
495 | SCM_UNPACK (denominator), 0); | |
496 | } | |
f92e85f7 | 497 | } |
c60e130c | 498 | #undef FUNC_NAME |
f92e85f7 | 499 | |
f92e85f7 MV |
500 | double |
501 | scm_i_fraction2double (SCM z) | |
502 | { | |
55f26379 MV |
503 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
504 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
505 | } |
506 | ||
2e274311 MW |
507 | static int |
508 | double_is_non_negative_zero (double x) | |
509 | { | |
510 | static double zero = 0.0; | |
511 | ||
512 | return !memcmp (&x, &zero, sizeof(double)); | |
513 | } | |
514 | ||
2519490c MW |
515 | SCM_PRIMITIVE_GENERIC (scm_exact_p, "exact?", 1, 0, 0, |
516 | (SCM x), | |
942e5b91 MG |
517 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
518 | "otherwise.") | |
1bbd0b84 | 519 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 520 | { |
41df63cf MW |
521 | if (SCM_INEXACTP (x)) |
522 | return SCM_BOOL_F; | |
523 | else if (SCM_NUMBERP (x)) | |
0aacf84e | 524 | return SCM_BOOL_T; |
41df63cf | 525 | else |
2519490c | 526 | SCM_WTA_DISPATCH_1 (g_scm_exact_p, x, 1, s_scm_exact_p); |
41df63cf MW |
527 | } |
528 | #undef FUNC_NAME | |
529 | ||
530 | ||
2519490c | 531 | SCM_PRIMITIVE_GENERIC (scm_inexact_p, "inexact?", 1, 0, 0, |
41df63cf MW |
532 | (SCM x), |
533 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" | |
534 | "else.") | |
535 | #define FUNC_NAME s_scm_inexact_p | |
536 | { | |
537 | if (SCM_INEXACTP (x)) | |
f92e85f7 | 538 | return SCM_BOOL_T; |
41df63cf | 539 | else if (SCM_NUMBERP (x)) |
eb927cb9 | 540 | return SCM_BOOL_F; |
41df63cf | 541 | else |
2519490c | 542 | SCM_WTA_DISPATCH_1 (g_scm_inexact_p, x, 1, s_scm_inexact_p); |
0f2d19dd | 543 | } |
1bbd0b84 | 544 | #undef FUNC_NAME |
0f2d19dd | 545 | |
4219f20d | 546 | |
2519490c | 547 | SCM_PRIMITIVE_GENERIC (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 548 | (SCM n), |
942e5b91 MG |
549 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
550 | "otherwise.") | |
1bbd0b84 | 551 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 552 | { |
e11e83f3 | 553 | if (SCM_I_INUMP (n)) |
0aacf84e | 554 | { |
e25f3727 | 555 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 556 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
557 | } |
558 | else if (SCM_BIGP (n)) | |
559 | { | |
560 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
561 | scm_remember_upto_here_1 (n); | |
73e4de09 | 562 | return scm_from_bool (odd_p); |
0aacf84e | 563 | } |
f92e85f7 MV |
564 | else if (SCM_REALP (n)) |
565 | { | |
2519490c MW |
566 | double val = SCM_REAL_VALUE (n); |
567 | if (DOUBLE_IS_FINITE (val)) | |
568 | { | |
569 | double rem = fabs (fmod (val, 2.0)); | |
570 | if (rem == 1.0) | |
571 | return SCM_BOOL_T; | |
572 | else if (rem == 0.0) | |
573 | return SCM_BOOL_F; | |
574 | } | |
f92e85f7 | 575 | } |
2519490c | 576 | SCM_WTA_DISPATCH_1 (g_scm_odd_p, n, 1, s_scm_odd_p); |
0f2d19dd | 577 | } |
1bbd0b84 | 578 | #undef FUNC_NAME |
0f2d19dd | 579 | |
4219f20d | 580 | |
2519490c | 581 | SCM_PRIMITIVE_GENERIC (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 582 | (SCM n), |
942e5b91 MG |
583 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
584 | "otherwise.") | |
1bbd0b84 | 585 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 586 | { |
e11e83f3 | 587 | if (SCM_I_INUMP (n)) |
0aacf84e | 588 | { |
e25f3727 | 589 | scm_t_inum val = SCM_I_INUM (n); |
73e4de09 | 590 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
591 | } |
592 | else if (SCM_BIGP (n)) | |
593 | { | |
594 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
595 | scm_remember_upto_here_1 (n); | |
73e4de09 | 596 | return scm_from_bool (even_p); |
0aacf84e | 597 | } |
f92e85f7 MV |
598 | else if (SCM_REALP (n)) |
599 | { | |
2519490c MW |
600 | double val = SCM_REAL_VALUE (n); |
601 | if (DOUBLE_IS_FINITE (val)) | |
602 | { | |
603 | double rem = fabs (fmod (val, 2.0)); | |
604 | if (rem == 1.0) | |
605 | return SCM_BOOL_F; | |
606 | else if (rem == 0.0) | |
607 | return SCM_BOOL_T; | |
608 | } | |
f92e85f7 | 609 | } |
2519490c | 610 | SCM_WTA_DISPATCH_1 (g_scm_even_p, n, 1, s_scm_even_p); |
0f2d19dd | 611 | } |
1bbd0b84 | 612 | #undef FUNC_NAME |
0f2d19dd | 613 | |
2519490c MW |
614 | SCM_PRIMITIVE_GENERIC (scm_finite_p, "finite?", 1, 0, 0, |
615 | (SCM x), | |
10391e06 AW |
616 | "Return @code{#t} if the real number @var{x} is neither\n" |
617 | "infinite nor a NaN, @code{#f} otherwise.") | |
7112615f MW |
618 | #define FUNC_NAME s_scm_finite_p |
619 | { | |
620 | if (SCM_REALP (x)) | |
621 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
10391e06 | 622 | else if (scm_is_real (x)) |
7112615f MW |
623 | return SCM_BOOL_T; |
624 | else | |
2519490c | 625 | SCM_WTA_DISPATCH_1 (g_scm_finite_p, x, 1, s_scm_finite_p); |
7112615f MW |
626 | } |
627 | #undef FUNC_NAME | |
628 | ||
2519490c MW |
629 | SCM_PRIMITIVE_GENERIC (scm_inf_p, "inf?", 1, 0, 0, |
630 | (SCM x), | |
631 | "Return @code{#t} if the real number @var{x} is @samp{+inf.0} or\n" | |
632 | "@samp{-inf.0}. Otherwise return @code{#f}.") | |
7351e207 MV |
633 | #define FUNC_NAME s_scm_inf_p |
634 | { | |
b1092b3a | 635 | if (SCM_REALP (x)) |
2e65b52f | 636 | return scm_from_bool (isinf (SCM_REAL_VALUE (x))); |
10391e06 | 637 | else if (scm_is_real (x)) |
7351e207 | 638 | return SCM_BOOL_F; |
10391e06 | 639 | else |
2519490c | 640 | SCM_WTA_DISPATCH_1 (g_scm_inf_p, x, 1, s_scm_inf_p); |
7351e207 MV |
641 | } |
642 | #undef FUNC_NAME | |
643 | ||
2519490c MW |
644 | SCM_PRIMITIVE_GENERIC (scm_nan_p, "nan?", 1, 0, 0, |
645 | (SCM x), | |
10391e06 AW |
646 | "Return @code{#t} if the real number @var{x} is a NaN,\n" |
647 | "or @code{#f} otherwise.") | |
7351e207 MV |
648 | #define FUNC_NAME s_scm_nan_p |
649 | { | |
10391e06 AW |
650 | if (SCM_REALP (x)) |
651 | return scm_from_bool (isnan (SCM_REAL_VALUE (x))); | |
652 | else if (scm_is_real (x)) | |
7351e207 | 653 | return SCM_BOOL_F; |
10391e06 | 654 | else |
2519490c | 655 | SCM_WTA_DISPATCH_1 (g_scm_nan_p, x, 1, s_scm_nan_p); |
7351e207 MV |
656 | } |
657 | #undef FUNC_NAME | |
658 | ||
659 | /* Guile's idea of infinity. */ | |
660 | static double guile_Inf; | |
661 | ||
662 | /* Guile's idea of not a number. */ | |
663 | static double guile_NaN; | |
664 | ||
665 | static void | |
666 | guile_ieee_init (void) | |
667 | { | |
7351e207 MV |
668 | /* Some version of gcc on some old version of Linux used to crash when |
669 | trying to make Inf and NaN. */ | |
670 | ||
240a27d2 KR |
671 | #ifdef INFINITY |
672 | /* C99 INFINITY, when available. | |
673 | FIXME: The standard allows for INFINITY to be something that overflows | |
674 | at compile time. We ought to have a configure test to check for that | |
675 | before trying to use it. (But in practice we believe this is not a | |
676 | problem on any system guile is likely to target.) */ | |
677 | guile_Inf = INFINITY; | |
56a3dcd4 | 678 | #elif defined HAVE_DINFINITY |
240a27d2 | 679 | /* OSF */ |
7351e207 | 680 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 681 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
682 | #else |
683 | double tmp = 1e+10; | |
684 | guile_Inf = tmp; | |
685 | for (;;) | |
686 | { | |
687 | guile_Inf *= 1e+10; | |
688 | if (guile_Inf == tmp) | |
689 | break; | |
690 | tmp = guile_Inf; | |
691 | } | |
692 | #endif | |
693 | ||
240a27d2 KR |
694 | #ifdef NAN |
695 | /* C99 NAN, when available */ | |
696 | guile_NaN = NAN; | |
56a3dcd4 | 697 | #elif defined HAVE_DQNAN |
eaa94eaa LC |
698 | { |
699 | /* OSF */ | |
700 | extern unsigned int DQNAN[2]; | |
701 | guile_NaN = (*((double *)(DQNAN))); | |
702 | } | |
7351e207 MV |
703 | #else |
704 | guile_NaN = guile_Inf / guile_Inf; | |
705 | #endif | |
7351e207 MV |
706 | } |
707 | ||
708 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
709 | (void), | |
710 | "Return Inf.") | |
711 | #define FUNC_NAME s_scm_inf | |
712 | { | |
713 | static int initialized = 0; | |
714 | if (! initialized) | |
715 | { | |
716 | guile_ieee_init (); | |
717 | initialized = 1; | |
718 | } | |
55f26379 | 719 | return scm_from_double (guile_Inf); |
7351e207 MV |
720 | } |
721 | #undef FUNC_NAME | |
722 | ||
723 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
724 | (void), | |
725 | "Return NaN.") | |
726 | #define FUNC_NAME s_scm_nan | |
727 | { | |
728 | static int initialized = 0; | |
0aacf84e | 729 | if (!initialized) |
7351e207 MV |
730 | { |
731 | guile_ieee_init (); | |
732 | initialized = 1; | |
733 | } | |
55f26379 | 734 | return scm_from_double (guile_NaN); |
7351e207 MV |
735 | } |
736 | #undef FUNC_NAME | |
737 | ||
4219f20d | 738 | |
a48d60b1 MD |
739 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
740 | (SCM x), | |
741 | "Return the absolute value of @var{x}.") | |
2519490c | 742 | #define FUNC_NAME s_scm_abs |
0f2d19dd | 743 | { |
e11e83f3 | 744 | if (SCM_I_INUMP (x)) |
0aacf84e | 745 | { |
e25f3727 | 746 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
747 | if (xx >= 0) |
748 | return x; | |
749 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 750 | return SCM_I_MAKINUM (-xx); |
0aacf84e | 751 | else |
e25f3727 | 752 | return scm_i_inum2big (-xx); |
4219f20d | 753 | } |
9b9ef10c MW |
754 | else if (SCM_LIKELY (SCM_REALP (x))) |
755 | { | |
756 | double xx = SCM_REAL_VALUE (x); | |
757 | /* If x is a NaN then xx<0 is false so we return x unchanged */ | |
758 | if (xx < 0.0) | |
759 | return scm_from_double (-xx); | |
760 | /* Handle signed zeroes properly */ | |
761 | else if (SCM_UNLIKELY (xx == 0.0)) | |
762 | return flo0; | |
763 | else | |
764 | return x; | |
765 | } | |
0aacf84e MD |
766 | else if (SCM_BIGP (x)) |
767 | { | |
768 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
769 | if (sgn < 0) | |
770 | return scm_i_clonebig (x, 0); | |
771 | else | |
772 | return x; | |
4219f20d | 773 | } |
f92e85f7 MV |
774 | else if (SCM_FRACTIONP (x)) |
775 | { | |
73e4de09 | 776 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 777 | return x; |
cba42c93 | 778 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
779 | SCM_FRACTION_DENOMINATOR (x)); |
780 | } | |
0aacf84e | 781 | else |
a48d60b1 | 782 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 783 | } |
a48d60b1 | 784 | #undef FUNC_NAME |
0f2d19dd | 785 | |
4219f20d | 786 | |
2519490c MW |
787 | SCM_PRIMITIVE_GENERIC (scm_quotient, "quotient", 2, 0, 0, |
788 | (SCM x, SCM y), | |
789 | "Return the quotient of the numbers @var{x} and @var{y}.") | |
790 | #define FUNC_NAME s_scm_quotient | |
0f2d19dd | 791 | { |
a8da6d93 | 792 | if (SCM_LIKELY (SCM_I_INUMP (x)) || SCM_LIKELY (SCM_BIGP (x))) |
0aacf84e | 793 | { |
a8da6d93 MW |
794 | if (SCM_LIKELY (SCM_I_INUMP (y)) || SCM_LIKELY (SCM_BIGP (y))) |
795 | return scm_truncate_quotient (x, y); | |
0aacf84e | 796 | else |
2519490c | 797 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG2, s_scm_quotient); |
f872b822 | 798 | } |
0aacf84e | 799 | else |
2519490c | 800 | SCM_WTA_DISPATCH_2 (g_scm_quotient, x, y, SCM_ARG1, s_scm_quotient); |
0f2d19dd | 801 | } |
2519490c | 802 | #undef FUNC_NAME |
0f2d19dd | 803 | |
2519490c MW |
804 | SCM_PRIMITIVE_GENERIC (scm_remainder, "remainder", 2, 0, 0, |
805 | (SCM x, SCM y), | |
806 | "Return the remainder of the numbers @var{x} and @var{y}.\n" | |
807 | "@lisp\n" | |
808 | "(remainder 13 4) @result{} 1\n" | |
809 | "(remainder -13 4) @result{} -1\n" | |
810 | "@end lisp") | |
811 | #define FUNC_NAME s_scm_remainder | |
0f2d19dd | 812 | { |
a8da6d93 | 813 | if (SCM_LIKELY (SCM_I_INUMP (x)) || SCM_LIKELY (SCM_BIGP (x))) |
0aacf84e | 814 | { |
a8da6d93 MW |
815 | if (SCM_LIKELY (SCM_I_INUMP (y)) || SCM_LIKELY (SCM_BIGP (y))) |
816 | return scm_truncate_remainder (x, y); | |
0aacf84e | 817 | else |
2519490c | 818 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG2, s_scm_remainder); |
f872b822 | 819 | } |
0aacf84e | 820 | else |
2519490c | 821 | SCM_WTA_DISPATCH_2 (g_scm_remainder, x, y, SCM_ARG1, s_scm_remainder); |
0f2d19dd | 822 | } |
2519490c | 823 | #undef FUNC_NAME |
0f2d19dd | 824 | |
89a7e495 | 825 | |
2519490c MW |
826 | SCM_PRIMITIVE_GENERIC (scm_modulo, "modulo", 2, 0, 0, |
827 | (SCM x, SCM y), | |
828 | "Return the modulo of the numbers @var{x} and @var{y}.\n" | |
829 | "@lisp\n" | |
830 | "(modulo 13 4) @result{} 1\n" | |
831 | "(modulo -13 4) @result{} 3\n" | |
832 | "@end lisp") | |
833 | #define FUNC_NAME s_scm_modulo | |
0f2d19dd | 834 | { |
a8da6d93 | 835 | if (SCM_LIKELY (SCM_I_INUMP (x)) || SCM_LIKELY (SCM_BIGP (x))) |
0aacf84e | 836 | { |
a8da6d93 MW |
837 | if (SCM_LIKELY (SCM_I_INUMP (y)) || SCM_LIKELY (SCM_BIGP (y))) |
838 | return scm_floor_remainder (x, y); | |
0aacf84e | 839 | else |
2519490c | 840 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG2, s_scm_modulo); |
828865c3 | 841 | } |
0aacf84e | 842 | else |
2519490c | 843 | SCM_WTA_DISPATCH_2 (g_scm_modulo, x, y, SCM_ARG1, s_scm_modulo); |
0f2d19dd | 844 | } |
2519490c | 845 | #undef FUNC_NAME |
0f2d19dd | 846 | |
5fbf680b MW |
847 | /* two_valued_wta_dispatch_2 is a version of SCM_WTA_DISPATCH_2 for |
848 | two-valued functions. It is called from primitive generics that take | |
849 | two arguments and return two values, when the core procedure is | |
850 | unable to handle the given argument types. If there are GOOPS | |
851 | methods for this primitive generic, it dispatches to GOOPS and, if | |
852 | successful, expects two values to be returned, which are placed in | |
853 | *rp1 and *rp2. If there are no GOOPS methods, it throws a | |
854 | wrong-type-arg exception. | |
855 | ||
856 | FIXME: This obviously belongs somewhere else, but until we decide on | |
857 | the right API, it is here as a static function, because it is needed | |
858 | by the *_divide functions below. | |
859 | */ | |
860 | static void | |
861 | two_valued_wta_dispatch_2 (SCM gf, SCM a1, SCM a2, int pos, | |
862 | const char *subr, SCM *rp1, SCM *rp2) | |
863 | { | |
864 | if (SCM_UNPACK (gf)) | |
865 | scm_i_extract_values_2 (scm_call_generic_2 (gf, a1, a2), rp1, rp2); | |
866 | else | |
867 | scm_wrong_type_arg (subr, pos, (pos == SCM_ARG1) ? a1 : a2); | |
868 | } | |
869 | ||
a8da6d93 MW |
870 | SCM_DEFINE (scm_euclidean_quotient, "euclidean-quotient", 2, 0, 0, |
871 | (SCM x, SCM y), | |
872 | "Return the integer @var{q} such that\n" | |
873 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
874 | "where @math{0 <= @var{r} < abs(@var{y})}.\n" | |
875 | "@lisp\n" | |
876 | "(euclidean-quotient 123 10) @result{} 12\n" | |
877 | "(euclidean-quotient 123 -10) @result{} -12\n" | |
878 | "(euclidean-quotient -123 10) @result{} -13\n" | |
879 | "(euclidean-quotient -123 -10) @result{} 13\n" | |
880 | "(euclidean-quotient -123.2 -63.5) @result{} 2.0\n" | |
881 | "(euclidean-quotient 16/3 -10/7) @result{} -3\n" | |
882 | "@end lisp") | |
ff62c168 MW |
883 | #define FUNC_NAME s_scm_euclidean_quotient |
884 | { | |
a8da6d93 MW |
885 | if (scm_is_false (scm_negative_p (y))) |
886 | return scm_floor_quotient (x, y); | |
ff62c168 | 887 | else |
a8da6d93 | 888 | return scm_ceiling_quotient (x, y); |
ff62c168 MW |
889 | } |
890 | #undef FUNC_NAME | |
891 | ||
a8da6d93 MW |
892 | SCM_DEFINE (scm_euclidean_remainder, "euclidean-remainder", 2, 0, 0, |
893 | (SCM x, SCM y), | |
894 | "Return the real number @var{r} such that\n" | |
895 | "@math{0 <= @var{r} < abs(@var{y})} and\n" | |
896 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
897 | "for some integer @var{q}.\n" | |
898 | "@lisp\n" | |
899 | "(euclidean-remainder 123 10) @result{} 3\n" | |
900 | "(euclidean-remainder 123 -10) @result{} 3\n" | |
901 | "(euclidean-remainder -123 10) @result{} 7\n" | |
902 | "(euclidean-remainder -123 -10) @result{} 7\n" | |
903 | "(euclidean-remainder -123.2 -63.5) @result{} 3.8\n" | |
904 | "(euclidean-remainder 16/3 -10/7) @result{} 22/21\n" | |
905 | "@end lisp") | |
ff62c168 MW |
906 | #define FUNC_NAME s_scm_euclidean_remainder |
907 | { | |
a8da6d93 MW |
908 | if (scm_is_false (scm_negative_p (y))) |
909 | return scm_floor_remainder (x, y); | |
ff62c168 | 910 | else |
a8da6d93 | 911 | return scm_ceiling_remainder (x, y); |
ff62c168 MW |
912 | } |
913 | #undef FUNC_NAME | |
914 | ||
a8da6d93 MW |
915 | SCM_DEFINE (scm_i_euclidean_divide, "euclidean/", 2, 0, 0, |
916 | (SCM x, SCM y), | |
917 | "Return the integer @var{q} and the real number @var{r}\n" | |
918 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
919 | "and @math{0 <= @var{r} < abs(@var{y})}.\n" | |
920 | "@lisp\n" | |
921 | "(euclidean/ 123 10) @result{} 12 and 3\n" | |
922 | "(euclidean/ 123 -10) @result{} -12 and 3\n" | |
923 | "(euclidean/ -123 10) @result{} -13 and 7\n" | |
924 | "(euclidean/ -123 -10) @result{} 13 and 7\n" | |
925 | "(euclidean/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
926 | "(euclidean/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
927 | "@end lisp") | |
5fbf680b MW |
928 | #define FUNC_NAME s_scm_i_euclidean_divide |
929 | { | |
a8da6d93 MW |
930 | if (scm_is_false (scm_negative_p (y))) |
931 | return scm_i_floor_divide (x, y); | |
932 | else | |
933 | return scm_i_ceiling_divide (x, y); | |
5fbf680b MW |
934 | } |
935 | #undef FUNC_NAME | |
936 | ||
5fbf680b MW |
937 | void |
938 | scm_euclidean_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
ff62c168 | 939 | { |
a8da6d93 MW |
940 | if (scm_is_false (scm_negative_p (y))) |
941 | return scm_floor_divide (x, y, qp, rp); | |
ff62c168 | 942 | else |
a8da6d93 | 943 | return scm_ceiling_divide (x, y, qp, rp); |
ff62c168 MW |
944 | } |
945 | ||
8f9da340 MW |
946 | static SCM scm_i_inexact_floor_quotient (double x, double y); |
947 | static SCM scm_i_exact_rational_floor_quotient (SCM x, SCM y); | |
948 | ||
949 | SCM_PRIMITIVE_GENERIC (scm_floor_quotient, "floor-quotient", 2, 0, 0, | |
950 | (SCM x, SCM y), | |
951 | "Return the floor of @math{@var{x} / @var{y}}.\n" | |
952 | "@lisp\n" | |
953 | "(floor-quotient 123 10) @result{} 12\n" | |
954 | "(floor-quotient 123 -10) @result{} -13\n" | |
955 | "(floor-quotient -123 10) @result{} -13\n" | |
956 | "(floor-quotient -123 -10) @result{} 12\n" | |
957 | "(floor-quotient -123.2 -63.5) @result{} 1.0\n" | |
958 | "(floor-quotient 16/3 -10/7) @result{} -4\n" | |
959 | "@end lisp") | |
960 | #define FUNC_NAME s_scm_floor_quotient | |
961 | { | |
962 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
963 | { | |
964 | scm_t_inum xx = SCM_I_INUM (x); | |
965 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
966 | { | |
967 | scm_t_inum yy = SCM_I_INUM (y); | |
968 | scm_t_inum xx1 = xx; | |
969 | scm_t_inum qq; | |
970 | if (SCM_LIKELY (yy > 0)) | |
971 | { | |
972 | if (SCM_UNLIKELY (xx < 0)) | |
973 | xx1 = xx - yy + 1; | |
974 | } | |
975 | else if (SCM_UNLIKELY (yy == 0)) | |
976 | scm_num_overflow (s_scm_floor_quotient); | |
977 | else if (xx > 0) | |
978 | xx1 = xx - yy - 1; | |
979 | qq = xx1 / yy; | |
980 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
981 | return SCM_I_MAKINUM (qq); | |
982 | else | |
983 | return scm_i_inum2big (qq); | |
984 | } | |
985 | else if (SCM_BIGP (y)) | |
986 | { | |
987 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
988 | scm_remember_upto_here_1 (y); | |
989 | if (sign > 0) | |
990 | return SCM_I_MAKINUM ((xx < 0) ? -1 : 0); | |
991 | else | |
992 | return SCM_I_MAKINUM ((xx > 0) ? -1 : 0); | |
993 | } | |
994 | else if (SCM_REALP (y)) | |
995 | return scm_i_inexact_floor_quotient (xx, SCM_REAL_VALUE (y)); | |
996 | else if (SCM_FRACTIONP (y)) | |
997 | return scm_i_exact_rational_floor_quotient (x, y); | |
998 | else | |
999 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1000 | s_scm_floor_quotient); | |
1001 | } | |
1002 | else if (SCM_BIGP (x)) | |
1003 | { | |
1004 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1005 | { | |
1006 | scm_t_inum yy = SCM_I_INUM (y); | |
1007 | if (SCM_UNLIKELY (yy == 0)) | |
1008 | scm_num_overflow (s_scm_floor_quotient); | |
1009 | else if (SCM_UNLIKELY (yy == 1)) | |
1010 | return x; | |
1011 | else | |
1012 | { | |
1013 | SCM q = scm_i_mkbig (); | |
1014 | if (yy > 0) | |
1015 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1016 | else | |
1017 | { | |
1018 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1019 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1020 | } | |
1021 | scm_remember_upto_here_1 (x); | |
1022 | return scm_i_normbig (q); | |
1023 | } | |
1024 | } | |
1025 | else if (SCM_BIGP (y)) | |
1026 | { | |
1027 | SCM q = scm_i_mkbig (); | |
1028 | mpz_fdiv_q (SCM_I_BIG_MPZ (q), | |
1029 | SCM_I_BIG_MPZ (x), | |
1030 | SCM_I_BIG_MPZ (y)); | |
1031 | scm_remember_upto_here_2 (x, y); | |
1032 | return scm_i_normbig (q); | |
1033 | } | |
1034 | else if (SCM_REALP (y)) | |
1035 | return scm_i_inexact_floor_quotient | |
1036 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1037 | else if (SCM_FRACTIONP (y)) | |
1038 | return scm_i_exact_rational_floor_quotient (x, y); | |
1039 | else | |
1040 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1041 | s_scm_floor_quotient); | |
1042 | } | |
1043 | else if (SCM_REALP (x)) | |
1044 | { | |
1045 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1046 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1047 | return scm_i_inexact_floor_quotient | |
1048 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1049 | else | |
1050 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1051 | s_scm_floor_quotient); | |
1052 | } | |
1053 | else if (SCM_FRACTIONP (x)) | |
1054 | { | |
1055 | if (SCM_REALP (y)) | |
1056 | return scm_i_inexact_floor_quotient | |
1057 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1058 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1059 | return scm_i_exact_rational_floor_quotient (x, y); | |
1060 | else | |
1061 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG2, | |
1062 | s_scm_floor_quotient); | |
1063 | } | |
1064 | else | |
1065 | SCM_WTA_DISPATCH_2 (g_scm_floor_quotient, x, y, SCM_ARG1, | |
1066 | s_scm_floor_quotient); | |
1067 | } | |
1068 | #undef FUNC_NAME | |
1069 | ||
1070 | static SCM | |
1071 | scm_i_inexact_floor_quotient (double x, double y) | |
1072 | { | |
1073 | if (SCM_UNLIKELY (y == 0)) | |
1074 | scm_num_overflow (s_scm_floor_quotient); /* or return a NaN? */ | |
1075 | else | |
1076 | return scm_from_double (floor (x / y)); | |
1077 | } | |
1078 | ||
1079 | static SCM | |
1080 | scm_i_exact_rational_floor_quotient (SCM x, SCM y) | |
1081 | { | |
1082 | return scm_floor_quotient | |
1083 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1084 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1085 | } | |
1086 | ||
1087 | static SCM scm_i_inexact_floor_remainder (double x, double y); | |
1088 | static SCM scm_i_exact_rational_floor_remainder (SCM x, SCM y); | |
1089 | ||
1090 | SCM_PRIMITIVE_GENERIC (scm_floor_remainder, "floor-remainder", 2, 0, 0, | |
1091 | (SCM x, SCM y), | |
1092 | "Return the real number @var{r} such that\n" | |
1093 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1094 | "where @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1095 | "@lisp\n" | |
1096 | "(floor-remainder 123 10) @result{} 3\n" | |
1097 | "(floor-remainder 123 -10) @result{} -7\n" | |
1098 | "(floor-remainder -123 10) @result{} 7\n" | |
1099 | "(floor-remainder -123 -10) @result{} -3\n" | |
1100 | "(floor-remainder -123.2 -63.5) @result{} -59.7\n" | |
1101 | "(floor-remainder 16/3 -10/7) @result{} -8/21\n" | |
1102 | "@end lisp") | |
1103 | #define FUNC_NAME s_scm_floor_remainder | |
1104 | { | |
1105 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1106 | { | |
1107 | scm_t_inum xx = SCM_I_INUM (x); | |
1108 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1109 | { | |
1110 | scm_t_inum yy = SCM_I_INUM (y); | |
1111 | if (SCM_UNLIKELY (yy == 0)) | |
1112 | scm_num_overflow (s_scm_floor_remainder); | |
1113 | else | |
1114 | { | |
1115 | scm_t_inum rr = xx % yy; | |
1116 | int needs_adjustment; | |
1117 | ||
1118 | if (SCM_LIKELY (yy > 0)) | |
1119 | needs_adjustment = (rr < 0); | |
1120 | else | |
1121 | needs_adjustment = (rr > 0); | |
1122 | ||
1123 | if (needs_adjustment) | |
1124 | rr += yy; | |
1125 | return SCM_I_MAKINUM (rr); | |
1126 | } | |
1127 | } | |
1128 | else if (SCM_BIGP (y)) | |
1129 | { | |
1130 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1131 | scm_remember_upto_here_1 (y); | |
1132 | if (sign > 0) | |
1133 | { | |
1134 | if (xx < 0) | |
1135 | { | |
1136 | SCM r = scm_i_mkbig (); | |
1137 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1138 | scm_remember_upto_here_1 (y); | |
1139 | return scm_i_normbig (r); | |
1140 | } | |
1141 | else | |
1142 | return x; | |
1143 | } | |
1144 | else if (xx <= 0) | |
1145 | return x; | |
1146 | else | |
1147 | { | |
1148 | SCM r = scm_i_mkbig (); | |
1149 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1150 | scm_remember_upto_here_1 (y); | |
1151 | return scm_i_normbig (r); | |
1152 | } | |
1153 | } | |
1154 | else if (SCM_REALP (y)) | |
1155 | return scm_i_inexact_floor_remainder (xx, SCM_REAL_VALUE (y)); | |
1156 | else if (SCM_FRACTIONP (y)) | |
1157 | return scm_i_exact_rational_floor_remainder (x, y); | |
1158 | else | |
1159 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1160 | s_scm_floor_remainder); | |
1161 | } | |
1162 | else if (SCM_BIGP (x)) | |
1163 | { | |
1164 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1165 | { | |
1166 | scm_t_inum yy = SCM_I_INUM (y); | |
1167 | if (SCM_UNLIKELY (yy == 0)) | |
1168 | scm_num_overflow (s_scm_floor_remainder); | |
1169 | else | |
1170 | { | |
1171 | scm_t_inum rr; | |
1172 | if (yy > 0) | |
1173 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1174 | else | |
1175 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1176 | scm_remember_upto_here_1 (x); | |
1177 | return SCM_I_MAKINUM (rr); | |
1178 | } | |
1179 | } | |
1180 | else if (SCM_BIGP (y)) | |
1181 | { | |
1182 | SCM r = scm_i_mkbig (); | |
1183 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
1184 | SCM_I_BIG_MPZ (x), | |
1185 | SCM_I_BIG_MPZ (y)); | |
1186 | scm_remember_upto_here_2 (x, y); | |
1187 | return scm_i_normbig (r); | |
1188 | } | |
1189 | else if (SCM_REALP (y)) | |
1190 | return scm_i_inexact_floor_remainder | |
1191 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1192 | else if (SCM_FRACTIONP (y)) | |
1193 | return scm_i_exact_rational_floor_remainder (x, y); | |
1194 | else | |
1195 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1196 | s_scm_floor_remainder); | |
1197 | } | |
1198 | else if (SCM_REALP (x)) | |
1199 | { | |
1200 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1201 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1202 | return scm_i_inexact_floor_remainder | |
1203 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1204 | else | |
1205 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1206 | s_scm_floor_remainder); | |
1207 | } | |
1208 | else if (SCM_FRACTIONP (x)) | |
1209 | { | |
1210 | if (SCM_REALP (y)) | |
1211 | return scm_i_inexact_floor_remainder | |
1212 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1213 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1214 | return scm_i_exact_rational_floor_remainder (x, y); | |
1215 | else | |
1216 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG2, | |
1217 | s_scm_floor_remainder); | |
1218 | } | |
1219 | else | |
1220 | SCM_WTA_DISPATCH_2 (g_scm_floor_remainder, x, y, SCM_ARG1, | |
1221 | s_scm_floor_remainder); | |
1222 | } | |
1223 | #undef FUNC_NAME | |
1224 | ||
1225 | static SCM | |
1226 | scm_i_inexact_floor_remainder (double x, double y) | |
1227 | { | |
1228 | /* Although it would be more efficient to use fmod here, we can't | |
1229 | because it would in some cases produce results inconsistent with | |
1230 | scm_i_inexact_floor_quotient, such that x != q * y + r (not even | |
1231 | close). In particular, when x is very close to a multiple of y, | |
1232 | then r might be either 0.0 or y, but those two cases must | |
1233 | correspond to different choices of q. If r = 0.0 then q must be | |
1234 | x/y, and if r = y then q must be x/y-1. If quotient chooses one | |
1235 | and remainder chooses the other, it would be bad. */ | |
1236 | if (SCM_UNLIKELY (y == 0)) | |
1237 | scm_num_overflow (s_scm_floor_remainder); /* or return a NaN? */ | |
1238 | else | |
1239 | return scm_from_double (x - y * floor (x / y)); | |
1240 | } | |
1241 | ||
1242 | static SCM | |
1243 | scm_i_exact_rational_floor_remainder (SCM x, SCM y) | |
1244 | { | |
1245 | SCM xd = scm_denominator (x); | |
1246 | SCM yd = scm_denominator (y); | |
1247 | SCM r1 = scm_floor_remainder (scm_product (scm_numerator (x), yd), | |
1248 | scm_product (scm_numerator (y), xd)); | |
1249 | return scm_divide (r1, scm_product (xd, yd)); | |
1250 | } | |
1251 | ||
1252 | ||
1253 | static void scm_i_inexact_floor_divide (double x, double y, | |
1254 | SCM *qp, SCM *rp); | |
1255 | static void scm_i_exact_rational_floor_divide (SCM x, SCM y, | |
1256 | SCM *qp, SCM *rp); | |
1257 | ||
1258 | SCM_PRIMITIVE_GENERIC (scm_i_floor_divide, "floor/", 2, 0, 0, | |
1259 | (SCM x, SCM y), | |
1260 | "Return the integer @var{q} and the real number @var{r}\n" | |
1261 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1262 | "and @math{@var{q} = floor(@var{x} / @var{y})}.\n" | |
1263 | "@lisp\n" | |
1264 | "(floor/ 123 10) @result{} 12 and 3\n" | |
1265 | "(floor/ 123 -10) @result{} -13 and -7\n" | |
1266 | "(floor/ -123 10) @result{} -13 and 7\n" | |
1267 | "(floor/ -123 -10) @result{} 12 and -3\n" | |
1268 | "(floor/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
1269 | "(floor/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
1270 | "@end lisp") | |
1271 | #define FUNC_NAME s_scm_i_floor_divide | |
1272 | { | |
1273 | SCM q, r; | |
1274 | ||
1275 | scm_floor_divide(x, y, &q, &r); | |
1276 | return scm_values (scm_list_2 (q, r)); | |
1277 | } | |
1278 | #undef FUNC_NAME | |
1279 | ||
1280 | #define s_scm_floor_divide s_scm_i_floor_divide | |
1281 | #define g_scm_floor_divide g_scm_i_floor_divide | |
1282 | ||
1283 | void | |
1284 | scm_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1285 | { | |
1286 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1287 | { | |
1288 | scm_t_inum xx = SCM_I_INUM (x); | |
1289 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1290 | { | |
1291 | scm_t_inum yy = SCM_I_INUM (y); | |
1292 | if (SCM_UNLIKELY (yy == 0)) | |
1293 | scm_num_overflow (s_scm_floor_divide); | |
1294 | else | |
1295 | { | |
1296 | scm_t_inum qq = xx / yy; | |
1297 | scm_t_inum rr = xx % yy; | |
1298 | int needs_adjustment; | |
1299 | ||
1300 | if (SCM_LIKELY (yy > 0)) | |
1301 | needs_adjustment = (rr < 0); | |
1302 | else | |
1303 | needs_adjustment = (rr > 0); | |
1304 | ||
1305 | if (needs_adjustment) | |
1306 | { | |
1307 | rr += yy; | |
1308 | qq--; | |
1309 | } | |
1310 | ||
1311 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1312 | *qp = SCM_I_MAKINUM (qq); | |
1313 | else | |
1314 | *qp = scm_i_inum2big (qq); | |
1315 | *rp = SCM_I_MAKINUM (rr); | |
1316 | } | |
1317 | return; | |
1318 | } | |
1319 | else if (SCM_BIGP (y)) | |
1320 | { | |
1321 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1322 | scm_remember_upto_here_1 (y); | |
1323 | if (sign > 0) | |
1324 | { | |
1325 | if (xx < 0) | |
1326 | { | |
1327 | SCM r = scm_i_mkbig (); | |
1328 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1329 | scm_remember_upto_here_1 (y); | |
1330 | *qp = SCM_I_MAKINUM (-1); | |
1331 | *rp = scm_i_normbig (r); | |
1332 | } | |
1333 | else | |
1334 | { | |
1335 | *qp = SCM_INUM0; | |
1336 | *rp = x; | |
1337 | } | |
1338 | } | |
1339 | else if (xx <= 0) | |
1340 | { | |
1341 | *qp = SCM_INUM0; | |
1342 | *rp = x; | |
1343 | } | |
1344 | else | |
1345 | { | |
1346 | SCM r = scm_i_mkbig (); | |
1347 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1348 | scm_remember_upto_here_1 (y); | |
1349 | *qp = SCM_I_MAKINUM (-1); | |
1350 | *rp = scm_i_normbig (r); | |
1351 | } | |
1352 | return; | |
1353 | } | |
1354 | else if (SCM_REALP (y)) | |
1355 | return scm_i_inexact_floor_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1356 | else if (SCM_FRACTIONP (y)) | |
1357 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1358 | else | |
1359 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1360 | s_scm_floor_divide, qp, rp); | |
1361 | } | |
1362 | else if (SCM_BIGP (x)) | |
1363 | { | |
1364 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1365 | { | |
1366 | scm_t_inum yy = SCM_I_INUM (y); | |
1367 | if (SCM_UNLIKELY (yy == 0)) | |
1368 | scm_num_overflow (s_scm_floor_divide); | |
1369 | else | |
1370 | { | |
1371 | SCM q = scm_i_mkbig (); | |
1372 | SCM r = scm_i_mkbig (); | |
1373 | if (yy > 0) | |
1374 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1375 | SCM_I_BIG_MPZ (x), yy); | |
1376 | else | |
1377 | { | |
1378 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1379 | SCM_I_BIG_MPZ (x), -yy); | |
1380 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1381 | } | |
1382 | scm_remember_upto_here_1 (x); | |
1383 | *qp = scm_i_normbig (q); | |
1384 | *rp = scm_i_normbig (r); | |
1385 | } | |
1386 | return; | |
1387 | } | |
1388 | else if (SCM_BIGP (y)) | |
1389 | { | |
1390 | SCM q = scm_i_mkbig (); | |
1391 | SCM r = scm_i_mkbig (); | |
1392 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1393 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1394 | scm_remember_upto_here_2 (x, y); | |
1395 | *qp = scm_i_normbig (q); | |
1396 | *rp = scm_i_normbig (r); | |
1397 | return; | |
1398 | } | |
1399 | else if (SCM_REALP (y)) | |
1400 | return scm_i_inexact_floor_divide | |
1401 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1402 | else if (SCM_FRACTIONP (y)) | |
1403 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1404 | else | |
1405 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1406 | s_scm_floor_divide, qp, rp); | |
1407 | } | |
1408 | else if (SCM_REALP (x)) | |
1409 | { | |
1410 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1411 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1412 | return scm_i_inexact_floor_divide | |
1413 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
1414 | else | |
1415 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1416 | s_scm_floor_divide, qp, rp); | |
1417 | } | |
1418 | else if (SCM_FRACTIONP (x)) | |
1419 | { | |
1420 | if (SCM_REALP (y)) | |
1421 | return scm_i_inexact_floor_divide | |
1422 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
1423 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1424 | return scm_i_exact_rational_floor_divide (x, y, qp, rp); | |
1425 | else | |
1426 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG2, | |
1427 | s_scm_floor_divide, qp, rp); | |
1428 | } | |
1429 | else | |
1430 | return two_valued_wta_dispatch_2 (g_scm_floor_divide, x, y, SCM_ARG1, | |
1431 | s_scm_floor_divide, qp, rp); | |
1432 | } | |
1433 | ||
1434 | static void | |
1435 | scm_i_inexact_floor_divide (double x, double y, SCM *qp, SCM *rp) | |
1436 | { | |
1437 | if (SCM_UNLIKELY (y == 0)) | |
1438 | scm_num_overflow (s_scm_floor_divide); /* or return a NaN? */ | |
1439 | else | |
1440 | { | |
1441 | double q = floor (x / y); | |
1442 | double r = x - q * y; | |
1443 | *qp = scm_from_double (q); | |
1444 | *rp = scm_from_double (r); | |
1445 | } | |
1446 | } | |
1447 | ||
1448 | static void | |
1449 | scm_i_exact_rational_floor_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1450 | { | |
1451 | SCM r1; | |
1452 | SCM xd = scm_denominator (x); | |
1453 | SCM yd = scm_denominator (y); | |
1454 | ||
1455 | scm_floor_divide (scm_product (scm_numerator (x), yd), | |
1456 | scm_product (scm_numerator (y), xd), | |
1457 | qp, &r1); | |
1458 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
1459 | } | |
1460 | ||
1461 | static SCM scm_i_inexact_ceiling_quotient (double x, double y); | |
1462 | static SCM scm_i_exact_rational_ceiling_quotient (SCM x, SCM y); | |
1463 | ||
1464 | SCM_PRIMITIVE_GENERIC (scm_ceiling_quotient, "ceiling-quotient", 2, 0, 0, | |
1465 | (SCM x, SCM y), | |
1466 | "Return the ceiling of @math{@var{x} / @var{y}}.\n" | |
1467 | "@lisp\n" | |
1468 | "(ceiling-quotient 123 10) @result{} 13\n" | |
1469 | "(ceiling-quotient 123 -10) @result{} -12\n" | |
1470 | "(ceiling-quotient -123 10) @result{} -12\n" | |
1471 | "(ceiling-quotient -123 -10) @result{} 13\n" | |
1472 | "(ceiling-quotient -123.2 -63.5) @result{} 2.0\n" | |
1473 | "(ceiling-quotient 16/3 -10/7) @result{} -3\n" | |
1474 | "@end lisp") | |
1475 | #define FUNC_NAME s_scm_ceiling_quotient | |
1476 | { | |
1477 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1478 | { | |
1479 | scm_t_inum xx = SCM_I_INUM (x); | |
1480 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1481 | { | |
1482 | scm_t_inum yy = SCM_I_INUM (y); | |
1483 | if (SCM_UNLIKELY (yy == 0)) | |
1484 | scm_num_overflow (s_scm_ceiling_quotient); | |
1485 | else | |
1486 | { | |
1487 | scm_t_inum xx1 = xx; | |
1488 | scm_t_inum qq; | |
1489 | if (SCM_LIKELY (yy > 0)) | |
1490 | { | |
1491 | if (SCM_LIKELY (xx >= 0)) | |
1492 | xx1 = xx + yy - 1; | |
1493 | } | |
1494 | else if (SCM_UNLIKELY (yy == 0)) | |
1495 | scm_num_overflow (s_scm_ceiling_quotient); | |
1496 | else if (xx < 0) | |
1497 | xx1 = xx + yy + 1; | |
1498 | qq = xx1 / yy; | |
1499 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1500 | return SCM_I_MAKINUM (qq); | |
1501 | else | |
1502 | return scm_i_inum2big (qq); | |
1503 | } | |
1504 | } | |
1505 | else if (SCM_BIGP (y)) | |
1506 | { | |
1507 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1508 | scm_remember_upto_here_1 (y); | |
1509 | if (SCM_LIKELY (sign > 0)) | |
1510 | { | |
1511 | if (SCM_LIKELY (xx > 0)) | |
1512 | return SCM_INUM1; | |
1513 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1514 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1515 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1516 | { | |
1517 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1518 | scm_remember_upto_here_1 (y); | |
1519 | return SCM_I_MAKINUM (-1); | |
1520 | } | |
1521 | else | |
1522 | return SCM_INUM0; | |
1523 | } | |
1524 | else if (xx >= 0) | |
1525 | return SCM_INUM0; | |
1526 | else | |
1527 | return SCM_INUM1; | |
1528 | } | |
1529 | else if (SCM_REALP (y)) | |
1530 | return scm_i_inexact_ceiling_quotient (xx, SCM_REAL_VALUE (y)); | |
1531 | else if (SCM_FRACTIONP (y)) | |
1532 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1533 | else | |
1534 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1535 | s_scm_ceiling_quotient); | |
1536 | } | |
1537 | else if (SCM_BIGP (x)) | |
1538 | { | |
1539 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1540 | { | |
1541 | scm_t_inum yy = SCM_I_INUM (y); | |
1542 | if (SCM_UNLIKELY (yy == 0)) | |
1543 | scm_num_overflow (s_scm_ceiling_quotient); | |
1544 | else if (SCM_UNLIKELY (yy == 1)) | |
1545 | return x; | |
1546 | else | |
1547 | { | |
1548 | SCM q = scm_i_mkbig (); | |
1549 | if (yy > 0) | |
1550 | mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
1551 | else | |
1552 | { | |
1553 | mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
1554 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1555 | } | |
1556 | scm_remember_upto_here_1 (x); | |
1557 | return scm_i_normbig (q); | |
1558 | } | |
1559 | } | |
1560 | else if (SCM_BIGP (y)) | |
1561 | { | |
1562 | SCM q = scm_i_mkbig (); | |
1563 | mpz_cdiv_q (SCM_I_BIG_MPZ (q), | |
1564 | SCM_I_BIG_MPZ (x), | |
1565 | SCM_I_BIG_MPZ (y)); | |
1566 | scm_remember_upto_here_2 (x, y); | |
1567 | return scm_i_normbig (q); | |
1568 | } | |
1569 | else if (SCM_REALP (y)) | |
1570 | return scm_i_inexact_ceiling_quotient | |
1571 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1572 | else if (SCM_FRACTIONP (y)) | |
1573 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1574 | else | |
1575 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1576 | s_scm_ceiling_quotient); | |
1577 | } | |
1578 | else if (SCM_REALP (x)) | |
1579 | { | |
1580 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1581 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1582 | return scm_i_inexact_ceiling_quotient | |
1583 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1584 | else | |
1585 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1586 | s_scm_ceiling_quotient); | |
1587 | } | |
1588 | else if (SCM_FRACTIONP (x)) | |
1589 | { | |
1590 | if (SCM_REALP (y)) | |
1591 | return scm_i_inexact_ceiling_quotient | |
1592 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1593 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1594 | return scm_i_exact_rational_ceiling_quotient (x, y); | |
1595 | else | |
1596 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG2, | |
1597 | s_scm_ceiling_quotient); | |
1598 | } | |
1599 | else | |
1600 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_quotient, x, y, SCM_ARG1, | |
1601 | s_scm_ceiling_quotient); | |
1602 | } | |
1603 | #undef FUNC_NAME | |
1604 | ||
1605 | static SCM | |
1606 | scm_i_inexact_ceiling_quotient (double x, double y) | |
1607 | { | |
1608 | if (SCM_UNLIKELY (y == 0)) | |
1609 | scm_num_overflow (s_scm_ceiling_quotient); /* or return a NaN? */ | |
1610 | else | |
1611 | return scm_from_double (ceil (x / y)); | |
1612 | } | |
1613 | ||
1614 | static SCM | |
1615 | scm_i_exact_rational_ceiling_quotient (SCM x, SCM y) | |
1616 | { | |
1617 | return scm_ceiling_quotient | |
1618 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
1619 | scm_product (scm_numerator (y), scm_denominator (x))); | |
1620 | } | |
1621 | ||
1622 | static SCM scm_i_inexact_ceiling_remainder (double x, double y); | |
1623 | static SCM scm_i_exact_rational_ceiling_remainder (SCM x, SCM y); | |
1624 | ||
1625 | SCM_PRIMITIVE_GENERIC (scm_ceiling_remainder, "ceiling-remainder", 2, 0, 0, | |
1626 | (SCM x, SCM y), | |
1627 | "Return the real number @var{r} such that\n" | |
1628 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1629 | "where @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1630 | "@lisp\n" | |
1631 | "(ceiling-remainder 123 10) @result{} -7\n" | |
1632 | "(ceiling-remainder 123 -10) @result{} 3\n" | |
1633 | "(ceiling-remainder -123 10) @result{} -3\n" | |
1634 | "(ceiling-remainder -123 -10) @result{} 7\n" | |
1635 | "(ceiling-remainder -123.2 -63.5) @result{} 3.8\n" | |
1636 | "(ceiling-remainder 16/3 -10/7) @result{} 22/21\n" | |
1637 | "@end lisp") | |
1638 | #define FUNC_NAME s_scm_ceiling_remainder | |
1639 | { | |
1640 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1641 | { | |
1642 | scm_t_inum xx = SCM_I_INUM (x); | |
1643 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1644 | { | |
1645 | scm_t_inum yy = SCM_I_INUM (y); | |
1646 | if (SCM_UNLIKELY (yy == 0)) | |
1647 | scm_num_overflow (s_scm_ceiling_remainder); | |
1648 | else | |
1649 | { | |
1650 | scm_t_inum rr = xx % yy; | |
1651 | int needs_adjustment; | |
1652 | ||
1653 | if (SCM_LIKELY (yy > 0)) | |
1654 | needs_adjustment = (rr > 0); | |
1655 | else | |
1656 | needs_adjustment = (rr < 0); | |
1657 | ||
1658 | if (needs_adjustment) | |
1659 | rr -= yy; | |
1660 | return SCM_I_MAKINUM (rr); | |
1661 | } | |
1662 | } | |
1663 | else if (SCM_BIGP (y)) | |
1664 | { | |
1665 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1666 | scm_remember_upto_here_1 (y); | |
1667 | if (SCM_LIKELY (sign > 0)) | |
1668 | { | |
1669 | if (SCM_LIKELY (xx > 0)) | |
1670 | { | |
1671 | SCM r = scm_i_mkbig (); | |
1672 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1673 | scm_remember_upto_here_1 (y); | |
1674 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1675 | return scm_i_normbig (r); | |
1676 | } | |
1677 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1678 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1679 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1680 | { | |
1681 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1682 | scm_remember_upto_here_1 (y); | |
1683 | return SCM_INUM0; | |
1684 | } | |
1685 | else | |
1686 | return x; | |
1687 | } | |
1688 | else if (xx >= 0) | |
1689 | return x; | |
1690 | else | |
1691 | { | |
1692 | SCM r = scm_i_mkbig (); | |
1693 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1694 | scm_remember_upto_here_1 (y); | |
1695 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1696 | return scm_i_normbig (r); | |
1697 | } | |
1698 | } | |
1699 | else if (SCM_REALP (y)) | |
1700 | return scm_i_inexact_ceiling_remainder (xx, SCM_REAL_VALUE (y)); | |
1701 | else if (SCM_FRACTIONP (y)) | |
1702 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1703 | else | |
1704 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1705 | s_scm_ceiling_remainder); | |
1706 | } | |
1707 | else if (SCM_BIGP (x)) | |
1708 | { | |
1709 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1710 | { | |
1711 | scm_t_inum yy = SCM_I_INUM (y); | |
1712 | if (SCM_UNLIKELY (yy == 0)) | |
1713 | scm_num_overflow (s_scm_ceiling_remainder); | |
1714 | else | |
1715 | { | |
1716 | scm_t_inum rr; | |
1717 | if (yy > 0) | |
1718 | rr = -mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
1719 | else | |
1720 | rr = mpz_fdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
1721 | scm_remember_upto_here_1 (x); | |
1722 | return SCM_I_MAKINUM (rr); | |
1723 | } | |
1724 | } | |
1725 | else if (SCM_BIGP (y)) | |
1726 | { | |
1727 | SCM r = scm_i_mkbig (); | |
1728 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
1729 | SCM_I_BIG_MPZ (x), | |
1730 | SCM_I_BIG_MPZ (y)); | |
1731 | scm_remember_upto_here_2 (x, y); | |
1732 | return scm_i_normbig (r); | |
1733 | } | |
1734 | else if (SCM_REALP (y)) | |
1735 | return scm_i_inexact_ceiling_remainder | |
1736 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
1737 | else if (SCM_FRACTIONP (y)) | |
1738 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1739 | else | |
1740 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1741 | s_scm_ceiling_remainder); | |
1742 | } | |
1743 | else if (SCM_REALP (x)) | |
1744 | { | |
1745 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1746 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1747 | return scm_i_inexact_ceiling_remainder | |
1748 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
1749 | else | |
1750 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1751 | s_scm_ceiling_remainder); | |
1752 | } | |
1753 | else if (SCM_FRACTIONP (x)) | |
1754 | { | |
1755 | if (SCM_REALP (y)) | |
1756 | return scm_i_inexact_ceiling_remainder | |
1757 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
1758 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1759 | return scm_i_exact_rational_ceiling_remainder (x, y); | |
1760 | else | |
1761 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG2, | |
1762 | s_scm_ceiling_remainder); | |
1763 | } | |
1764 | else | |
1765 | SCM_WTA_DISPATCH_2 (g_scm_ceiling_remainder, x, y, SCM_ARG1, | |
1766 | s_scm_ceiling_remainder); | |
1767 | } | |
1768 | #undef FUNC_NAME | |
1769 | ||
1770 | static SCM | |
1771 | scm_i_inexact_ceiling_remainder (double x, double y) | |
1772 | { | |
1773 | /* Although it would be more efficient to use fmod here, we can't | |
1774 | because it would in some cases produce results inconsistent with | |
1775 | scm_i_inexact_ceiling_quotient, such that x != q * y + r (not even | |
1776 | close). In particular, when x is very close to a multiple of y, | |
1777 | then r might be either 0.0 or -y, but those two cases must | |
1778 | correspond to different choices of q. If r = 0.0 then q must be | |
1779 | x/y, and if r = -y then q must be x/y+1. If quotient chooses one | |
1780 | and remainder chooses the other, it would be bad. */ | |
1781 | if (SCM_UNLIKELY (y == 0)) | |
1782 | scm_num_overflow (s_scm_ceiling_remainder); /* or return a NaN? */ | |
1783 | else | |
1784 | return scm_from_double (x - y * ceil (x / y)); | |
1785 | } | |
1786 | ||
1787 | static SCM | |
1788 | scm_i_exact_rational_ceiling_remainder (SCM x, SCM y) | |
1789 | { | |
1790 | SCM xd = scm_denominator (x); | |
1791 | SCM yd = scm_denominator (y); | |
1792 | SCM r1 = scm_ceiling_remainder (scm_product (scm_numerator (x), yd), | |
1793 | scm_product (scm_numerator (y), xd)); | |
1794 | return scm_divide (r1, scm_product (xd, yd)); | |
1795 | } | |
1796 | ||
1797 | static void scm_i_inexact_ceiling_divide (double x, double y, | |
1798 | SCM *qp, SCM *rp); | |
1799 | static void scm_i_exact_rational_ceiling_divide (SCM x, SCM y, | |
1800 | SCM *qp, SCM *rp); | |
1801 | ||
1802 | SCM_PRIMITIVE_GENERIC (scm_i_ceiling_divide, "ceiling/", 2, 0, 0, | |
1803 | (SCM x, SCM y), | |
1804 | "Return the integer @var{q} and the real number @var{r}\n" | |
1805 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
1806 | "and @math{@var{q} = ceiling(@var{x} / @var{y})}.\n" | |
1807 | "@lisp\n" | |
1808 | "(ceiling/ 123 10) @result{} 13 and -7\n" | |
1809 | "(ceiling/ 123 -10) @result{} -12 and 3\n" | |
1810 | "(ceiling/ -123 10) @result{} -12 and -3\n" | |
1811 | "(ceiling/ -123 -10) @result{} 13 and 7\n" | |
1812 | "(ceiling/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
1813 | "(ceiling/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
1814 | "@end lisp") | |
1815 | #define FUNC_NAME s_scm_i_ceiling_divide | |
1816 | { | |
1817 | SCM q, r; | |
1818 | ||
1819 | scm_ceiling_divide(x, y, &q, &r); | |
1820 | return scm_values (scm_list_2 (q, r)); | |
1821 | } | |
1822 | #undef FUNC_NAME | |
1823 | ||
1824 | #define s_scm_ceiling_divide s_scm_i_ceiling_divide | |
1825 | #define g_scm_ceiling_divide g_scm_i_ceiling_divide | |
1826 | ||
1827 | void | |
1828 | scm_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
1829 | { | |
1830 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
1831 | { | |
1832 | scm_t_inum xx = SCM_I_INUM (x); | |
1833 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1834 | { | |
1835 | scm_t_inum yy = SCM_I_INUM (y); | |
1836 | if (SCM_UNLIKELY (yy == 0)) | |
1837 | scm_num_overflow (s_scm_ceiling_divide); | |
1838 | else | |
1839 | { | |
1840 | scm_t_inum qq = xx / yy; | |
1841 | scm_t_inum rr = xx % yy; | |
1842 | int needs_adjustment; | |
1843 | ||
1844 | if (SCM_LIKELY (yy > 0)) | |
1845 | needs_adjustment = (rr > 0); | |
1846 | else | |
1847 | needs_adjustment = (rr < 0); | |
1848 | ||
1849 | if (needs_adjustment) | |
1850 | { | |
1851 | rr -= yy; | |
1852 | qq++; | |
1853 | } | |
1854 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
1855 | *qp = SCM_I_MAKINUM (qq); | |
1856 | else | |
1857 | *qp = scm_i_inum2big (qq); | |
1858 | *rp = SCM_I_MAKINUM (rr); | |
1859 | } | |
1860 | return; | |
1861 | } | |
1862 | else if (SCM_BIGP (y)) | |
1863 | { | |
1864 | int sign = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
1865 | scm_remember_upto_here_1 (y); | |
1866 | if (SCM_LIKELY (sign > 0)) | |
1867 | { | |
1868 | if (SCM_LIKELY (xx > 0)) | |
1869 | { | |
1870 | SCM r = scm_i_mkbig (); | |
1871 | mpz_sub_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), xx); | |
1872 | scm_remember_upto_here_1 (y); | |
1873 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1874 | *qp = SCM_INUM1; | |
1875 | *rp = scm_i_normbig (r); | |
1876 | } | |
1877 | else if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
1878 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
1879 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
1880 | { | |
1881 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
1882 | scm_remember_upto_here_1 (y); | |
1883 | *qp = SCM_I_MAKINUM (-1); | |
1884 | *rp = SCM_INUM0; | |
1885 | } | |
1886 | else | |
1887 | { | |
1888 | *qp = SCM_INUM0; | |
1889 | *rp = x; | |
1890 | } | |
1891 | } | |
1892 | else if (xx >= 0) | |
1893 | { | |
1894 | *qp = SCM_INUM0; | |
1895 | *rp = x; | |
1896 | } | |
1897 | else | |
1898 | { | |
1899 | SCM r = scm_i_mkbig (); | |
1900 | mpz_add_ui (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y), -xx); | |
1901 | scm_remember_upto_here_1 (y); | |
1902 | mpz_neg (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r)); | |
1903 | *qp = SCM_INUM1; | |
1904 | *rp = scm_i_normbig (r); | |
1905 | } | |
1906 | return; | |
1907 | } | |
1908 | else if (SCM_REALP (y)) | |
1909 | return scm_i_inexact_ceiling_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
1910 | else if (SCM_FRACTIONP (y)) | |
1911 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
1912 | else | |
1913 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1914 | s_scm_ceiling_divide, qp, rp); | |
1915 | } | |
1916 | else if (SCM_BIGP (x)) | |
1917 | { | |
1918 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
1919 | { | |
1920 | scm_t_inum yy = SCM_I_INUM (y); | |
1921 | if (SCM_UNLIKELY (yy == 0)) | |
1922 | scm_num_overflow (s_scm_ceiling_divide); | |
1923 | else | |
1924 | { | |
1925 | SCM q = scm_i_mkbig (); | |
1926 | SCM r = scm_i_mkbig (); | |
1927 | if (yy > 0) | |
1928 | mpz_cdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1929 | SCM_I_BIG_MPZ (x), yy); | |
1930 | else | |
1931 | { | |
1932 | mpz_fdiv_qr_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1933 | SCM_I_BIG_MPZ (x), -yy); | |
1934 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
1935 | } | |
1936 | scm_remember_upto_here_1 (x); | |
1937 | *qp = scm_i_normbig (q); | |
1938 | *rp = scm_i_normbig (r); | |
1939 | } | |
1940 | return; | |
1941 | } | |
1942 | else if (SCM_BIGP (y)) | |
1943 | { | |
1944 | SCM q = scm_i_mkbig (); | |
1945 | SCM r = scm_i_mkbig (); | |
1946 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
1947 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
1948 | scm_remember_upto_here_2 (x, y); | |
1949 | *qp = scm_i_normbig (q); | |
1950 | *rp = scm_i_normbig (r); | |
1951 | return; | |
1952 | } | |
1953 | else if (SCM_REALP (y)) | |
1954 | return scm_i_inexact_ceiling_divide | |
1955 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
1956 | else if (SCM_FRACTIONP (y)) | |
1957 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
1958 | else | |
1959 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1960 | s_scm_ceiling_divide, qp, rp); | |
1961 | } | |
1962 | else if (SCM_REALP (x)) | |
1963 | { | |
1964 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
1965 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1966 | return scm_i_inexact_ceiling_divide | |
1967 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
1968 | else | |
1969 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1970 | s_scm_ceiling_divide, qp, rp); | |
1971 | } | |
1972 | else if (SCM_FRACTIONP (x)) | |
1973 | { | |
1974 | if (SCM_REALP (y)) | |
1975 | return scm_i_inexact_ceiling_divide | |
1976 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
1977 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
1978 | return scm_i_exact_rational_ceiling_divide (x, y, qp, rp); | |
1979 | else | |
1980 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG2, | |
1981 | s_scm_ceiling_divide, qp, rp); | |
1982 | } | |
1983 | else | |
1984 | return two_valued_wta_dispatch_2 (g_scm_ceiling_divide, x, y, SCM_ARG1, | |
1985 | s_scm_ceiling_divide, qp, rp); | |
1986 | } | |
1987 | ||
1988 | static void | |
1989 | scm_i_inexact_ceiling_divide (double x, double y, SCM *qp, SCM *rp) | |
1990 | { | |
1991 | if (SCM_UNLIKELY (y == 0)) | |
1992 | scm_num_overflow (s_scm_ceiling_divide); /* or return a NaN? */ | |
1993 | else | |
1994 | { | |
1995 | double q = ceil (x / y); | |
1996 | double r = x - q * y; | |
1997 | *qp = scm_from_double (q); | |
1998 | *rp = scm_from_double (r); | |
1999 | } | |
2000 | } | |
2001 | ||
2002 | static void | |
2003 | scm_i_exact_rational_ceiling_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2004 | { | |
2005 | SCM r1; | |
2006 | SCM xd = scm_denominator (x); | |
2007 | SCM yd = scm_denominator (y); | |
2008 | ||
2009 | scm_ceiling_divide (scm_product (scm_numerator (x), yd), | |
2010 | scm_product (scm_numerator (y), xd), | |
2011 | qp, &r1); | |
2012 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2013 | } | |
2014 | ||
2015 | static SCM scm_i_inexact_truncate_quotient (double x, double y); | |
2016 | static SCM scm_i_exact_rational_truncate_quotient (SCM x, SCM y); | |
2017 | ||
2018 | SCM_PRIMITIVE_GENERIC (scm_truncate_quotient, "truncate-quotient", 2, 0, 0, | |
2019 | (SCM x, SCM y), | |
2020 | "Return @math{@var{x} / @var{y}} rounded toward zero.\n" | |
2021 | "@lisp\n" | |
2022 | "(truncate-quotient 123 10) @result{} 12\n" | |
2023 | "(truncate-quotient 123 -10) @result{} -12\n" | |
2024 | "(truncate-quotient -123 10) @result{} -12\n" | |
2025 | "(truncate-quotient -123 -10) @result{} 12\n" | |
2026 | "(truncate-quotient -123.2 -63.5) @result{} 1.0\n" | |
2027 | "(truncate-quotient 16/3 -10/7) @result{} -3\n" | |
2028 | "@end lisp") | |
2029 | #define FUNC_NAME s_scm_truncate_quotient | |
2030 | { | |
2031 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2032 | { | |
2033 | scm_t_inum xx = SCM_I_INUM (x); | |
2034 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2035 | { | |
2036 | scm_t_inum yy = SCM_I_INUM (y); | |
2037 | if (SCM_UNLIKELY (yy == 0)) | |
2038 | scm_num_overflow (s_scm_truncate_quotient); | |
2039 | else | |
2040 | { | |
2041 | scm_t_inum qq = xx / yy; | |
2042 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2043 | return SCM_I_MAKINUM (qq); | |
2044 | else | |
2045 | return scm_i_inum2big (qq); | |
2046 | } | |
2047 | } | |
2048 | else if (SCM_BIGP (y)) | |
2049 | { | |
2050 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2051 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2052 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2053 | { | |
2054 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2055 | scm_remember_upto_here_1 (y); | |
2056 | return SCM_I_MAKINUM (-1); | |
2057 | } | |
2058 | else | |
2059 | return SCM_INUM0; | |
2060 | } | |
2061 | else if (SCM_REALP (y)) | |
2062 | return scm_i_inexact_truncate_quotient (xx, SCM_REAL_VALUE (y)); | |
2063 | else if (SCM_FRACTIONP (y)) | |
2064 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2065 | else | |
2066 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2067 | s_scm_truncate_quotient); | |
2068 | } | |
2069 | else if (SCM_BIGP (x)) | |
2070 | { | |
2071 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2072 | { | |
2073 | scm_t_inum yy = SCM_I_INUM (y); | |
2074 | if (SCM_UNLIKELY (yy == 0)) | |
2075 | scm_num_overflow (s_scm_truncate_quotient); | |
2076 | else if (SCM_UNLIKELY (yy == 1)) | |
2077 | return x; | |
2078 | else | |
2079 | { | |
2080 | SCM q = scm_i_mkbig (); | |
2081 | if (yy > 0) | |
2082 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), yy); | |
2083 | else | |
2084 | { | |
2085 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (x), -yy); | |
2086 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2087 | } | |
2088 | scm_remember_upto_here_1 (x); | |
2089 | return scm_i_normbig (q); | |
2090 | } | |
2091 | } | |
2092 | else if (SCM_BIGP (y)) | |
2093 | { | |
2094 | SCM q = scm_i_mkbig (); | |
2095 | mpz_tdiv_q (SCM_I_BIG_MPZ (q), | |
2096 | SCM_I_BIG_MPZ (x), | |
2097 | SCM_I_BIG_MPZ (y)); | |
2098 | scm_remember_upto_here_2 (x, y); | |
2099 | return scm_i_normbig (q); | |
2100 | } | |
2101 | else if (SCM_REALP (y)) | |
2102 | return scm_i_inexact_truncate_quotient | |
2103 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2104 | else if (SCM_FRACTIONP (y)) | |
2105 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2106 | else | |
2107 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2108 | s_scm_truncate_quotient); | |
2109 | } | |
2110 | else if (SCM_REALP (x)) | |
2111 | { | |
2112 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2113 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2114 | return scm_i_inexact_truncate_quotient | |
2115 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2116 | else | |
2117 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2118 | s_scm_truncate_quotient); | |
2119 | } | |
2120 | else if (SCM_FRACTIONP (x)) | |
2121 | { | |
2122 | if (SCM_REALP (y)) | |
2123 | return scm_i_inexact_truncate_quotient | |
2124 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2125 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2126 | return scm_i_exact_rational_truncate_quotient (x, y); | |
2127 | else | |
2128 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG2, | |
2129 | s_scm_truncate_quotient); | |
2130 | } | |
2131 | else | |
2132 | SCM_WTA_DISPATCH_2 (g_scm_truncate_quotient, x, y, SCM_ARG1, | |
2133 | s_scm_truncate_quotient); | |
2134 | } | |
2135 | #undef FUNC_NAME | |
2136 | ||
2137 | static SCM | |
2138 | scm_i_inexact_truncate_quotient (double x, double y) | |
2139 | { | |
2140 | if (SCM_UNLIKELY (y == 0)) | |
2141 | scm_num_overflow (s_scm_truncate_quotient); /* or return a NaN? */ | |
2142 | else | |
c251ab63 | 2143 | return scm_from_double (trunc (x / y)); |
8f9da340 MW |
2144 | } |
2145 | ||
2146 | static SCM | |
2147 | scm_i_exact_rational_truncate_quotient (SCM x, SCM y) | |
2148 | { | |
2149 | return scm_truncate_quotient | |
2150 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2151 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2152 | } | |
2153 | ||
2154 | static SCM scm_i_inexact_truncate_remainder (double x, double y); | |
2155 | static SCM scm_i_exact_rational_truncate_remainder (SCM x, SCM y); | |
2156 | ||
2157 | SCM_PRIMITIVE_GENERIC (scm_truncate_remainder, "truncate-remainder", 2, 0, 0, | |
2158 | (SCM x, SCM y), | |
2159 | "Return the real number @var{r} such that\n" | |
2160 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2161 | "where @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2162 | "@lisp\n" | |
2163 | "(truncate-remainder 123 10) @result{} 3\n" | |
2164 | "(truncate-remainder 123 -10) @result{} 3\n" | |
2165 | "(truncate-remainder -123 10) @result{} -3\n" | |
2166 | "(truncate-remainder -123 -10) @result{} -3\n" | |
2167 | "(truncate-remainder -123.2 -63.5) @result{} -59.7\n" | |
2168 | "(truncate-remainder 16/3 -10/7) @result{} 22/21\n" | |
2169 | "@end lisp") | |
2170 | #define FUNC_NAME s_scm_truncate_remainder | |
2171 | { | |
2172 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2173 | { | |
2174 | scm_t_inum xx = SCM_I_INUM (x); | |
2175 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2176 | { | |
2177 | scm_t_inum yy = SCM_I_INUM (y); | |
2178 | if (SCM_UNLIKELY (yy == 0)) | |
2179 | scm_num_overflow (s_scm_truncate_remainder); | |
2180 | else | |
2181 | return SCM_I_MAKINUM (xx % yy); | |
2182 | } | |
2183 | else if (SCM_BIGP (y)) | |
2184 | { | |
2185 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2186 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2187 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2188 | { | |
2189 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2190 | scm_remember_upto_here_1 (y); | |
2191 | return SCM_INUM0; | |
2192 | } | |
2193 | else | |
2194 | return x; | |
2195 | } | |
2196 | else if (SCM_REALP (y)) | |
2197 | return scm_i_inexact_truncate_remainder (xx, SCM_REAL_VALUE (y)); | |
2198 | else if (SCM_FRACTIONP (y)) | |
2199 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2200 | else | |
2201 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2202 | s_scm_truncate_remainder); | |
2203 | } | |
2204 | else if (SCM_BIGP (x)) | |
2205 | { | |
2206 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2207 | { | |
2208 | scm_t_inum yy = SCM_I_INUM (y); | |
2209 | if (SCM_UNLIKELY (yy == 0)) | |
2210 | scm_num_overflow (s_scm_truncate_remainder); | |
2211 | else | |
2212 | { | |
2213 | scm_t_inum rr = (mpz_tdiv_ui (SCM_I_BIG_MPZ (x), | |
2214 | (yy > 0) ? yy : -yy) | |
2215 | * mpz_sgn (SCM_I_BIG_MPZ (x))); | |
2216 | scm_remember_upto_here_1 (x); | |
2217 | return SCM_I_MAKINUM (rr); | |
2218 | } | |
2219 | } | |
2220 | else if (SCM_BIGP (y)) | |
2221 | { | |
2222 | SCM r = scm_i_mkbig (); | |
2223 | mpz_tdiv_r (SCM_I_BIG_MPZ (r), | |
2224 | SCM_I_BIG_MPZ (x), | |
2225 | SCM_I_BIG_MPZ (y)); | |
2226 | scm_remember_upto_here_2 (x, y); | |
2227 | return scm_i_normbig (r); | |
2228 | } | |
2229 | else if (SCM_REALP (y)) | |
2230 | return scm_i_inexact_truncate_remainder | |
2231 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2232 | else if (SCM_FRACTIONP (y)) | |
2233 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2234 | else | |
2235 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2236 | s_scm_truncate_remainder); | |
2237 | } | |
2238 | else if (SCM_REALP (x)) | |
2239 | { | |
2240 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2241 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2242 | return scm_i_inexact_truncate_remainder | |
2243 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2244 | else | |
2245 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2246 | s_scm_truncate_remainder); | |
2247 | } | |
2248 | else if (SCM_FRACTIONP (x)) | |
2249 | { | |
2250 | if (SCM_REALP (y)) | |
2251 | return scm_i_inexact_truncate_remainder | |
2252 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2253 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2254 | return scm_i_exact_rational_truncate_remainder (x, y); | |
2255 | else | |
2256 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG2, | |
2257 | s_scm_truncate_remainder); | |
2258 | } | |
2259 | else | |
2260 | SCM_WTA_DISPATCH_2 (g_scm_truncate_remainder, x, y, SCM_ARG1, | |
2261 | s_scm_truncate_remainder); | |
2262 | } | |
2263 | #undef FUNC_NAME | |
2264 | ||
2265 | static SCM | |
2266 | scm_i_inexact_truncate_remainder (double x, double y) | |
2267 | { | |
2268 | /* Although it would be more efficient to use fmod here, we can't | |
2269 | because it would in some cases produce results inconsistent with | |
2270 | scm_i_inexact_truncate_quotient, such that x != q * y + r (not even | |
2271 | close). In particular, when x is very close to a multiple of y, | |
2272 | then r might be either 0.0 or sgn(x)*|y|, but those two cases must | |
2273 | correspond to different choices of q. If quotient chooses one and | |
2274 | remainder chooses the other, it would be bad. */ | |
2275 | if (SCM_UNLIKELY (y == 0)) | |
2276 | scm_num_overflow (s_scm_truncate_remainder); /* or return a NaN? */ | |
2277 | else | |
c251ab63 | 2278 | return scm_from_double (x - y * trunc (x / y)); |
8f9da340 MW |
2279 | } |
2280 | ||
2281 | static SCM | |
2282 | scm_i_exact_rational_truncate_remainder (SCM x, SCM y) | |
2283 | { | |
2284 | SCM xd = scm_denominator (x); | |
2285 | SCM yd = scm_denominator (y); | |
2286 | SCM r1 = scm_truncate_remainder (scm_product (scm_numerator (x), yd), | |
2287 | scm_product (scm_numerator (y), xd)); | |
2288 | return scm_divide (r1, scm_product (xd, yd)); | |
2289 | } | |
2290 | ||
2291 | ||
2292 | static void scm_i_inexact_truncate_divide (double x, double y, | |
2293 | SCM *qp, SCM *rp); | |
2294 | static void scm_i_exact_rational_truncate_divide (SCM x, SCM y, | |
2295 | SCM *qp, SCM *rp); | |
2296 | ||
2297 | SCM_PRIMITIVE_GENERIC (scm_i_truncate_divide, "truncate/", 2, 0, 0, | |
2298 | (SCM x, SCM y), | |
2299 | "Return the integer @var{q} and the real number @var{r}\n" | |
2300 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2301 | "and @math{@var{q} = truncate(@var{x} / @var{y})}.\n" | |
2302 | "@lisp\n" | |
2303 | "(truncate/ 123 10) @result{} 12 and 3\n" | |
2304 | "(truncate/ 123 -10) @result{} -12 and 3\n" | |
2305 | "(truncate/ -123 10) @result{} -12 and -3\n" | |
2306 | "(truncate/ -123 -10) @result{} 12 and -3\n" | |
2307 | "(truncate/ -123.2 -63.5) @result{} 1.0 and -59.7\n" | |
2308 | "(truncate/ 16/3 -10/7) @result{} -3 and 22/21\n" | |
2309 | "@end lisp") | |
2310 | #define FUNC_NAME s_scm_i_truncate_divide | |
2311 | { | |
2312 | SCM q, r; | |
2313 | ||
2314 | scm_truncate_divide(x, y, &q, &r); | |
2315 | return scm_values (scm_list_2 (q, r)); | |
2316 | } | |
2317 | #undef FUNC_NAME | |
2318 | ||
2319 | #define s_scm_truncate_divide s_scm_i_truncate_divide | |
2320 | #define g_scm_truncate_divide g_scm_i_truncate_divide | |
2321 | ||
2322 | void | |
2323 | scm_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2324 | { | |
2325 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2326 | { | |
2327 | scm_t_inum xx = SCM_I_INUM (x); | |
2328 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2329 | { | |
2330 | scm_t_inum yy = SCM_I_INUM (y); | |
2331 | if (SCM_UNLIKELY (yy == 0)) | |
2332 | scm_num_overflow (s_scm_truncate_divide); | |
2333 | else | |
2334 | { | |
2335 | scm_t_inum qq = xx / yy; | |
2336 | scm_t_inum rr = xx % yy; | |
2337 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2338 | *qp = SCM_I_MAKINUM (qq); | |
2339 | else | |
2340 | *qp = scm_i_inum2big (qq); | |
2341 | *rp = SCM_I_MAKINUM (rr); | |
2342 | } | |
2343 | return; | |
2344 | } | |
2345 | else if (SCM_BIGP (y)) | |
2346 | { | |
2347 | if (SCM_UNLIKELY (xx == SCM_MOST_NEGATIVE_FIXNUM) | |
2348 | && SCM_UNLIKELY (mpz_cmp_ui (SCM_I_BIG_MPZ (y), | |
2349 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
2350 | { | |
2351 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
2352 | scm_remember_upto_here_1 (y); | |
2353 | *qp = SCM_I_MAKINUM (-1); | |
2354 | *rp = SCM_INUM0; | |
2355 | } | |
2356 | else | |
2357 | { | |
2358 | *qp = SCM_INUM0; | |
2359 | *rp = x; | |
2360 | } | |
2361 | return; | |
2362 | } | |
2363 | else if (SCM_REALP (y)) | |
2364 | return scm_i_inexact_truncate_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2365 | else if (SCM_FRACTIONP (y)) | |
2366 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2367 | else | |
2368 | return two_valued_wta_dispatch_2 | |
2369 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2370 | s_scm_truncate_divide, qp, rp); | |
2371 | } | |
2372 | else if (SCM_BIGP (x)) | |
2373 | { | |
2374 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2375 | { | |
2376 | scm_t_inum yy = SCM_I_INUM (y); | |
2377 | if (SCM_UNLIKELY (yy == 0)) | |
2378 | scm_num_overflow (s_scm_truncate_divide); | |
2379 | else | |
2380 | { | |
2381 | SCM q = scm_i_mkbig (); | |
2382 | scm_t_inum rr; | |
2383 | if (yy > 0) | |
2384 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2385 | SCM_I_BIG_MPZ (x), yy); | |
2386 | else | |
2387 | { | |
2388 | rr = mpz_tdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2389 | SCM_I_BIG_MPZ (x), -yy); | |
2390 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2391 | } | |
2392 | rr *= mpz_sgn (SCM_I_BIG_MPZ (x)); | |
2393 | scm_remember_upto_here_1 (x); | |
2394 | *qp = scm_i_normbig (q); | |
2395 | *rp = SCM_I_MAKINUM (rr); | |
2396 | } | |
2397 | return; | |
2398 | } | |
2399 | else if (SCM_BIGP (y)) | |
2400 | { | |
2401 | SCM q = scm_i_mkbig (); | |
2402 | SCM r = scm_i_mkbig (); | |
2403 | mpz_tdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2404 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2405 | scm_remember_upto_here_2 (x, y); | |
2406 | *qp = scm_i_normbig (q); | |
2407 | *rp = scm_i_normbig (r); | |
2408 | } | |
2409 | else if (SCM_REALP (y)) | |
2410 | return scm_i_inexact_truncate_divide | |
2411 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
2412 | else if (SCM_FRACTIONP (y)) | |
2413 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2414 | else | |
2415 | return two_valued_wta_dispatch_2 | |
2416 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2417 | s_scm_truncate_divide, qp, rp); | |
2418 | } | |
2419 | else if (SCM_REALP (x)) | |
2420 | { | |
2421 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2422 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2423 | return scm_i_inexact_truncate_divide | |
2424 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
2425 | else | |
2426 | return two_valued_wta_dispatch_2 | |
2427 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2428 | s_scm_truncate_divide, qp, rp); | |
2429 | } | |
2430 | else if (SCM_FRACTIONP (x)) | |
2431 | { | |
2432 | if (SCM_REALP (y)) | |
2433 | return scm_i_inexact_truncate_divide | |
2434 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
2435 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2436 | return scm_i_exact_rational_truncate_divide (x, y, qp, rp); | |
2437 | else | |
2438 | return two_valued_wta_dispatch_2 | |
2439 | (g_scm_truncate_divide, x, y, SCM_ARG2, | |
2440 | s_scm_truncate_divide, qp, rp); | |
2441 | } | |
2442 | else | |
2443 | return two_valued_wta_dispatch_2 (g_scm_truncate_divide, x, y, SCM_ARG1, | |
2444 | s_scm_truncate_divide, qp, rp); | |
2445 | } | |
2446 | ||
2447 | static void | |
2448 | scm_i_inexact_truncate_divide (double x, double y, SCM *qp, SCM *rp) | |
2449 | { | |
2450 | if (SCM_UNLIKELY (y == 0)) | |
2451 | scm_num_overflow (s_scm_truncate_divide); /* or return a NaN? */ | |
2452 | else | |
2453 | { | |
c15fe499 MW |
2454 | double q = trunc (x / y); |
2455 | double r = x - q * y; | |
8f9da340 MW |
2456 | *qp = scm_from_double (q); |
2457 | *rp = scm_from_double (r); | |
2458 | } | |
2459 | } | |
2460 | ||
2461 | static void | |
2462 | scm_i_exact_rational_truncate_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2463 | { | |
2464 | SCM r1; | |
2465 | SCM xd = scm_denominator (x); | |
2466 | SCM yd = scm_denominator (y); | |
2467 | ||
2468 | scm_truncate_divide (scm_product (scm_numerator (x), yd), | |
2469 | scm_product (scm_numerator (y), xd), | |
2470 | qp, &r1); | |
2471 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
2472 | } | |
2473 | ||
ff62c168 MW |
2474 | static SCM scm_i_inexact_centered_quotient (double x, double y); |
2475 | static SCM scm_i_bigint_centered_quotient (SCM x, SCM y); | |
03ddd15b | 2476 | static SCM scm_i_exact_rational_centered_quotient (SCM x, SCM y); |
ff62c168 | 2477 | |
8f9da340 MW |
2478 | SCM_PRIMITIVE_GENERIC (scm_centered_quotient, "centered-quotient", 2, 0, 0, |
2479 | (SCM x, SCM y), | |
2480 | "Return the integer @var{q} such that\n" | |
2481 | "@math{@var{x} = @var{q}*@var{y} + @var{r}} where\n" | |
2482 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2483 | "@lisp\n" | |
2484 | "(centered-quotient 123 10) @result{} 12\n" | |
2485 | "(centered-quotient 123 -10) @result{} -12\n" | |
2486 | "(centered-quotient -123 10) @result{} -12\n" | |
2487 | "(centered-quotient -123 -10) @result{} 12\n" | |
2488 | "(centered-quotient -123.2 -63.5) @result{} 2.0\n" | |
2489 | "(centered-quotient 16/3 -10/7) @result{} -4\n" | |
2490 | "@end lisp") | |
2491 | #define FUNC_NAME s_scm_centered_quotient | |
2492 | { | |
2493 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2494 | { | |
2495 | scm_t_inum xx = SCM_I_INUM (x); | |
2496 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2497 | { | |
2498 | scm_t_inum yy = SCM_I_INUM (y); | |
2499 | if (SCM_UNLIKELY (yy == 0)) | |
2500 | scm_num_overflow (s_scm_centered_quotient); | |
2501 | else | |
2502 | { | |
2503 | scm_t_inum qq = xx / yy; | |
2504 | scm_t_inum rr = xx % yy; | |
2505 | if (SCM_LIKELY (xx > 0)) | |
2506 | { | |
2507 | if (SCM_LIKELY (yy > 0)) | |
2508 | { | |
2509 | if (rr >= (yy + 1) / 2) | |
2510 | qq++; | |
2511 | } | |
2512 | else | |
2513 | { | |
2514 | if (rr >= (1 - yy) / 2) | |
2515 | qq--; | |
2516 | } | |
2517 | } | |
2518 | else | |
2519 | { | |
2520 | if (SCM_LIKELY (yy > 0)) | |
2521 | { | |
2522 | if (rr < -yy / 2) | |
2523 | qq--; | |
2524 | } | |
2525 | else | |
2526 | { | |
2527 | if (rr < yy / 2) | |
2528 | qq++; | |
2529 | } | |
2530 | } | |
2531 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2532 | return SCM_I_MAKINUM (qq); | |
2533 | else | |
2534 | return scm_i_inum2big (qq); | |
2535 | } | |
2536 | } | |
2537 | else if (SCM_BIGP (y)) | |
2538 | { | |
2539 | /* Pass a denormalized bignum version of x (even though it | |
2540 | can fit in a fixnum) to scm_i_bigint_centered_quotient */ | |
2541 | return scm_i_bigint_centered_quotient (scm_i_long2big (xx), y); | |
2542 | } | |
2543 | else if (SCM_REALP (y)) | |
2544 | return scm_i_inexact_centered_quotient (xx, SCM_REAL_VALUE (y)); | |
2545 | else if (SCM_FRACTIONP (y)) | |
2546 | return scm_i_exact_rational_centered_quotient (x, y); | |
2547 | else | |
2548 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2549 | s_scm_centered_quotient); | |
2550 | } | |
2551 | else if (SCM_BIGP (x)) | |
2552 | { | |
2553 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2554 | { | |
2555 | scm_t_inum yy = SCM_I_INUM (y); | |
2556 | if (SCM_UNLIKELY (yy == 0)) | |
2557 | scm_num_overflow (s_scm_centered_quotient); | |
2558 | else if (SCM_UNLIKELY (yy == 1)) | |
2559 | return x; | |
2560 | else | |
2561 | { | |
2562 | SCM q = scm_i_mkbig (); | |
2563 | scm_t_inum rr; | |
2564 | /* Arrange for rr to initially be non-positive, | |
2565 | because that simplifies the test to see | |
2566 | if it is within the needed bounds. */ | |
2567 | if (yy > 0) | |
2568 | { | |
2569 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2570 | SCM_I_BIG_MPZ (x), yy); | |
2571 | scm_remember_upto_here_1 (x); | |
2572 | if (rr < -yy / 2) | |
2573 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2574 | SCM_I_BIG_MPZ (q), 1); | |
2575 | } | |
2576 | else | |
2577 | { | |
2578 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
2579 | SCM_I_BIG_MPZ (x), -yy); | |
2580 | scm_remember_upto_here_1 (x); | |
2581 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
2582 | if (rr < yy / 2) | |
2583 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2584 | SCM_I_BIG_MPZ (q), 1); | |
2585 | } | |
2586 | return scm_i_normbig (q); | |
2587 | } | |
2588 | } | |
2589 | else if (SCM_BIGP (y)) | |
2590 | return scm_i_bigint_centered_quotient (x, y); | |
2591 | else if (SCM_REALP (y)) | |
2592 | return scm_i_inexact_centered_quotient | |
2593 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2594 | else if (SCM_FRACTIONP (y)) | |
2595 | return scm_i_exact_rational_centered_quotient (x, y); | |
2596 | else | |
2597 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2598 | s_scm_centered_quotient); | |
2599 | } | |
2600 | else if (SCM_REALP (x)) | |
2601 | { | |
2602 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2603 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2604 | return scm_i_inexact_centered_quotient | |
2605 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2606 | else | |
2607 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2608 | s_scm_centered_quotient); | |
2609 | } | |
2610 | else if (SCM_FRACTIONP (x)) | |
2611 | { | |
2612 | if (SCM_REALP (y)) | |
2613 | return scm_i_inexact_centered_quotient | |
2614 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2615 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2616 | return scm_i_exact_rational_centered_quotient (x, y); | |
2617 | else | |
2618 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG2, | |
2619 | s_scm_centered_quotient); | |
2620 | } | |
2621 | else | |
2622 | SCM_WTA_DISPATCH_2 (g_scm_centered_quotient, x, y, SCM_ARG1, | |
2623 | s_scm_centered_quotient); | |
2624 | } | |
2625 | #undef FUNC_NAME | |
2626 | ||
2627 | static SCM | |
2628 | scm_i_inexact_centered_quotient (double x, double y) | |
2629 | { | |
2630 | if (SCM_LIKELY (y > 0)) | |
2631 | return scm_from_double (floor (x/y + 0.5)); | |
2632 | else if (SCM_LIKELY (y < 0)) | |
2633 | return scm_from_double (ceil (x/y - 0.5)); | |
2634 | else if (y == 0) | |
2635 | scm_num_overflow (s_scm_centered_quotient); /* or return a NaN? */ | |
2636 | else | |
2637 | return scm_nan (); | |
2638 | } | |
2639 | ||
2640 | /* Assumes that both x and y are bigints, though | |
2641 | x might be able to fit into a fixnum. */ | |
2642 | static SCM | |
2643 | scm_i_bigint_centered_quotient (SCM x, SCM y) | |
2644 | { | |
2645 | SCM q, r, min_r; | |
2646 | ||
2647 | /* Note that x might be small enough to fit into a | |
2648 | fixnum, so we must not let it escape into the wild */ | |
2649 | q = scm_i_mkbig (); | |
2650 | r = scm_i_mkbig (); | |
2651 | ||
2652 | /* min_r will eventually become -abs(y)/2 */ | |
2653 | min_r = scm_i_mkbig (); | |
2654 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2655 | SCM_I_BIG_MPZ (y), 1); | |
2656 | ||
2657 | /* Arrange for rr to initially be non-positive, | |
2658 | because that simplifies the test to see | |
2659 | if it is within the needed bounds. */ | |
2660 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2661 | { | |
2662 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2663 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2664 | scm_remember_upto_here_2 (x, y); | |
2665 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2666 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2667 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
2668 | SCM_I_BIG_MPZ (q), 1); | |
2669 | } | |
2670 | else | |
2671 | { | |
2672 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
2673 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2674 | scm_remember_upto_here_2 (x, y); | |
2675 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2676 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
2677 | SCM_I_BIG_MPZ (q), 1); | |
2678 | } | |
2679 | scm_remember_upto_here_2 (r, min_r); | |
2680 | return scm_i_normbig (q); | |
2681 | } | |
2682 | ||
2683 | static SCM | |
2684 | scm_i_exact_rational_centered_quotient (SCM x, SCM y) | |
2685 | { | |
2686 | return scm_centered_quotient | |
2687 | (scm_product (scm_numerator (x), scm_denominator (y)), | |
2688 | scm_product (scm_numerator (y), scm_denominator (x))); | |
2689 | } | |
2690 | ||
2691 | static SCM scm_i_inexact_centered_remainder (double x, double y); | |
2692 | static SCM scm_i_bigint_centered_remainder (SCM x, SCM y); | |
2693 | static SCM scm_i_exact_rational_centered_remainder (SCM x, SCM y); | |
2694 | ||
2695 | SCM_PRIMITIVE_GENERIC (scm_centered_remainder, "centered-remainder", 2, 0, 0, | |
2696 | (SCM x, SCM y), | |
2697 | "Return the real number @var{r} such that\n" | |
2698 | "@math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}\n" | |
2699 | "and @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2700 | "for some integer @var{q}.\n" | |
2701 | "@lisp\n" | |
2702 | "(centered-remainder 123 10) @result{} 3\n" | |
2703 | "(centered-remainder 123 -10) @result{} 3\n" | |
2704 | "(centered-remainder -123 10) @result{} -3\n" | |
2705 | "(centered-remainder -123 -10) @result{} -3\n" | |
2706 | "(centered-remainder -123.2 -63.5) @result{} 3.8\n" | |
2707 | "(centered-remainder 16/3 -10/7) @result{} -8/21\n" | |
2708 | "@end lisp") | |
2709 | #define FUNC_NAME s_scm_centered_remainder | |
2710 | { | |
2711 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2712 | { | |
2713 | scm_t_inum xx = SCM_I_INUM (x); | |
2714 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2715 | { | |
2716 | scm_t_inum yy = SCM_I_INUM (y); | |
2717 | if (SCM_UNLIKELY (yy == 0)) | |
2718 | scm_num_overflow (s_scm_centered_remainder); | |
2719 | else | |
2720 | { | |
2721 | scm_t_inum rr = xx % yy; | |
2722 | if (SCM_LIKELY (xx > 0)) | |
2723 | { | |
2724 | if (SCM_LIKELY (yy > 0)) | |
2725 | { | |
2726 | if (rr >= (yy + 1) / 2) | |
2727 | rr -= yy; | |
2728 | } | |
2729 | else | |
2730 | { | |
2731 | if (rr >= (1 - yy) / 2) | |
2732 | rr += yy; | |
2733 | } | |
2734 | } | |
2735 | else | |
2736 | { | |
2737 | if (SCM_LIKELY (yy > 0)) | |
2738 | { | |
2739 | if (rr < -yy / 2) | |
2740 | rr += yy; | |
2741 | } | |
2742 | else | |
2743 | { | |
2744 | if (rr < yy / 2) | |
2745 | rr -= yy; | |
2746 | } | |
2747 | } | |
2748 | return SCM_I_MAKINUM (rr); | |
2749 | } | |
2750 | } | |
2751 | else if (SCM_BIGP (y)) | |
2752 | { | |
2753 | /* Pass a denormalized bignum version of x (even though it | |
2754 | can fit in a fixnum) to scm_i_bigint_centered_remainder */ | |
2755 | return scm_i_bigint_centered_remainder (scm_i_long2big (xx), y); | |
2756 | } | |
2757 | else if (SCM_REALP (y)) | |
2758 | return scm_i_inexact_centered_remainder (xx, SCM_REAL_VALUE (y)); | |
2759 | else if (SCM_FRACTIONP (y)) | |
2760 | return scm_i_exact_rational_centered_remainder (x, y); | |
2761 | else | |
2762 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2763 | s_scm_centered_remainder); | |
2764 | } | |
2765 | else if (SCM_BIGP (x)) | |
2766 | { | |
2767 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2768 | { | |
2769 | scm_t_inum yy = SCM_I_INUM (y); | |
2770 | if (SCM_UNLIKELY (yy == 0)) | |
2771 | scm_num_overflow (s_scm_centered_remainder); | |
2772 | else | |
2773 | { | |
2774 | scm_t_inum rr; | |
2775 | /* Arrange for rr to initially be non-positive, | |
2776 | because that simplifies the test to see | |
2777 | if it is within the needed bounds. */ | |
2778 | if (yy > 0) | |
2779 | { | |
2780 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), yy); | |
2781 | scm_remember_upto_here_1 (x); | |
2782 | if (rr < -yy / 2) | |
2783 | rr += yy; | |
2784 | } | |
2785 | else | |
2786 | { | |
2787 | rr = - mpz_cdiv_ui (SCM_I_BIG_MPZ (x), -yy); | |
2788 | scm_remember_upto_here_1 (x); | |
2789 | if (rr < yy / 2) | |
2790 | rr -= yy; | |
2791 | } | |
2792 | return SCM_I_MAKINUM (rr); | |
2793 | } | |
2794 | } | |
2795 | else if (SCM_BIGP (y)) | |
2796 | return scm_i_bigint_centered_remainder (x, y); | |
2797 | else if (SCM_REALP (y)) | |
2798 | return scm_i_inexact_centered_remainder | |
2799 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); | |
2800 | else if (SCM_FRACTIONP (y)) | |
2801 | return scm_i_exact_rational_centered_remainder (x, y); | |
2802 | else | |
2803 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2804 | s_scm_centered_remainder); | |
2805 | } | |
2806 | else if (SCM_REALP (x)) | |
2807 | { | |
2808 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
2809 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2810 | return scm_i_inexact_centered_remainder | |
2811 | (SCM_REAL_VALUE (x), scm_to_double (y)); | |
2812 | else | |
2813 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2814 | s_scm_centered_remainder); | |
2815 | } | |
2816 | else if (SCM_FRACTIONP (x)) | |
2817 | { | |
2818 | if (SCM_REALP (y)) | |
2819 | return scm_i_inexact_centered_remainder | |
2820 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); | |
2821 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
2822 | return scm_i_exact_rational_centered_remainder (x, y); | |
2823 | else | |
2824 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG2, | |
2825 | s_scm_centered_remainder); | |
2826 | } | |
2827 | else | |
2828 | SCM_WTA_DISPATCH_2 (g_scm_centered_remainder, x, y, SCM_ARG1, | |
2829 | s_scm_centered_remainder); | |
2830 | } | |
2831 | #undef FUNC_NAME | |
2832 | ||
2833 | static SCM | |
2834 | scm_i_inexact_centered_remainder (double x, double y) | |
2835 | { | |
2836 | double q; | |
2837 | ||
2838 | /* Although it would be more efficient to use fmod here, we can't | |
2839 | because it would in some cases produce results inconsistent with | |
2840 | scm_i_inexact_centered_quotient, such that x != r + q * y (not even | |
2841 | close). In particular, when x-y/2 is very close to a multiple of | |
2842 | y, then r might be either -abs(y/2) or abs(y/2)-epsilon, but those | |
2843 | two cases must correspond to different choices of q. If quotient | |
2844 | chooses one and remainder chooses the other, it would be bad. */ | |
2845 | if (SCM_LIKELY (y > 0)) | |
2846 | q = floor (x/y + 0.5); | |
2847 | else if (SCM_LIKELY (y < 0)) | |
2848 | q = ceil (x/y - 0.5); | |
2849 | else if (y == 0) | |
2850 | scm_num_overflow (s_scm_centered_remainder); /* or return a NaN? */ | |
2851 | else | |
2852 | return scm_nan (); | |
2853 | return scm_from_double (x - q * y); | |
2854 | } | |
2855 | ||
2856 | /* Assumes that both x and y are bigints, though | |
2857 | x might be able to fit into a fixnum. */ | |
2858 | static SCM | |
2859 | scm_i_bigint_centered_remainder (SCM x, SCM y) | |
2860 | { | |
2861 | SCM r, min_r; | |
2862 | ||
2863 | /* Note that x might be small enough to fit into a | |
2864 | fixnum, so we must not let it escape into the wild */ | |
2865 | r = scm_i_mkbig (); | |
2866 | ||
2867 | /* min_r will eventually become -abs(y)/2 */ | |
2868 | min_r = scm_i_mkbig (); | |
2869 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
2870 | SCM_I_BIG_MPZ (y), 1); | |
2871 | ||
2872 | /* Arrange for rr to initially be non-positive, | |
2873 | because that simplifies the test to see | |
2874 | if it is within the needed bounds. */ | |
2875 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
2876 | { | |
2877 | mpz_cdiv_r (SCM_I_BIG_MPZ (r), | |
2878 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2879 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
2880 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2881 | mpz_add (SCM_I_BIG_MPZ (r), | |
2882 | SCM_I_BIG_MPZ (r), | |
2883 | SCM_I_BIG_MPZ (y)); | |
2884 | } | |
2885 | else | |
2886 | { | |
2887 | mpz_fdiv_r (SCM_I_BIG_MPZ (r), | |
2888 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2889 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
2890 | mpz_sub (SCM_I_BIG_MPZ (r), | |
2891 | SCM_I_BIG_MPZ (r), | |
2892 | SCM_I_BIG_MPZ (y)); | |
2893 | } | |
2894 | scm_remember_upto_here_2 (x, y); | |
2895 | return scm_i_normbig (r); | |
2896 | } | |
2897 | ||
2898 | static SCM | |
2899 | scm_i_exact_rational_centered_remainder (SCM x, SCM y) | |
2900 | { | |
2901 | SCM xd = scm_denominator (x); | |
2902 | SCM yd = scm_denominator (y); | |
2903 | SCM r1 = scm_centered_remainder (scm_product (scm_numerator (x), yd), | |
2904 | scm_product (scm_numerator (y), xd)); | |
2905 | return scm_divide (r1, scm_product (xd, yd)); | |
2906 | } | |
2907 | ||
2908 | ||
2909 | static void scm_i_inexact_centered_divide (double x, double y, | |
2910 | SCM *qp, SCM *rp); | |
2911 | static void scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
2912 | static void scm_i_exact_rational_centered_divide (SCM x, SCM y, | |
2913 | SCM *qp, SCM *rp); | |
2914 | ||
2915 | SCM_PRIMITIVE_GENERIC (scm_i_centered_divide, "centered/", 2, 0, 0, | |
2916 | (SCM x, SCM y), | |
2917 | "Return the integer @var{q} and the real number @var{r}\n" | |
2918 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
2919 | "and @math{-abs(@var{y}/2) <= @var{r} < abs(@var{y}/2)}.\n" | |
2920 | "@lisp\n" | |
2921 | "(centered/ 123 10) @result{} 12 and 3\n" | |
2922 | "(centered/ 123 -10) @result{} -12 and 3\n" | |
2923 | "(centered/ -123 10) @result{} -12 and -3\n" | |
2924 | "(centered/ -123 -10) @result{} 12 and -3\n" | |
2925 | "(centered/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
2926 | "(centered/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
2927 | "@end lisp") | |
2928 | #define FUNC_NAME s_scm_i_centered_divide | |
2929 | { | |
2930 | SCM q, r; | |
2931 | ||
2932 | scm_centered_divide(x, y, &q, &r); | |
2933 | return scm_values (scm_list_2 (q, r)); | |
2934 | } | |
2935 | #undef FUNC_NAME | |
2936 | ||
2937 | #define s_scm_centered_divide s_scm_i_centered_divide | |
2938 | #define g_scm_centered_divide g_scm_i_centered_divide | |
2939 | ||
2940 | void | |
2941 | scm_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
2942 | { | |
2943 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
2944 | { | |
2945 | scm_t_inum xx = SCM_I_INUM (x); | |
2946 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
2947 | { | |
2948 | scm_t_inum yy = SCM_I_INUM (y); | |
2949 | if (SCM_UNLIKELY (yy == 0)) | |
2950 | scm_num_overflow (s_scm_centered_divide); | |
2951 | else | |
2952 | { | |
2953 | scm_t_inum qq = xx / yy; | |
2954 | scm_t_inum rr = xx % yy; | |
2955 | if (SCM_LIKELY (xx > 0)) | |
2956 | { | |
2957 | if (SCM_LIKELY (yy > 0)) | |
2958 | { | |
2959 | if (rr >= (yy + 1) / 2) | |
2960 | { qq++; rr -= yy; } | |
2961 | } | |
2962 | else | |
2963 | { | |
2964 | if (rr >= (1 - yy) / 2) | |
2965 | { qq--; rr += yy; } | |
2966 | } | |
2967 | } | |
2968 | else | |
2969 | { | |
2970 | if (SCM_LIKELY (yy > 0)) | |
2971 | { | |
2972 | if (rr < -yy / 2) | |
2973 | { qq--; rr += yy; } | |
2974 | } | |
2975 | else | |
2976 | { | |
2977 | if (rr < yy / 2) | |
2978 | { qq++; rr -= yy; } | |
2979 | } | |
2980 | } | |
2981 | if (SCM_LIKELY (SCM_FIXABLE (qq))) | |
2982 | *qp = SCM_I_MAKINUM (qq); | |
2983 | else | |
2984 | *qp = scm_i_inum2big (qq); | |
2985 | *rp = SCM_I_MAKINUM (rr); | |
2986 | } | |
2987 | return; | |
2988 | } | |
2989 | else if (SCM_BIGP (y)) | |
2990 | { | |
2991 | /* Pass a denormalized bignum version of x (even though it | |
2992 | can fit in a fixnum) to scm_i_bigint_centered_divide */ | |
2993 | return scm_i_bigint_centered_divide (scm_i_long2big (xx), y, qp, rp); | |
2994 | } | |
2995 | else if (SCM_REALP (y)) | |
2996 | return scm_i_inexact_centered_divide (xx, SCM_REAL_VALUE (y), qp, rp); | |
2997 | else if (SCM_FRACTIONP (y)) | |
2998 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
2999 | else | |
3000 | return two_valued_wta_dispatch_2 | |
3001 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3002 | s_scm_centered_divide, qp, rp); | |
3003 | } | |
3004 | else if (SCM_BIGP (x)) | |
3005 | { | |
3006 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3007 | { | |
3008 | scm_t_inum yy = SCM_I_INUM (y); | |
3009 | if (SCM_UNLIKELY (yy == 0)) | |
3010 | scm_num_overflow (s_scm_centered_divide); | |
3011 | else | |
3012 | { | |
3013 | SCM q = scm_i_mkbig (); | |
3014 | scm_t_inum rr; | |
3015 | /* Arrange for rr to initially be non-positive, | |
3016 | because that simplifies the test to see | |
3017 | if it is within the needed bounds. */ | |
3018 | if (yy > 0) | |
3019 | { | |
3020 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3021 | SCM_I_BIG_MPZ (x), yy); | |
3022 | scm_remember_upto_here_1 (x); | |
3023 | if (rr < -yy / 2) | |
3024 | { | |
3025 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3026 | SCM_I_BIG_MPZ (q), 1); | |
3027 | rr += yy; | |
3028 | } | |
3029 | } | |
3030 | else | |
3031 | { | |
3032 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3033 | SCM_I_BIG_MPZ (x), -yy); | |
3034 | scm_remember_upto_here_1 (x); | |
3035 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); | |
3036 | if (rr < yy / 2) | |
3037 | { | |
3038 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3039 | SCM_I_BIG_MPZ (q), 1); | |
3040 | rr -= yy; | |
3041 | } | |
3042 | } | |
3043 | *qp = scm_i_normbig (q); | |
3044 | *rp = SCM_I_MAKINUM (rr); | |
3045 | } | |
3046 | return; | |
3047 | } | |
3048 | else if (SCM_BIGP (y)) | |
3049 | return scm_i_bigint_centered_divide (x, y, qp, rp); | |
3050 | else if (SCM_REALP (y)) | |
3051 | return scm_i_inexact_centered_divide | |
3052 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); | |
3053 | else if (SCM_FRACTIONP (y)) | |
3054 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3055 | else | |
3056 | return two_valued_wta_dispatch_2 | |
3057 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3058 | s_scm_centered_divide, qp, rp); | |
3059 | } | |
3060 | else if (SCM_REALP (x)) | |
3061 | { | |
3062 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3063 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3064 | return scm_i_inexact_centered_divide | |
3065 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); | |
3066 | else | |
3067 | return two_valued_wta_dispatch_2 | |
3068 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3069 | s_scm_centered_divide, qp, rp); | |
3070 | } | |
3071 | else if (SCM_FRACTIONP (x)) | |
3072 | { | |
3073 | if (SCM_REALP (y)) | |
3074 | return scm_i_inexact_centered_divide | |
3075 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); | |
3076 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
3077 | return scm_i_exact_rational_centered_divide (x, y, qp, rp); | |
3078 | else | |
3079 | return two_valued_wta_dispatch_2 | |
3080 | (g_scm_centered_divide, x, y, SCM_ARG2, | |
3081 | s_scm_centered_divide, qp, rp); | |
3082 | } | |
3083 | else | |
3084 | return two_valued_wta_dispatch_2 (g_scm_centered_divide, x, y, SCM_ARG1, | |
3085 | s_scm_centered_divide, qp, rp); | |
3086 | } | |
3087 | ||
3088 | static void | |
3089 | scm_i_inexact_centered_divide (double x, double y, SCM *qp, SCM *rp) | |
3090 | { | |
3091 | double q, r; | |
3092 | ||
3093 | if (SCM_LIKELY (y > 0)) | |
3094 | q = floor (x/y + 0.5); | |
3095 | else if (SCM_LIKELY (y < 0)) | |
3096 | q = ceil (x/y - 0.5); | |
3097 | else if (y == 0) | |
3098 | scm_num_overflow (s_scm_centered_divide); /* or return a NaN? */ | |
3099 | else | |
3100 | q = guile_NaN; | |
3101 | r = x - q * y; | |
3102 | *qp = scm_from_double (q); | |
3103 | *rp = scm_from_double (r); | |
3104 | } | |
3105 | ||
3106 | /* Assumes that both x and y are bigints, though | |
3107 | x might be able to fit into a fixnum. */ | |
3108 | static void | |
3109 | scm_i_bigint_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3110 | { | |
3111 | SCM q, r, min_r; | |
3112 | ||
3113 | /* Note that x might be small enough to fit into a | |
3114 | fixnum, so we must not let it escape into the wild */ | |
3115 | q = scm_i_mkbig (); | |
3116 | r = scm_i_mkbig (); | |
3117 | ||
3118 | /* min_r will eventually become -abs(y/2) */ | |
3119 | min_r = scm_i_mkbig (); | |
3120 | mpz_tdiv_q_2exp (SCM_I_BIG_MPZ (min_r), | |
3121 | SCM_I_BIG_MPZ (y), 1); | |
3122 | ||
3123 | /* Arrange for rr to initially be non-positive, | |
3124 | because that simplifies the test to see | |
3125 | if it is within the needed bounds. */ | |
3126 | if (mpz_sgn (SCM_I_BIG_MPZ (y)) > 0) | |
3127 | { | |
3128 | mpz_cdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3129 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3130 | mpz_neg (SCM_I_BIG_MPZ (min_r), SCM_I_BIG_MPZ (min_r)); | |
3131 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3132 | { | |
3133 | mpz_sub_ui (SCM_I_BIG_MPZ (q), | |
3134 | SCM_I_BIG_MPZ (q), 1); | |
3135 | mpz_add (SCM_I_BIG_MPZ (r), | |
3136 | SCM_I_BIG_MPZ (r), | |
3137 | SCM_I_BIG_MPZ (y)); | |
3138 | } | |
3139 | } | |
3140 | else | |
3141 | { | |
3142 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), | |
3143 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3144 | if (mpz_cmp (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (min_r)) < 0) | |
3145 | { | |
3146 | mpz_add_ui (SCM_I_BIG_MPZ (q), | |
3147 | SCM_I_BIG_MPZ (q), 1); | |
3148 | mpz_sub (SCM_I_BIG_MPZ (r), | |
3149 | SCM_I_BIG_MPZ (r), | |
3150 | SCM_I_BIG_MPZ (y)); | |
3151 | } | |
3152 | } | |
3153 | scm_remember_upto_here_2 (x, y); | |
3154 | *qp = scm_i_normbig (q); | |
3155 | *rp = scm_i_normbig (r); | |
3156 | } | |
3157 | ||
3158 | static void | |
3159 | scm_i_exact_rational_centered_divide (SCM x, SCM y, SCM *qp, SCM *rp) | |
3160 | { | |
3161 | SCM r1; | |
3162 | SCM xd = scm_denominator (x); | |
3163 | SCM yd = scm_denominator (y); | |
3164 | ||
3165 | scm_centered_divide (scm_product (scm_numerator (x), yd), | |
3166 | scm_product (scm_numerator (y), xd), | |
3167 | qp, &r1); | |
3168 | *rp = scm_divide (r1, scm_product (xd, yd)); | |
3169 | } | |
3170 | ||
3171 | static SCM scm_i_inexact_round_quotient (double x, double y); | |
3172 | static SCM scm_i_bigint_round_quotient (SCM x, SCM y); | |
3173 | static SCM scm_i_exact_rational_round_quotient (SCM x, SCM y); | |
3174 | ||
3175 | SCM_PRIMITIVE_GENERIC (scm_round_quotient, "round-quotient", 2, 0, 0, | |
ff62c168 | 3176 | (SCM x, SCM y), |
8f9da340 MW |
3177 | "Return @math{@var{x} / @var{y}} to the nearest integer,\n" |
3178 | "with ties going to the nearest even integer.\n" | |
ff62c168 | 3179 | "@lisp\n" |
8f9da340 MW |
3180 | "(round-quotient 123 10) @result{} 12\n" |
3181 | "(round-quotient 123 -10) @result{} -12\n" | |
3182 | "(round-quotient -123 10) @result{} -12\n" | |
3183 | "(round-quotient -123 -10) @result{} 12\n" | |
3184 | "(round-quotient 125 10) @result{} 12\n" | |
3185 | "(round-quotient 127 10) @result{} 13\n" | |
3186 | "(round-quotient 135 10) @result{} 14\n" | |
3187 | "(round-quotient -123.2 -63.5) @result{} 2.0\n" | |
3188 | "(round-quotient 16/3 -10/7) @result{} -4\n" | |
ff62c168 | 3189 | "@end lisp") |
8f9da340 | 3190 | #define FUNC_NAME s_scm_round_quotient |
ff62c168 MW |
3191 | { |
3192 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3193 | { | |
4a46bc2a | 3194 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3195 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3196 | { | |
3197 | scm_t_inum yy = SCM_I_INUM (y); | |
3198 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3199 | scm_num_overflow (s_scm_round_quotient); |
ff62c168 MW |
3200 | else |
3201 | { | |
ff62c168 | 3202 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3203 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3204 | scm_t_inum ay = yy; |
3205 | scm_t_inum r2 = 2 * rr; | |
3206 | ||
3207 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3208 | { |
8f9da340 MW |
3209 | ay = -ay; |
3210 | r2 = -r2; | |
3211 | } | |
3212 | ||
3213 | if (qq & 1L) | |
3214 | { | |
3215 | if (r2 >= ay) | |
3216 | qq++; | |
3217 | else if (r2 <= -ay) | |
3218 | qq--; | |
ff62c168 MW |
3219 | } |
3220 | else | |
3221 | { | |
8f9da340 MW |
3222 | if (r2 > ay) |
3223 | qq++; | |
3224 | else if (r2 < -ay) | |
3225 | qq--; | |
ff62c168 | 3226 | } |
4a46bc2a MW |
3227 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
3228 | return SCM_I_MAKINUM (qq); | |
3229 | else | |
3230 | return scm_i_inum2big (qq); | |
ff62c168 MW |
3231 | } |
3232 | } | |
3233 | else if (SCM_BIGP (y)) | |
3234 | { | |
3235 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3236 | can fit in a fixnum) to scm_i_bigint_round_quotient */ |
3237 | return scm_i_bigint_round_quotient (scm_i_long2big (xx), y); | |
ff62c168 MW |
3238 | } |
3239 | else if (SCM_REALP (y)) | |
8f9da340 | 3240 | return scm_i_inexact_round_quotient (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3241 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3242 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3243 | else |
8f9da340 MW |
3244 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3245 | s_scm_round_quotient); | |
ff62c168 MW |
3246 | } |
3247 | else if (SCM_BIGP (x)) | |
3248 | { | |
3249 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3250 | { | |
3251 | scm_t_inum yy = SCM_I_INUM (y); | |
3252 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3253 | scm_num_overflow (s_scm_round_quotient); |
4a46bc2a MW |
3254 | else if (SCM_UNLIKELY (yy == 1)) |
3255 | return x; | |
ff62c168 MW |
3256 | else |
3257 | { | |
3258 | SCM q = scm_i_mkbig (); | |
3259 | scm_t_inum rr; | |
8f9da340 MW |
3260 | int needs_adjustment; |
3261 | ||
ff62c168 MW |
3262 | if (yy > 0) |
3263 | { | |
8f9da340 MW |
3264 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3265 | SCM_I_BIG_MPZ (x), yy); | |
3266 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3267 | needs_adjustment = (2*rr >= yy); | |
3268 | else | |
3269 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3270 | } |
3271 | else | |
3272 | { | |
3273 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3274 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3275 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3276 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3277 | needs_adjustment = (2*rr <= yy); | |
3278 | else | |
3279 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3280 | } |
8f9da340 MW |
3281 | scm_remember_upto_here_1 (x); |
3282 | if (needs_adjustment) | |
3283 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
ff62c168 MW |
3284 | return scm_i_normbig (q); |
3285 | } | |
3286 | } | |
3287 | else if (SCM_BIGP (y)) | |
8f9da340 | 3288 | return scm_i_bigint_round_quotient (x, y); |
ff62c168 | 3289 | else if (SCM_REALP (y)) |
8f9da340 | 3290 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3291 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3292 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3293 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3294 | else |
8f9da340 MW |
3295 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3296 | s_scm_round_quotient); | |
ff62c168 MW |
3297 | } |
3298 | else if (SCM_REALP (x)) | |
3299 | { | |
3300 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3301 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3302 | return scm_i_inexact_round_quotient |
ff62c168 MW |
3303 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3304 | else | |
8f9da340 MW |
3305 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3306 | s_scm_round_quotient); | |
ff62c168 MW |
3307 | } |
3308 | else if (SCM_FRACTIONP (x)) | |
3309 | { | |
3310 | if (SCM_REALP (y)) | |
8f9da340 | 3311 | return scm_i_inexact_round_quotient |
ff62c168 | 3312 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3313 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3314 | return scm_i_exact_rational_round_quotient (x, y); |
ff62c168 | 3315 | else |
8f9da340 MW |
3316 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG2, |
3317 | s_scm_round_quotient); | |
ff62c168 MW |
3318 | } |
3319 | else | |
8f9da340 MW |
3320 | SCM_WTA_DISPATCH_2 (g_scm_round_quotient, x, y, SCM_ARG1, |
3321 | s_scm_round_quotient); | |
ff62c168 MW |
3322 | } |
3323 | #undef FUNC_NAME | |
3324 | ||
3325 | static SCM | |
8f9da340 | 3326 | scm_i_inexact_round_quotient (double x, double y) |
ff62c168 | 3327 | { |
8f9da340 MW |
3328 | if (SCM_UNLIKELY (y == 0)) |
3329 | scm_num_overflow (s_scm_round_quotient); /* or return a NaN? */ | |
ff62c168 | 3330 | else |
8f9da340 | 3331 | return scm_from_double (scm_c_round (x / y)); |
ff62c168 MW |
3332 | } |
3333 | ||
3334 | /* Assumes that both x and y are bigints, though | |
3335 | x might be able to fit into a fixnum. */ | |
3336 | static SCM | |
8f9da340 | 3337 | scm_i_bigint_round_quotient (SCM x, SCM y) |
ff62c168 | 3338 | { |
8f9da340 MW |
3339 | SCM q, r, r2; |
3340 | int cmp, needs_adjustment; | |
ff62c168 MW |
3341 | |
3342 | /* Note that x might be small enough to fit into a | |
3343 | fixnum, so we must not let it escape into the wild */ | |
3344 | q = scm_i_mkbig (); | |
3345 | r = scm_i_mkbig (); | |
8f9da340 | 3346 | r2 = scm_i_mkbig (); |
ff62c168 | 3347 | |
8f9da340 MW |
3348 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3349 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3350 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
3351 | scm_remember_upto_here_2 (x, r); | |
ff62c168 | 3352 | |
8f9da340 MW |
3353 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3354 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3355 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3356 | else |
8f9da340 MW |
3357 | needs_adjustment = (cmp > 0); |
3358 | scm_remember_upto_here_2 (r2, y); | |
3359 | ||
3360 | if (needs_adjustment) | |
3361 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3362 | ||
ff62c168 MW |
3363 | return scm_i_normbig (q); |
3364 | } | |
3365 | ||
ff62c168 | 3366 | static SCM |
8f9da340 | 3367 | scm_i_exact_rational_round_quotient (SCM x, SCM y) |
ff62c168 | 3368 | { |
8f9da340 | 3369 | return scm_round_quotient |
03ddd15b MW |
3370 | (scm_product (scm_numerator (x), scm_denominator (y)), |
3371 | scm_product (scm_numerator (y), scm_denominator (x))); | |
ff62c168 MW |
3372 | } |
3373 | ||
8f9da340 MW |
3374 | static SCM scm_i_inexact_round_remainder (double x, double y); |
3375 | static SCM scm_i_bigint_round_remainder (SCM x, SCM y); | |
3376 | static SCM scm_i_exact_rational_round_remainder (SCM x, SCM y); | |
ff62c168 | 3377 | |
8f9da340 | 3378 | SCM_PRIMITIVE_GENERIC (scm_round_remainder, "round-remainder", 2, 0, 0, |
ff62c168 MW |
3379 | (SCM x, SCM y), |
3380 | "Return the real number @var{r} such that\n" | |
8f9da340 MW |
3381 | "@math{@var{x} = @var{q}*@var{y} + @var{r}}, where\n" |
3382 | "@var{q} is @math{@var{x} / @var{y}} rounded to the\n" | |
3383 | "nearest integer, with ties going to the nearest\n" | |
3384 | "even integer.\n" | |
ff62c168 | 3385 | "@lisp\n" |
8f9da340 MW |
3386 | "(round-remainder 123 10) @result{} 3\n" |
3387 | "(round-remainder 123 -10) @result{} 3\n" | |
3388 | "(round-remainder -123 10) @result{} -3\n" | |
3389 | "(round-remainder -123 -10) @result{} -3\n" | |
3390 | "(round-remainder 125 10) @result{} 5\n" | |
3391 | "(round-remainder 127 10) @result{} -3\n" | |
3392 | "(round-remainder 135 10) @result{} -5\n" | |
3393 | "(round-remainder -123.2 -63.5) @result{} 3.8\n" | |
3394 | "(round-remainder 16/3 -10/7) @result{} -8/21\n" | |
ff62c168 | 3395 | "@end lisp") |
8f9da340 | 3396 | #define FUNC_NAME s_scm_round_remainder |
ff62c168 MW |
3397 | { |
3398 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3399 | { | |
4a46bc2a | 3400 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3401 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3402 | { | |
3403 | scm_t_inum yy = SCM_I_INUM (y); | |
3404 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3405 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3406 | else |
3407 | { | |
8f9da340 | 3408 | scm_t_inum qq = xx / yy; |
ff62c168 | 3409 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3410 | scm_t_inum ay = yy; |
3411 | scm_t_inum r2 = 2 * rr; | |
3412 | ||
3413 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3414 | { |
8f9da340 MW |
3415 | ay = -ay; |
3416 | r2 = -r2; | |
3417 | } | |
3418 | ||
3419 | if (qq & 1L) | |
3420 | { | |
3421 | if (r2 >= ay) | |
3422 | rr -= yy; | |
3423 | else if (r2 <= -ay) | |
3424 | rr += yy; | |
ff62c168 MW |
3425 | } |
3426 | else | |
3427 | { | |
8f9da340 MW |
3428 | if (r2 > ay) |
3429 | rr -= yy; | |
3430 | else if (r2 < -ay) | |
3431 | rr += yy; | |
ff62c168 MW |
3432 | } |
3433 | return SCM_I_MAKINUM (rr); | |
3434 | } | |
3435 | } | |
3436 | else if (SCM_BIGP (y)) | |
3437 | { | |
3438 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3439 | can fit in a fixnum) to scm_i_bigint_round_remainder */ |
3440 | return scm_i_bigint_round_remainder | |
3441 | (scm_i_long2big (xx), y); | |
ff62c168 MW |
3442 | } |
3443 | else if (SCM_REALP (y)) | |
8f9da340 | 3444 | return scm_i_inexact_round_remainder (xx, SCM_REAL_VALUE (y)); |
ff62c168 | 3445 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3446 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3447 | else |
8f9da340 MW |
3448 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3449 | s_scm_round_remainder); | |
ff62c168 MW |
3450 | } |
3451 | else if (SCM_BIGP (x)) | |
3452 | { | |
3453 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3454 | { | |
3455 | scm_t_inum yy = SCM_I_INUM (y); | |
3456 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3457 | scm_num_overflow (s_scm_round_remainder); |
ff62c168 MW |
3458 | else |
3459 | { | |
8f9da340 | 3460 | SCM q = scm_i_mkbig (); |
ff62c168 | 3461 | scm_t_inum rr; |
8f9da340 MW |
3462 | int needs_adjustment; |
3463 | ||
ff62c168 MW |
3464 | if (yy > 0) |
3465 | { | |
8f9da340 MW |
3466 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3467 | SCM_I_BIG_MPZ (x), yy); | |
3468 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3469 | needs_adjustment = (2*rr >= yy); | |
3470 | else | |
3471 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3472 | } |
3473 | else | |
3474 | { | |
8f9da340 MW |
3475 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), |
3476 | SCM_I_BIG_MPZ (x), -yy); | |
3477 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3478 | needs_adjustment = (2*rr <= yy); | |
3479 | else | |
3480 | needs_adjustment = (2*rr < yy); | |
ff62c168 | 3481 | } |
8f9da340 MW |
3482 | scm_remember_upto_here_2 (x, q); |
3483 | if (needs_adjustment) | |
3484 | rr -= yy; | |
ff62c168 MW |
3485 | return SCM_I_MAKINUM (rr); |
3486 | } | |
3487 | } | |
3488 | else if (SCM_BIGP (y)) | |
8f9da340 | 3489 | return scm_i_bigint_round_remainder (x, y); |
ff62c168 | 3490 | else if (SCM_REALP (y)) |
8f9da340 | 3491 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3492 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y)); |
3493 | else if (SCM_FRACTIONP (y)) | |
8f9da340 | 3494 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3495 | else |
8f9da340 MW |
3496 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3497 | s_scm_round_remainder); | |
ff62c168 MW |
3498 | } |
3499 | else if (SCM_REALP (x)) | |
3500 | { | |
3501 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3502 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3503 | return scm_i_inexact_round_remainder |
ff62c168 MW |
3504 | (SCM_REAL_VALUE (x), scm_to_double (y)); |
3505 | else | |
8f9da340 MW |
3506 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3507 | s_scm_round_remainder); | |
ff62c168 MW |
3508 | } |
3509 | else if (SCM_FRACTIONP (x)) | |
3510 | { | |
3511 | if (SCM_REALP (y)) | |
8f9da340 | 3512 | return scm_i_inexact_round_remainder |
ff62c168 | 3513 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y)); |
03ddd15b | 3514 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3515 | return scm_i_exact_rational_round_remainder (x, y); |
ff62c168 | 3516 | else |
8f9da340 MW |
3517 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG2, |
3518 | s_scm_round_remainder); | |
ff62c168 MW |
3519 | } |
3520 | else | |
8f9da340 MW |
3521 | SCM_WTA_DISPATCH_2 (g_scm_round_remainder, x, y, SCM_ARG1, |
3522 | s_scm_round_remainder); | |
ff62c168 MW |
3523 | } |
3524 | #undef FUNC_NAME | |
3525 | ||
3526 | static SCM | |
8f9da340 | 3527 | scm_i_inexact_round_remainder (double x, double y) |
ff62c168 | 3528 | { |
ff62c168 MW |
3529 | /* Although it would be more efficient to use fmod here, we can't |
3530 | because it would in some cases produce results inconsistent with | |
8f9da340 | 3531 | scm_i_inexact_round_quotient, such that x != r + q * y (not even |
ff62c168 | 3532 | close). In particular, when x-y/2 is very close to a multiple of |
8f9da340 MW |
3533 | y, then r might be either -abs(y/2) or abs(y/2), but those two |
3534 | cases must correspond to different choices of q. If quotient | |
ff62c168 | 3535 | chooses one and remainder chooses the other, it would be bad. */ |
8f9da340 MW |
3536 | |
3537 | if (SCM_UNLIKELY (y == 0)) | |
3538 | scm_num_overflow (s_scm_round_remainder); /* or return a NaN? */ | |
ff62c168 | 3539 | else |
8f9da340 MW |
3540 | { |
3541 | double q = scm_c_round (x / y); | |
3542 | return scm_from_double (x - q * y); | |
3543 | } | |
ff62c168 MW |
3544 | } |
3545 | ||
3546 | /* Assumes that both x and y are bigints, though | |
3547 | x might be able to fit into a fixnum. */ | |
3548 | static SCM | |
8f9da340 | 3549 | scm_i_bigint_round_remainder (SCM x, SCM y) |
ff62c168 | 3550 | { |
8f9da340 MW |
3551 | SCM q, r, r2; |
3552 | int cmp, needs_adjustment; | |
ff62c168 MW |
3553 | |
3554 | /* Note that x might be small enough to fit into a | |
3555 | fixnum, so we must not let it escape into the wild */ | |
8f9da340 | 3556 | q = scm_i_mkbig (); |
ff62c168 | 3557 | r = scm_i_mkbig (); |
8f9da340 | 3558 | r2 = scm_i_mkbig (); |
ff62c168 | 3559 | |
8f9da340 MW |
3560 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3561 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3562 | scm_remember_upto_here_1 (x); | |
3563 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3564 | |
8f9da340 MW |
3565 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3566 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3567 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3568 | else |
8f9da340 MW |
3569 | needs_adjustment = (cmp > 0); |
3570 | scm_remember_upto_here_2 (q, r2); | |
3571 | ||
3572 | if (needs_adjustment) | |
3573 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
3574 | ||
3575 | scm_remember_upto_here_1 (y); | |
ff62c168 MW |
3576 | return scm_i_normbig (r); |
3577 | } | |
3578 | ||
ff62c168 | 3579 | static SCM |
8f9da340 | 3580 | scm_i_exact_rational_round_remainder (SCM x, SCM y) |
ff62c168 | 3581 | { |
03ddd15b MW |
3582 | SCM xd = scm_denominator (x); |
3583 | SCM yd = scm_denominator (y); | |
8f9da340 MW |
3584 | SCM r1 = scm_round_remainder (scm_product (scm_numerator (x), yd), |
3585 | scm_product (scm_numerator (y), xd)); | |
03ddd15b | 3586 | return scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3587 | } |
3588 | ||
3589 | ||
8f9da340 MW |
3590 | static void scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp); |
3591 | static void scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
3592 | static void scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp); | |
ff62c168 | 3593 | |
8f9da340 | 3594 | SCM_PRIMITIVE_GENERIC (scm_i_round_divide, "round/", 2, 0, 0, |
ff62c168 MW |
3595 | (SCM x, SCM y), |
3596 | "Return the integer @var{q} and the real number @var{r}\n" | |
3597 | "such that @math{@var{x} = @var{q}*@var{y} + @var{r}}\n" | |
8f9da340 MW |
3598 | "and @var{q} is @math{@var{x} / @var{y}} rounded to the\n" |
3599 | "nearest integer, with ties going to the nearest even integer.\n" | |
ff62c168 | 3600 | "@lisp\n" |
8f9da340 MW |
3601 | "(round/ 123 10) @result{} 12 and 3\n" |
3602 | "(round/ 123 -10) @result{} -12 and 3\n" | |
3603 | "(round/ -123 10) @result{} -12 and -3\n" | |
3604 | "(round/ -123 -10) @result{} 12 and -3\n" | |
3605 | "(round/ 125 10) @result{} 12 and 5\n" | |
3606 | "(round/ 127 10) @result{} 13 and -3\n" | |
3607 | "(round/ 135 10) @result{} 14 and -5\n" | |
3608 | "(round/ -123.2 -63.5) @result{} 2.0 and 3.8\n" | |
3609 | "(round/ 16/3 -10/7) @result{} -4 and -8/21\n" | |
ff62c168 | 3610 | "@end lisp") |
8f9da340 | 3611 | #define FUNC_NAME s_scm_i_round_divide |
5fbf680b MW |
3612 | { |
3613 | SCM q, r; | |
3614 | ||
8f9da340 | 3615 | scm_round_divide(x, y, &q, &r); |
5fbf680b MW |
3616 | return scm_values (scm_list_2 (q, r)); |
3617 | } | |
3618 | #undef FUNC_NAME | |
3619 | ||
8f9da340 MW |
3620 | #define s_scm_round_divide s_scm_i_round_divide |
3621 | #define g_scm_round_divide g_scm_i_round_divide | |
5fbf680b MW |
3622 | |
3623 | void | |
8f9da340 | 3624 | scm_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 MW |
3625 | { |
3626 | if (SCM_LIKELY (SCM_I_INUMP (x))) | |
3627 | { | |
4a46bc2a | 3628 | scm_t_inum xx = SCM_I_INUM (x); |
ff62c168 MW |
3629 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
3630 | { | |
3631 | scm_t_inum yy = SCM_I_INUM (y); | |
3632 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3633 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3634 | else |
3635 | { | |
ff62c168 | 3636 | scm_t_inum qq = xx / yy; |
4a46bc2a | 3637 | scm_t_inum rr = xx % yy; |
8f9da340 MW |
3638 | scm_t_inum ay = yy; |
3639 | scm_t_inum r2 = 2 * rr; | |
3640 | ||
3641 | if (SCM_LIKELY (yy < 0)) | |
ff62c168 | 3642 | { |
8f9da340 MW |
3643 | ay = -ay; |
3644 | r2 = -r2; | |
3645 | } | |
3646 | ||
3647 | if (qq & 1L) | |
3648 | { | |
3649 | if (r2 >= ay) | |
3650 | { qq++; rr -= yy; } | |
3651 | else if (r2 <= -ay) | |
3652 | { qq--; rr += yy; } | |
ff62c168 MW |
3653 | } |
3654 | else | |
3655 | { | |
8f9da340 MW |
3656 | if (r2 > ay) |
3657 | { qq++; rr -= yy; } | |
3658 | else if (r2 < -ay) | |
3659 | { qq--; rr += yy; } | |
ff62c168 | 3660 | } |
4a46bc2a | 3661 | if (SCM_LIKELY (SCM_FIXABLE (qq))) |
5fbf680b | 3662 | *qp = SCM_I_MAKINUM (qq); |
4a46bc2a | 3663 | else |
5fbf680b MW |
3664 | *qp = scm_i_inum2big (qq); |
3665 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3666 | } |
5fbf680b | 3667 | return; |
ff62c168 MW |
3668 | } |
3669 | else if (SCM_BIGP (y)) | |
3670 | { | |
3671 | /* Pass a denormalized bignum version of x (even though it | |
8f9da340 MW |
3672 | can fit in a fixnum) to scm_i_bigint_round_divide */ |
3673 | return scm_i_bigint_round_divide | |
3674 | (scm_i_long2big (SCM_I_INUM (x)), y, qp, rp); | |
ff62c168 MW |
3675 | } |
3676 | else if (SCM_REALP (y)) | |
8f9da340 | 3677 | return scm_i_inexact_round_divide (xx, SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3678 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3679 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3680 | else |
8f9da340 MW |
3681 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3682 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3683 | } |
3684 | else if (SCM_BIGP (x)) | |
3685 | { | |
3686 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
3687 | { | |
3688 | scm_t_inum yy = SCM_I_INUM (y); | |
3689 | if (SCM_UNLIKELY (yy == 0)) | |
8f9da340 | 3690 | scm_num_overflow (s_scm_round_divide); |
ff62c168 MW |
3691 | else |
3692 | { | |
3693 | SCM q = scm_i_mkbig (); | |
3694 | scm_t_inum rr; | |
8f9da340 MW |
3695 | int needs_adjustment; |
3696 | ||
ff62c168 MW |
3697 | if (yy > 0) |
3698 | { | |
8f9da340 MW |
3699 | rr = mpz_fdiv_q_ui (SCM_I_BIG_MPZ (q), |
3700 | SCM_I_BIG_MPZ (x), yy); | |
3701 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3702 | needs_adjustment = (2*rr >= yy); | |
3703 | else | |
3704 | needs_adjustment = (2*rr > yy); | |
ff62c168 MW |
3705 | } |
3706 | else | |
3707 | { | |
3708 | rr = - mpz_cdiv_q_ui (SCM_I_BIG_MPZ (q), | |
3709 | SCM_I_BIG_MPZ (x), -yy); | |
ff62c168 | 3710 | mpz_neg (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q)); |
8f9da340 MW |
3711 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) |
3712 | needs_adjustment = (2*rr <= yy); | |
3713 | else | |
3714 | needs_adjustment = (2*rr < yy); | |
3715 | } | |
3716 | scm_remember_upto_here_1 (x); | |
3717 | if (needs_adjustment) | |
3718 | { | |
3719 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); | |
3720 | rr -= yy; | |
ff62c168 | 3721 | } |
5fbf680b MW |
3722 | *qp = scm_i_normbig (q); |
3723 | *rp = SCM_I_MAKINUM (rr); | |
ff62c168 | 3724 | } |
5fbf680b | 3725 | return; |
ff62c168 MW |
3726 | } |
3727 | else if (SCM_BIGP (y)) | |
8f9da340 | 3728 | return scm_i_bigint_round_divide (x, y, qp, rp); |
ff62c168 | 3729 | else if (SCM_REALP (y)) |
8f9da340 | 3730 | return scm_i_inexact_round_divide |
5fbf680b | 3731 | (scm_i_big2dbl (x), SCM_REAL_VALUE (y), qp, rp); |
ff62c168 | 3732 | else if (SCM_FRACTIONP (y)) |
8f9da340 | 3733 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3734 | else |
8f9da340 MW |
3735 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3736 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3737 | } |
3738 | else if (SCM_REALP (x)) | |
3739 | { | |
3740 | if (SCM_REALP (y) || SCM_I_INUMP (y) || | |
3741 | SCM_BIGP (y) || SCM_FRACTIONP (y)) | |
8f9da340 | 3742 | return scm_i_inexact_round_divide |
5fbf680b | 3743 | (SCM_REAL_VALUE (x), scm_to_double (y), qp, rp); |
03ddd15b | 3744 | else |
8f9da340 MW |
3745 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3746 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3747 | } |
3748 | else if (SCM_FRACTIONP (x)) | |
3749 | { | |
3750 | if (SCM_REALP (y)) | |
8f9da340 | 3751 | return scm_i_inexact_round_divide |
5fbf680b | 3752 | (scm_i_fraction2double (x), SCM_REAL_VALUE (y), qp, rp); |
03ddd15b | 3753 | else if (SCM_I_INUMP (y) || SCM_BIGP (y) || SCM_FRACTIONP (y)) |
8f9da340 | 3754 | return scm_i_exact_rational_round_divide (x, y, qp, rp); |
ff62c168 | 3755 | else |
8f9da340 MW |
3756 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG2, |
3757 | s_scm_round_divide, qp, rp); | |
ff62c168 MW |
3758 | } |
3759 | else | |
8f9da340 MW |
3760 | return two_valued_wta_dispatch_2 (g_scm_round_divide, x, y, SCM_ARG1, |
3761 | s_scm_round_divide, qp, rp); | |
ff62c168 | 3762 | } |
ff62c168 | 3763 | |
5fbf680b | 3764 | static void |
8f9da340 | 3765 | scm_i_inexact_round_divide (double x, double y, SCM *qp, SCM *rp) |
ff62c168 | 3766 | { |
8f9da340 MW |
3767 | if (SCM_UNLIKELY (y == 0)) |
3768 | scm_num_overflow (s_scm_round_divide); /* or return a NaN? */ | |
ff62c168 | 3769 | else |
8f9da340 MW |
3770 | { |
3771 | double q = scm_c_round (x / y); | |
3772 | double r = x - q * y; | |
3773 | *qp = scm_from_double (q); | |
3774 | *rp = scm_from_double (r); | |
3775 | } | |
ff62c168 MW |
3776 | } |
3777 | ||
3778 | /* Assumes that both x and y are bigints, though | |
3779 | x might be able to fit into a fixnum. */ | |
5fbf680b | 3780 | static void |
8f9da340 | 3781 | scm_i_bigint_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3782 | { |
8f9da340 MW |
3783 | SCM q, r, r2; |
3784 | int cmp, needs_adjustment; | |
ff62c168 MW |
3785 | |
3786 | /* Note that x might be small enough to fit into a | |
3787 | fixnum, so we must not let it escape into the wild */ | |
3788 | q = scm_i_mkbig (); | |
3789 | r = scm_i_mkbig (); | |
8f9da340 | 3790 | r2 = scm_i_mkbig (); |
ff62c168 | 3791 | |
8f9da340 MW |
3792 | mpz_fdiv_qr (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (r), |
3793 | SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3794 | scm_remember_upto_here_1 (x); | |
3795 | mpz_mul_2exp (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (r), 1); /* r2 = 2*r */ | |
ff62c168 | 3796 | |
8f9da340 MW |
3797 | cmp = mpz_cmpabs (SCM_I_BIG_MPZ (r2), SCM_I_BIG_MPZ (y)); |
3798 | if (mpz_odd_p (SCM_I_BIG_MPZ (q))) | |
3799 | needs_adjustment = (cmp >= 0); | |
ff62c168 | 3800 | else |
8f9da340 MW |
3801 | needs_adjustment = (cmp > 0); |
3802 | ||
3803 | if (needs_adjustment) | |
ff62c168 | 3804 | { |
8f9da340 MW |
3805 | mpz_add_ui (SCM_I_BIG_MPZ (q), SCM_I_BIG_MPZ (q), 1); |
3806 | mpz_sub (SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (r), SCM_I_BIG_MPZ (y)); | |
ff62c168 | 3807 | } |
8f9da340 MW |
3808 | |
3809 | scm_remember_upto_here_2 (r2, y); | |
5fbf680b MW |
3810 | *qp = scm_i_normbig (q); |
3811 | *rp = scm_i_normbig (r); | |
ff62c168 MW |
3812 | } |
3813 | ||
5fbf680b | 3814 | static void |
8f9da340 | 3815 | scm_i_exact_rational_round_divide (SCM x, SCM y, SCM *qp, SCM *rp) |
ff62c168 | 3816 | { |
03ddd15b MW |
3817 | SCM r1; |
3818 | SCM xd = scm_denominator (x); | |
3819 | SCM yd = scm_denominator (y); | |
3820 | ||
8f9da340 MW |
3821 | scm_round_divide (scm_product (scm_numerator (x), yd), |
3822 | scm_product (scm_numerator (y), xd), | |
3823 | qp, &r1); | |
03ddd15b | 3824 | *rp = scm_divide (r1, scm_product (xd, yd)); |
ff62c168 MW |
3825 | } |
3826 | ||
3827 | ||
78d3deb1 AW |
3828 | SCM_PRIMITIVE_GENERIC (scm_i_gcd, "gcd", 0, 2, 1, |
3829 | (SCM x, SCM y, SCM rest), | |
3830 | "Return the greatest common divisor of all parameter values.\n" | |
3831 | "If called without arguments, 0 is returned.") | |
3832 | #define FUNC_NAME s_scm_i_gcd | |
3833 | { | |
3834 | while (!scm_is_null (rest)) | |
3835 | { x = scm_gcd (x, y); | |
3836 | y = scm_car (rest); | |
3837 | rest = scm_cdr (rest); | |
3838 | } | |
3839 | return scm_gcd (x, y); | |
3840 | } | |
3841 | #undef FUNC_NAME | |
3842 | ||
3843 | #define s_gcd s_scm_i_gcd | |
3844 | #define g_gcd g_scm_i_gcd | |
3845 | ||
0f2d19dd | 3846 | SCM |
6e8d25a6 | 3847 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 3848 | { |
ca46fb90 | 3849 | if (SCM_UNBNDP (y)) |
1dd79792 | 3850 | return SCM_UNBNDP (x) ? SCM_INUM0 : scm_abs (x); |
ca46fb90 | 3851 | |
e11e83f3 | 3852 | if (SCM_I_INUMP (x)) |
ca46fb90 | 3853 | { |
e11e83f3 | 3854 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3855 | { |
e25f3727 AW |
3856 | scm_t_inum xx = SCM_I_INUM (x); |
3857 | scm_t_inum yy = SCM_I_INUM (y); | |
3858 | scm_t_inum u = xx < 0 ? -xx : xx; | |
3859 | scm_t_inum v = yy < 0 ? -yy : yy; | |
3860 | scm_t_inum result; | |
0aacf84e MD |
3861 | if (xx == 0) |
3862 | result = v; | |
3863 | else if (yy == 0) | |
3864 | result = u; | |
3865 | else | |
3866 | { | |
e25f3727 AW |
3867 | scm_t_inum k = 1; |
3868 | scm_t_inum t; | |
0aacf84e MD |
3869 | /* Determine a common factor 2^k */ |
3870 | while (!(1 & (u | v))) | |
3871 | { | |
3872 | k <<= 1; | |
3873 | u >>= 1; | |
3874 | v >>= 1; | |
3875 | } | |
3876 | /* Now, any factor 2^n can be eliminated */ | |
3877 | if (u & 1) | |
3878 | t = -v; | |
3879 | else | |
3880 | { | |
3881 | t = u; | |
3882 | b3: | |
3883 | t = SCM_SRS (t, 1); | |
3884 | } | |
3885 | if (!(1 & t)) | |
3886 | goto b3; | |
3887 | if (t > 0) | |
3888 | u = t; | |
3889 | else | |
3890 | v = -t; | |
3891 | t = u - v; | |
3892 | if (t != 0) | |
3893 | goto b3; | |
3894 | result = u * k; | |
3895 | } | |
3896 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 3897 | ? SCM_I_MAKINUM (result) |
e25f3727 | 3898 | : scm_i_inum2big (result)); |
ca46fb90 RB |
3899 | } |
3900 | else if (SCM_BIGP (y)) | |
3901 | { | |
0bff4dce KR |
3902 | SCM_SWAP (x, y); |
3903 | goto big_inum; | |
ca46fb90 RB |
3904 | } |
3905 | else | |
3906 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 3907 | } |
ca46fb90 RB |
3908 | else if (SCM_BIGP (x)) |
3909 | { | |
e11e83f3 | 3910 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3911 | { |
e25f3727 AW |
3912 | scm_t_bits result; |
3913 | scm_t_inum yy; | |
0bff4dce | 3914 | big_inum: |
e11e83f3 | 3915 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
3916 | if (yy == 0) |
3917 | return scm_abs (x); | |
0aacf84e MD |
3918 | if (yy < 0) |
3919 | yy = -yy; | |
ca46fb90 RB |
3920 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
3921 | scm_remember_upto_here_1 (x); | |
0aacf84e | 3922 | return (SCM_POSFIXABLE (result) |
d956fa6f | 3923 | ? SCM_I_MAKINUM (result) |
e25f3727 | 3924 | : scm_from_unsigned_integer (result)); |
ca46fb90 RB |
3925 | } |
3926 | else if (SCM_BIGP (y)) | |
3927 | { | |
3928 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
3929 | mpz_gcd (SCM_I_BIG_MPZ (result), |
3930 | SCM_I_BIG_MPZ (x), | |
3931 | SCM_I_BIG_MPZ (y)); | |
3932 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
3933 | return scm_i_normbig (result); |
3934 | } | |
3935 | else | |
3936 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 3937 | } |
ca46fb90 | 3938 | else |
09fb7599 | 3939 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
3940 | } |
3941 | ||
78d3deb1 AW |
3942 | SCM_PRIMITIVE_GENERIC (scm_i_lcm, "lcm", 0, 2, 1, |
3943 | (SCM x, SCM y, SCM rest), | |
3944 | "Return the least common multiple of the arguments.\n" | |
3945 | "If called without arguments, 1 is returned.") | |
3946 | #define FUNC_NAME s_scm_i_lcm | |
3947 | { | |
3948 | while (!scm_is_null (rest)) | |
3949 | { x = scm_lcm (x, y); | |
3950 | y = scm_car (rest); | |
3951 | rest = scm_cdr (rest); | |
3952 | } | |
3953 | return scm_lcm (x, y); | |
3954 | } | |
3955 | #undef FUNC_NAME | |
3956 | ||
3957 | #define s_lcm s_scm_i_lcm | |
3958 | #define g_lcm g_scm_i_lcm | |
3959 | ||
0f2d19dd | 3960 | SCM |
6e8d25a6 | 3961 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 3962 | { |
ca46fb90 RB |
3963 | if (SCM_UNBNDP (n2)) |
3964 | { | |
3965 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
3966 | return SCM_I_MAKINUM (1L); |
3967 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 3968 | } |
09fb7599 | 3969 | |
e11e83f3 | 3970 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 3971 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 3972 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 3973 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 3974 | |
e11e83f3 | 3975 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 3976 | { |
e11e83f3 | 3977 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
3978 | { |
3979 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 3980 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
3981 | return d; |
3982 | else | |
3983 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
3984 | } | |
3985 | else | |
3986 | { | |
3987 | /* inum n1, big n2 */ | |
3988 | inumbig: | |
3989 | { | |
3990 | SCM result = scm_i_mkbig (); | |
e25f3727 | 3991 | scm_t_inum nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
3992 | if (nn1 == 0) return SCM_INUM0; |
3993 | if (nn1 < 0) nn1 = - nn1; | |
3994 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
3995 | scm_remember_upto_here_1 (n2); | |
3996 | return result; | |
3997 | } | |
3998 | } | |
3999 | } | |
4000 | else | |
4001 | { | |
4002 | /* big n1 */ | |
e11e83f3 | 4003 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
4004 | { |
4005 | SCM_SWAP (n1, n2); | |
4006 | goto inumbig; | |
4007 | } | |
4008 | else | |
4009 | { | |
4010 | SCM result = scm_i_mkbig (); | |
4011 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
4012 | SCM_I_BIG_MPZ (n1), | |
4013 | SCM_I_BIG_MPZ (n2)); | |
4014 | scm_remember_upto_here_2(n1, n2); | |
4015 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
4016 | return result; | |
4017 | } | |
f872b822 | 4018 | } |
0f2d19dd JB |
4019 | } |
4020 | ||
8a525303 GB |
4021 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
4022 | ||
4023 | Logand: | |
4024 | X Y Result Method: | |
4025 | (len) | |
4026 | + + + x (map digit:logand X Y) | |
4027 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
4028 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
4029 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
4030 | ||
4031 | Logior: | |
4032 | X Y Result Method: | |
4033 | ||
4034 | + + + (map digit:logior X Y) | |
4035 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
4036 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
4037 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
4038 | ||
4039 | Logxor: | |
4040 | X Y Result Method: | |
4041 | ||
4042 | + + + (map digit:logxor X Y) | |
4043 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
4044 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
4045 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
4046 | ||
4047 | Logtest: | |
4048 | X Y Result | |
4049 | ||
4050 | + + (any digit:logand X Y) | |
4051 | + - (any digit:logand X (lognot (+ -1 Y))) | |
4052 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
4053 | - - #t | |
4054 | ||
4055 | */ | |
4056 | ||
78d3deb1 AW |
4057 | SCM_DEFINE (scm_i_logand, "logand", 0, 2, 1, |
4058 | (SCM x, SCM y, SCM rest), | |
4059 | "Return the bitwise AND of the integer arguments.\n\n" | |
4060 | "@lisp\n" | |
4061 | "(logand) @result{} -1\n" | |
4062 | "(logand 7) @result{} 7\n" | |
4063 | "(logand #b111 #b011 #b001) @result{} 1\n" | |
4064 | "@end lisp") | |
4065 | #define FUNC_NAME s_scm_i_logand | |
4066 | { | |
4067 | while (!scm_is_null (rest)) | |
4068 | { x = scm_logand (x, y); | |
4069 | y = scm_car (rest); | |
4070 | rest = scm_cdr (rest); | |
4071 | } | |
4072 | return scm_logand (x, y); | |
4073 | } | |
4074 | #undef FUNC_NAME | |
4075 | ||
4076 | #define s_scm_logand s_scm_i_logand | |
4077 | ||
4078 | SCM scm_logand (SCM n1, SCM n2) | |
1bbd0b84 | 4079 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 4080 | { |
e25f3727 | 4081 | scm_t_inum nn1; |
9a00c9fc | 4082 | |
0aacf84e MD |
4083 | if (SCM_UNBNDP (n2)) |
4084 | { | |
4085 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 4086 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
4087 | else if (!SCM_NUMBERP (n1)) |
4088 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
4089 | else if (SCM_NUMBERP (n1)) | |
4090 | return n1; | |
4091 | else | |
4092 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4093 | } |
09fb7599 | 4094 | |
e11e83f3 | 4095 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4096 | { |
e11e83f3 MV |
4097 | nn1 = SCM_I_INUM (n1); |
4098 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4099 | { |
e25f3727 | 4100 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4101 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
4102 | } |
4103 | else if SCM_BIGP (n2) | |
4104 | { | |
4105 | intbig: | |
4106 | if (n1 == 0) | |
4107 | return SCM_INUM0; | |
4108 | { | |
4109 | SCM result_z = scm_i_mkbig (); | |
4110 | mpz_t nn1_z; | |
4111 | mpz_init_set_si (nn1_z, nn1); | |
4112 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4113 | scm_remember_upto_here_1 (n2); | |
4114 | mpz_clear (nn1_z); | |
4115 | return scm_i_normbig (result_z); | |
4116 | } | |
4117 | } | |
4118 | else | |
4119 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4120 | } | |
4121 | else if (SCM_BIGP (n1)) | |
4122 | { | |
e11e83f3 | 4123 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4124 | { |
4125 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4126 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4127 | goto intbig; |
4128 | } | |
4129 | else if (SCM_BIGP (n2)) | |
4130 | { | |
4131 | SCM result_z = scm_i_mkbig (); | |
4132 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
4133 | SCM_I_BIG_MPZ (n1), | |
4134 | SCM_I_BIG_MPZ (n2)); | |
4135 | scm_remember_upto_here_2 (n1, n2); | |
4136 | return scm_i_normbig (result_z); | |
4137 | } | |
4138 | else | |
4139 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4140 | } |
0aacf84e | 4141 | else |
09fb7599 | 4142 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4143 | } |
1bbd0b84 | 4144 | #undef FUNC_NAME |
0f2d19dd | 4145 | |
09fb7599 | 4146 | |
78d3deb1 AW |
4147 | SCM_DEFINE (scm_i_logior, "logior", 0, 2, 1, |
4148 | (SCM x, SCM y, SCM rest), | |
4149 | "Return the bitwise OR of the integer arguments.\n\n" | |
4150 | "@lisp\n" | |
4151 | "(logior) @result{} 0\n" | |
4152 | "(logior 7) @result{} 7\n" | |
4153 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
4154 | "@end lisp") | |
4155 | #define FUNC_NAME s_scm_i_logior | |
4156 | { | |
4157 | while (!scm_is_null (rest)) | |
4158 | { x = scm_logior (x, y); | |
4159 | y = scm_car (rest); | |
4160 | rest = scm_cdr (rest); | |
4161 | } | |
4162 | return scm_logior (x, y); | |
4163 | } | |
4164 | #undef FUNC_NAME | |
4165 | ||
4166 | #define s_scm_logior s_scm_i_logior | |
4167 | ||
4168 | SCM scm_logior (SCM n1, SCM n2) | |
1bbd0b84 | 4169 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 4170 | { |
e25f3727 | 4171 | scm_t_inum nn1; |
9a00c9fc | 4172 | |
0aacf84e MD |
4173 | if (SCM_UNBNDP (n2)) |
4174 | { | |
4175 | if (SCM_UNBNDP (n1)) | |
4176 | return SCM_INUM0; | |
4177 | else if (SCM_NUMBERP (n1)) | |
4178 | return n1; | |
4179 | else | |
4180 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4181 | } |
09fb7599 | 4182 | |
e11e83f3 | 4183 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4184 | { |
e11e83f3 MV |
4185 | nn1 = SCM_I_INUM (n1); |
4186 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4187 | { |
e11e83f3 | 4188 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 4189 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
4190 | } |
4191 | else if (SCM_BIGP (n2)) | |
4192 | { | |
4193 | intbig: | |
4194 | if (nn1 == 0) | |
4195 | return n2; | |
4196 | { | |
4197 | SCM result_z = scm_i_mkbig (); | |
4198 | mpz_t nn1_z; | |
4199 | mpz_init_set_si (nn1_z, nn1); | |
4200 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4201 | scm_remember_upto_here_1 (n2); | |
4202 | mpz_clear (nn1_z); | |
9806de0d | 4203 | return scm_i_normbig (result_z); |
0aacf84e MD |
4204 | } |
4205 | } | |
4206 | else | |
4207 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4208 | } | |
4209 | else if (SCM_BIGP (n1)) | |
4210 | { | |
e11e83f3 | 4211 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4212 | { |
4213 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4214 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4215 | goto intbig; |
4216 | } | |
4217 | else if (SCM_BIGP (n2)) | |
4218 | { | |
4219 | SCM result_z = scm_i_mkbig (); | |
4220 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
4221 | SCM_I_BIG_MPZ (n1), | |
4222 | SCM_I_BIG_MPZ (n2)); | |
4223 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 4224 | return scm_i_normbig (result_z); |
0aacf84e MD |
4225 | } |
4226 | else | |
4227 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4228 | } |
0aacf84e | 4229 | else |
09fb7599 | 4230 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4231 | } |
1bbd0b84 | 4232 | #undef FUNC_NAME |
0f2d19dd | 4233 | |
09fb7599 | 4234 | |
78d3deb1 AW |
4235 | SCM_DEFINE (scm_i_logxor, "logxor", 0, 2, 1, |
4236 | (SCM x, SCM y, SCM rest), | |
3c3db128 GH |
4237 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
4238 | "set in the result if it is set in an odd number of arguments.\n" | |
4239 | "@lisp\n" | |
4240 | "(logxor) @result{} 0\n" | |
4241 | "(logxor 7) @result{} 7\n" | |
4242 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
4243 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 4244 | "@end lisp") |
78d3deb1 AW |
4245 | #define FUNC_NAME s_scm_i_logxor |
4246 | { | |
4247 | while (!scm_is_null (rest)) | |
4248 | { x = scm_logxor (x, y); | |
4249 | y = scm_car (rest); | |
4250 | rest = scm_cdr (rest); | |
4251 | } | |
4252 | return scm_logxor (x, y); | |
4253 | } | |
4254 | #undef FUNC_NAME | |
4255 | ||
4256 | #define s_scm_logxor s_scm_i_logxor | |
4257 | ||
4258 | SCM scm_logxor (SCM n1, SCM n2) | |
1bbd0b84 | 4259 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 4260 | { |
e25f3727 | 4261 | scm_t_inum nn1; |
9a00c9fc | 4262 | |
0aacf84e MD |
4263 | if (SCM_UNBNDP (n2)) |
4264 | { | |
4265 | if (SCM_UNBNDP (n1)) | |
4266 | return SCM_INUM0; | |
4267 | else if (SCM_NUMBERP (n1)) | |
4268 | return n1; | |
4269 | else | |
4270 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 4271 | } |
09fb7599 | 4272 | |
e11e83f3 | 4273 | if (SCM_I_INUMP (n1)) |
0aacf84e | 4274 | { |
e11e83f3 MV |
4275 | nn1 = SCM_I_INUM (n1); |
4276 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 4277 | { |
e25f3727 | 4278 | scm_t_inum nn2 = SCM_I_INUM (n2); |
d956fa6f | 4279 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
4280 | } |
4281 | else if (SCM_BIGP (n2)) | |
4282 | { | |
4283 | intbig: | |
4284 | { | |
4285 | SCM result_z = scm_i_mkbig (); | |
4286 | mpz_t nn1_z; | |
4287 | mpz_init_set_si (nn1_z, nn1); | |
4288 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
4289 | scm_remember_upto_here_1 (n2); | |
4290 | mpz_clear (nn1_z); | |
4291 | return scm_i_normbig (result_z); | |
4292 | } | |
4293 | } | |
4294 | else | |
4295 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
4296 | } | |
4297 | else if (SCM_BIGP (n1)) | |
4298 | { | |
e11e83f3 | 4299 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
4300 | { |
4301 | SCM_SWAP (n1, n2); | |
e11e83f3 | 4302 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
4303 | goto intbig; |
4304 | } | |
4305 | else if (SCM_BIGP (n2)) | |
4306 | { | |
4307 | SCM result_z = scm_i_mkbig (); | |
4308 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
4309 | SCM_I_BIG_MPZ (n1), | |
4310 | SCM_I_BIG_MPZ (n2)); | |
4311 | scm_remember_upto_here_2 (n1, n2); | |
4312 | return scm_i_normbig (result_z); | |
4313 | } | |
4314 | else | |
4315 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 4316 | } |
0aacf84e | 4317 | else |
09fb7599 | 4318 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 4319 | } |
1bbd0b84 | 4320 | #undef FUNC_NAME |
0f2d19dd | 4321 | |
09fb7599 | 4322 | |
a1ec6916 | 4323 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 4324 | (SCM j, SCM k), |
ba6e7231 KR |
4325 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
4326 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
4327 | "without actually calculating the @code{logand}, just testing\n" | |
4328 | "for non-zero.\n" | |
4329 | "\n" | |
1e6808ea | 4330 | "@lisp\n" |
b380b885 MD |
4331 | "(logtest #b0100 #b1011) @result{} #f\n" |
4332 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 4333 | "@end lisp") |
1bbd0b84 | 4334 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 4335 | { |
e25f3727 | 4336 | scm_t_inum nj; |
9a00c9fc | 4337 | |
e11e83f3 | 4338 | if (SCM_I_INUMP (j)) |
0aacf84e | 4339 | { |
e11e83f3 MV |
4340 | nj = SCM_I_INUM (j); |
4341 | if (SCM_I_INUMP (k)) | |
0aacf84e | 4342 | { |
e25f3727 | 4343 | scm_t_inum nk = SCM_I_INUM (k); |
73e4de09 | 4344 | return scm_from_bool (nj & nk); |
0aacf84e MD |
4345 | } |
4346 | else if (SCM_BIGP (k)) | |
4347 | { | |
4348 | intbig: | |
4349 | if (nj == 0) | |
4350 | return SCM_BOOL_F; | |
4351 | { | |
4352 | SCM result; | |
4353 | mpz_t nj_z; | |
4354 | mpz_init_set_si (nj_z, nj); | |
4355 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
4356 | scm_remember_upto_here_1 (k); | |
73e4de09 | 4357 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
4358 | mpz_clear (nj_z); |
4359 | return result; | |
4360 | } | |
4361 | } | |
4362 | else | |
4363 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4364 | } | |
4365 | else if (SCM_BIGP (j)) | |
4366 | { | |
e11e83f3 | 4367 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
4368 | { |
4369 | SCM_SWAP (j, k); | |
e11e83f3 | 4370 | nj = SCM_I_INUM (j); |
0aacf84e MD |
4371 | goto intbig; |
4372 | } | |
4373 | else if (SCM_BIGP (k)) | |
4374 | { | |
4375 | SCM result; | |
4376 | mpz_t result_z; | |
4377 | mpz_init (result_z); | |
4378 | mpz_and (result_z, | |
4379 | SCM_I_BIG_MPZ (j), | |
4380 | SCM_I_BIG_MPZ (k)); | |
4381 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 4382 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
4383 | mpz_clear (result_z); |
4384 | return result; | |
4385 | } | |
4386 | else | |
4387 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
4388 | } | |
4389 | else | |
4390 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 4391 | } |
1bbd0b84 | 4392 | #undef FUNC_NAME |
0f2d19dd | 4393 | |
c1bfcf60 | 4394 | |
a1ec6916 | 4395 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 4396 | (SCM index, SCM j), |
ba6e7231 KR |
4397 | "Test whether bit number @var{index} in @var{j} is set.\n" |
4398 | "@var{index} starts from 0 for the least significant bit.\n" | |
4399 | "\n" | |
1e6808ea | 4400 | "@lisp\n" |
b380b885 MD |
4401 | "(logbit? 0 #b1101) @result{} #t\n" |
4402 | "(logbit? 1 #b1101) @result{} #f\n" | |
4403 | "(logbit? 2 #b1101) @result{} #t\n" | |
4404 | "(logbit? 3 #b1101) @result{} #t\n" | |
4405 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 4406 | "@end lisp") |
1bbd0b84 | 4407 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 4408 | { |
78166ad5 | 4409 | unsigned long int iindex; |
5efd3c7d | 4410 | iindex = scm_to_ulong (index); |
78166ad5 | 4411 | |
e11e83f3 | 4412 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
4413 | { |
4414 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 4415 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 4416 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 4417 | } |
0aacf84e MD |
4418 | else if (SCM_BIGP (j)) |
4419 | { | |
4420 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
4421 | scm_remember_upto_here_1 (j); | |
73e4de09 | 4422 | return scm_from_bool (val); |
0aacf84e MD |
4423 | } |
4424 | else | |
78166ad5 | 4425 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 4426 | } |
1bbd0b84 | 4427 | #undef FUNC_NAME |
0f2d19dd | 4428 | |
78166ad5 | 4429 | |
a1ec6916 | 4430 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 4431 | (SCM n), |
4d814788 | 4432 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
4433 | "argument.\n" |
4434 | "\n" | |
b380b885 MD |
4435 | "@lisp\n" |
4436 | "(number->string (lognot #b10000000) 2)\n" | |
4437 | " @result{} \"-10000001\"\n" | |
4438 | "(number->string (lognot #b0) 2)\n" | |
4439 | " @result{} \"-1\"\n" | |
1e6808ea | 4440 | "@end lisp") |
1bbd0b84 | 4441 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 4442 | { |
e11e83f3 | 4443 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
4444 | /* No overflow here, just need to toggle all the bits making up the inum. |
4445 | Enhancement: No need to strip the tag and add it back, could just xor | |
4446 | a block of 1 bits, if that worked with the various debug versions of | |
4447 | the SCM typedef. */ | |
e11e83f3 | 4448 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
4449 | |
4450 | } else if (SCM_BIGP (n)) { | |
4451 | SCM result = scm_i_mkbig (); | |
4452 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
4453 | scm_remember_upto_here_1 (n); | |
4454 | return result; | |
4455 | ||
4456 | } else { | |
4457 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4458 | } | |
0f2d19dd | 4459 | } |
1bbd0b84 | 4460 | #undef FUNC_NAME |
0f2d19dd | 4461 | |
518b7508 KR |
4462 | /* returns 0 if IN is not an integer. OUT must already be |
4463 | initialized. */ | |
4464 | static int | |
4465 | coerce_to_big (SCM in, mpz_t out) | |
4466 | { | |
4467 | if (SCM_BIGP (in)) | |
4468 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
4469 | else if (SCM_I_INUMP (in)) |
4470 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
4471 | else |
4472 | return 0; | |
4473 | ||
4474 | return 1; | |
4475 | } | |
4476 | ||
d885e204 | 4477 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
4478 | (SCM n, SCM k, SCM m), |
4479 | "Return @var{n} raised to the integer exponent\n" | |
4480 | "@var{k}, modulo @var{m}.\n" | |
4481 | "\n" | |
4482 | "@lisp\n" | |
4483 | "(modulo-expt 2 3 5)\n" | |
4484 | " @result{} 3\n" | |
4485 | "@end lisp") | |
d885e204 | 4486 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
4487 | { |
4488 | mpz_t n_tmp; | |
4489 | mpz_t k_tmp; | |
4490 | mpz_t m_tmp; | |
4491 | ||
4492 | /* There are two classes of error we might encounter -- | |
4493 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
4494 | and | |
4495 | 2) wrong-type errors, which of course we'll report by calling | |
4496 | SCM_WRONG_TYPE_ARG. | |
4497 | We don't report those errors immediately, however; instead we do | |
4498 | some cleanup first. These variables tell us which error (if | |
4499 | any) we should report after cleaning up. | |
4500 | */ | |
4501 | int report_overflow = 0; | |
4502 | ||
4503 | int position_of_wrong_type = 0; | |
4504 | SCM value_of_wrong_type = SCM_INUM0; | |
4505 | ||
4506 | SCM result = SCM_UNDEFINED; | |
4507 | ||
4508 | mpz_init (n_tmp); | |
4509 | mpz_init (k_tmp); | |
4510 | mpz_init (m_tmp); | |
4511 | ||
bc36d050 | 4512 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
4513 | { |
4514 | report_overflow = 1; | |
4515 | goto cleanup; | |
4516 | } | |
4517 | ||
4518 | if (!coerce_to_big (n, n_tmp)) | |
4519 | { | |
4520 | value_of_wrong_type = n; | |
4521 | position_of_wrong_type = 1; | |
4522 | goto cleanup; | |
4523 | } | |
4524 | ||
4525 | if (!coerce_to_big (k, k_tmp)) | |
4526 | { | |
4527 | value_of_wrong_type = k; | |
4528 | position_of_wrong_type = 2; | |
4529 | goto cleanup; | |
4530 | } | |
4531 | ||
4532 | if (!coerce_to_big (m, m_tmp)) | |
4533 | { | |
4534 | value_of_wrong_type = m; | |
4535 | position_of_wrong_type = 3; | |
4536 | goto cleanup; | |
4537 | } | |
4538 | ||
4539 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
4540 | will get a divide-by-zero exception when an inverse 1/n mod m | |
4541 | doesn't exist (or is not unique). Since exceptions are hard to | |
4542 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
4543 | a simple failure code, which is easy to handle. */ | |
4544 | ||
4545 | if (-1 == mpz_sgn (k_tmp)) | |
4546 | { | |
4547 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
4548 | { | |
4549 | report_overflow = 1; | |
4550 | goto cleanup; | |
4551 | } | |
4552 | mpz_neg (k_tmp, k_tmp); | |
4553 | } | |
4554 | ||
4555 | result = scm_i_mkbig (); | |
4556 | mpz_powm (SCM_I_BIG_MPZ (result), | |
4557 | n_tmp, | |
4558 | k_tmp, | |
4559 | m_tmp); | |
b7b8c575 KR |
4560 | |
4561 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
4562 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
4563 | ||
518b7508 KR |
4564 | cleanup: |
4565 | mpz_clear (m_tmp); | |
4566 | mpz_clear (k_tmp); | |
4567 | mpz_clear (n_tmp); | |
4568 | ||
4569 | if (report_overflow) | |
4570 | scm_num_overflow (FUNC_NAME); | |
4571 | ||
4572 | if (position_of_wrong_type) | |
4573 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
4574 | value_of_wrong_type); | |
4575 | ||
4576 | return scm_i_normbig (result); | |
4577 | } | |
4578 | #undef FUNC_NAME | |
4579 | ||
a1ec6916 | 4580 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 4581 | (SCM n, SCM k), |
ba6e7231 KR |
4582 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
4583 | "exact integer, @var{n} can be any number.\n" | |
4584 | "\n" | |
2519490c MW |
4585 | "Negative @var{k} is supported, and results in\n" |
4586 | "@math{1/@var{n}^abs(@var{k})} in the usual way.\n" | |
4587 | "@math{@var{n}^0} is 1, as usual, and that\n" | |
ba6e7231 | 4588 | "includes @math{0^0} is 1.\n" |
1e6808ea | 4589 | "\n" |
b380b885 | 4590 | "@lisp\n" |
ba6e7231 KR |
4591 | "(integer-expt 2 5) @result{} 32\n" |
4592 | "(integer-expt -3 3) @result{} -27\n" | |
4593 | "(integer-expt 5 -3) @result{} 1/125\n" | |
4594 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 4595 | "@end lisp") |
1bbd0b84 | 4596 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 4597 | { |
e25f3727 | 4598 | scm_t_inum i2 = 0; |
1c35cb19 RB |
4599 | SCM z_i2 = SCM_BOOL_F; |
4600 | int i2_is_big = 0; | |
d956fa6f | 4601 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 4602 | |
bfe1f03a MW |
4603 | /* Specifically refrain from checking the type of the first argument. |
4604 | This allows us to exponentiate any object that can be multiplied. | |
4605 | If we must raise to a negative power, we must also be able to | |
4606 | take its reciprocal. */ | |
4607 | if (!SCM_LIKELY (SCM_I_INUMP (k)) && !SCM_LIKELY (SCM_BIGP (k))) | |
01c7284a | 4608 | SCM_WRONG_TYPE_ARG (2, k); |
5a8fc758 | 4609 | |
bfe1f03a MW |
4610 | if (SCM_UNLIKELY (scm_is_eq (k, SCM_INUM0))) |
4611 | return SCM_INUM1; /* n^(exact0) is exact 1, regardless of n */ | |
4612 | else if (SCM_UNLIKELY (scm_is_eq (n, SCM_I_MAKINUM (-1L)))) | |
4613 | return scm_is_false (scm_even_p (k)) ? n : SCM_INUM1; | |
4614 | /* The next check is necessary only because R6RS specifies different | |
4615 | behavior for 0^(-k) than for (/ 0). If n is not a scheme number, | |
4616 | we simply skip this case and move on. */ | |
4617 | else if (SCM_NUMBERP (n) && scm_is_true (scm_zero_p (n))) | |
4618 | { | |
4619 | /* k cannot be 0 at this point, because we | |
4620 | have already checked for that case above */ | |
4621 | if (scm_is_true (scm_positive_p (k))) | |
01c7284a MW |
4622 | return n; |
4623 | else /* return NaN for (0 ^ k) for negative k per R6RS */ | |
4624 | return scm_nan (); | |
4625 | } | |
ca46fb90 | 4626 | |
e11e83f3 MV |
4627 | if (SCM_I_INUMP (k)) |
4628 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
4629 | else if (SCM_BIGP (k)) |
4630 | { | |
4631 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
4632 | scm_remember_upto_here_1 (k); |
4633 | i2_is_big = 1; | |
4634 | } | |
2830fd91 | 4635 | else |
ca46fb90 RB |
4636 | SCM_WRONG_TYPE_ARG (2, k); |
4637 | ||
4638 | if (i2_is_big) | |
f872b822 | 4639 | { |
ca46fb90 RB |
4640 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
4641 | { | |
4642 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
4643 | n = scm_divide (n, SCM_UNDEFINED); | |
4644 | } | |
4645 | while (1) | |
4646 | { | |
4647 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
4648 | { | |
ca46fb90 RB |
4649 | return acc; |
4650 | } | |
4651 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
4652 | { | |
ca46fb90 RB |
4653 | return scm_product (acc, n); |
4654 | } | |
4655 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
4656 | acc = scm_product (acc, n); | |
4657 | n = scm_product (n, n); | |
4658 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
4659 | } | |
f872b822 | 4660 | } |
ca46fb90 | 4661 | else |
f872b822 | 4662 | { |
ca46fb90 RB |
4663 | if (i2 < 0) |
4664 | { | |
4665 | i2 = -i2; | |
4666 | n = scm_divide (n, SCM_UNDEFINED); | |
4667 | } | |
4668 | while (1) | |
4669 | { | |
4670 | if (0 == i2) | |
4671 | return acc; | |
4672 | if (1 == i2) | |
4673 | return scm_product (acc, n); | |
4674 | if (i2 & 1) | |
4675 | acc = scm_product (acc, n); | |
4676 | n = scm_product (n, n); | |
4677 | i2 >>= 1; | |
4678 | } | |
f872b822 | 4679 | } |
0f2d19dd | 4680 | } |
1bbd0b84 | 4681 | #undef FUNC_NAME |
0f2d19dd | 4682 | |
a1ec6916 | 4683 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 4684 | (SCM n, SCM cnt), |
32f19569 KR |
4685 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
4686 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 4687 | "\n" |
e7644cb2 | 4688 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
4689 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
4690 | "infinity. (Note that this is not the same rounding as\n" | |
4691 | "@code{quotient} does.)\n" | |
4692 | "\n" | |
4693 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
4694 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
4695 | "shift dropping bits.\n" | |
1e6808ea | 4696 | "\n" |
b380b885 | 4697 | "@lisp\n" |
1e6808ea MG |
4698 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
4699 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
4700 | "\n" |
4701 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
4702 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 4703 | "@end lisp") |
1bbd0b84 | 4704 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 4705 | { |
3ab9f56e | 4706 | long bits_to_shift; |
5efd3c7d | 4707 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 4708 | |
788aca27 KR |
4709 | if (SCM_I_INUMP (n)) |
4710 | { | |
e25f3727 | 4711 | scm_t_inum nn = SCM_I_INUM (n); |
788aca27 KR |
4712 | |
4713 | if (bits_to_shift > 0) | |
4714 | { | |
4715 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
4716 | overflow a non-zero fixnum. For smaller shifts we check the | |
4717 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
4718 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
4719 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
4720 | bits_to_shift)". */ | |
4721 | ||
4722 | if (nn == 0) | |
4723 | return n; | |
4724 | ||
4725 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 4726 | && ((scm_t_bits) |
788aca27 KR |
4727 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) |
4728 | <= 1)) | |
4729 | { | |
4730 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
4731 | } | |
4732 | else | |
4733 | { | |
e25f3727 | 4734 | SCM result = scm_i_inum2big (nn); |
788aca27 KR |
4735 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
4736 | bits_to_shift); | |
4737 | return result; | |
4738 | } | |
4739 | } | |
4740 | else | |
4741 | { | |
4742 | bits_to_shift = -bits_to_shift; | |
4743 | if (bits_to_shift >= SCM_LONG_BIT) | |
cff5fa33 | 4744 | return (nn >= 0 ? SCM_INUM0 : SCM_I_MAKINUM(-1)); |
788aca27 KR |
4745 | else |
4746 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
4747 | } | |
4748 | ||
4749 | } | |
4750 | else if (SCM_BIGP (n)) | |
ca46fb90 | 4751 | { |
788aca27 KR |
4752 | SCM result; |
4753 | ||
4754 | if (bits_to_shift == 0) | |
4755 | return n; | |
4756 | ||
4757 | result = scm_i_mkbig (); | |
4758 | if (bits_to_shift >= 0) | |
4759 | { | |
4760 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
4761 | bits_to_shift); | |
4762 | return result; | |
4763 | } | |
ca46fb90 | 4764 | else |
788aca27 KR |
4765 | { |
4766 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
4767 | we have to allocate a bignum even if the result is going to be a | |
4768 | fixnum. */ | |
4769 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
4770 | -bits_to_shift); | |
4771 | return scm_i_normbig (result); | |
4772 | } | |
4773 | ||
ca46fb90 RB |
4774 | } |
4775 | else | |
788aca27 KR |
4776 | { |
4777 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
4778 | } | |
0f2d19dd | 4779 | } |
1bbd0b84 | 4780 | #undef FUNC_NAME |
0f2d19dd | 4781 | |
3c9f20f8 | 4782 | |
a1ec6916 | 4783 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 4784 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
4785 | "Return the integer composed of the @var{start} (inclusive)\n" |
4786 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
4787 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
4788 | "\n" | |
b380b885 MD |
4789 | "@lisp\n" |
4790 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
4791 | " @result{} \"1010\"\n" | |
4792 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
4793 | " @result{} \"10110\"\n" | |
4794 | "@end lisp") | |
1bbd0b84 | 4795 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 4796 | { |
7f848242 | 4797 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
4798 | istart = scm_to_ulong (start); |
4799 | iend = scm_to_ulong (end); | |
c1bfcf60 | 4800 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 4801 | |
7f848242 KR |
4802 | /* how many bits to keep */ |
4803 | bits = iend - istart; | |
4804 | ||
e11e83f3 | 4805 | if (SCM_I_INUMP (n)) |
0aacf84e | 4806 | { |
e25f3727 | 4807 | scm_t_inum in = SCM_I_INUM (n); |
7f848242 KR |
4808 | |
4809 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 4810 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 4811 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 4812 | |
0aacf84e MD |
4813 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
4814 | { | |
4815 | /* Since we emulate two's complement encoded numbers, this | |
4816 | * special case requires us to produce a result that has | |
7f848242 | 4817 | * more bits than can be stored in a fixnum. |
0aacf84e | 4818 | */ |
e25f3727 | 4819 | SCM result = scm_i_inum2big (in); |
7f848242 KR |
4820 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), |
4821 | bits); | |
4822 | return result; | |
0aacf84e | 4823 | } |
ac0c002c | 4824 | |
7f848242 | 4825 | /* mask down to requisite bits */ |
857ae6af | 4826 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 4827 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
4828 | } |
4829 | else if (SCM_BIGP (n)) | |
ac0c002c | 4830 | { |
7f848242 KR |
4831 | SCM result; |
4832 | if (bits == 1) | |
4833 | { | |
d956fa6f | 4834 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
4835 | } |
4836 | else | |
4837 | { | |
4838 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
4839 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
4840 | such bits into a ulong. */ | |
4841 | result = scm_i_mkbig (); | |
4842 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
4843 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
4844 | result = scm_i_normbig (result); | |
4845 | } | |
4846 | scm_remember_upto_here_1 (n); | |
4847 | return result; | |
ac0c002c | 4848 | } |
0aacf84e | 4849 | else |
78166ad5 | 4850 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 4851 | } |
1bbd0b84 | 4852 | #undef FUNC_NAME |
0f2d19dd | 4853 | |
7f848242 | 4854 | |
e4755e5c JB |
4855 | static const char scm_logtab[] = { |
4856 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
4857 | }; | |
1cc91f1b | 4858 | |
a1ec6916 | 4859 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 4860 | (SCM n), |
1e6808ea MG |
4861 | "Return the number of bits in integer @var{n}. If integer is\n" |
4862 | "positive, the 1-bits in its binary representation are counted.\n" | |
4863 | "If negative, the 0-bits in its two's-complement binary\n" | |
4864 | "representation are counted. If 0, 0 is returned.\n" | |
4865 | "\n" | |
b380b885 MD |
4866 | "@lisp\n" |
4867 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
4868 | " @result{} 4\n" |
4869 | "(logcount 0)\n" | |
4870 | " @result{} 0\n" | |
4871 | "(logcount -2)\n" | |
4872 | " @result{} 1\n" | |
4873 | "@end lisp") | |
4874 | #define FUNC_NAME s_scm_logcount | |
4875 | { | |
e11e83f3 | 4876 | if (SCM_I_INUMP (n)) |
f872b822 | 4877 | { |
e25f3727 AW |
4878 | unsigned long c = 0; |
4879 | scm_t_inum nn = SCM_I_INUM (n); | |
ca46fb90 RB |
4880 | if (nn < 0) |
4881 | nn = -1 - nn; | |
4882 | while (nn) | |
4883 | { | |
4884 | c += scm_logtab[15 & nn]; | |
4885 | nn >>= 4; | |
4886 | } | |
d956fa6f | 4887 | return SCM_I_MAKINUM (c); |
f872b822 | 4888 | } |
ca46fb90 | 4889 | else if (SCM_BIGP (n)) |
f872b822 | 4890 | { |
ca46fb90 | 4891 | unsigned long count; |
713a4259 KR |
4892 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
4893 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 4894 | else |
713a4259 KR |
4895 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
4896 | scm_remember_upto_here_1 (n); | |
d956fa6f | 4897 | return SCM_I_MAKINUM (count); |
f872b822 | 4898 | } |
ca46fb90 RB |
4899 | else |
4900 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 4901 | } |
ca46fb90 | 4902 | #undef FUNC_NAME |
0f2d19dd JB |
4903 | |
4904 | ||
ca46fb90 RB |
4905 | static const char scm_ilentab[] = { |
4906 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
4907 | }; | |
4908 | ||
0f2d19dd | 4909 | |
ca46fb90 RB |
4910 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
4911 | (SCM n), | |
4912 | "Return the number of bits necessary to represent @var{n}.\n" | |
4913 | "\n" | |
4914 | "@lisp\n" | |
4915 | "(integer-length #b10101010)\n" | |
4916 | " @result{} 8\n" | |
4917 | "(integer-length 0)\n" | |
4918 | " @result{} 0\n" | |
4919 | "(integer-length #b1111)\n" | |
4920 | " @result{} 4\n" | |
4921 | "@end lisp") | |
4922 | #define FUNC_NAME s_scm_integer_length | |
4923 | { | |
e11e83f3 | 4924 | if (SCM_I_INUMP (n)) |
0aacf84e | 4925 | { |
e25f3727 | 4926 | unsigned long c = 0; |
0aacf84e | 4927 | unsigned int l = 4; |
e25f3727 | 4928 | scm_t_inum nn = SCM_I_INUM (n); |
0aacf84e MD |
4929 | if (nn < 0) |
4930 | nn = -1 - nn; | |
4931 | while (nn) | |
4932 | { | |
4933 | c += 4; | |
4934 | l = scm_ilentab [15 & nn]; | |
4935 | nn >>= 4; | |
4936 | } | |
d956fa6f | 4937 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
4938 | } |
4939 | else if (SCM_BIGP (n)) | |
4940 | { | |
4941 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
4942 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
4943 | 1 too big, so check for that and adjust. */ | |
4944 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
4945 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
4946 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
4947 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
4948 | size--; | |
4949 | scm_remember_upto_here_1 (n); | |
d956fa6f | 4950 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
4951 | } |
4952 | else | |
ca46fb90 | 4953 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
4954 | } |
4955 | #undef FUNC_NAME | |
0f2d19dd JB |
4956 | |
4957 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
4958 | #define SCM_MAX_DBL_PREC 60 |
4959 | #define SCM_MAX_DBL_RADIX 36 | |
4960 | ||
4961 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
4962 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
4963 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
4964 | ||
4965 | static | |
4966 | void init_dblprec(int *prec, int radix) { | |
4967 | /* determine floating point precision by adding successively | |
4968 | smaller increments to 1.0 until it is considered == 1.0 */ | |
4969 | double f = ((double)1.0)/radix; | |
4970 | double fsum = 1.0 + f; | |
4971 | ||
4972 | *prec = 0; | |
4973 | while (fsum != 1.0) | |
4974 | { | |
4975 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
4976 | fsum = 1.0; | |
4977 | else | |
4978 | { | |
4979 | f /= radix; | |
4980 | fsum = f + 1.0; | |
4981 | } | |
4982 | } | |
4983 | (*prec) -= 1; | |
4984 | } | |
4985 | ||
4986 | static | |
4987 | void init_fx_radix(double *fx_list, int radix) | |
4988 | { | |
4989 | /* initialize a per-radix list of tolerances. When added | |
4990 | to a number < 1.0, we can determine if we should raund | |
4991 | up and quit converting a number to a string. */ | |
4992 | int i; | |
4993 | fx_list[0] = 0.0; | |
4994 | fx_list[1] = 0.5; | |
4995 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
4996 | fx_list[i] = (fx_list[i-1] / radix); | |
4997 | } | |
4998 | ||
4999 | /* use this array as a way to generate a single digit */ | |
9b5fcde6 | 5000 | static const char number_chars[] = "0123456789abcdefghijklmnopqrstuvwxyz"; |
0f2d19dd | 5001 | |
1be6b49c | 5002 | static size_t |
0b799eea | 5003 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 5004 | { |
0b799eea MV |
5005 | int efmt, dpt, d, i, wp; |
5006 | double *fx; | |
5007 | #ifdef DBL_MIN_10_EXP | |
5008 | double f_cpy; | |
5009 | int exp_cpy; | |
5010 | #endif /* DBL_MIN_10_EXP */ | |
5011 | size_t ch = 0; | |
5012 | int exp = 0; | |
5013 | ||
5014 | if(radix < 2 || | |
5015 | radix > SCM_MAX_DBL_RADIX) | |
5016 | { | |
5017 | /* revert to existing behavior */ | |
5018 | radix = 10; | |
5019 | } | |
5020 | ||
5021 | wp = scm_dblprec[radix-2]; | |
5022 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 5023 | |
f872b822 | 5024 | if (f == 0.0) |
abb7e44d MV |
5025 | { |
5026 | #ifdef HAVE_COPYSIGN | |
5027 | double sgn = copysign (1.0, f); | |
5028 | ||
5029 | if (sgn < 0.0) | |
5030 | a[ch++] = '-'; | |
5031 | #endif | |
abb7e44d MV |
5032 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
5033 | } | |
7351e207 | 5034 | |
2e65b52f | 5035 | if (isinf (f)) |
7351e207 MV |
5036 | { |
5037 | if (f < 0) | |
5038 | strcpy (a, "-inf.0"); | |
5039 | else | |
5040 | strcpy (a, "+inf.0"); | |
5041 | return ch+6; | |
5042 | } | |
2e65b52f | 5043 | else if (isnan (f)) |
7351e207 MV |
5044 | { |
5045 | strcpy (a, "+nan.0"); | |
5046 | return ch+6; | |
5047 | } | |
5048 | ||
f872b822 MD |
5049 | if (f < 0.0) |
5050 | { | |
5051 | f = -f; | |
5052 | a[ch++] = '-'; | |
5053 | } | |
7351e207 | 5054 | |
f872b822 MD |
5055 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
5056 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
5057 | /* just do the checking...if it passes, we do the conversion for our |
5058 | radix again below */ | |
5059 | f_cpy = f; | |
5060 | exp_cpy = exp; | |
5061 | ||
5062 | while (f_cpy < 1.0) | |
f872b822 | 5063 | { |
0b799eea MV |
5064 | f_cpy *= 10.0; |
5065 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
5066 | { |
5067 | a[ch++] = '#'; | |
5068 | a[ch++] = '.'; | |
5069 | a[ch++] = '#'; | |
5070 | return ch; | |
5071 | } | |
f872b822 | 5072 | } |
0b799eea | 5073 | while (f_cpy > 10.0) |
f872b822 | 5074 | { |
0b799eea MV |
5075 | f_cpy *= 0.10; |
5076 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
5077 | { |
5078 | a[ch++] = '#'; | |
5079 | a[ch++] = '.'; | |
5080 | a[ch++] = '#'; | |
5081 | return ch; | |
5082 | } | |
f872b822 | 5083 | } |
0b799eea MV |
5084 | #endif |
5085 | ||
f872b822 MD |
5086 | while (f < 1.0) |
5087 | { | |
0b799eea | 5088 | f *= radix; |
f872b822 MD |
5089 | exp--; |
5090 | } | |
0b799eea | 5091 | while (f > radix) |
f872b822 | 5092 | { |
0b799eea | 5093 | f /= radix; |
f872b822 MD |
5094 | exp++; |
5095 | } | |
0b799eea MV |
5096 | |
5097 | if (f + fx[wp] >= radix) | |
f872b822 MD |
5098 | { |
5099 | f = 1.0; | |
5100 | exp++; | |
5101 | } | |
0f2d19dd | 5102 | zero: |
0b799eea MV |
5103 | #ifdef ENGNOT |
5104 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 5105 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
5106 | exp -= dpt++; |
5107 | efmt = 1; | |
f872b822 MD |
5108 | #else |
5109 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 5110 | if (!efmt) |
cda139a7 MD |
5111 | { |
5112 | if (exp < 0) | |
5113 | { | |
5114 | a[ch++] = '0'; | |
5115 | a[ch++] = '.'; | |
5116 | dpt = exp; | |
f872b822 MD |
5117 | while (++dpt) |
5118 | a[ch++] = '0'; | |
cda139a7 MD |
5119 | } |
5120 | else | |
f872b822 | 5121 | dpt = exp + 1; |
cda139a7 | 5122 | } |
0f2d19dd JB |
5123 | else |
5124 | dpt = 1; | |
f872b822 MD |
5125 | #endif |
5126 | ||
5127 | do | |
5128 | { | |
5129 | d = f; | |
5130 | f -= d; | |
0b799eea | 5131 | a[ch++] = number_chars[d]; |
f872b822 MD |
5132 | if (f < fx[wp]) |
5133 | break; | |
5134 | if (f + fx[wp] >= 1.0) | |
5135 | { | |
0b799eea | 5136 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
5137 | break; |
5138 | } | |
0b799eea | 5139 | f *= radix; |
f872b822 MD |
5140 | if (!(--dpt)) |
5141 | a[ch++] = '.'; | |
0f2d19dd | 5142 | } |
f872b822 | 5143 | while (wp--); |
0f2d19dd JB |
5144 | |
5145 | if (dpt > 0) | |
cda139a7 | 5146 | { |
f872b822 | 5147 | #ifndef ENGNOT |
cda139a7 MD |
5148 | if ((dpt > 4) && (exp > 6)) |
5149 | { | |
f872b822 | 5150 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 5151 | for (i = ch++; i > d; i--) |
f872b822 | 5152 | a[i] = a[i - 1]; |
cda139a7 MD |
5153 | a[d] = '.'; |
5154 | efmt = 1; | |
5155 | } | |
5156 | else | |
f872b822 | 5157 | #endif |
cda139a7 | 5158 | { |
f872b822 MD |
5159 | while (--dpt) |
5160 | a[ch++] = '0'; | |
cda139a7 MD |
5161 | a[ch++] = '.'; |
5162 | } | |
5163 | } | |
f872b822 MD |
5164 | if (a[ch - 1] == '.') |
5165 | a[ch++] = '0'; /* trailing zero */ | |
5166 | if (efmt && exp) | |
5167 | { | |
5168 | a[ch++] = 'e'; | |
5169 | if (exp < 0) | |
5170 | { | |
5171 | exp = -exp; | |
5172 | a[ch++] = '-'; | |
5173 | } | |
0b799eea MV |
5174 | for (i = radix; i <= exp; i *= radix); |
5175 | for (i /= radix; i; i /= radix) | |
f872b822 | 5176 | { |
0b799eea | 5177 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
5178 | exp %= i; |
5179 | } | |
0f2d19dd | 5180 | } |
0f2d19dd JB |
5181 | return ch; |
5182 | } | |
5183 | ||
7a1aba42 MV |
5184 | |
5185 | static size_t | |
5186 | icmplx2str (double real, double imag, char *str, int radix) | |
5187 | { | |
5188 | size_t i; | |
c7218482 | 5189 | double sgn; |
7a1aba42 MV |
5190 | |
5191 | i = idbl2str (real, str, radix); | |
c7218482 MW |
5192 | #ifdef HAVE_COPYSIGN |
5193 | sgn = copysign (1.0, imag); | |
5194 | #else | |
5195 | sgn = imag; | |
5196 | #endif | |
5197 | /* Don't output a '+' for negative numbers or for Inf and | |
5198 | NaN. They will provide their own sign. */ | |
5199 | if (sgn >= 0 && DOUBLE_IS_FINITE (imag)) | |
5200 | str[i++] = '+'; | |
5201 | i += idbl2str (imag, &str[i], radix); | |
5202 | str[i++] = 'i'; | |
7a1aba42 MV |
5203 | return i; |
5204 | } | |
5205 | ||
1be6b49c | 5206 | static size_t |
0b799eea | 5207 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 5208 | { |
1be6b49c | 5209 | size_t i; |
3c9a524f | 5210 | if (SCM_REALP (flt)) |
0b799eea | 5211 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 5212 | else |
7a1aba42 MV |
5213 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
5214 | str, radix); | |
0f2d19dd JB |
5215 | return i; |
5216 | } | |
0f2d19dd | 5217 | |
2881e77b | 5218 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
5219 | characters in the result. |
5220 | rad is output base | |
5221 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 5222 | size_t |
2881e77b MV |
5223 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
5224 | { | |
5225 | if (num < 0) | |
5226 | { | |
5227 | *p++ = '-'; | |
5228 | return scm_iuint2str (-num, rad, p) + 1; | |
5229 | } | |
5230 | else | |
5231 | return scm_iuint2str (num, rad, p); | |
5232 | } | |
5233 | ||
5234 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
5235 | characters in the result. | |
5236 | rad is output base | |
5237 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
5238 | size_t | |
5239 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 5240 | { |
1be6b49c ML |
5241 | size_t j = 1; |
5242 | size_t i; | |
2881e77b | 5243 | scm_t_uintmax n = num; |
5c11cc9d | 5244 | |
a6f3af16 AW |
5245 | if (rad < 2 || rad > 36) |
5246 | scm_out_of_range ("scm_iuint2str", scm_from_int (rad)); | |
5247 | ||
f872b822 | 5248 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
5249 | j++; |
5250 | ||
5251 | i = j; | |
2881e77b | 5252 | n = num; |
f872b822 MD |
5253 | while (i--) |
5254 | { | |
5c11cc9d GH |
5255 | int d = n % rad; |
5256 | ||
f872b822 | 5257 | n /= rad; |
a6f3af16 | 5258 | p[i] = number_chars[d]; |
f872b822 | 5259 | } |
0f2d19dd JB |
5260 | return j; |
5261 | } | |
5262 | ||
a1ec6916 | 5263 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
5264 | (SCM n, SCM radix), |
5265 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
5266 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
5267 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 5268 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 5269 | { |
1bbd0b84 | 5270 | int base; |
98cb6e75 | 5271 | |
0aacf84e | 5272 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 5273 | base = 10; |
0aacf84e | 5274 | else |
5efd3c7d | 5275 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 5276 | |
e11e83f3 | 5277 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
5278 | { |
5279 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 5280 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 5281 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
5282 | } |
5283 | else if (SCM_BIGP (n)) | |
5284 | { | |
5285 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
5286 | scm_remember_upto_here_1 (n); | |
cc95e00a | 5287 | return scm_take_locale_string (str); |
0aacf84e | 5288 | } |
f92e85f7 MV |
5289 | else if (SCM_FRACTIONP (n)) |
5290 | { | |
f92e85f7 | 5291 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 5292 | scm_from_locale_string ("/"), |
f92e85f7 MV |
5293 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
5294 | } | |
0aacf84e MD |
5295 | else if (SCM_INEXACTP (n)) |
5296 | { | |
5297 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 5298 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
5299 | } |
5300 | else | |
bb628794 | 5301 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 5302 | } |
1bbd0b84 | 5303 | #undef FUNC_NAME |
0f2d19dd JB |
5304 | |
5305 | ||
ca46fb90 RB |
5306 | /* These print routines used to be stubbed here so that scm_repl.c |
5307 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 5308 | |
0f2d19dd | 5309 | int |
e81d98ec | 5310 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5311 | { |
56e55ac7 | 5312 | char num_buf[FLOBUFLEN]; |
0b799eea | 5313 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
5314 | return !0; |
5315 | } | |
5316 | ||
b479fe9a MV |
5317 | void |
5318 | scm_i_print_double (double val, SCM port) | |
5319 | { | |
5320 | char num_buf[FLOBUFLEN]; | |
5321 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
5322 | } | |
5323 | ||
f3ae5d60 | 5324 | int |
e81d98ec | 5325 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 5326 | |
f3ae5d60 | 5327 | { |
56e55ac7 | 5328 | char num_buf[FLOBUFLEN]; |
0b799eea | 5329 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
5330 | return !0; |
5331 | } | |
1cc91f1b | 5332 | |
7a1aba42 MV |
5333 | void |
5334 | scm_i_print_complex (double real, double imag, SCM port) | |
5335 | { | |
5336 | char num_buf[FLOBUFLEN]; | |
5337 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
5338 | } | |
5339 | ||
f92e85f7 MV |
5340 | int |
5341 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
5342 | { | |
5343 | SCM str; | |
f92e85f7 | 5344 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
a9178715 | 5345 | scm_display (str, port); |
f92e85f7 MV |
5346 | scm_remember_upto_here_1 (str); |
5347 | return !0; | |
5348 | } | |
5349 | ||
0f2d19dd | 5350 | int |
e81d98ec | 5351 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 5352 | { |
ca46fb90 RB |
5353 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
5354 | scm_remember_upto_here_1 (exp); | |
5355 | scm_lfwrite (str, (size_t) strlen (str), port); | |
5356 | free (str); | |
0f2d19dd JB |
5357 | return !0; |
5358 | } | |
5359 | /*** END nums->strs ***/ | |
5360 | ||
3c9a524f | 5361 | |
0f2d19dd | 5362 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 5363 | |
3c9a524f DH |
5364 | /* The following functions implement the conversion from strings to numbers. |
5365 | * The implementation somehow follows the grammar for numbers as it is given | |
5366 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
5367 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
5368 | * points should be noted about the implementation: | |
bc3d34f5 | 5369 | * |
3c9a524f DH |
5370 | * * Each function keeps a local index variable 'idx' that points at the |
5371 | * current position within the parsed string. The global index is only | |
5372 | * updated if the function could parse the corresponding syntactic unit | |
5373 | * successfully. | |
bc3d34f5 | 5374 | * |
3c9a524f | 5375 | * * Similarly, the functions keep track of indicators of inexactness ('#', |
bc3d34f5 MW |
5376 | * '.' or exponents) using local variables ('hash_seen', 'x'). |
5377 | * | |
3c9a524f DH |
5378 | * * Sequences of digits are parsed into temporary variables holding fixnums. |
5379 | * Only if these fixnums would overflow, the result variables are updated | |
5380 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
5381 | * the temporary variables holding the fixnums are cleared, and the process | |
5382 | * starts over again. If for example fixnums were able to store five decimal | |
5383 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
5384 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
5385 | * only every five digits two bignum operations were performed. | |
bc3d34f5 MW |
5386 | * |
5387 | * Notes on the handling of exactness specifiers: | |
5388 | * | |
5389 | * When parsing non-real complex numbers, we apply exactness specifiers on | |
5390 | * per-component basis, as is done in PLT Scheme. For complex numbers | |
5391 | * written in rectangular form, exactness specifiers are applied to the | |
5392 | * real and imaginary parts before calling scm_make_rectangular. For | |
5393 | * complex numbers written in polar form, exactness specifiers are applied | |
5394 | * to the magnitude and angle before calling scm_make_polar. | |
5395 | * | |
5396 | * There are two kinds of exactness specifiers: forced and implicit. A | |
5397 | * forced exactness specifier is a "#e" or "#i" prefix at the beginning of | |
5398 | * the entire number, and applies to both components of a complex number. | |
5399 | * "#e" causes each component to be made exact, and "#i" causes each | |
5400 | * component to be made inexact. If no forced exactness specifier is | |
5401 | * present, then the exactness of each component is determined | |
5402 | * independently by the presence or absence of a decimal point or hash mark | |
5403 | * within that component. If a decimal point or hash mark is present, the | |
5404 | * component is made inexact, otherwise it is made exact. | |
5405 | * | |
5406 | * After the exactness specifiers have been applied to each component, they | |
5407 | * are passed to either scm_make_rectangular or scm_make_polar to produce | |
5408 | * the final result. Note that this will result in a real number if the | |
5409 | * imaginary part, magnitude, or angle is an exact 0. | |
5410 | * | |
5411 | * For example, (string->number "#i5.0+0i") does the equivalent of: | |
5412 | * | |
5413 | * (make-rectangular (exact->inexact 5) (exact->inexact 0)) | |
3c9a524f DH |
5414 | */ |
5415 | ||
5416 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
5417 | ||
5418 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
5419 | ||
a6f3af16 AW |
5420 | /* Caller is responsible for checking that the return value is in range |
5421 | for the given radix, which should be <= 36. */ | |
5422 | static unsigned int | |
5423 | char_decimal_value (scm_t_uint32 c) | |
5424 | { | |
5425 | /* uc_decimal_value returns -1 on error. When cast to an unsigned int, | |
5426 | that's certainly above any valid decimal, so we take advantage of | |
5427 | that to elide some tests. */ | |
5428 | unsigned int d = (unsigned int) uc_decimal_value (c); | |
5429 | ||
5430 | /* If that failed, try extended hexadecimals, then. Only accept ascii | |
5431 | hexadecimals. */ | |
5432 | if (d >= 10U) | |
5433 | { | |
5434 | c = uc_tolower (c); | |
5435 | if (c >= (scm_t_uint32) 'a') | |
5436 | d = c - (scm_t_uint32)'a' + 10U; | |
5437 | } | |
5438 | return d; | |
5439 | } | |
3c9a524f | 5440 | |
2a8fecee | 5441 | static SCM |
3f47e526 | 5442 | mem2uinteger (SCM mem, unsigned int *p_idx, |
3c9a524f | 5443 | unsigned int radix, enum t_exactness *p_exactness) |
2a8fecee | 5444 | { |
3c9a524f DH |
5445 | unsigned int idx = *p_idx; |
5446 | unsigned int hash_seen = 0; | |
5447 | scm_t_bits shift = 1; | |
5448 | scm_t_bits add = 0; | |
5449 | unsigned int digit_value; | |
5450 | SCM result; | |
5451 | char c; | |
3f47e526 | 5452 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5453 | |
5454 | if (idx == len) | |
5455 | return SCM_BOOL_F; | |
2a8fecee | 5456 | |
3f47e526 | 5457 | c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5458 | digit_value = char_decimal_value (c); |
3c9a524f DH |
5459 | if (digit_value >= radix) |
5460 | return SCM_BOOL_F; | |
5461 | ||
5462 | idx++; | |
d956fa6f | 5463 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 5464 | while (idx != len) |
f872b822 | 5465 | { |
3f47e526 | 5466 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
a6f3af16 | 5467 | if (c == '#') |
3c9a524f DH |
5468 | { |
5469 | hash_seen = 1; | |
5470 | digit_value = 0; | |
5471 | } | |
a6f3af16 AW |
5472 | else if (hash_seen) |
5473 | break; | |
3c9a524f | 5474 | else |
a6f3af16 AW |
5475 | { |
5476 | digit_value = char_decimal_value (c); | |
5477 | /* This check catches non-decimals in addition to out-of-range | |
5478 | decimals. */ | |
5479 | if (digit_value >= radix) | |
5480 | break; | |
5481 | } | |
3c9a524f DH |
5482 | |
5483 | idx++; | |
5484 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
5485 | { | |
d956fa6f | 5486 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5487 | if (add > 0) |
d956fa6f | 5488 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5489 | |
5490 | shift = radix; | |
5491 | add = digit_value; | |
5492 | } | |
5493 | else | |
5494 | { | |
5495 | shift = shift * radix; | |
5496 | add = add * radix + digit_value; | |
5497 | } | |
5498 | }; | |
5499 | ||
5500 | if (shift > 1) | |
d956fa6f | 5501 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 5502 | if (add > 0) |
d956fa6f | 5503 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5504 | |
5505 | *p_idx = idx; | |
5506 | if (hash_seen) | |
5507 | *p_exactness = INEXACT; | |
5508 | ||
5509 | return result; | |
2a8fecee JB |
5510 | } |
5511 | ||
5512 | ||
3c9a524f DH |
5513 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
5514 | * covers the parts of the rules that start at a potential point. The value | |
5515 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
5516 | * in variable result. The content of *p_exactness indicates, whether a hash |
5517 | * has already been seen in the digits before the point. | |
3c9a524f | 5518 | */ |
1cc91f1b | 5519 | |
3f47e526 | 5520 | #define DIGIT2UINT(d) (uc_numeric_value(d).numerator) |
3c9a524f DH |
5521 | |
5522 | static SCM | |
3f47e526 | 5523 | mem2decimal_from_point (SCM result, SCM mem, |
3c9a524f | 5524 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 5525 | { |
3c9a524f DH |
5526 | unsigned int idx = *p_idx; |
5527 | enum t_exactness x = *p_exactness; | |
3f47e526 | 5528 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5529 | |
5530 | if (idx == len) | |
79d34f68 | 5531 | return result; |
3c9a524f | 5532 | |
3f47e526 | 5533 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5534 | { |
5535 | scm_t_bits shift = 1; | |
5536 | scm_t_bits add = 0; | |
5537 | unsigned int digit_value; | |
cff5fa33 | 5538 | SCM big_shift = SCM_INUM1; |
3c9a524f DH |
5539 | |
5540 | idx++; | |
5541 | while (idx != len) | |
5542 | { | |
3f47e526 MG |
5543 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5544 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5545 | { |
5546 | if (x == INEXACT) | |
5547 | return SCM_BOOL_F; | |
5548 | else | |
5549 | digit_value = DIGIT2UINT (c); | |
5550 | } | |
5551 | else if (c == '#') | |
5552 | { | |
5553 | x = INEXACT; | |
5554 | digit_value = 0; | |
5555 | } | |
5556 | else | |
5557 | break; | |
5558 | ||
5559 | idx++; | |
5560 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
5561 | { | |
d956fa6f MV |
5562 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5563 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 5564 | if (add > 0) |
d956fa6f | 5565 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
5566 | |
5567 | shift = 10; | |
5568 | add = digit_value; | |
5569 | } | |
5570 | else | |
5571 | { | |
5572 | shift = shift * 10; | |
5573 | add = add * 10 + digit_value; | |
5574 | } | |
5575 | }; | |
5576 | ||
5577 | if (add > 0) | |
5578 | { | |
d956fa6f MV |
5579 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
5580 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
5581 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
5582 | } |
5583 | ||
d8592269 | 5584 | result = scm_divide (result, big_shift); |
79d34f68 | 5585 | |
3c9a524f DH |
5586 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
5587 | x = INEXACT; | |
f872b822 | 5588 | } |
3c9a524f | 5589 | |
3c9a524f | 5590 | if (idx != len) |
f872b822 | 5591 | { |
3c9a524f DH |
5592 | int sign = 1; |
5593 | unsigned int start; | |
3f47e526 | 5594 | scm_t_wchar c; |
3c9a524f DH |
5595 | int exponent; |
5596 | SCM e; | |
5597 | ||
5598 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
5599 | ||
3f47e526 | 5600 | switch (scm_i_string_ref (mem, idx)) |
f872b822 | 5601 | { |
3c9a524f DH |
5602 | case 'd': case 'D': |
5603 | case 'e': case 'E': | |
5604 | case 'f': case 'F': | |
5605 | case 'l': case 'L': | |
5606 | case 's': case 'S': | |
5607 | idx++; | |
ee0ddd21 AW |
5608 | if (idx == len) |
5609 | return SCM_BOOL_F; | |
5610 | ||
3c9a524f | 5611 | start = idx; |
3f47e526 | 5612 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5613 | if (c == '-') |
5614 | { | |
5615 | idx++; | |
ee0ddd21 AW |
5616 | if (idx == len) |
5617 | return SCM_BOOL_F; | |
5618 | ||
3c9a524f | 5619 | sign = -1; |
3f47e526 | 5620 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5621 | } |
5622 | else if (c == '+') | |
5623 | { | |
5624 | idx++; | |
ee0ddd21 AW |
5625 | if (idx == len) |
5626 | return SCM_BOOL_F; | |
5627 | ||
3c9a524f | 5628 | sign = 1; |
3f47e526 | 5629 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5630 | } |
5631 | else | |
5632 | sign = 1; | |
5633 | ||
3f47e526 | 5634 | if (!uc_is_property_decimal_digit ((scm_t_uint32) c)) |
3c9a524f DH |
5635 | return SCM_BOOL_F; |
5636 | ||
5637 | idx++; | |
5638 | exponent = DIGIT2UINT (c); | |
5639 | while (idx != len) | |
f872b822 | 5640 | { |
3f47e526 MG |
5641 | scm_t_wchar c = scm_i_string_ref (mem, idx); |
5642 | if (uc_is_property_decimal_digit ((scm_t_uint32) c)) | |
3c9a524f DH |
5643 | { |
5644 | idx++; | |
5645 | if (exponent <= SCM_MAXEXP) | |
5646 | exponent = exponent * 10 + DIGIT2UINT (c); | |
5647 | } | |
5648 | else | |
5649 | break; | |
f872b822 | 5650 | } |
3c9a524f DH |
5651 | |
5652 | if (exponent > SCM_MAXEXP) | |
f872b822 | 5653 | { |
3c9a524f | 5654 | size_t exp_len = idx - start; |
3f47e526 | 5655 | SCM exp_string = scm_i_substring_copy (mem, start, start + exp_len); |
3c9a524f DH |
5656 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
5657 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 5658 | } |
3c9a524f | 5659 | |
d956fa6f | 5660 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
5661 | if (sign == 1) |
5662 | result = scm_product (result, e); | |
5663 | else | |
f92e85f7 | 5664 | result = scm_divide2real (result, e); |
3c9a524f DH |
5665 | |
5666 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
5667 | x = INEXACT; | |
5668 | ||
f872b822 | 5669 | break; |
3c9a524f | 5670 | |
f872b822 | 5671 | default: |
3c9a524f | 5672 | break; |
f872b822 | 5673 | } |
0f2d19dd | 5674 | } |
3c9a524f DH |
5675 | |
5676 | *p_idx = idx; | |
5677 | if (x == INEXACT) | |
5678 | *p_exactness = x; | |
5679 | ||
5680 | return result; | |
0f2d19dd | 5681 | } |
0f2d19dd | 5682 | |
3c9a524f DH |
5683 | |
5684 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
5685 | ||
5686 | static SCM | |
3f47e526 | 5687 | mem2ureal (SCM mem, unsigned int *p_idx, |
9d427b2c | 5688 | unsigned int radix, enum t_exactness forced_x) |
0f2d19dd | 5689 | { |
3c9a524f | 5690 | unsigned int idx = *p_idx; |
164d2481 | 5691 | SCM result; |
3f47e526 | 5692 | size_t len = scm_i_string_length (mem); |
3c9a524f | 5693 | |
40f89215 NJ |
5694 | /* Start off believing that the number will be exact. This changes |
5695 | to INEXACT if we see a decimal point or a hash. */ | |
9d427b2c | 5696 | enum t_exactness implicit_x = EXACT; |
40f89215 | 5697 | |
3c9a524f DH |
5698 | if (idx == len) |
5699 | return SCM_BOOL_F; | |
5700 | ||
3f47e526 | 5701 | if (idx+5 <= len && !scm_i_string_strcmp (mem, idx, "inf.0")) |
7351e207 MV |
5702 | { |
5703 | *p_idx = idx+5; | |
5704 | return scm_inf (); | |
5705 | } | |
5706 | ||
3f47e526 | 5707 | if (idx+4 < len && !scm_i_string_strcmp (mem, idx, "nan.")) |
7351e207 | 5708 | { |
d8592269 MV |
5709 | /* Cobble up the fractional part. We might want to set the |
5710 | NaN's mantissa from it. */ | |
7351e207 | 5711 | idx += 4; |
9d427b2c | 5712 | mem2uinteger (mem, &idx, 10, &implicit_x); |
7351e207 MV |
5713 | *p_idx = idx; |
5714 | return scm_nan (); | |
5715 | } | |
5716 | ||
3f47e526 | 5717 | if (scm_i_string_ref (mem, idx) == '.') |
3c9a524f DH |
5718 | { |
5719 | if (radix != 10) | |
5720 | return SCM_BOOL_F; | |
5721 | else if (idx + 1 == len) | |
5722 | return SCM_BOOL_F; | |
3f47e526 | 5723 | else if (!uc_is_property_decimal_digit ((scm_t_uint32) scm_i_string_ref (mem, idx+1))) |
3c9a524f DH |
5724 | return SCM_BOOL_F; |
5725 | else | |
cff5fa33 | 5726 | result = mem2decimal_from_point (SCM_INUM0, mem, |
9d427b2c | 5727 | p_idx, &implicit_x); |
f872b822 | 5728 | } |
3c9a524f DH |
5729 | else |
5730 | { | |
3c9a524f | 5731 | SCM uinteger; |
3c9a524f | 5732 | |
9d427b2c | 5733 | uinteger = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 5734 | if (scm_is_false (uinteger)) |
3c9a524f DH |
5735 | return SCM_BOOL_F; |
5736 | ||
5737 | if (idx == len) | |
5738 | result = uinteger; | |
3f47e526 | 5739 | else if (scm_i_string_ref (mem, idx) == '/') |
f872b822 | 5740 | { |
3c9a524f DH |
5741 | SCM divisor; |
5742 | ||
5743 | idx++; | |
ee0ddd21 AW |
5744 | if (idx == len) |
5745 | return SCM_BOOL_F; | |
3c9a524f | 5746 | |
9d427b2c | 5747 | divisor = mem2uinteger (mem, &idx, radix, &implicit_x); |
73e4de09 | 5748 | if (scm_is_false (divisor)) |
3c9a524f DH |
5749 | return SCM_BOOL_F; |
5750 | ||
f92e85f7 | 5751 | /* both are int/big here, I assume */ |
cba42c93 | 5752 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 5753 | } |
3c9a524f DH |
5754 | else if (radix == 10) |
5755 | { | |
9d427b2c | 5756 | result = mem2decimal_from_point (uinteger, mem, &idx, &implicit_x); |
73e4de09 | 5757 | if (scm_is_false (result)) |
3c9a524f DH |
5758 | return SCM_BOOL_F; |
5759 | } | |
5760 | else | |
5761 | result = uinteger; | |
5762 | ||
5763 | *p_idx = idx; | |
f872b822 | 5764 | } |
164d2481 | 5765 | |
9d427b2c MW |
5766 | switch (forced_x) |
5767 | { | |
5768 | case EXACT: | |
5769 | if (SCM_INEXACTP (result)) | |
5770 | return scm_inexact_to_exact (result); | |
5771 | else | |
5772 | return result; | |
5773 | case INEXACT: | |
5774 | if (SCM_INEXACTP (result)) | |
5775 | return result; | |
5776 | else | |
5777 | return scm_exact_to_inexact (result); | |
5778 | case NO_EXACTNESS: | |
5779 | if (implicit_x == INEXACT) | |
5780 | { | |
5781 | if (SCM_INEXACTP (result)) | |
5782 | return result; | |
5783 | else | |
5784 | return scm_exact_to_inexact (result); | |
5785 | } | |
5786 | else | |
5787 | return result; | |
5788 | } | |
164d2481 | 5789 | |
9d427b2c MW |
5790 | /* We should never get here */ |
5791 | scm_syserror ("mem2ureal"); | |
3c9a524f | 5792 | } |
0f2d19dd | 5793 | |
0f2d19dd | 5794 | |
3c9a524f | 5795 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 5796 | |
3c9a524f | 5797 | static SCM |
3f47e526 | 5798 | mem2complex (SCM mem, unsigned int idx, |
9d427b2c | 5799 | unsigned int radix, enum t_exactness forced_x) |
3c9a524f | 5800 | { |
3f47e526 | 5801 | scm_t_wchar c; |
3c9a524f DH |
5802 | int sign = 0; |
5803 | SCM ureal; | |
3f47e526 | 5804 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5805 | |
5806 | if (idx == len) | |
5807 | return SCM_BOOL_F; | |
5808 | ||
3f47e526 | 5809 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5810 | if (c == '+') |
5811 | { | |
5812 | idx++; | |
5813 | sign = 1; | |
5814 | } | |
5815 | else if (c == '-') | |
5816 | { | |
5817 | idx++; | |
5818 | sign = -1; | |
0f2d19dd | 5819 | } |
0f2d19dd | 5820 | |
3c9a524f DH |
5821 | if (idx == len) |
5822 | return SCM_BOOL_F; | |
5823 | ||
9d427b2c | 5824 | ureal = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 5825 | if (scm_is_false (ureal)) |
f872b822 | 5826 | { |
3c9a524f DH |
5827 | /* input must be either +i or -i */ |
5828 | ||
5829 | if (sign == 0) | |
5830 | return SCM_BOOL_F; | |
5831 | ||
3f47e526 MG |
5832 | if (scm_i_string_ref (mem, idx) == 'i' |
5833 | || scm_i_string_ref (mem, idx) == 'I') | |
f872b822 | 5834 | { |
3c9a524f DH |
5835 | idx++; |
5836 | if (idx != len) | |
5837 | return SCM_BOOL_F; | |
5838 | ||
cff5fa33 | 5839 | return scm_make_rectangular (SCM_INUM0, SCM_I_MAKINUM (sign)); |
f872b822 | 5840 | } |
3c9a524f DH |
5841 | else |
5842 | return SCM_BOOL_F; | |
0f2d19dd | 5843 | } |
3c9a524f DH |
5844 | else |
5845 | { | |
73e4de09 | 5846 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 5847 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 5848 | |
3c9a524f DH |
5849 | if (idx == len) |
5850 | return ureal; | |
5851 | ||
3f47e526 | 5852 | c = scm_i_string_ref (mem, idx); |
3c9a524f | 5853 | switch (c) |
f872b822 | 5854 | { |
3c9a524f DH |
5855 | case 'i': case 'I': |
5856 | /* either +<ureal>i or -<ureal>i */ | |
5857 | ||
5858 | idx++; | |
5859 | if (sign == 0) | |
5860 | return SCM_BOOL_F; | |
5861 | if (idx != len) | |
5862 | return SCM_BOOL_F; | |
cff5fa33 | 5863 | return scm_make_rectangular (SCM_INUM0, ureal); |
3c9a524f DH |
5864 | |
5865 | case '@': | |
5866 | /* polar input: <real>@<real>. */ | |
5867 | ||
5868 | idx++; | |
5869 | if (idx == len) | |
5870 | return SCM_BOOL_F; | |
5871 | else | |
f872b822 | 5872 | { |
3c9a524f DH |
5873 | int sign; |
5874 | SCM angle; | |
5875 | SCM result; | |
5876 | ||
3f47e526 | 5877 | c = scm_i_string_ref (mem, idx); |
3c9a524f DH |
5878 | if (c == '+') |
5879 | { | |
5880 | idx++; | |
ee0ddd21 AW |
5881 | if (idx == len) |
5882 | return SCM_BOOL_F; | |
3c9a524f DH |
5883 | sign = 1; |
5884 | } | |
5885 | else if (c == '-') | |
5886 | { | |
5887 | idx++; | |
ee0ddd21 AW |
5888 | if (idx == len) |
5889 | return SCM_BOOL_F; | |
3c9a524f DH |
5890 | sign = -1; |
5891 | } | |
5892 | else | |
5893 | sign = 1; | |
5894 | ||
9d427b2c | 5895 | angle = mem2ureal (mem, &idx, radix, forced_x); |
73e4de09 | 5896 | if (scm_is_false (angle)) |
3c9a524f DH |
5897 | return SCM_BOOL_F; |
5898 | if (idx != len) | |
5899 | return SCM_BOOL_F; | |
5900 | ||
73e4de09 | 5901 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
5902 | angle = scm_difference (angle, SCM_UNDEFINED); |
5903 | ||
5904 | result = scm_make_polar (ureal, angle); | |
5905 | return result; | |
f872b822 | 5906 | } |
3c9a524f DH |
5907 | case '+': |
5908 | case '-': | |
5909 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 5910 | |
3c9a524f DH |
5911 | idx++; |
5912 | if (idx == len) | |
5913 | return SCM_BOOL_F; | |
5914 | else | |
5915 | { | |
5916 | int sign = (c == '+') ? 1 : -1; | |
9d427b2c | 5917 | SCM imag = mem2ureal (mem, &idx, radix, forced_x); |
0f2d19dd | 5918 | |
73e4de09 | 5919 | if (scm_is_false (imag)) |
d956fa6f | 5920 | imag = SCM_I_MAKINUM (sign); |
23295dc3 | 5921 | else if (sign == -1 && scm_is_false (scm_nan_p (imag))) |
1fe5e088 | 5922 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 5923 | |
3c9a524f DH |
5924 | if (idx == len) |
5925 | return SCM_BOOL_F; | |
3f47e526 MG |
5926 | if (scm_i_string_ref (mem, idx) != 'i' |
5927 | && scm_i_string_ref (mem, idx) != 'I') | |
3c9a524f | 5928 | return SCM_BOOL_F; |
0f2d19dd | 5929 | |
3c9a524f DH |
5930 | idx++; |
5931 | if (idx != len) | |
5932 | return SCM_BOOL_F; | |
0f2d19dd | 5933 | |
1fe5e088 | 5934 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
5935 | } |
5936 | default: | |
5937 | return SCM_BOOL_F; | |
5938 | } | |
5939 | } | |
0f2d19dd | 5940 | } |
0f2d19dd JB |
5941 | |
5942 | ||
3c9a524f DH |
5943 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
5944 | ||
5945 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 5946 | |
0f2d19dd | 5947 | SCM |
3f47e526 | 5948 | scm_i_string_to_number (SCM mem, unsigned int default_radix) |
0f2d19dd | 5949 | { |
3c9a524f DH |
5950 | unsigned int idx = 0; |
5951 | unsigned int radix = NO_RADIX; | |
5952 | enum t_exactness forced_x = NO_EXACTNESS; | |
3f47e526 | 5953 | size_t len = scm_i_string_length (mem); |
3c9a524f DH |
5954 | |
5955 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
3f47e526 | 5956 | while (idx + 2 < len && scm_i_string_ref (mem, idx) == '#') |
3c9a524f | 5957 | { |
3f47e526 | 5958 | switch (scm_i_string_ref (mem, idx + 1)) |
3c9a524f DH |
5959 | { |
5960 | case 'b': case 'B': | |
5961 | if (radix != NO_RADIX) | |
5962 | return SCM_BOOL_F; | |
5963 | radix = DUAL; | |
5964 | break; | |
5965 | case 'd': case 'D': | |
5966 | if (radix != NO_RADIX) | |
5967 | return SCM_BOOL_F; | |
5968 | radix = DEC; | |
5969 | break; | |
5970 | case 'i': case 'I': | |
5971 | if (forced_x != NO_EXACTNESS) | |
5972 | return SCM_BOOL_F; | |
5973 | forced_x = INEXACT; | |
5974 | break; | |
5975 | case 'e': case 'E': | |
5976 | if (forced_x != NO_EXACTNESS) | |
5977 | return SCM_BOOL_F; | |
5978 | forced_x = EXACT; | |
5979 | break; | |
5980 | case 'o': case 'O': | |
5981 | if (radix != NO_RADIX) | |
5982 | return SCM_BOOL_F; | |
5983 | radix = OCT; | |
5984 | break; | |
5985 | case 'x': case 'X': | |
5986 | if (radix != NO_RADIX) | |
5987 | return SCM_BOOL_F; | |
5988 | radix = HEX; | |
5989 | break; | |
5990 | default: | |
f872b822 | 5991 | return SCM_BOOL_F; |
3c9a524f DH |
5992 | } |
5993 | idx += 2; | |
5994 | } | |
5995 | ||
5996 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
5997 | if (radix == NO_RADIX) | |
9d427b2c | 5998 | radix = default_radix; |
f872b822 | 5999 | |
9d427b2c | 6000 | return mem2complex (mem, idx, radix, forced_x); |
0f2d19dd JB |
6001 | } |
6002 | ||
3f47e526 MG |
6003 | SCM |
6004 | scm_c_locale_stringn_to_number (const char* mem, size_t len, | |
6005 | unsigned int default_radix) | |
6006 | { | |
6007 | SCM str = scm_from_locale_stringn (mem, len); | |
6008 | ||
6009 | return scm_i_string_to_number (str, default_radix); | |
6010 | } | |
6011 | ||
0f2d19dd | 6012 | |
a1ec6916 | 6013 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 6014 | (SCM string, SCM radix), |
1e6808ea | 6015 | "Return a number of the maximally precise representation\n" |
942e5b91 | 6016 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
6017 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
6018 | "is a default radix that may be overridden by an explicit radix\n" | |
6019 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
6020 | "supplied, then the default radix is 10. If string is not a\n" | |
6021 | "syntactically valid notation for a number, then\n" | |
6022 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 6023 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
6024 | { |
6025 | SCM answer; | |
5efd3c7d | 6026 | unsigned int base; |
a6d9e5ab | 6027 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
6028 | |
6029 | if (SCM_UNBNDP (radix)) | |
6030 | base = 10; | |
6031 | else | |
6032 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
6033 | ||
3f47e526 | 6034 | answer = scm_i_string_to_number (string, base); |
8824ac88 MV |
6035 | scm_remember_upto_here_1 (string); |
6036 | return answer; | |
0f2d19dd | 6037 | } |
1bbd0b84 | 6038 | #undef FUNC_NAME |
3c9a524f DH |
6039 | |
6040 | ||
0f2d19dd JB |
6041 | /*** END strs->nums ***/ |
6042 | ||
5986c47d | 6043 | |
8507ec80 MV |
6044 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
6045 | (SCM x), | |
6046 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
6047 | "otherwise.") | |
6048 | #define FUNC_NAME s_scm_number_p | |
6049 | { | |
6050 | return scm_from_bool (SCM_NUMBERP (x)); | |
6051 | } | |
6052 | #undef FUNC_NAME | |
6053 | ||
6054 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 6055 | (SCM x), |
942e5b91 | 6056 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 6057 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
6058 | "values form subsets of the set of complex numbers, i. e. the\n" |
6059 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
6060 | "rational or integer number.") | |
8507ec80 | 6061 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 6062 | { |
8507ec80 MV |
6063 | /* all numbers are complex. */ |
6064 | return scm_number_p (x); | |
0f2d19dd | 6065 | } |
1bbd0b84 | 6066 | #undef FUNC_NAME |
0f2d19dd | 6067 | |
f92e85f7 MV |
6068 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
6069 | (SCM x), | |
6070 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
6071 | "otherwise. Note that the set of integer values forms a subset of\n" | |
6072 | "the set of real numbers, i. e. the predicate will also be\n" | |
6073 | "fulfilled if @var{x} is an integer number.") | |
6074 | #define FUNC_NAME s_scm_real_p | |
6075 | { | |
c960e556 MW |
6076 | return scm_from_bool |
6077 | (SCM_I_INUMP (x) || SCM_REALP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)); | |
f92e85f7 MV |
6078 | } |
6079 | #undef FUNC_NAME | |
6080 | ||
6081 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 6082 | (SCM x), |
942e5b91 | 6083 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 6084 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 6085 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
6086 | "fulfilled if @var{x} is an integer number.") |
6087 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 6088 | { |
c960e556 | 6089 | if (SCM_I_INUMP (x) || SCM_BIGP (x) || SCM_FRACTIONP (x)) |
f92e85f7 MV |
6090 | return SCM_BOOL_T; |
6091 | else if (SCM_REALP (x)) | |
c960e556 MW |
6092 | /* due to their limited precision, finite floating point numbers are |
6093 | rational as well. (finite means neither infinity nor a NaN) */ | |
6094 | return scm_from_bool (DOUBLE_IS_FINITE (SCM_REAL_VALUE (x))); | |
0aacf84e | 6095 | else |
bb628794 | 6096 | return SCM_BOOL_F; |
0f2d19dd | 6097 | } |
1bbd0b84 | 6098 | #undef FUNC_NAME |
0f2d19dd | 6099 | |
a1ec6916 | 6100 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 6101 | (SCM x), |
942e5b91 MG |
6102 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
6103 | "else.") | |
1bbd0b84 | 6104 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd | 6105 | { |
c960e556 | 6106 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f872b822 | 6107 | return SCM_BOOL_T; |
c960e556 MW |
6108 | else if (SCM_REALP (x)) |
6109 | { | |
6110 | double val = SCM_REAL_VALUE (x); | |
6111 | return scm_from_bool (!isinf (val) && (val == floor (val))); | |
6112 | } | |
6113 | else | |
8e43ed5d | 6114 | return SCM_BOOL_F; |
0f2d19dd | 6115 | } |
1bbd0b84 | 6116 | #undef FUNC_NAME |
0f2d19dd JB |
6117 | |
6118 | ||
8a1f4f98 AW |
6119 | SCM scm_i_num_eq_p (SCM, SCM, SCM); |
6120 | SCM_PRIMITIVE_GENERIC (scm_i_num_eq_p, "=", 0, 2, 1, | |
6121 | (SCM x, SCM y, SCM rest), | |
6122 | "Return @code{#t} if all parameters are numerically equal.") | |
6123 | #define FUNC_NAME s_scm_i_num_eq_p | |
6124 | { | |
6125 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6126 | return SCM_BOOL_T; | |
6127 | while (!scm_is_null (rest)) | |
6128 | { | |
6129 | if (scm_is_false (scm_num_eq_p (x, y))) | |
6130 | return SCM_BOOL_F; | |
6131 | x = y; | |
6132 | y = scm_car (rest); | |
6133 | rest = scm_cdr (rest); | |
6134 | } | |
6135 | return scm_num_eq_p (x, y); | |
6136 | } | |
6137 | #undef FUNC_NAME | |
0f2d19dd | 6138 | SCM |
6e8d25a6 | 6139 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 6140 | { |
d8b95e27 | 6141 | again: |
e11e83f3 | 6142 | if (SCM_I_INUMP (x)) |
0aacf84e | 6143 | { |
e25f3727 | 6144 | scm_t_signed_bits xx = SCM_I_INUM (x); |
e11e83f3 | 6145 | if (SCM_I_INUMP (y)) |
0aacf84e | 6146 | { |
e25f3727 | 6147 | scm_t_signed_bits yy = SCM_I_INUM (y); |
73e4de09 | 6148 | return scm_from_bool (xx == yy); |
0aacf84e MD |
6149 | } |
6150 | else if (SCM_BIGP (y)) | |
6151 | return SCM_BOOL_F; | |
6152 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
6153 | { |
6154 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
6155 | to a double and compare. | |
6156 | ||
6157 | But on a 64-bit system an inum is bigger than a double and | |
6158 | casting it to a double (call that dxx) will round. dxx is at | |
6159 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
6160 | an integer and fits a long. So we cast yy to a long and | |
6161 | compare with plain xx. | |
6162 | ||
6163 | An alternative (for any size system actually) would be to check | |
6164 | yy is an integer (with floor) and is in range of an inum | |
6165 | (compare against appropriate powers of 2) then test | |
e25f3727 AW |
6166 | xx==(scm_t_signed_bits)yy. It's just a matter of which |
6167 | casts/comparisons might be fastest or easiest for the cpu. */ | |
e8c5b1f2 KR |
6168 | |
6169 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
6170 | return scm_from_bool ((double) xx == yy |
6171 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6172 | || xx == (scm_t_signed_bits) yy)); |
e8c5b1f2 | 6173 | } |
0aacf84e | 6174 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6175 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6176 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
6177 | else if (SCM_FRACTIONP (y)) |
6178 | return SCM_BOOL_F; | |
0aacf84e | 6179 | else |
8a1f4f98 | 6180 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6181 | } |
0aacf84e MD |
6182 | else if (SCM_BIGP (x)) |
6183 | { | |
e11e83f3 | 6184 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6185 | return SCM_BOOL_F; |
6186 | else if (SCM_BIGP (y)) | |
6187 | { | |
6188 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6189 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6190 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6191 | } |
6192 | else if (SCM_REALP (y)) | |
6193 | { | |
6194 | int cmp; | |
2e65b52f | 6195 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6196 | return SCM_BOOL_F; |
6197 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6198 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6199 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6200 | } |
6201 | else if (SCM_COMPLEXP (y)) | |
6202 | { | |
6203 | int cmp; | |
6204 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
6205 | return SCM_BOOL_F; | |
2e65b52f | 6206 | if (isnan (SCM_COMPLEX_REAL (y))) |
0aacf84e MD |
6207 | return SCM_BOOL_F; |
6208 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
6209 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6210 | return scm_from_bool (0 == cmp); |
0aacf84e | 6211 | } |
f92e85f7 MV |
6212 | else if (SCM_FRACTIONP (y)) |
6213 | return SCM_BOOL_F; | |
0aacf84e | 6214 | else |
8a1f4f98 | 6215 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6216 | } |
0aacf84e MD |
6217 | else if (SCM_REALP (x)) |
6218 | { | |
e8c5b1f2 | 6219 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 6220 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
6221 | { |
6222 | /* see comments with inum/real above */ | |
e25f3727 | 6223 | scm_t_signed_bits yy = SCM_I_INUM (y); |
3a1b45fd MV |
6224 | return scm_from_bool (xx == (double) yy |
6225 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
e25f3727 | 6226 | || (scm_t_signed_bits) xx == yy)); |
e8c5b1f2 | 6227 | } |
0aacf84e MD |
6228 | else if (SCM_BIGP (y)) |
6229 | { | |
6230 | int cmp; | |
2e65b52f | 6231 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6232 | return SCM_BOOL_F; |
6233 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6234 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6235 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6236 | } |
6237 | else if (SCM_REALP (y)) | |
73e4de09 | 6238 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 6239 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 6240 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6241 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6242 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6243 | { |
6244 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6245 | if (isnan (xx)) |
d8b95e27 | 6246 | return SCM_BOOL_F; |
2e65b52f | 6247 | if (isinf (xx)) |
73e4de09 | 6248 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6249 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6250 | goto again; | |
6251 | } | |
0aacf84e | 6252 | else |
8a1f4f98 | 6253 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f872b822 | 6254 | } |
0aacf84e MD |
6255 | else if (SCM_COMPLEXP (x)) |
6256 | { | |
e11e83f3 MV |
6257 | if (SCM_I_INUMP (y)) |
6258 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
6259 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6260 | else if (SCM_BIGP (y)) | |
6261 | { | |
6262 | int cmp; | |
6263 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
6264 | return SCM_BOOL_F; | |
2e65b52f | 6265 | if (isnan (SCM_COMPLEX_REAL (x))) |
0aacf84e MD |
6266 | return SCM_BOOL_F; |
6267 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
6268 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6269 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
6270 | } |
6271 | else if (SCM_REALP (y)) | |
73e4de09 | 6272 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
6273 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
6274 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 6275 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 6276 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 6277 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
6278 | { |
6279 | double xx; | |
6280 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
6281 | return SCM_BOOL_F; | |
6282 | xx = SCM_COMPLEX_REAL (x); | |
2e65b52f | 6283 | if (isnan (xx)) |
d8b95e27 | 6284 | return SCM_BOOL_F; |
2e65b52f | 6285 | if (isinf (xx)) |
73e4de09 | 6286 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
6287 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6288 | goto again; | |
6289 | } | |
f92e85f7 | 6290 | else |
8a1f4f98 | 6291 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f92e85f7 MV |
6292 | } |
6293 | else if (SCM_FRACTIONP (x)) | |
6294 | { | |
e11e83f3 | 6295 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
6296 | return SCM_BOOL_F; |
6297 | else if (SCM_BIGP (y)) | |
6298 | return SCM_BOOL_F; | |
6299 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
6300 | { |
6301 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6302 | if (isnan (yy)) |
d8b95e27 | 6303 | return SCM_BOOL_F; |
2e65b52f | 6304 | if (isinf (yy)) |
73e4de09 | 6305 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6306 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6307 | goto again; | |
6308 | } | |
f92e85f7 | 6309 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
6310 | { |
6311 | double yy; | |
6312 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
6313 | return SCM_BOOL_F; | |
6314 | yy = SCM_COMPLEX_REAL (y); | |
2e65b52f | 6315 | if (isnan (yy)) |
d8b95e27 | 6316 | return SCM_BOOL_F; |
2e65b52f | 6317 | if (isinf (yy)) |
73e4de09 | 6318 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
6319 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6320 | goto again; | |
6321 | } | |
f92e85f7 MV |
6322 | else if (SCM_FRACTIONP (y)) |
6323 | return scm_i_fraction_equalp (x, y); | |
0aacf84e | 6324 | else |
8a1f4f98 | 6325 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARGn, s_scm_i_num_eq_p); |
f4c627b3 | 6326 | } |
0aacf84e | 6327 | else |
8a1f4f98 | 6328 | SCM_WTA_DISPATCH_2 (g_scm_i_num_eq_p, x, y, SCM_ARG1, s_scm_i_num_eq_p); |
0f2d19dd JB |
6329 | } |
6330 | ||
6331 | ||
a5f0b599 KR |
6332 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
6333 | done are good for inums, but for bignums an answer can almost always be | |
6334 | had by just examining a few high bits of the operands, as done by GMP in | |
6335 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
6336 | of the float exponent to take into account. */ | |
6337 | ||
8c93b597 | 6338 | SCM_INTERNAL SCM scm_i_num_less_p (SCM, SCM, SCM); |
8a1f4f98 AW |
6339 | SCM_PRIMITIVE_GENERIC (scm_i_num_less_p, "<", 0, 2, 1, |
6340 | (SCM x, SCM y, SCM rest), | |
6341 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6342 | "increasing.") | |
6343 | #define FUNC_NAME s_scm_i_num_less_p | |
6344 | { | |
6345 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6346 | return SCM_BOOL_T; | |
6347 | while (!scm_is_null (rest)) | |
6348 | { | |
6349 | if (scm_is_false (scm_less_p (x, y))) | |
6350 | return SCM_BOOL_F; | |
6351 | x = y; | |
6352 | y = scm_car (rest); | |
6353 | rest = scm_cdr (rest); | |
6354 | } | |
6355 | return scm_less_p (x, y); | |
6356 | } | |
6357 | #undef FUNC_NAME | |
0f2d19dd | 6358 | SCM |
6e8d25a6 | 6359 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 6360 | { |
a5f0b599 | 6361 | again: |
e11e83f3 | 6362 | if (SCM_I_INUMP (x)) |
0aacf84e | 6363 | { |
e25f3727 | 6364 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6365 | if (SCM_I_INUMP (y)) |
0aacf84e | 6366 | { |
e25f3727 | 6367 | scm_t_inum yy = SCM_I_INUM (y); |
73e4de09 | 6368 | return scm_from_bool (xx < yy); |
0aacf84e MD |
6369 | } |
6370 | else if (SCM_BIGP (y)) | |
6371 | { | |
6372 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6373 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6374 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6375 | } |
6376 | else if (SCM_REALP (y)) | |
73e4de09 | 6377 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 6378 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6379 | { |
6380 | /* "x < a/b" becomes "x*b < a" */ | |
6381 | int_frac: | |
6382 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
6383 | y = SCM_FRACTION_NUMERATOR (y); | |
6384 | goto again; | |
6385 | } | |
0aacf84e | 6386 | else |
8a1f4f98 | 6387 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6388 | } |
0aacf84e MD |
6389 | else if (SCM_BIGP (x)) |
6390 | { | |
e11e83f3 | 6391 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6392 | { |
6393 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6394 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6395 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6396 | } |
6397 | else if (SCM_BIGP (y)) | |
6398 | { | |
6399 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6400 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 6401 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
6402 | } |
6403 | else if (SCM_REALP (y)) | |
6404 | { | |
6405 | int cmp; | |
2e65b52f | 6406 | if (isnan (SCM_REAL_VALUE (y))) |
0aacf84e MD |
6407 | return SCM_BOOL_F; |
6408 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
6409 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6410 | return scm_from_bool (cmp < 0); |
0aacf84e | 6411 | } |
f92e85f7 | 6412 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 6413 | goto int_frac; |
0aacf84e | 6414 | else |
8a1f4f98 | 6415 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f4c627b3 | 6416 | } |
0aacf84e MD |
6417 | else if (SCM_REALP (x)) |
6418 | { | |
e11e83f3 MV |
6419 | if (SCM_I_INUMP (y)) |
6420 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
6421 | else if (SCM_BIGP (y)) |
6422 | { | |
6423 | int cmp; | |
2e65b52f | 6424 | if (isnan (SCM_REAL_VALUE (x))) |
0aacf84e MD |
6425 | return SCM_BOOL_F; |
6426 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
6427 | scm_remember_upto_here_1 (y); | |
73e4de09 | 6428 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
6429 | } |
6430 | else if (SCM_REALP (y)) | |
73e4de09 | 6431 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 6432 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6433 | { |
6434 | double xx = SCM_REAL_VALUE (x); | |
2e65b52f | 6435 | if (isnan (xx)) |
a5f0b599 | 6436 | return SCM_BOOL_F; |
2e65b52f | 6437 | if (isinf (xx)) |
73e4de09 | 6438 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
6439 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
6440 | goto again; | |
6441 | } | |
f92e85f7 | 6442 | else |
8a1f4f98 | 6443 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f92e85f7 MV |
6444 | } |
6445 | else if (SCM_FRACTIONP (x)) | |
6446 | { | |
e11e83f3 | 6447 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
6448 | { |
6449 | /* "a/b < y" becomes "a < y*b" */ | |
6450 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
6451 | x = SCM_FRACTION_NUMERATOR (x); | |
6452 | goto again; | |
6453 | } | |
f92e85f7 | 6454 | else if (SCM_REALP (y)) |
a5f0b599 KR |
6455 | { |
6456 | double yy = SCM_REAL_VALUE (y); | |
2e65b52f | 6457 | if (isnan (yy)) |
a5f0b599 | 6458 | return SCM_BOOL_F; |
2e65b52f | 6459 | if (isinf (yy)) |
73e4de09 | 6460 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
6461 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
6462 | goto again; | |
6463 | } | |
f92e85f7 | 6464 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
6465 | { |
6466 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
6467 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
6468 | SCM_FRACTION_DENOMINATOR (y)); | |
6469 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
6470 | SCM_FRACTION_DENOMINATOR (x)); | |
6471 | x = new_x; | |
6472 | y = new_y; | |
6473 | goto again; | |
6474 | } | |
0aacf84e | 6475 | else |
8a1f4f98 | 6476 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARGn, s_scm_i_num_less_p); |
f872b822 | 6477 | } |
0aacf84e | 6478 | else |
8a1f4f98 | 6479 | SCM_WTA_DISPATCH_2 (g_scm_i_num_less_p, x, y, SCM_ARG1, s_scm_i_num_less_p); |
0f2d19dd JB |
6480 | } |
6481 | ||
6482 | ||
8a1f4f98 AW |
6483 | SCM scm_i_num_gr_p (SCM, SCM, SCM); |
6484 | SCM_PRIMITIVE_GENERIC (scm_i_num_gr_p, ">", 0, 2, 1, | |
6485 | (SCM x, SCM y, SCM rest), | |
6486 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6487 | "decreasing.") | |
6488 | #define FUNC_NAME s_scm_i_num_gr_p | |
6489 | { | |
6490 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6491 | return SCM_BOOL_T; | |
6492 | while (!scm_is_null (rest)) | |
6493 | { | |
6494 | if (scm_is_false (scm_gr_p (x, y))) | |
6495 | return SCM_BOOL_F; | |
6496 | x = y; | |
6497 | y = scm_car (rest); | |
6498 | rest = scm_cdr (rest); | |
6499 | } | |
6500 | return scm_gr_p (x, y); | |
6501 | } | |
6502 | #undef FUNC_NAME | |
6503 | #define FUNC_NAME s_scm_i_num_gr_p | |
c76b1eaf MD |
6504 | SCM |
6505 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 6506 | { |
c76b1eaf | 6507 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6508 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6509 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6510 | SCM_WTA_DISPATCH_2 (g_scm_i_num_gr_p, x, y, SCM_ARG2, FUNC_NAME); |
c76b1eaf MD |
6511 | else |
6512 | return scm_less_p (y, x); | |
0f2d19dd | 6513 | } |
1bbd0b84 | 6514 | #undef FUNC_NAME |
0f2d19dd JB |
6515 | |
6516 | ||
8a1f4f98 AW |
6517 | SCM scm_i_num_leq_p (SCM, SCM, SCM); |
6518 | SCM_PRIMITIVE_GENERIC (scm_i_num_leq_p, "<=", 0, 2, 1, | |
6519 | (SCM x, SCM y, SCM rest), | |
6520 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6521 | "non-decreasing.") | |
6522 | #define FUNC_NAME s_scm_i_num_leq_p | |
6523 | { | |
6524 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6525 | return SCM_BOOL_T; | |
6526 | while (!scm_is_null (rest)) | |
6527 | { | |
6528 | if (scm_is_false (scm_leq_p (x, y))) | |
6529 | return SCM_BOOL_F; | |
6530 | x = y; | |
6531 | y = scm_car (rest); | |
6532 | rest = scm_cdr (rest); | |
6533 | } | |
6534 | return scm_leq_p (x, y); | |
6535 | } | |
6536 | #undef FUNC_NAME | |
6537 | #define FUNC_NAME s_scm_i_num_leq_p | |
c76b1eaf MD |
6538 | SCM |
6539 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 6540 | { |
c76b1eaf | 6541 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6542 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6543 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6544 | SCM_WTA_DISPATCH_2 (g_scm_i_num_leq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6545 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6546 | return SCM_BOOL_F; |
c76b1eaf | 6547 | else |
73e4de09 | 6548 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 6549 | } |
1bbd0b84 | 6550 | #undef FUNC_NAME |
0f2d19dd JB |
6551 | |
6552 | ||
8a1f4f98 AW |
6553 | SCM scm_i_num_geq_p (SCM, SCM, SCM); |
6554 | SCM_PRIMITIVE_GENERIC (scm_i_num_geq_p, ">=", 0, 2, 1, | |
6555 | (SCM x, SCM y, SCM rest), | |
6556 | "Return @code{#t} if the list of parameters is monotonically\n" | |
6557 | "non-increasing.") | |
6558 | #define FUNC_NAME s_scm_i_num_geq_p | |
6559 | { | |
6560 | if (SCM_UNBNDP (x) || SCM_UNBNDP (y)) | |
6561 | return SCM_BOOL_T; | |
6562 | while (!scm_is_null (rest)) | |
6563 | { | |
6564 | if (scm_is_false (scm_geq_p (x, y))) | |
6565 | return SCM_BOOL_F; | |
6566 | x = y; | |
6567 | y = scm_car (rest); | |
6568 | rest = scm_cdr (rest); | |
6569 | } | |
6570 | return scm_geq_p (x, y); | |
6571 | } | |
6572 | #undef FUNC_NAME | |
6573 | #define FUNC_NAME s_scm_i_num_geq_p | |
c76b1eaf MD |
6574 | SCM |
6575 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 6576 | { |
c76b1eaf | 6577 | if (!SCM_NUMBERP (x)) |
8a1f4f98 | 6578 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG1, FUNC_NAME); |
c76b1eaf | 6579 | else if (!SCM_NUMBERP (y)) |
8a1f4f98 | 6580 | SCM_WTA_DISPATCH_2 (g_scm_i_num_geq_p, x, y, SCM_ARG2, FUNC_NAME); |
73e4de09 | 6581 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 6582 | return SCM_BOOL_F; |
c76b1eaf | 6583 | else |
73e4de09 | 6584 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 6585 | } |
1bbd0b84 | 6586 | #undef FUNC_NAME |
0f2d19dd JB |
6587 | |
6588 | ||
2519490c MW |
6589 | SCM_PRIMITIVE_GENERIC (scm_zero_p, "zero?", 1, 0, 0, |
6590 | (SCM z), | |
6591 | "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" | |
6592 | "zero.") | |
6593 | #define FUNC_NAME s_scm_zero_p | |
0f2d19dd | 6594 | { |
e11e83f3 | 6595 | if (SCM_I_INUMP (z)) |
bc36d050 | 6596 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 6597 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 6598 | return SCM_BOOL_F; |
0aacf84e | 6599 | else if (SCM_REALP (z)) |
73e4de09 | 6600 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 6601 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 6602 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 6603 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
6604 | else if (SCM_FRACTIONP (z)) |
6605 | return SCM_BOOL_F; | |
0aacf84e | 6606 | else |
2519490c | 6607 | SCM_WTA_DISPATCH_1 (g_scm_zero_p, z, SCM_ARG1, s_scm_zero_p); |
0f2d19dd | 6608 | } |
2519490c | 6609 | #undef FUNC_NAME |
0f2d19dd JB |
6610 | |
6611 | ||
2519490c MW |
6612 | SCM_PRIMITIVE_GENERIC (scm_positive_p, "positive?", 1, 0, 0, |
6613 | (SCM x), | |
6614 | "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" | |
6615 | "zero.") | |
6616 | #define FUNC_NAME s_scm_positive_p | |
0f2d19dd | 6617 | { |
e11e83f3 MV |
6618 | if (SCM_I_INUMP (x)) |
6619 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
6620 | else if (SCM_BIGP (x)) |
6621 | { | |
6622 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6623 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6624 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
6625 | } |
6626 | else if (SCM_REALP (x)) | |
73e4de09 | 6627 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
6628 | else if (SCM_FRACTIONP (x)) |
6629 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6630 | else |
2519490c | 6631 | SCM_WTA_DISPATCH_1 (g_scm_positive_p, x, SCM_ARG1, s_scm_positive_p); |
0f2d19dd | 6632 | } |
2519490c | 6633 | #undef FUNC_NAME |
0f2d19dd JB |
6634 | |
6635 | ||
2519490c MW |
6636 | SCM_PRIMITIVE_GENERIC (scm_negative_p, "negative?", 1, 0, 0, |
6637 | (SCM x), | |
6638 | "Return @code{#t} if @var{x} is an exact or inexact number less than\n" | |
6639 | "zero.") | |
6640 | #define FUNC_NAME s_scm_negative_p | |
0f2d19dd | 6641 | { |
e11e83f3 MV |
6642 | if (SCM_I_INUMP (x)) |
6643 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
6644 | else if (SCM_BIGP (x)) |
6645 | { | |
6646 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6647 | scm_remember_upto_here_1 (x); | |
73e4de09 | 6648 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
6649 | } |
6650 | else if (SCM_REALP (x)) | |
73e4de09 | 6651 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
6652 | else if (SCM_FRACTIONP (x)) |
6653 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 6654 | else |
2519490c | 6655 | SCM_WTA_DISPATCH_1 (g_scm_negative_p, x, SCM_ARG1, s_scm_negative_p); |
0f2d19dd | 6656 | } |
2519490c | 6657 | #undef FUNC_NAME |
0f2d19dd JB |
6658 | |
6659 | ||
2a06f791 KR |
6660 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
6661 | required by r5rs. On that basis, for exact/inexact combinations the | |
6662 | exact is converted to inexact to compare and possibly return. This is | |
6663 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
6664 | its test, such trouble is not required for min and max. */ | |
6665 | ||
78d3deb1 AW |
6666 | SCM_PRIMITIVE_GENERIC (scm_i_max, "max", 0, 2, 1, |
6667 | (SCM x, SCM y, SCM rest), | |
6668 | "Return the maximum of all parameter values.") | |
6669 | #define FUNC_NAME s_scm_i_max | |
6670 | { | |
6671 | while (!scm_is_null (rest)) | |
6672 | { x = scm_max (x, y); | |
6673 | y = scm_car (rest); | |
6674 | rest = scm_cdr (rest); | |
6675 | } | |
6676 | return scm_max (x, y); | |
6677 | } | |
6678 | #undef FUNC_NAME | |
6679 | ||
6680 | #define s_max s_scm_i_max | |
6681 | #define g_max g_scm_i_max | |
6682 | ||
0f2d19dd | 6683 | SCM |
6e8d25a6 | 6684 | scm_max (SCM x, SCM y) |
0f2d19dd | 6685 | { |
0aacf84e MD |
6686 | if (SCM_UNBNDP (y)) |
6687 | { | |
6688 | if (SCM_UNBNDP (x)) | |
6689 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 6690 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
6691 | return x; |
6692 | else | |
6693 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 6694 | } |
f4c627b3 | 6695 | |
e11e83f3 | 6696 | if (SCM_I_INUMP (x)) |
0aacf84e | 6697 | { |
e25f3727 | 6698 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6699 | if (SCM_I_INUMP (y)) |
0aacf84e | 6700 | { |
e25f3727 | 6701 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6702 | return (xx < yy) ? y : x; |
6703 | } | |
6704 | else if (SCM_BIGP (y)) | |
6705 | { | |
6706 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6707 | scm_remember_upto_here_1 (y); | |
6708 | return (sgn < 0) ? x : y; | |
6709 | } | |
6710 | else if (SCM_REALP (y)) | |
6711 | { | |
2e274311 MW |
6712 | double xxd = xx; |
6713 | double yyd = SCM_REAL_VALUE (y); | |
6714 | ||
6715 | if (xxd > yyd) | |
6716 | return scm_from_double (xxd); | |
6717 | /* If y is a NaN, then "==" is false and we return the NaN */ | |
6718 | else if (SCM_LIKELY (!(xxd == yyd))) | |
6719 | return y; | |
6720 | /* Handle signed zeroes properly */ | |
6721 | else if (xx == 0) | |
6722 | return flo0; | |
6723 | else | |
6724 | return y; | |
0aacf84e | 6725 | } |
f92e85f7 MV |
6726 | else if (SCM_FRACTIONP (y)) |
6727 | { | |
e4bc5d6c | 6728 | use_less: |
73e4de09 | 6729 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 6730 | } |
0aacf84e MD |
6731 | else |
6732 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 6733 | } |
0aacf84e MD |
6734 | else if (SCM_BIGP (x)) |
6735 | { | |
e11e83f3 | 6736 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6737 | { |
6738 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6739 | scm_remember_upto_here_1 (x); | |
6740 | return (sgn < 0) ? y : x; | |
6741 | } | |
6742 | else if (SCM_BIGP (y)) | |
6743 | { | |
6744 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6745 | scm_remember_upto_here_2 (x, y); | |
6746 | return (cmp > 0) ? x : y; | |
6747 | } | |
6748 | else if (SCM_REALP (y)) | |
6749 | { | |
2a06f791 KR |
6750 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
6751 | double xx, yy; | |
6752 | big_real: | |
6753 | xx = scm_i_big2dbl (x); | |
6754 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 6755 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 6756 | } |
f92e85f7 MV |
6757 | else if (SCM_FRACTIONP (y)) |
6758 | { | |
e4bc5d6c | 6759 | goto use_less; |
f92e85f7 | 6760 | } |
0aacf84e MD |
6761 | else |
6762 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 6763 | } |
0aacf84e MD |
6764 | else if (SCM_REALP (x)) |
6765 | { | |
e11e83f3 | 6766 | if (SCM_I_INUMP (y)) |
0aacf84e | 6767 | { |
2e274311 MW |
6768 | scm_t_inum yy = SCM_I_INUM (y); |
6769 | double xxd = SCM_REAL_VALUE (x); | |
6770 | double yyd = yy; | |
6771 | ||
6772 | if (yyd > xxd) | |
6773 | return scm_from_double (yyd); | |
6774 | /* If x is a NaN, then "==" is false and we return the NaN */ | |
6775 | else if (SCM_LIKELY (!(xxd == yyd))) | |
6776 | return x; | |
6777 | /* Handle signed zeroes properly */ | |
6778 | else if (yy == 0) | |
6779 | return flo0; | |
6780 | else | |
6781 | return x; | |
0aacf84e MD |
6782 | } |
6783 | else if (SCM_BIGP (y)) | |
6784 | { | |
b6f8f763 | 6785 | SCM_SWAP (x, y); |
2a06f791 | 6786 | goto big_real; |
0aacf84e MD |
6787 | } |
6788 | else if (SCM_REALP (y)) | |
6789 | { | |
0aacf84e | 6790 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
6791 | double yy = SCM_REAL_VALUE (y); |
6792 | ||
6793 | /* For purposes of max: +inf.0 > nan > everything else, per R6RS */ | |
6794 | if (xx > yy) | |
6795 | return x; | |
6796 | else if (SCM_LIKELY (xx < yy)) | |
6797 | return y; | |
6798 | /* If neither (xx > yy) nor (xx < yy), then | |
6799 | either they're equal or one is a NaN */ | |
6800 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 6801 | return DOUBLE_IS_POSITIVE_INFINITY (yy) ? y : x; |
2e274311 | 6802 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 6803 | return DOUBLE_IS_POSITIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
6804 | /* xx == yy, but handle signed zeroes properly */ |
6805 | else if (double_is_non_negative_zero (yy)) | |
6806 | return y; | |
6807 | else | |
6808 | return x; | |
0aacf84e | 6809 | } |
f92e85f7 MV |
6810 | else if (SCM_FRACTIONP (y)) |
6811 | { | |
6812 | double yy = scm_i_fraction2double (y); | |
6813 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 6814 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
6815 | } |
6816 | else | |
6817 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
6818 | } | |
6819 | else if (SCM_FRACTIONP (x)) | |
6820 | { | |
e11e83f3 | 6821 | if (SCM_I_INUMP (y)) |
f92e85f7 | 6822 | { |
e4bc5d6c | 6823 | goto use_less; |
f92e85f7 MV |
6824 | } |
6825 | else if (SCM_BIGP (y)) | |
6826 | { | |
e4bc5d6c | 6827 | goto use_less; |
f92e85f7 MV |
6828 | } |
6829 | else if (SCM_REALP (y)) | |
6830 | { | |
6831 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
6832 | /* if y==NaN then ">" is false, so we return the NaN y */ |
6833 | return (xx > SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
6834 | } |
6835 | else if (SCM_FRACTIONP (y)) | |
6836 | { | |
e4bc5d6c | 6837 | goto use_less; |
f92e85f7 | 6838 | } |
0aacf84e MD |
6839 | else |
6840 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 6841 | } |
0aacf84e | 6842 | else |
f4c627b3 | 6843 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
6844 | } |
6845 | ||
6846 | ||
78d3deb1 AW |
6847 | SCM_PRIMITIVE_GENERIC (scm_i_min, "min", 0, 2, 1, |
6848 | (SCM x, SCM y, SCM rest), | |
6849 | "Return the minimum of all parameter values.") | |
6850 | #define FUNC_NAME s_scm_i_min | |
6851 | { | |
6852 | while (!scm_is_null (rest)) | |
6853 | { x = scm_min (x, y); | |
6854 | y = scm_car (rest); | |
6855 | rest = scm_cdr (rest); | |
6856 | } | |
6857 | return scm_min (x, y); | |
6858 | } | |
6859 | #undef FUNC_NAME | |
6860 | ||
6861 | #define s_min s_scm_i_min | |
6862 | #define g_min g_scm_i_min | |
6863 | ||
0f2d19dd | 6864 | SCM |
6e8d25a6 | 6865 | scm_min (SCM x, SCM y) |
0f2d19dd | 6866 | { |
0aacf84e MD |
6867 | if (SCM_UNBNDP (y)) |
6868 | { | |
6869 | if (SCM_UNBNDP (x)) | |
6870 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 6871 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
6872 | return x; |
6873 | else | |
6874 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 6875 | } |
f4c627b3 | 6876 | |
e11e83f3 | 6877 | if (SCM_I_INUMP (x)) |
0aacf84e | 6878 | { |
e25f3727 | 6879 | scm_t_inum xx = SCM_I_INUM (x); |
e11e83f3 | 6880 | if (SCM_I_INUMP (y)) |
0aacf84e | 6881 | { |
e25f3727 | 6882 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
6883 | return (xx < yy) ? x : y; |
6884 | } | |
6885 | else if (SCM_BIGP (y)) | |
6886 | { | |
6887 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
6888 | scm_remember_upto_here_1 (y); | |
6889 | return (sgn < 0) ? y : x; | |
6890 | } | |
6891 | else if (SCM_REALP (y)) | |
6892 | { | |
6893 | double z = xx; | |
6894 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 6895 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 6896 | } |
f92e85f7 MV |
6897 | else if (SCM_FRACTIONP (y)) |
6898 | { | |
e4bc5d6c | 6899 | use_less: |
73e4de09 | 6900 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 6901 | } |
0aacf84e MD |
6902 | else |
6903 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 6904 | } |
0aacf84e MD |
6905 | else if (SCM_BIGP (x)) |
6906 | { | |
e11e83f3 | 6907 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
6908 | { |
6909 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
6910 | scm_remember_upto_here_1 (x); | |
6911 | return (sgn < 0) ? x : y; | |
6912 | } | |
6913 | else if (SCM_BIGP (y)) | |
6914 | { | |
6915 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
6916 | scm_remember_upto_here_2 (x, y); | |
6917 | return (cmp > 0) ? y : x; | |
6918 | } | |
6919 | else if (SCM_REALP (y)) | |
6920 | { | |
2a06f791 KR |
6921 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
6922 | double xx, yy; | |
6923 | big_real: | |
6924 | xx = scm_i_big2dbl (x); | |
6925 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 6926 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 6927 | } |
f92e85f7 MV |
6928 | else if (SCM_FRACTIONP (y)) |
6929 | { | |
e4bc5d6c | 6930 | goto use_less; |
f92e85f7 | 6931 | } |
0aacf84e MD |
6932 | else |
6933 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 6934 | } |
0aacf84e MD |
6935 | else if (SCM_REALP (x)) |
6936 | { | |
e11e83f3 | 6937 | if (SCM_I_INUMP (y)) |
0aacf84e | 6938 | { |
e11e83f3 | 6939 | double z = SCM_I_INUM (y); |
0aacf84e | 6940 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 6941 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
6942 | } |
6943 | else if (SCM_BIGP (y)) | |
6944 | { | |
b6f8f763 | 6945 | SCM_SWAP (x, y); |
2a06f791 | 6946 | goto big_real; |
0aacf84e MD |
6947 | } |
6948 | else if (SCM_REALP (y)) | |
6949 | { | |
0aacf84e | 6950 | double xx = SCM_REAL_VALUE (x); |
2e274311 MW |
6951 | double yy = SCM_REAL_VALUE (y); |
6952 | ||
6953 | /* For purposes of min: -inf.0 < nan < everything else, per R6RS */ | |
6954 | if (xx < yy) | |
6955 | return x; | |
6956 | else if (SCM_LIKELY (xx > yy)) | |
6957 | return y; | |
6958 | /* If neither (xx < yy) nor (xx > yy), then | |
6959 | either they're equal or one is a NaN */ | |
6960 | else if (SCM_UNLIKELY (isnan (xx))) | |
041fccf6 | 6961 | return DOUBLE_IS_NEGATIVE_INFINITY (yy) ? y : x; |
2e274311 | 6962 | else if (SCM_UNLIKELY (isnan (yy))) |
041fccf6 | 6963 | return DOUBLE_IS_NEGATIVE_INFINITY (xx) ? x : y; |
2e274311 MW |
6964 | /* xx == yy, but handle signed zeroes properly */ |
6965 | else if (double_is_non_negative_zero (xx)) | |
6966 | return y; | |
6967 | else | |
6968 | return x; | |
0aacf84e | 6969 | } |
f92e85f7 MV |
6970 | else if (SCM_FRACTIONP (y)) |
6971 | { | |
6972 | double yy = scm_i_fraction2double (y); | |
6973 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 6974 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 6975 | } |
0aacf84e MD |
6976 | else |
6977 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 6978 | } |
f92e85f7 MV |
6979 | else if (SCM_FRACTIONP (x)) |
6980 | { | |
e11e83f3 | 6981 | if (SCM_I_INUMP (y)) |
f92e85f7 | 6982 | { |
e4bc5d6c | 6983 | goto use_less; |
f92e85f7 MV |
6984 | } |
6985 | else if (SCM_BIGP (y)) | |
6986 | { | |
e4bc5d6c | 6987 | goto use_less; |
f92e85f7 MV |
6988 | } |
6989 | else if (SCM_REALP (y)) | |
6990 | { | |
6991 | double xx = scm_i_fraction2double (x); | |
2e274311 MW |
6992 | /* if y==NaN then "<" is false, so we return the NaN y */ |
6993 | return (xx < SCM_REAL_VALUE (y)) ? scm_from_double (xx) : y; | |
f92e85f7 MV |
6994 | } |
6995 | else if (SCM_FRACTIONP (y)) | |
6996 | { | |
e4bc5d6c | 6997 | goto use_less; |
f92e85f7 MV |
6998 | } |
6999 | else | |
78d3deb1 | 7000 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); |
f92e85f7 | 7001 | } |
0aacf84e | 7002 | else |
f4c627b3 | 7003 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
7004 | } |
7005 | ||
7006 | ||
8ccd24f7 AW |
7007 | SCM_PRIMITIVE_GENERIC (scm_i_sum, "+", 0, 2, 1, |
7008 | (SCM x, SCM y, SCM rest), | |
7009 | "Return the sum of all parameter values. Return 0 if called without\n" | |
7010 | "any parameters." ) | |
7011 | #define FUNC_NAME s_scm_i_sum | |
7012 | { | |
7013 | while (!scm_is_null (rest)) | |
7014 | { x = scm_sum (x, y); | |
7015 | y = scm_car (rest); | |
7016 | rest = scm_cdr (rest); | |
7017 | } | |
7018 | return scm_sum (x, y); | |
7019 | } | |
7020 | #undef FUNC_NAME | |
7021 | ||
7022 | #define s_sum s_scm_i_sum | |
7023 | #define g_sum g_scm_i_sum | |
7024 | ||
0f2d19dd | 7025 | SCM |
6e8d25a6 | 7026 | scm_sum (SCM x, SCM y) |
0f2d19dd | 7027 | { |
9cc37597 | 7028 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7029 | { |
7030 | if (SCM_NUMBERP (x)) return x; | |
7031 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 7032 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 7033 | } |
c209c88e | 7034 | |
9cc37597 | 7035 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 7036 | { |
9cc37597 | 7037 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 7038 | { |
e25f3727 AW |
7039 | scm_t_inum xx = SCM_I_INUM (x); |
7040 | scm_t_inum yy = SCM_I_INUM (y); | |
7041 | scm_t_inum z = xx + yy; | |
7042 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_inum2big (z); | |
ca46fb90 RB |
7043 | } |
7044 | else if (SCM_BIGP (y)) | |
7045 | { | |
7046 | SCM_SWAP (x, y); | |
7047 | goto add_big_inum; | |
7048 | } | |
7049 | else if (SCM_REALP (y)) | |
7050 | { | |
e25f3727 | 7051 | scm_t_inum xx = SCM_I_INUM (x); |
55f26379 | 7052 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
7053 | } |
7054 | else if (SCM_COMPLEXP (y)) | |
7055 | { | |
e25f3727 | 7056 | scm_t_inum xx = SCM_I_INUM (x); |
8507ec80 | 7057 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
7058 | SCM_COMPLEX_IMAG (y)); |
7059 | } | |
f92e85f7 | 7060 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7061 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7062 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7063 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
7064 | else |
7065 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
7066 | } else if (SCM_BIGP (x)) |
7067 | { | |
e11e83f3 | 7068 | if (SCM_I_INUMP (y)) |
0aacf84e | 7069 | { |
e25f3727 | 7070 | scm_t_inum inum; |
0aacf84e MD |
7071 | int bigsgn; |
7072 | add_big_inum: | |
e11e83f3 | 7073 | inum = SCM_I_INUM (y); |
0aacf84e MD |
7074 | if (inum == 0) |
7075 | return x; | |
7076 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7077 | if (inum < 0) | |
7078 | { | |
7079 | SCM result = scm_i_mkbig (); | |
7080 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
7081 | scm_remember_upto_here_1 (x); | |
7082 | /* we know the result will have to be a bignum */ | |
7083 | if (bigsgn == -1) | |
7084 | return result; | |
7085 | return scm_i_normbig (result); | |
7086 | } | |
7087 | else | |
7088 | { | |
7089 | SCM result = scm_i_mkbig (); | |
7090 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
7091 | scm_remember_upto_here_1 (x); | |
7092 | /* we know the result will have to be a bignum */ | |
7093 | if (bigsgn == 1) | |
7094 | return result; | |
7095 | return scm_i_normbig (result); | |
7096 | } | |
7097 | } | |
7098 | else if (SCM_BIGP (y)) | |
7099 | { | |
7100 | SCM result = scm_i_mkbig (); | |
7101 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7102 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7103 | mpz_add (SCM_I_BIG_MPZ (result), | |
7104 | SCM_I_BIG_MPZ (x), | |
7105 | SCM_I_BIG_MPZ (y)); | |
7106 | scm_remember_upto_here_2 (x, y); | |
7107 | /* we know the result will have to be a bignum */ | |
7108 | if (sgn_x == sgn_y) | |
7109 | return result; | |
7110 | return scm_i_normbig (result); | |
7111 | } | |
7112 | else if (SCM_REALP (y)) | |
7113 | { | |
7114 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
7115 | scm_remember_upto_here_1 (x); | |
55f26379 | 7116 | return scm_from_double (result); |
0aacf84e MD |
7117 | } |
7118 | else if (SCM_COMPLEXP (y)) | |
7119 | { | |
7120 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7121 | + SCM_COMPLEX_REAL (y)); | |
7122 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7123 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7124 | } |
f92e85f7 | 7125 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7126 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
7127 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
7128 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7129 | else |
7130 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 7131 | } |
0aacf84e MD |
7132 | else if (SCM_REALP (x)) |
7133 | { | |
e11e83f3 | 7134 | if (SCM_I_INUMP (y)) |
55f26379 | 7135 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
7136 | else if (SCM_BIGP (y)) |
7137 | { | |
7138 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
7139 | scm_remember_upto_here_1 (y); | |
55f26379 | 7140 | return scm_from_double (result); |
0aacf84e MD |
7141 | } |
7142 | else if (SCM_REALP (y)) | |
55f26379 | 7143 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 7144 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7145 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7146 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7147 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7148 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
7149 | else |
7150 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 7151 | } |
0aacf84e MD |
7152 | else if (SCM_COMPLEXP (x)) |
7153 | { | |
e11e83f3 | 7154 | if (SCM_I_INUMP (y)) |
8507ec80 | 7155 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
7156 | SCM_COMPLEX_IMAG (x)); |
7157 | else if (SCM_BIGP (y)) | |
7158 | { | |
7159 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
7160 | + SCM_COMPLEX_REAL (x)); | |
7161 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7162 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7163 | } |
7164 | else if (SCM_REALP (y)) | |
8507ec80 | 7165 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
7166 | SCM_COMPLEX_IMAG (x)); |
7167 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7168 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 7169 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7170 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7171 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
7172 | SCM_COMPLEX_IMAG (x)); |
7173 | else | |
7174 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
7175 | } | |
7176 | else if (SCM_FRACTIONP (x)) | |
7177 | { | |
e11e83f3 | 7178 | if (SCM_I_INUMP (y)) |
cba42c93 | 7179 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7180 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7181 | SCM_FRACTION_DENOMINATOR (x)); | |
7182 | else if (SCM_BIGP (y)) | |
cba42c93 | 7183 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7184 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
7185 | SCM_FRACTION_DENOMINATOR (x)); | |
7186 | else if (SCM_REALP (y)) | |
55f26379 | 7187 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 7188 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7189 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
7190 | SCM_COMPLEX_IMAG (y)); |
7191 | else if (SCM_FRACTIONP (y)) | |
7192 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 7193 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7194 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7195 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7196 | else |
7197 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 7198 | } |
0aacf84e | 7199 | else |
98cb6e75 | 7200 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
7201 | } |
7202 | ||
7203 | ||
40882e3d KR |
7204 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
7205 | (SCM x), | |
7206 | "Return @math{@var{x}+1}.") | |
7207 | #define FUNC_NAME s_scm_oneplus | |
7208 | { | |
cff5fa33 | 7209 | return scm_sum (x, SCM_INUM1); |
40882e3d KR |
7210 | } |
7211 | #undef FUNC_NAME | |
7212 | ||
7213 | ||
78d3deb1 AW |
7214 | SCM_PRIMITIVE_GENERIC (scm_i_difference, "-", 0, 2, 1, |
7215 | (SCM x, SCM y, SCM rest), | |
7216 | "If called with one argument @var{z1}, -@var{z1} returned. Otherwise\n" | |
7217 | "the sum of all but the first argument are subtracted from the first\n" | |
7218 | "argument.") | |
7219 | #define FUNC_NAME s_scm_i_difference | |
7220 | { | |
7221 | while (!scm_is_null (rest)) | |
7222 | { x = scm_difference (x, y); | |
7223 | y = scm_car (rest); | |
7224 | rest = scm_cdr (rest); | |
7225 | } | |
7226 | return scm_difference (x, y); | |
7227 | } | |
7228 | #undef FUNC_NAME | |
7229 | ||
7230 | #define s_difference s_scm_i_difference | |
7231 | #define g_difference g_scm_i_difference | |
7232 | ||
0f2d19dd | 7233 | SCM |
6e8d25a6 | 7234 | scm_difference (SCM x, SCM y) |
78d3deb1 | 7235 | #define FUNC_NAME s_difference |
0f2d19dd | 7236 | { |
9cc37597 | 7237 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
7238 | { |
7239 | if (SCM_UNBNDP (x)) | |
7240 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
7241 | else | |
e11e83f3 | 7242 | if (SCM_I_INUMP (x)) |
ca46fb90 | 7243 | { |
e25f3727 | 7244 | scm_t_inum xx = -SCM_I_INUM (x); |
ca46fb90 | 7245 | if (SCM_FIXABLE (xx)) |
d956fa6f | 7246 | return SCM_I_MAKINUM (xx); |
ca46fb90 | 7247 | else |
e25f3727 | 7248 | return scm_i_inum2big (xx); |
ca46fb90 RB |
7249 | } |
7250 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
7251 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
7252 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
7253 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
7254 | else if (SCM_REALP (x)) | |
55f26379 | 7255 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 7256 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 7257 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 7258 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 7259 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 7260 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 7261 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
7262 | else |
7263 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 7264 | } |
ca46fb90 | 7265 | |
9cc37597 | 7266 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7267 | { |
9cc37597 | 7268 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7269 | { |
e25f3727 AW |
7270 | scm_t_inum xx = SCM_I_INUM (x); |
7271 | scm_t_inum yy = SCM_I_INUM (y); | |
7272 | scm_t_inum z = xx - yy; | |
0aacf84e | 7273 | if (SCM_FIXABLE (z)) |
d956fa6f | 7274 | return SCM_I_MAKINUM (z); |
0aacf84e | 7275 | else |
e25f3727 | 7276 | return scm_i_inum2big (z); |
0aacf84e MD |
7277 | } |
7278 | else if (SCM_BIGP (y)) | |
7279 | { | |
7280 | /* inum-x - big-y */ | |
e25f3727 | 7281 | scm_t_inum xx = SCM_I_INUM (x); |
ca46fb90 | 7282 | |
0aacf84e | 7283 | if (xx == 0) |
b5c40589 MW |
7284 | { |
7285 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a | |
7286 | bignum, but negating that gives a fixnum. */ | |
7287 | return scm_i_normbig (scm_i_clonebig (y, 0)); | |
7288 | } | |
0aacf84e MD |
7289 | else |
7290 | { | |
7291 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7292 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7293 | |
0aacf84e MD |
7294 | if (xx >= 0) |
7295 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
7296 | else | |
7297 | { | |
7298 | /* x - y == -(y + -x) */ | |
7299 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
7300 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7301 | } | |
7302 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 7303 | |
0aacf84e MD |
7304 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
7305 | /* we know the result will have to be a bignum */ | |
7306 | return result; | |
7307 | else | |
7308 | return scm_i_normbig (result); | |
7309 | } | |
7310 | } | |
7311 | else if (SCM_REALP (y)) | |
7312 | { | |
e25f3727 | 7313 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7314 | |
7315 | /* | |
7316 | * We need to handle x == exact 0 | |
7317 | * specially because R6RS states that: | |
7318 | * (- 0.0) ==> -0.0 and | |
7319 | * (- 0.0 0.0) ==> 0.0 | |
7320 | * and the scheme compiler changes | |
7321 | * (- 0.0) into (- 0 0.0) | |
7322 | * So we need to treat (- 0 0.0) like (- 0.0). | |
7323 | * At the C level, (-x) is different than (0.0 - x). | |
7324 | * (0.0 - 0.0) ==> 0.0, but (- 0.0) ==> -0.0. | |
7325 | */ | |
7326 | if (xx == 0) | |
7327 | return scm_from_double (- SCM_REAL_VALUE (y)); | |
7328 | else | |
7329 | return scm_from_double (xx - SCM_REAL_VALUE (y)); | |
0aacf84e MD |
7330 | } |
7331 | else if (SCM_COMPLEXP (y)) | |
7332 | { | |
e25f3727 | 7333 | scm_t_inum xx = SCM_I_INUM (x); |
9b9ef10c MW |
7334 | |
7335 | /* We need to handle x == exact 0 specially. | |
7336 | See the comment above (for SCM_REALP (y)) */ | |
7337 | if (xx == 0) | |
7338 | return scm_c_make_rectangular (- SCM_COMPLEX_REAL (y), | |
7339 | - SCM_COMPLEX_IMAG (y)); | |
7340 | else | |
7341 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), | |
7342 | - SCM_COMPLEX_IMAG (y)); | |
0aacf84e | 7343 | } |
f92e85f7 MV |
7344 | else if (SCM_FRACTIONP (y)) |
7345 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 7346 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7347 | SCM_FRACTION_NUMERATOR (y)), |
7348 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
7349 | else |
7350 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 7351 | } |
0aacf84e MD |
7352 | else if (SCM_BIGP (x)) |
7353 | { | |
e11e83f3 | 7354 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7355 | { |
7356 | /* big-x - inum-y */ | |
e25f3727 | 7357 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e | 7358 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 7359 | |
0aacf84e MD |
7360 | scm_remember_upto_here_1 (x); |
7361 | if (sgn_x == 0) | |
c71b0706 | 7362 | return (SCM_FIXABLE (-yy) ? |
e25f3727 | 7363 | SCM_I_MAKINUM (-yy) : scm_from_inum (-yy)); |
0aacf84e MD |
7364 | else |
7365 | { | |
7366 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 7367 | |
708f22c6 KR |
7368 | if (yy >= 0) |
7369 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
7370 | else | |
7371 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 7372 | scm_remember_upto_here_1 (x); |
ca46fb90 | 7373 | |
0aacf84e MD |
7374 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
7375 | /* we know the result will have to be a bignum */ | |
7376 | return result; | |
7377 | else | |
7378 | return scm_i_normbig (result); | |
7379 | } | |
7380 | } | |
7381 | else if (SCM_BIGP (y)) | |
7382 | { | |
7383 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
7384 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
7385 | SCM result = scm_i_mkbig (); | |
7386 | mpz_sub (SCM_I_BIG_MPZ (result), | |
7387 | SCM_I_BIG_MPZ (x), | |
7388 | SCM_I_BIG_MPZ (y)); | |
7389 | scm_remember_upto_here_2 (x, y); | |
7390 | /* we know the result will have to be a bignum */ | |
7391 | if ((sgn_x == 1) && (sgn_y == -1)) | |
7392 | return result; | |
7393 | if ((sgn_x == -1) && (sgn_y == 1)) | |
7394 | return result; | |
7395 | return scm_i_normbig (result); | |
7396 | } | |
7397 | else if (SCM_REALP (y)) | |
7398 | { | |
7399 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
7400 | scm_remember_upto_here_1 (x); | |
55f26379 | 7401 | return scm_from_double (result); |
0aacf84e MD |
7402 | } |
7403 | else if (SCM_COMPLEXP (y)) | |
7404 | { | |
7405 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
7406 | - SCM_COMPLEX_REAL (y)); | |
7407 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7408 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 7409 | } |
f92e85f7 | 7410 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7411 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7412 | SCM_FRACTION_NUMERATOR (y)), |
7413 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 7414 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 7415 | } |
0aacf84e MD |
7416 | else if (SCM_REALP (x)) |
7417 | { | |
e11e83f3 | 7418 | if (SCM_I_INUMP (y)) |
55f26379 | 7419 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
7420 | else if (SCM_BIGP (y)) |
7421 | { | |
7422 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7423 | scm_remember_upto_here_1 (x); | |
55f26379 | 7424 | return scm_from_double (result); |
0aacf84e MD |
7425 | } |
7426 | else if (SCM_REALP (y)) | |
55f26379 | 7427 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 7428 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7429 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7430 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7431 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7432 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
7433 | else |
7434 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7435 | } |
0aacf84e MD |
7436 | else if (SCM_COMPLEXP (x)) |
7437 | { | |
e11e83f3 | 7438 | if (SCM_I_INUMP (y)) |
8507ec80 | 7439 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
7440 | SCM_COMPLEX_IMAG (x)); |
7441 | else if (SCM_BIGP (y)) | |
7442 | { | |
7443 | double real_part = (SCM_COMPLEX_REAL (x) | |
7444 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
7445 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7446 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
7447 | } |
7448 | else if (SCM_REALP (y)) | |
8507ec80 | 7449 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
7450 | SCM_COMPLEX_IMAG (x)); |
7451 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 7452 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 7453 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7454 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 7455 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
7456 | SCM_COMPLEX_IMAG (x)); |
7457 | else | |
7458 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
7459 | } | |
7460 | else if (SCM_FRACTIONP (x)) | |
7461 | { | |
e11e83f3 | 7462 | if (SCM_I_INUMP (y)) |
f92e85f7 | 7463 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 7464 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7465 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7466 | SCM_FRACTION_DENOMINATOR (x)); | |
7467 | else if (SCM_BIGP (y)) | |
cba42c93 | 7468 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7469 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
7470 | SCM_FRACTION_DENOMINATOR (x)); | |
7471 | else if (SCM_REALP (y)) | |
55f26379 | 7472 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 7473 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7474 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7475 | -SCM_COMPLEX_IMAG (y)); |
7476 | else if (SCM_FRACTIONP (y)) | |
7477 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 7478 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
7479 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
7480 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7481 | else |
7482 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 7483 | } |
0aacf84e | 7484 | else |
98cb6e75 | 7485 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 7486 | } |
c05e97b7 | 7487 | #undef FUNC_NAME |
0f2d19dd | 7488 | |
ca46fb90 | 7489 | |
40882e3d KR |
7490 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
7491 | (SCM x), | |
7492 | "Return @math{@var{x}-1}.") | |
7493 | #define FUNC_NAME s_scm_oneminus | |
7494 | { | |
cff5fa33 | 7495 | return scm_difference (x, SCM_INUM1); |
40882e3d KR |
7496 | } |
7497 | #undef FUNC_NAME | |
7498 | ||
7499 | ||
78d3deb1 AW |
7500 | SCM_PRIMITIVE_GENERIC (scm_i_product, "*", 0, 2, 1, |
7501 | (SCM x, SCM y, SCM rest), | |
7502 | "Return the product of all arguments. If called without arguments,\n" | |
7503 | "1 is returned.") | |
7504 | #define FUNC_NAME s_scm_i_product | |
7505 | { | |
7506 | while (!scm_is_null (rest)) | |
7507 | { x = scm_product (x, y); | |
7508 | y = scm_car (rest); | |
7509 | rest = scm_cdr (rest); | |
7510 | } | |
7511 | return scm_product (x, y); | |
7512 | } | |
7513 | #undef FUNC_NAME | |
7514 | ||
7515 | #define s_product s_scm_i_product | |
7516 | #define g_product g_scm_i_product | |
7517 | ||
0f2d19dd | 7518 | SCM |
6e8d25a6 | 7519 | scm_product (SCM x, SCM y) |
0f2d19dd | 7520 | { |
9cc37597 | 7521 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7522 | { |
7523 | if (SCM_UNBNDP (x)) | |
d956fa6f | 7524 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
7525 | else if (SCM_NUMBERP (x)) |
7526 | return x; | |
7527 | else | |
7528 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 7529 | } |
ca46fb90 | 7530 | |
9cc37597 | 7531 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7532 | { |
e25f3727 | 7533 | scm_t_inum xx; |
f4c627b3 | 7534 | |
5e791807 | 7535 | xinum: |
e11e83f3 | 7536 | xx = SCM_I_INUM (x); |
f4c627b3 | 7537 | |
0aacf84e MD |
7538 | switch (xx) |
7539 | { | |
5e791807 MW |
7540 | case 1: |
7541 | /* exact1 is the universal multiplicative identity */ | |
7542 | return y; | |
7543 | break; | |
7544 | case 0: | |
7545 | /* exact0 times a fixnum is exact0: optimize this case */ | |
7546 | if (SCM_LIKELY (SCM_I_INUMP (y))) | |
7547 | return SCM_INUM0; | |
7548 | /* if the other argument is inexact, the result is inexact, | |
7549 | and we must do the multiplication in order to handle | |
7550 | infinities and NaNs properly. */ | |
7551 | else if (SCM_REALP (y)) | |
7552 | return scm_from_double (0.0 * SCM_REAL_VALUE (y)); | |
7553 | else if (SCM_COMPLEXP (y)) | |
7554 | return scm_c_make_rectangular (0.0 * SCM_COMPLEX_REAL (y), | |
7555 | 0.0 * SCM_COMPLEX_IMAG (y)); | |
7556 | /* we've already handled inexact numbers, | |
7557 | so y must be exact, and we return exact0 */ | |
7558 | else if (SCM_NUMP (y)) | |
7559 | return SCM_INUM0; | |
7560 | else | |
7561 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
7562 | break; | |
7563 | case -1: | |
b5c40589 | 7564 | /* |
5e791807 MW |
7565 | * This case is important for more than just optimization. |
7566 | * It handles the case of negating | |
b5c40589 MW |
7567 | * (+ 1 most-positive-fixnum) aka (- most-negative-fixnum), |
7568 | * which is a bignum that must be changed back into a fixnum. | |
7569 | * Failure to do so will cause the following to return #f: | |
7570 | * (= most-negative-fixnum (* -1 (- most-negative-fixnum))) | |
7571 | */ | |
b5c40589 MW |
7572 | return scm_difference(y, SCM_UNDEFINED); |
7573 | break; | |
0aacf84e | 7574 | } |
f4c627b3 | 7575 | |
9cc37597 | 7576 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7577 | { |
e25f3727 AW |
7578 | scm_t_inum yy = SCM_I_INUM (y); |
7579 | scm_t_inum kk = xx * yy; | |
d956fa6f | 7580 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 7581 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
7582 | return k; |
7583 | else | |
7584 | { | |
e25f3727 | 7585 | SCM result = scm_i_inum2big (xx); |
0aacf84e MD |
7586 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); |
7587 | return scm_i_normbig (result); | |
7588 | } | |
7589 | } | |
7590 | else if (SCM_BIGP (y)) | |
7591 | { | |
7592 | SCM result = scm_i_mkbig (); | |
7593 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
7594 | scm_remember_upto_here_1 (y); | |
7595 | return result; | |
7596 | } | |
7597 | else if (SCM_REALP (y)) | |
55f26379 | 7598 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 7599 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7600 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 7601 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7602 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7603 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7604 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7605 | else |
7606 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7607 | } |
0aacf84e MD |
7608 | else if (SCM_BIGP (x)) |
7609 | { | |
e11e83f3 | 7610 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
7611 | { |
7612 | SCM_SWAP (x, y); | |
5e791807 | 7613 | goto xinum; |
0aacf84e MD |
7614 | } |
7615 | else if (SCM_BIGP (y)) | |
7616 | { | |
7617 | SCM result = scm_i_mkbig (); | |
7618 | mpz_mul (SCM_I_BIG_MPZ (result), | |
7619 | SCM_I_BIG_MPZ (x), | |
7620 | SCM_I_BIG_MPZ (y)); | |
7621 | scm_remember_upto_here_2 (x, y); | |
7622 | return result; | |
7623 | } | |
7624 | else if (SCM_REALP (y)) | |
7625 | { | |
7626 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
7627 | scm_remember_upto_here_1 (x); | |
55f26379 | 7628 | return scm_from_double (result); |
0aacf84e MD |
7629 | } |
7630 | else if (SCM_COMPLEXP (y)) | |
7631 | { | |
7632 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
7633 | scm_remember_upto_here_1 (x); | |
8507ec80 | 7634 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
7635 | z * SCM_COMPLEX_IMAG (y)); |
7636 | } | |
f92e85f7 | 7637 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 7638 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 7639 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
7640 | else |
7641 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7642 | } |
0aacf84e MD |
7643 | else if (SCM_REALP (x)) |
7644 | { | |
e11e83f3 | 7645 | if (SCM_I_INUMP (y)) |
5e791807 MW |
7646 | { |
7647 | SCM_SWAP (x, y); | |
7648 | goto xinum; | |
7649 | } | |
0aacf84e MD |
7650 | else if (SCM_BIGP (y)) |
7651 | { | |
7652 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
7653 | scm_remember_upto_here_1 (y); | |
55f26379 | 7654 | return scm_from_double (result); |
0aacf84e MD |
7655 | } |
7656 | else if (SCM_REALP (y)) | |
55f26379 | 7657 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 7658 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 7659 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 7660 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 7661 | else if (SCM_FRACTIONP (y)) |
55f26379 | 7662 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
7663 | else |
7664 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7665 | } |
0aacf84e MD |
7666 | else if (SCM_COMPLEXP (x)) |
7667 | { | |
e11e83f3 | 7668 | if (SCM_I_INUMP (y)) |
5e791807 MW |
7669 | { |
7670 | SCM_SWAP (x, y); | |
7671 | goto xinum; | |
7672 | } | |
0aacf84e MD |
7673 | else if (SCM_BIGP (y)) |
7674 | { | |
7675 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
7676 | scm_remember_upto_here_1 (y); | |
8507ec80 | 7677 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 7678 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
7679 | } |
7680 | else if (SCM_REALP (y)) | |
8507ec80 | 7681 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
7682 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
7683 | else if (SCM_COMPLEXP (y)) | |
7684 | { | |
8507ec80 | 7685 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
7686 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
7687 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
7688 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
7689 | } | |
f92e85f7 MV |
7690 | else if (SCM_FRACTIONP (y)) |
7691 | { | |
7692 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 7693 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
7694 | yy * SCM_COMPLEX_IMAG (x)); |
7695 | } | |
7696 | else | |
7697 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
7698 | } | |
7699 | else if (SCM_FRACTIONP (x)) | |
7700 | { | |
e11e83f3 | 7701 | if (SCM_I_INUMP (y)) |
cba42c93 | 7702 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
7703 | SCM_FRACTION_DENOMINATOR (x)); |
7704 | else if (SCM_BIGP (y)) | |
cba42c93 | 7705 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
7706 | SCM_FRACTION_DENOMINATOR (x)); |
7707 | else if (SCM_REALP (y)) | |
55f26379 | 7708 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
7709 | else if (SCM_COMPLEXP (y)) |
7710 | { | |
7711 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 7712 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
7713 | xx * SCM_COMPLEX_IMAG (y)); |
7714 | } | |
7715 | else if (SCM_FRACTIONP (y)) | |
7716 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 7717 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
7718 | SCM_FRACTION_NUMERATOR (y)), |
7719 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
7720 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
7721 | else |
7722 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 7723 | } |
0aacf84e | 7724 | else |
f4c627b3 | 7725 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
7726 | } |
7727 | ||
7351e207 MV |
7728 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
7729 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
7730 | #define ALLOW_DIVIDE_BY_ZERO | |
7731 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
7732 | #endif | |
0f2d19dd | 7733 | |
ba74ef4e MV |
7734 | /* The code below for complex division is adapted from the GNU |
7735 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
7736 | this copyright: */ | |
7737 | ||
7738 | /**************************************************************** | |
7739 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
7740 | ||
7741 | Permission to use, copy, modify, and distribute this software | |
7742 | and its documentation for any purpose and without fee is hereby | |
7743 | granted, provided that the above copyright notice appear in all | |
7744 | copies and that both that the copyright notice and this | |
7745 | permission notice and warranty disclaimer appear in supporting | |
7746 | documentation, and that the names of AT&T Bell Laboratories or | |
7747 | Bellcore or any of their entities not be used in advertising or | |
7748 | publicity pertaining to distribution of the software without | |
7749 | specific, written prior permission. | |
7750 | ||
7751 | AT&T and Bellcore disclaim all warranties with regard to this | |
7752 | software, including all implied warranties of merchantability | |
7753 | and fitness. In no event shall AT&T or Bellcore be liable for | |
7754 | any special, indirect or consequential damages or any damages | |
7755 | whatsoever resulting from loss of use, data or profits, whether | |
7756 | in an action of contract, negligence or other tortious action, | |
7757 | arising out of or in connection with the use or performance of | |
7758 | this software. | |
7759 | ****************************************************************/ | |
7760 | ||
78d3deb1 AW |
7761 | SCM_PRIMITIVE_GENERIC (scm_i_divide, "/", 0, 2, 1, |
7762 | (SCM x, SCM y, SCM rest), | |
7763 | "Divide the first argument by the product of the remaining\n" | |
7764 | "arguments. If called with one argument @var{z1}, 1/@var{z1} is\n" | |
7765 | "returned.") | |
7766 | #define FUNC_NAME s_scm_i_divide | |
7767 | { | |
7768 | while (!scm_is_null (rest)) | |
7769 | { x = scm_divide (x, y); | |
7770 | y = scm_car (rest); | |
7771 | rest = scm_cdr (rest); | |
7772 | } | |
7773 | return scm_divide (x, y); | |
7774 | } | |
7775 | #undef FUNC_NAME | |
7776 | ||
7777 | #define s_divide s_scm_i_divide | |
7778 | #define g_divide g_scm_i_divide | |
7779 | ||
f92e85f7 | 7780 | static SCM |
78d3deb1 AW |
7781 | do_divide (SCM x, SCM y, int inexact) |
7782 | #define FUNC_NAME s_divide | |
0f2d19dd | 7783 | { |
f8de44c1 DH |
7784 | double a; |
7785 | ||
9cc37597 | 7786 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
7787 | { |
7788 | if (SCM_UNBNDP (x)) | |
7789 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 7790 | else if (SCM_I_INUMP (x)) |
0aacf84e | 7791 | { |
e25f3727 | 7792 | scm_t_inum xx = SCM_I_INUM (x); |
0aacf84e MD |
7793 | if (xx == 1 || xx == -1) |
7794 | return x; | |
7351e207 | 7795 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
7796 | else if (xx == 0) |
7797 | scm_num_overflow (s_divide); | |
7351e207 | 7798 | #endif |
0aacf84e | 7799 | else |
f92e85f7 MV |
7800 | { |
7801 | if (inexact) | |
55f26379 | 7802 | return scm_from_double (1.0 / (double) xx); |
cff5fa33 | 7803 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 7804 | } |
0aacf84e MD |
7805 | } |
7806 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
7807 | { |
7808 | if (inexact) | |
55f26379 | 7809 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cff5fa33 | 7810 | else return scm_i_make_ratio (SCM_INUM1, x); |
f92e85f7 | 7811 | } |
0aacf84e MD |
7812 | else if (SCM_REALP (x)) |
7813 | { | |
7814 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 7815 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
7816 | if (xx == 0.0) |
7817 | scm_num_overflow (s_divide); | |
7818 | else | |
7351e207 | 7819 | #endif |
55f26379 | 7820 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
7821 | } |
7822 | else if (SCM_COMPLEXP (x)) | |
7823 | { | |
7824 | double r = SCM_COMPLEX_REAL (x); | |
7825 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 7826 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
7827 | { |
7828 | double t = r / i; | |
7829 | double d = i * (1.0 + t * t); | |
8507ec80 | 7830 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
7831 | } |
7832 | else | |
7833 | { | |
7834 | double t = i / r; | |
7835 | double d = r * (1.0 + t * t); | |
8507ec80 | 7836 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
7837 | } |
7838 | } | |
f92e85f7 | 7839 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 7840 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 7841 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
7842 | else |
7843 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 7844 | } |
f8de44c1 | 7845 | |
9cc37597 | 7846 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 7847 | { |
e25f3727 | 7848 | scm_t_inum xx = SCM_I_INUM (x); |
9cc37597 | 7849 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 7850 | { |
e25f3727 | 7851 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7852 | if (yy == 0) |
7853 | { | |
7351e207 | 7854 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 7855 | scm_num_overflow (s_divide); |
7351e207 | 7856 | #else |
55f26379 | 7857 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 7858 | #endif |
0aacf84e MD |
7859 | } |
7860 | else if (xx % yy != 0) | |
f92e85f7 MV |
7861 | { |
7862 | if (inexact) | |
55f26379 | 7863 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 7864 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 7865 | } |
0aacf84e MD |
7866 | else |
7867 | { | |
e25f3727 | 7868 | scm_t_inum z = xx / yy; |
0aacf84e | 7869 | if (SCM_FIXABLE (z)) |
d956fa6f | 7870 | return SCM_I_MAKINUM (z); |
0aacf84e | 7871 | else |
e25f3727 | 7872 | return scm_i_inum2big (z); |
0aacf84e | 7873 | } |
f872b822 | 7874 | } |
0aacf84e | 7875 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
7876 | { |
7877 | if (inexact) | |
55f26379 | 7878 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 7879 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 7880 | } |
0aacf84e MD |
7881 | else if (SCM_REALP (y)) |
7882 | { | |
7883 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 7884 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
7885 | if (yy == 0.0) |
7886 | scm_num_overflow (s_divide); | |
7887 | else | |
7351e207 | 7888 | #endif |
55f26379 | 7889 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 7890 | } |
0aacf84e MD |
7891 | else if (SCM_COMPLEXP (y)) |
7892 | { | |
7893 | a = xx; | |
7894 | complex_div: /* y _must_ be a complex number */ | |
7895 | { | |
7896 | double r = SCM_COMPLEX_REAL (y); | |
7897 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 7898 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
7899 | { |
7900 | double t = r / i; | |
7901 | double d = i * (1.0 + t * t); | |
8507ec80 | 7902 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
7903 | } |
7904 | else | |
7905 | { | |
7906 | double t = i / r; | |
7907 | double d = r * (1.0 + t * t); | |
8507ec80 | 7908 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
7909 | } |
7910 | } | |
7911 | } | |
f92e85f7 MV |
7912 | else if (SCM_FRACTIONP (y)) |
7913 | /* a / b/c = ac / b */ | |
cba42c93 | 7914 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 7915 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
7916 | else |
7917 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 7918 | } |
0aacf84e MD |
7919 | else if (SCM_BIGP (x)) |
7920 | { | |
e11e83f3 | 7921 | if (SCM_I_INUMP (y)) |
0aacf84e | 7922 | { |
e25f3727 | 7923 | scm_t_inum yy = SCM_I_INUM (y); |
0aacf84e MD |
7924 | if (yy == 0) |
7925 | { | |
7351e207 | 7926 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 7927 | scm_num_overflow (s_divide); |
7351e207 | 7928 | #else |
0aacf84e MD |
7929 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
7930 | scm_remember_upto_here_1 (x); | |
7931 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 7932 | #endif |
0aacf84e MD |
7933 | } |
7934 | else if (yy == 1) | |
7935 | return x; | |
7936 | else | |
7937 | { | |
7938 | /* FIXME: HMM, what are the relative performance issues here? | |
7939 | We need to test. Is it faster on average to test | |
7940 | divisible_p, then perform whichever operation, or is it | |
7941 | faster to perform the integer div opportunistically and | |
7942 | switch to real if there's a remainder? For now we take the | |
7943 | middle ground: test, then if divisible, use the faster div | |
7944 | func. */ | |
7945 | ||
e25f3727 | 7946 | scm_t_inum abs_yy = yy < 0 ? -yy : yy; |
0aacf84e MD |
7947 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); |
7948 | ||
7949 | if (divisible_p) | |
7950 | { | |
7951 | SCM result = scm_i_mkbig (); | |
7952 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
7953 | scm_remember_upto_here_1 (x); | |
7954 | if (yy < 0) | |
7955 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
7956 | return scm_i_normbig (result); | |
7957 | } | |
7958 | else | |
f92e85f7 MV |
7959 | { |
7960 | if (inexact) | |
55f26379 | 7961 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 7962 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 7963 | } |
0aacf84e MD |
7964 | } |
7965 | } | |
7966 | else if (SCM_BIGP (y)) | |
7967 | { | |
a4955a04 MW |
7968 | /* big_x / big_y */ |
7969 | if (inexact) | |
0aacf84e | 7970 | { |
a4955a04 MW |
7971 | /* It's easily possible for the ratio x/y to fit a double |
7972 | but one or both x and y be too big to fit a double, | |
7973 | hence the use of mpq_get_d rather than converting and | |
7974 | dividing. */ | |
7975 | mpq_t q; | |
7976 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
7977 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
7978 | return scm_from_double (mpq_get_d (q)); | |
0aacf84e MD |
7979 | } |
7980 | else | |
7981 | { | |
a4955a04 MW |
7982 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), |
7983 | SCM_I_BIG_MPZ (y)); | |
7984 | if (divisible_p) | |
7985 | { | |
7986 | SCM result = scm_i_mkbig (); | |
7987 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
7988 | SCM_I_BIG_MPZ (x), | |
7989 | SCM_I_BIG_MPZ (y)); | |
7990 | scm_remember_upto_here_2 (x, y); | |
7991 | return scm_i_normbig (result); | |
7992 | } | |
7993 | else | |
7994 | return scm_i_make_ratio (x, y); | |
0aacf84e MD |
7995 | } |
7996 | } | |
7997 | else if (SCM_REALP (y)) | |
7998 | { | |
7999 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8000 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8001 | if (yy == 0.0) |
8002 | scm_num_overflow (s_divide); | |
8003 | else | |
7351e207 | 8004 | #endif |
55f26379 | 8005 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
8006 | } |
8007 | else if (SCM_COMPLEXP (y)) | |
8008 | { | |
8009 | a = scm_i_big2dbl (x); | |
8010 | goto complex_div; | |
8011 | } | |
f92e85f7 | 8012 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 8013 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 8014 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
8015 | else |
8016 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8017 | } |
0aacf84e MD |
8018 | else if (SCM_REALP (x)) |
8019 | { | |
8020 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 8021 | if (SCM_I_INUMP (y)) |
0aacf84e | 8022 | { |
e25f3727 | 8023 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8024 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8025 | if (yy == 0) |
8026 | scm_num_overflow (s_divide); | |
8027 | else | |
7351e207 | 8028 | #endif |
55f26379 | 8029 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
8030 | } |
8031 | else if (SCM_BIGP (y)) | |
8032 | { | |
8033 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8034 | scm_remember_upto_here_1 (y); | |
55f26379 | 8035 | return scm_from_double (rx / dby); |
0aacf84e MD |
8036 | } |
8037 | else if (SCM_REALP (y)) | |
8038 | { | |
8039 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8040 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8041 | if (yy == 0.0) |
8042 | scm_num_overflow (s_divide); | |
8043 | else | |
7351e207 | 8044 | #endif |
55f26379 | 8045 | return scm_from_double (rx / yy); |
0aacf84e MD |
8046 | } |
8047 | else if (SCM_COMPLEXP (y)) | |
8048 | { | |
8049 | a = rx; | |
8050 | goto complex_div; | |
8051 | } | |
f92e85f7 | 8052 | else if (SCM_FRACTIONP (y)) |
55f26379 | 8053 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
8054 | else |
8055 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 8056 | } |
0aacf84e MD |
8057 | else if (SCM_COMPLEXP (x)) |
8058 | { | |
8059 | double rx = SCM_COMPLEX_REAL (x); | |
8060 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 8061 | if (SCM_I_INUMP (y)) |
0aacf84e | 8062 | { |
e25f3727 | 8063 | scm_t_inum yy = SCM_I_INUM (y); |
7351e207 | 8064 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
8065 | if (yy == 0) |
8066 | scm_num_overflow (s_divide); | |
8067 | else | |
7351e207 | 8068 | #endif |
0aacf84e MD |
8069 | { |
8070 | double d = yy; | |
8507ec80 | 8071 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
8072 | } |
8073 | } | |
8074 | else if (SCM_BIGP (y)) | |
8075 | { | |
8076 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
8077 | scm_remember_upto_here_1 (y); | |
8507ec80 | 8078 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
8079 | } |
8080 | else if (SCM_REALP (y)) | |
8081 | { | |
8082 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 8083 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
8084 | if (yy == 0.0) |
8085 | scm_num_overflow (s_divide); | |
8086 | else | |
7351e207 | 8087 | #endif |
8507ec80 | 8088 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
8089 | } |
8090 | else if (SCM_COMPLEXP (y)) | |
8091 | { | |
8092 | double ry = SCM_COMPLEX_REAL (y); | |
8093 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 8094 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
8095 | { |
8096 | double t = ry / iy; | |
8097 | double d = iy * (1.0 + t * t); | |
8507ec80 | 8098 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
8099 | } |
8100 | else | |
8101 | { | |
8102 | double t = iy / ry; | |
8103 | double d = ry * (1.0 + t * t); | |
8507ec80 | 8104 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
8105 | } |
8106 | } | |
f92e85f7 MV |
8107 | else if (SCM_FRACTIONP (y)) |
8108 | { | |
8109 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 8110 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 8111 | } |
0aacf84e MD |
8112 | else |
8113 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 8114 | } |
f92e85f7 MV |
8115 | else if (SCM_FRACTIONP (x)) |
8116 | { | |
e11e83f3 | 8117 | if (SCM_I_INUMP (y)) |
f92e85f7 | 8118 | { |
e25f3727 | 8119 | scm_t_inum yy = SCM_I_INUM (y); |
f92e85f7 MV |
8120 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
8121 | if (yy == 0) | |
8122 | scm_num_overflow (s_divide); | |
8123 | else | |
8124 | #endif | |
cba42c93 | 8125 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8126 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8127 | } | |
8128 | else if (SCM_BIGP (y)) | |
8129 | { | |
cba42c93 | 8130 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
8131 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
8132 | } | |
8133 | else if (SCM_REALP (y)) | |
8134 | { | |
8135 | double yy = SCM_REAL_VALUE (y); | |
8136 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8137 | if (yy == 0.0) | |
8138 | scm_num_overflow (s_divide); | |
8139 | else | |
8140 | #endif | |
55f26379 | 8141 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
8142 | } |
8143 | else if (SCM_COMPLEXP (y)) | |
8144 | { | |
8145 | a = scm_i_fraction2double (x); | |
8146 | goto complex_div; | |
8147 | } | |
8148 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 8149 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
8150 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
8151 | else | |
8152 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
8153 | } | |
0aacf84e | 8154 | else |
f8de44c1 | 8155 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 8156 | } |
f92e85f7 MV |
8157 | |
8158 | SCM | |
8159 | scm_divide (SCM x, SCM y) | |
8160 | { | |
78d3deb1 | 8161 | return do_divide (x, y, 0); |
f92e85f7 MV |
8162 | } |
8163 | ||
8164 | static SCM scm_divide2real (SCM x, SCM y) | |
8165 | { | |
78d3deb1 | 8166 | return do_divide (x, y, 1); |
f92e85f7 | 8167 | } |
c05e97b7 | 8168 | #undef FUNC_NAME |
0f2d19dd | 8169 | |
fa605590 | 8170 | |
0f2d19dd | 8171 | double |
3101f40f | 8172 | scm_c_truncate (double x) |
0f2d19dd | 8173 | { |
fa605590 | 8174 | return trunc (x); |
0f2d19dd | 8175 | } |
0f2d19dd | 8176 | |
3101f40f MV |
8177 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
8178 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
8179 | Then half-way cases are identified and adjusted down if the | |
8180 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
8181 | |
8182 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
8183 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
8184 | ||
8185 | An odd "result" value is identified with result/2 != floor(result/2). | |
8186 | This is done with plus_half, since that value is ready for use sooner in | |
8187 | a pipelined cpu, and we're already requiring plus_half == result. | |
8188 | ||
8189 | Note however that we need to be careful when x is big and already an | |
8190 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
8191 | us to return such a value, incorrectly. For instance if the hardware is | |
8192 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
8193 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
8194 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
8195 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
8196 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
8197 | ||
8198 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
8199 | x is already an integer. If it is then clearly that's the desired result | |
8200 | already. And if it's not then the exponent must be small enough to allow | |
8201 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
8202 | ||
0f2d19dd | 8203 | double |
3101f40f | 8204 | scm_c_round (double x) |
0f2d19dd | 8205 | { |
6187f48b KR |
8206 | double plus_half, result; |
8207 | ||
8208 | if (x == floor (x)) | |
8209 | return x; | |
8210 | ||
8211 | plus_half = x + 0.5; | |
8212 | result = floor (plus_half); | |
3101f40f | 8213 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
8214 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
8215 | ? result - 1 | |
8216 | : result); | |
0f2d19dd JB |
8217 | } |
8218 | ||
8b56bcec MW |
8219 | SCM_PRIMITIVE_GENERIC (scm_truncate_number, "truncate", 1, 0, 0, |
8220 | (SCM x), | |
8221 | "Round the number @var{x} towards zero.") | |
f92e85f7 MV |
8222 | #define FUNC_NAME s_scm_truncate_number |
8223 | { | |
8b56bcec MW |
8224 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
8225 | return x; | |
8226 | else if (SCM_REALP (x)) | |
c251ab63 | 8227 | return scm_from_double (trunc (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8228 | else if (SCM_FRACTIONP (x)) |
8229 | return scm_truncate_quotient (SCM_FRACTION_NUMERATOR (x), | |
8230 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8231 | else |
8b56bcec MW |
8232 | SCM_WTA_DISPATCH_1 (g_scm_truncate_number, x, SCM_ARG1, |
8233 | s_scm_truncate_number); | |
f92e85f7 MV |
8234 | } |
8235 | #undef FUNC_NAME | |
8236 | ||
8b56bcec MW |
8237 | SCM_PRIMITIVE_GENERIC (scm_round_number, "round", 1, 0, 0, |
8238 | (SCM x), | |
8239 | "Round the number @var{x} towards the nearest integer. " | |
8240 | "When it is exactly halfway between two integers, " | |
8241 | "round towards the even one.") | |
f92e85f7 MV |
8242 | #define FUNC_NAME s_scm_round_number |
8243 | { | |
e11e83f3 | 8244 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
8245 | return x; |
8246 | else if (SCM_REALP (x)) | |
3101f40f | 8247 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
8b56bcec MW |
8248 | else if (SCM_FRACTIONP (x)) |
8249 | return scm_round_quotient (SCM_FRACTION_NUMERATOR (x), | |
8250 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 | 8251 | else |
8b56bcec MW |
8252 | SCM_WTA_DISPATCH_1 (g_scm_round_number, x, SCM_ARG1, |
8253 | s_scm_round_number); | |
f92e85f7 MV |
8254 | } |
8255 | #undef FUNC_NAME | |
8256 | ||
8257 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
8258 | (SCM x), | |
8259 | "Round the number @var{x} towards minus infinity.") | |
8260 | #define FUNC_NAME s_scm_floor | |
8261 | { | |
e11e83f3 | 8262 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8263 | return x; |
8264 | else if (SCM_REALP (x)) | |
55f26379 | 8265 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 | 8266 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8267 | return scm_floor_quotient (SCM_FRACTION_NUMERATOR (x), |
8268 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8269 | else |
8270 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
8271 | } | |
8272 | #undef FUNC_NAME | |
8273 | ||
8274 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
8275 | (SCM x), | |
8276 | "Round the number @var{x} towards infinity.") | |
8277 | #define FUNC_NAME s_scm_ceiling | |
8278 | { | |
e11e83f3 | 8279 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
8280 | return x; |
8281 | else if (SCM_REALP (x)) | |
55f26379 | 8282 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 | 8283 | else if (SCM_FRACTIONP (x)) |
8b56bcec MW |
8284 | return scm_ceiling_quotient (SCM_FRACTION_NUMERATOR (x), |
8285 | SCM_FRACTION_DENOMINATOR (x)); | |
f92e85f7 MV |
8286 | else |
8287 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
8288 | } | |
8289 | #undef FUNC_NAME | |
0f2d19dd | 8290 | |
2519490c MW |
8291 | SCM_PRIMITIVE_GENERIC (scm_expt, "expt", 2, 0, 0, |
8292 | (SCM x, SCM y), | |
8293 | "Return @var{x} raised to the power of @var{y}.") | |
6fc4d012 | 8294 | #define FUNC_NAME s_scm_expt |
0f2d19dd | 8295 | { |
01c7284a MW |
8296 | if (scm_is_integer (y)) |
8297 | { | |
8298 | if (scm_is_true (scm_exact_p (y))) | |
8299 | return scm_integer_expt (x, y); | |
8300 | else | |
8301 | { | |
8302 | /* Here we handle the case where the exponent is an inexact | |
8303 | integer. We make the exponent exact in order to use | |
8304 | scm_integer_expt, and thus avoid the spurious imaginary | |
8305 | parts that may result from round-off errors in the general | |
8306 | e^(y log x) method below (for example when squaring a large | |
8307 | negative number). In this case, we must return an inexact | |
8308 | result for correctness. We also make the base inexact so | |
8309 | that scm_integer_expt will use fast inexact arithmetic | |
8310 | internally. Note that making the base inexact is not | |
8311 | sufficient to guarantee an inexact result, because | |
8312 | scm_integer_expt will return an exact 1 when the exponent | |
8313 | is 0, even if the base is inexact. */ | |
8314 | return scm_exact_to_inexact | |
8315 | (scm_integer_expt (scm_exact_to_inexact (x), | |
8316 | scm_inexact_to_exact (y))); | |
8317 | } | |
8318 | } | |
6fc4d012 AW |
8319 | else if (scm_is_real (x) && scm_is_real (y) && scm_to_double (x) >= 0.0) |
8320 | { | |
8321 | return scm_from_double (pow (scm_to_double (x), scm_to_double (y))); | |
8322 | } | |
2519490c | 8323 | else if (scm_is_complex (x) && scm_is_complex (y)) |
6fc4d012 | 8324 | return scm_exp (scm_product (scm_log (x), y)); |
2519490c MW |
8325 | else if (scm_is_complex (x)) |
8326 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG2, s_scm_expt); | |
8327 | else | |
8328 | SCM_WTA_DISPATCH_2 (g_scm_expt, x, y, SCM_ARG1, s_scm_expt); | |
0f2d19dd | 8329 | } |
1bbd0b84 | 8330 | #undef FUNC_NAME |
0f2d19dd | 8331 | |
7f41099e MW |
8332 | /* sin/cos/tan/asin/acos/atan |
8333 | sinh/cosh/tanh/asinh/acosh/atanh | |
8334 | Derived from "Transcen.scm", Complex trancendental functions for SCM. | |
8335 | Written by Jerry D. Hedden, (C) FSF. | |
8336 | See the file `COPYING' for terms applying to this program. */ | |
8337 | ||
ad79736c AW |
8338 | SCM_PRIMITIVE_GENERIC (scm_sin, "sin", 1, 0, 0, |
8339 | (SCM z), | |
8340 | "Compute the sine of @var{z}.") | |
8341 | #define FUNC_NAME s_scm_sin | |
8342 | { | |
8deddc94 MW |
8343 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8344 | return z; /* sin(exact0) = exact0 */ | |
8345 | else if (scm_is_real (z)) | |
ad79736c AW |
8346 | return scm_from_double (sin (scm_to_double (z))); |
8347 | else if (SCM_COMPLEXP (z)) | |
8348 | { double x, y; | |
8349 | x = SCM_COMPLEX_REAL (z); | |
8350 | y = SCM_COMPLEX_IMAG (z); | |
8351 | return scm_c_make_rectangular (sin (x) * cosh (y), | |
8352 | cos (x) * sinh (y)); | |
8353 | } | |
8354 | else | |
8355 | SCM_WTA_DISPATCH_1 (g_scm_sin, z, 1, s_scm_sin); | |
8356 | } | |
8357 | #undef FUNC_NAME | |
0f2d19dd | 8358 | |
ad79736c AW |
8359 | SCM_PRIMITIVE_GENERIC (scm_cos, "cos", 1, 0, 0, |
8360 | (SCM z), | |
8361 | "Compute the cosine of @var{z}.") | |
8362 | #define FUNC_NAME s_scm_cos | |
8363 | { | |
8deddc94 MW |
8364 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8365 | return SCM_INUM1; /* cos(exact0) = exact1 */ | |
8366 | else if (scm_is_real (z)) | |
ad79736c AW |
8367 | return scm_from_double (cos (scm_to_double (z))); |
8368 | else if (SCM_COMPLEXP (z)) | |
8369 | { double x, y; | |
8370 | x = SCM_COMPLEX_REAL (z); | |
8371 | y = SCM_COMPLEX_IMAG (z); | |
8372 | return scm_c_make_rectangular (cos (x) * cosh (y), | |
8373 | -sin (x) * sinh (y)); | |
8374 | } | |
8375 | else | |
8376 | SCM_WTA_DISPATCH_1 (g_scm_cos, z, 1, s_scm_cos); | |
8377 | } | |
8378 | #undef FUNC_NAME | |
8379 | ||
8380 | SCM_PRIMITIVE_GENERIC (scm_tan, "tan", 1, 0, 0, | |
8381 | (SCM z), | |
8382 | "Compute the tangent of @var{z}.") | |
8383 | #define FUNC_NAME s_scm_tan | |
0f2d19dd | 8384 | { |
8deddc94 MW |
8385 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8386 | return z; /* tan(exact0) = exact0 */ | |
8387 | else if (scm_is_real (z)) | |
ad79736c AW |
8388 | return scm_from_double (tan (scm_to_double (z))); |
8389 | else if (SCM_COMPLEXP (z)) | |
8390 | { double x, y, w; | |
8391 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8392 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8393 | w = cos (x) + cosh (y); | |
8394 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8395 | if (w == 0.0) | |
8396 | scm_num_overflow (s_scm_tan); | |
8397 | #endif | |
8398 | return scm_c_make_rectangular (sin (x) / w, sinh (y) / w); | |
8399 | } | |
8400 | else | |
8401 | SCM_WTA_DISPATCH_1 (g_scm_tan, z, 1, s_scm_tan); | |
8402 | } | |
8403 | #undef FUNC_NAME | |
8404 | ||
8405 | SCM_PRIMITIVE_GENERIC (scm_sinh, "sinh", 1, 0, 0, | |
8406 | (SCM z), | |
8407 | "Compute the hyperbolic sine of @var{z}.") | |
8408 | #define FUNC_NAME s_scm_sinh | |
8409 | { | |
8deddc94 MW |
8410 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8411 | return z; /* sinh(exact0) = exact0 */ | |
8412 | else if (scm_is_real (z)) | |
ad79736c AW |
8413 | return scm_from_double (sinh (scm_to_double (z))); |
8414 | else if (SCM_COMPLEXP (z)) | |
8415 | { double x, y; | |
8416 | x = SCM_COMPLEX_REAL (z); | |
8417 | y = SCM_COMPLEX_IMAG (z); | |
8418 | return scm_c_make_rectangular (sinh (x) * cos (y), | |
8419 | cosh (x) * sin (y)); | |
8420 | } | |
8421 | else | |
8422 | SCM_WTA_DISPATCH_1 (g_scm_sinh, z, 1, s_scm_sinh); | |
8423 | } | |
8424 | #undef FUNC_NAME | |
8425 | ||
8426 | SCM_PRIMITIVE_GENERIC (scm_cosh, "cosh", 1, 0, 0, | |
8427 | (SCM z), | |
8428 | "Compute the hyperbolic cosine of @var{z}.") | |
8429 | #define FUNC_NAME s_scm_cosh | |
8430 | { | |
8deddc94 MW |
8431 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8432 | return SCM_INUM1; /* cosh(exact0) = exact1 */ | |
8433 | else if (scm_is_real (z)) | |
ad79736c AW |
8434 | return scm_from_double (cosh (scm_to_double (z))); |
8435 | else if (SCM_COMPLEXP (z)) | |
8436 | { double x, y; | |
8437 | x = SCM_COMPLEX_REAL (z); | |
8438 | y = SCM_COMPLEX_IMAG (z); | |
8439 | return scm_c_make_rectangular (cosh (x) * cos (y), | |
8440 | sinh (x) * sin (y)); | |
8441 | } | |
8442 | else | |
8443 | SCM_WTA_DISPATCH_1 (g_scm_cosh, z, 1, s_scm_cosh); | |
8444 | } | |
8445 | #undef FUNC_NAME | |
8446 | ||
8447 | SCM_PRIMITIVE_GENERIC (scm_tanh, "tanh", 1, 0, 0, | |
8448 | (SCM z), | |
8449 | "Compute the hyperbolic tangent of @var{z}.") | |
8450 | #define FUNC_NAME s_scm_tanh | |
8451 | { | |
8deddc94 MW |
8452 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8453 | return z; /* tanh(exact0) = exact0 */ | |
8454 | else if (scm_is_real (z)) | |
ad79736c AW |
8455 | return scm_from_double (tanh (scm_to_double (z))); |
8456 | else if (SCM_COMPLEXP (z)) | |
8457 | { double x, y, w; | |
8458 | x = 2.0 * SCM_COMPLEX_REAL (z); | |
8459 | y = 2.0 * SCM_COMPLEX_IMAG (z); | |
8460 | w = cosh (x) + cos (y); | |
8461 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
8462 | if (w == 0.0) | |
8463 | scm_num_overflow (s_scm_tanh); | |
8464 | #endif | |
8465 | return scm_c_make_rectangular (sinh (x) / w, sin (y) / w); | |
8466 | } | |
8467 | else | |
8468 | SCM_WTA_DISPATCH_1 (g_scm_tanh, z, 1, s_scm_tanh); | |
8469 | } | |
8470 | #undef FUNC_NAME | |
8471 | ||
8472 | SCM_PRIMITIVE_GENERIC (scm_asin, "asin", 1, 0, 0, | |
8473 | (SCM z), | |
8474 | "Compute the arc sine of @var{z}.") | |
8475 | #define FUNC_NAME s_scm_asin | |
8476 | { | |
8deddc94 MW |
8477 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8478 | return z; /* asin(exact0) = exact0 */ | |
8479 | else if (scm_is_real (z)) | |
ad79736c AW |
8480 | { |
8481 | double w = scm_to_double (z); | |
8482 | if (w >= -1.0 && w <= 1.0) | |
8483 | return scm_from_double (asin (w)); | |
8484 | else | |
8485 | return scm_product (scm_c_make_rectangular (0, -1), | |
8486 | scm_sys_asinh (scm_c_make_rectangular (0, w))); | |
8487 | } | |
8488 | else if (SCM_COMPLEXP (z)) | |
8489 | { double x, y; | |
8490 | x = SCM_COMPLEX_REAL (z); | |
8491 | y = SCM_COMPLEX_IMAG (z); | |
8492 | return scm_product (scm_c_make_rectangular (0, -1), | |
8493 | scm_sys_asinh (scm_c_make_rectangular (-y, x))); | |
8494 | } | |
8495 | else | |
8496 | SCM_WTA_DISPATCH_1 (g_scm_asin, z, 1, s_scm_asin); | |
8497 | } | |
8498 | #undef FUNC_NAME | |
8499 | ||
8500 | SCM_PRIMITIVE_GENERIC (scm_acos, "acos", 1, 0, 0, | |
8501 | (SCM z), | |
8502 | "Compute the arc cosine of @var{z}.") | |
8503 | #define FUNC_NAME s_scm_acos | |
8504 | { | |
8deddc94 MW |
8505 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8506 | return SCM_INUM0; /* acos(exact1) = exact0 */ | |
8507 | else if (scm_is_real (z)) | |
ad79736c AW |
8508 | { |
8509 | double w = scm_to_double (z); | |
8510 | if (w >= -1.0 && w <= 1.0) | |
8511 | return scm_from_double (acos (w)); | |
8512 | else | |
8513 | return scm_sum (scm_from_double (acos (0.0)), | |
8514 | scm_product (scm_c_make_rectangular (0, 1), | |
8515 | scm_sys_asinh (scm_c_make_rectangular (0, w)))); | |
8516 | } | |
8517 | else if (SCM_COMPLEXP (z)) | |
8518 | { double x, y; | |
8519 | x = SCM_COMPLEX_REAL (z); | |
8520 | y = SCM_COMPLEX_IMAG (z); | |
8521 | return scm_sum (scm_from_double (acos (0.0)), | |
8522 | scm_product (scm_c_make_rectangular (0, 1), | |
8523 | scm_sys_asinh (scm_c_make_rectangular (-y, x)))); | |
8524 | } | |
8525 | else | |
8526 | SCM_WTA_DISPATCH_1 (g_scm_acos, z, 1, s_scm_acos); | |
8527 | } | |
8528 | #undef FUNC_NAME | |
8529 | ||
8530 | SCM_PRIMITIVE_GENERIC (scm_atan, "atan", 1, 1, 0, | |
8531 | (SCM z, SCM y), | |
8532 | "With one argument, compute the arc tangent of @var{z}.\n" | |
8533 | "If @var{y} is present, compute the arc tangent of @var{z}/@var{y},\n" | |
8534 | "using the sign of @var{z} and @var{y} to determine the quadrant.") | |
8535 | #define FUNC_NAME s_scm_atan | |
8536 | { | |
8537 | if (SCM_UNBNDP (y)) | |
8538 | { | |
8deddc94 MW |
8539 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8540 | return z; /* atan(exact0) = exact0 */ | |
8541 | else if (scm_is_real (z)) | |
ad79736c AW |
8542 | return scm_from_double (atan (scm_to_double (z))); |
8543 | else if (SCM_COMPLEXP (z)) | |
8544 | { | |
8545 | double v, w; | |
8546 | v = SCM_COMPLEX_REAL (z); | |
8547 | w = SCM_COMPLEX_IMAG (z); | |
8548 | return scm_divide (scm_log (scm_divide (scm_c_make_rectangular (v, w - 1.0), | |
8549 | scm_c_make_rectangular (v, w + 1.0))), | |
8550 | scm_c_make_rectangular (0, 2)); | |
8551 | } | |
8552 | else | |
18104cac | 8553 | SCM_WTA_DISPATCH_1 (g_scm_atan, z, SCM_ARG1, s_scm_atan); |
ad79736c AW |
8554 | } |
8555 | else if (scm_is_real (z)) | |
8556 | { | |
8557 | if (scm_is_real (y)) | |
8558 | return scm_from_double (atan2 (scm_to_double (z), scm_to_double (y))); | |
8559 | else | |
8560 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG2, s_scm_atan); | |
8561 | } | |
8562 | else | |
8563 | SCM_WTA_DISPATCH_2 (g_scm_atan, z, y, SCM_ARG1, s_scm_atan); | |
8564 | } | |
8565 | #undef FUNC_NAME | |
8566 | ||
8567 | SCM_PRIMITIVE_GENERIC (scm_sys_asinh, "asinh", 1, 0, 0, | |
8568 | (SCM z), | |
8569 | "Compute the inverse hyperbolic sine of @var{z}.") | |
8570 | #define FUNC_NAME s_scm_sys_asinh | |
8571 | { | |
8deddc94 MW |
8572 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8573 | return z; /* asinh(exact0) = exact0 */ | |
8574 | else if (scm_is_real (z)) | |
ad79736c AW |
8575 | return scm_from_double (asinh (scm_to_double (z))); |
8576 | else if (scm_is_number (z)) | |
8577 | return scm_log (scm_sum (z, | |
8578 | scm_sqrt (scm_sum (scm_product (z, z), | |
cff5fa33 | 8579 | SCM_INUM1)))); |
ad79736c AW |
8580 | else |
8581 | SCM_WTA_DISPATCH_1 (g_scm_sys_asinh, z, 1, s_scm_sys_asinh); | |
8582 | } | |
8583 | #undef FUNC_NAME | |
8584 | ||
8585 | SCM_PRIMITIVE_GENERIC (scm_sys_acosh, "acosh", 1, 0, 0, | |
8586 | (SCM z), | |
8587 | "Compute the inverse hyperbolic cosine of @var{z}.") | |
8588 | #define FUNC_NAME s_scm_sys_acosh | |
8589 | { | |
8deddc94 MW |
8590 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM1))) |
8591 | return SCM_INUM0; /* acosh(exact1) = exact0 */ | |
8592 | else if (scm_is_real (z) && scm_to_double (z) >= 1.0) | |
ad79736c AW |
8593 | return scm_from_double (acosh (scm_to_double (z))); |
8594 | else if (scm_is_number (z)) | |
8595 | return scm_log (scm_sum (z, | |
8596 | scm_sqrt (scm_difference (scm_product (z, z), | |
cff5fa33 | 8597 | SCM_INUM1)))); |
ad79736c AW |
8598 | else |
8599 | SCM_WTA_DISPATCH_1 (g_scm_sys_acosh, z, 1, s_scm_sys_acosh); | |
8600 | } | |
8601 | #undef FUNC_NAME | |
8602 | ||
8603 | SCM_PRIMITIVE_GENERIC (scm_sys_atanh, "atanh", 1, 0, 0, | |
8604 | (SCM z), | |
8605 | "Compute the inverse hyperbolic tangent of @var{z}.") | |
8606 | #define FUNC_NAME s_scm_sys_atanh | |
8607 | { | |
8deddc94 MW |
8608 | if (SCM_UNLIKELY (scm_is_eq (z, SCM_INUM0))) |
8609 | return z; /* atanh(exact0) = exact0 */ | |
8610 | else if (scm_is_real (z) && scm_to_double (z) >= -1.0 && scm_to_double (z) <= 1.0) | |
ad79736c AW |
8611 | return scm_from_double (atanh (scm_to_double (z))); |
8612 | else if (scm_is_number (z)) | |
cff5fa33 MW |
8613 | return scm_divide (scm_log (scm_divide (scm_sum (SCM_INUM1, z), |
8614 | scm_difference (SCM_INUM1, z))), | |
ad79736c AW |
8615 | SCM_I_MAKINUM (2)); |
8616 | else | |
8617 | SCM_WTA_DISPATCH_1 (g_scm_sys_atanh, z, 1, s_scm_sys_atanh); | |
0f2d19dd | 8618 | } |
1bbd0b84 | 8619 | #undef FUNC_NAME |
0f2d19dd | 8620 | |
8507ec80 MV |
8621 | SCM |
8622 | scm_c_make_rectangular (double re, double im) | |
8623 | { | |
c7218482 | 8624 | SCM z; |
03604fcf | 8625 | |
c7218482 MW |
8626 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_complex), |
8627 | "complex")); | |
8628 | SCM_SET_CELL_TYPE (z, scm_tc16_complex); | |
8629 | SCM_COMPLEX_REAL (z) = re; | |
8630 | SCM_COMPLEX_IMAG (z) = im; | |
8631 | return z; | |
8507ec80 | 8632 | } |
0f2d19dd | 8633 | |
a1ec6916 | 8634 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
8635 | (SCM real_part, SCM imaginary_part), |
8636 | "Return a complex number constructed of the given @var{real-part} " | |
8637 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 8638 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd | 8639 | { |
ad79736c AW |
8640 | SCM_ASSERT_TYPE (scm_is_real (real_part), real_part, |
8641 | SCM_ARG1, FUNC_NAME, "real"); | |
8642 | SCM_ASSERT_TYPE (scm_is_real (imaginary_part), imaginary_part, | |
8643 | SCM_ARG2, FUNC_NAME, "real"); | |
c7218482 MW |
8644 | |
8645 | /* Return a real if and only if the imaginary_part is an _exact_ 0 */ | |
8646 | if (scm_is_eq (imaginary_part, SCM_INUM0)) | |
8647 | return real_part; | |
8648 | else | |
8649 | return scm_c_make_rectangular (scm_to_double (real_part), | |
8650 | scm_to_double (imaginary_part)); | |
0f2d19dd | 8651 | } |
1bbd0b84 | 8652 | #undef FUNC_NAME |
0f2d19dd | 8653 | |
8507ec80 MV |
8654 | SCM |
8655 | scm_c_make_polar (double mag, double ang) | |
8656 | { | |
8657 | double s, c; | |
5e647d08 LC |
8658 | |
8659 | /* The sincos(3) function is undocumented an broken on Tru64. Thus we only | |
8660 | use it on Glibc-based systems that have it (it's a GNU extension). See | |
8661 | http://lists.gnu.org/archive/html/guile-user/2009-04/msg00033.html for | |
8662 | details. */ | |
8663 | #if (defined HAVE_SINCOS) && (defined __GLIBC__) && (defined _GNU_SOURCE) | |
8507ec80 MV |
8664 | sincos (ang, &s, &c); |
8665 | #else | |
8666 | s = sin (ang); | |
8667 | c = cos (ang); | |
8668 | #endif | |
9d427b2c MW |
8669 | |
8670 | /* If s and c are NaNs, this indicates that the angle is a NaN, | |
8671 | infinite, or perhaps simply too large to determine its value | |
8672 | mod 2*pi. However, we know something that the floating-point | |
8673 | implementation doesn't know: We know that s and c are finite. | |
8674 | Therefore, if the magnitude is zero, return a complex zero. | |
8675 | ||
8676 | The reason we check for the NaNs instead of using this case | |
8677 | whenever mag == 0.0 is because when the angle is known, we'd | |
8678 | like to return the correct kind of non-real complex zero: | |
8679 | +0.0+0.0i, -0.0+0.0i, -0.0-0.0i, or +0.0-0.0i, depending | |
8680 | on which quadrant the angle is in. | |
8681 | */ | |
8682 | if (SCM_UNLIKELY (isnan(s)) && isnan(c) && (mag == 0.0)) | |
8683 | return scm_c_make_rectangular (0.0, 0.0); | |
8684 | else | |
8685 | return scm_c_make_rectangular (mag * c, mag * s); | |
8507ec80 | 8686 | } |
0f2d19dd | 8687 | |
a1ec6916 | 8688 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
c7218482 MW |
8689 | (SCM mag, SCM ang), |
8690 | "Return the complex number @var{mag} * e^(i * @var{ang}).") | |
1bbd0b84 | 8691 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd | 8692 | { |
c7218482 MW |
8693 | SCM_ASSERT_TYPE (scm_is_real (mag), mag, SCM_ARG1, FUNC_NAME, "real"); |
8694 | SCM_ASSERT_TYPE (scm_is_real (ang), ang, SCM_ARG2, FUNC_NAME, "real"); | |
8695 | ||
8696 | /* If mag is exact0, return exact0 */ | |
8697 | if (scm_is_eq (mag, SCM_INUM0)) | |
8698 | return SCM_INUM0; | |
8699 | /* Return a real if ang is exact0 */ | |
8700 | else if (scm_is_eq (ang, SCM_INUM0)) | |
8701 | return mag; | |
8702 | else | |
8703 | return scm_c_make_polar (scm_to_double (mag), scm_to_double (ang)); | |
0f2d19dd | 8704 | } |
1bbd0b84 | 8705 | #undef FUNC_NAME |
0f2d19dd JB |
8706 | |
8707 | ||
2519490c MW |
8708 | SCM_PRIMITIVE_GENERIC (scm_real_part, "real-part", 1, 0, 0, |
8709 | (SCM z), | |
8710 | "Return the real part of the number @var{z}.") | |
8711 | #define FUNC_NAME s_scm_real_part | |
0f2d19dd | 8712 | { |
2519490c | 8713 | if (SCM_COMPLEXP (z)) |
55f26379 | 8714 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
2519490c | 8715 | else if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_REALP (z) || SCM_FRACTIONP (z)) |
2fa2d879 | 8716 | return z; |
0aacf84e | 8717 | else |
2519490c | 8718 | SCM_WTA_DISPATCH_1 (g_scm_real_part, z, SCM_ARG1, s_scm_real_part); |
0f2d19dd | 8719 | } |
2519490c | 8720 | #undef FUNC_NAME |
0f2d19dd JB |
8721 | |
8722 | ||
2519490c MW |
8723 | SCM_PRIMITIVE_GENERIC (scm_imag_part, "imag-part", 1, 0, 0, |
8724 | (SCM z), | |
8725 | "Return the imaginary part of the number @var{z}.") | |
8726 | #define FUNC_NAME s_scm_imag_part | |
0f2d19dd | 8727 | { |
2519490c MW |
8728 | if (SCM_COMPLEXP (z)) |
8729 | return scm_from_double (SCM_COMPLEX_IMAG (z)); | |
c7218482 | 8730 | else if (SCM_I_INUMP (z) || SCM_REALP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f92e85f7 | 8731 | return SCM_INUM0; |
0aacf84e | 8732 | else |
2519490c | 8733 | SCM_WTA_DISPATCH_1 (g_scm_imag_part, z, SCM_ARG1, s_scm_imag_part); |
0f2d19dd | 8734 | } |
2519490c | 8735 | #undef FUNC_NAME |
0f2d19dd | 8736 | |
2519490c MW |
8737 | SCM_PRIMITIVE_GENERIC (scm_numerator, "numerator", 1, 0, 0, |
8738 | (SCM z), | |
8739 | "Return the numerator of the number @var{z}.") | |
8740 | #define FUNC_NAME s_scm_numerator | |
f92e85f7 | 8741 | { |
2519490c | 8742 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
f92e85f7 MV |
8743 | return z; |
8744 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 8745 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
8746 | else if (SCM_REALP (z)) |
8747 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
8748 | else | |
2519490c | 8749 | SCM_WTA_DISPATCH_1 (g_scm_numerator, z, SCM_ARG1, s_scm_numerator); |
f92e85f7 | 8750 | } |
2519490c | 8751 | #undef FUNC_NAME |
f92e85f7 MV |
8752 | |
8753 | ||
2519490c MW |
8754 | SCM_PRIMITIVE_GENERIC (scm_denominator, "denominator", 1, 0, 0, |
8755 | (SCM z), | |
8756 | "Return the denominator of the number @var{z}.") | |
8757 | #define FUNC_NAME s_scm_denominator | |
f92e85f7 | 8758 | { |
2519490c | 8759 | if (SCM_I_INUMP (z) || SCM_BIGP (z)) |
cff5fa33 | 8760 | return SCM_INUM1; |
f92e85f7 | 8761 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 8762 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
8763 | else if (SCM_REALP (z)) |
8764 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
8765 | else | |
2519490c | 8766 | SCM_WTA_DISPATCH_1 (g_scm_denominator, z, SCM_ARG1, s_scm_denominator); |
f92e85f7 | 8767 | } |
2519490c | 8768 | #undef FUNC_NAME |
0f2d19dd | 8769 | |
2519490c MW |
8770 | |
8771 | SCM_PRIMITIVE_GENERIC (scm_magnitude, "magnitude", 1, 0, 0, | |
8772 | (SCM z), | |
8773 | "Return the magnitude of the number @var{z}. This is the same as\n" | |
8774 | "@code{abs} for real arguments, but also allows complex numbers.") | |
8775 | #define FUNC_NAME s_scm_magnitude | |
0f2d19dd | 8776 | { |
e11e83f3 | 8777 | if (SCM_I_INUMP (z)) |
0aacf84e | 8778 | { |
e25f3727 | 8779 | scm_t_inum zz = SCM_I_INUM (z); |
0aacf84e MD |
8780 | if (zz >= 0) |
8781 | return z; | |
8782 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 8783 | return SCM_I_MAKINUM (-zz); |
0aacf84e | 8784 | else |
e25f3727 | 8785 | return scm_i_inum2big (-zz); |
5986c47d | 8786 | } |
0aacf84e MD |
8787 | else if (SCM_BIGP (z)) |
8788 | { | |
8789 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
8790 | scm_remember_upto_here_1 (z); | |
8791 | if (sgn < 0) | |
8792 | return scm_i_clonebig (z, 0); | |
8793 | else | |
8794 | return z; | |
5986c47d | 8795 | } |
0aacf84e | 8796 | else if (SCM_REALP (z)) |
55f26379 | 8797 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 8798 | else if (SCM_COMPLEXP (z)) |
55f26379 | 8799 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
8800 | else if (SCM_FRACTIONP (z)) |
8801 | { | |
73e4de09 | 8802 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 8803 | return z; |
cba42c93 | 8804 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
8805 | SCM_FRACTION_DENOMINATOR (z)); |
8806 | } | |
0aacf84e | 8807 | else |
2519490c | 8808 | SCM_WTA_DISPATCH_1 (g_scm_magnitude, z, SCM_ARG1, s_scm_magnitude); |
0f2d19dd | 8809 | } |
2519490c | 8810 | #undef FUNC_NAME |
0f2d19dd JB |
8811 | |
8812 | ||
2519490c MW |
8813 | SCM_PRIMITIVE_GENERIC (scm_angle, "angle", 1, 0, 0, |
8814 | (SCM z), | |
8815 | "Return the angle of the complex number @var{z}.") | |
8816 | #define FUNC_NAME s_scm_angle | |
0f2d19dd | 8817 | { |
c8ae173e | 8818 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
e7efe8e7 | 8819 | flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
8820 | But if atan2 follows the floating point rounding mode, then the value |
8821 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 8822 | if (SCM_I_INUMP (z)) |
0aacf84e | 8823 | { |
e11e83f3 | 8824 | if (SCM_I_INUM (z) >= 0) |
e7efe8e7 | 8825 | return flo0; |
0aacf84e | 8826 | else |
55f26379 | 8827 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 8828 | } |
0aacf84e MD |
8829 | else if (SCM_BIGP (z)) |
8830 | { | |
8831 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
8832 | scm_remember_upto_here_1 (z); | |
8833 | if (sgn < 0) | |
55f26379 | 8834 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 8835 | else |
e7efe8e7 | 8836 | return flo0; |
0f2d19dd | 8837 | } |
0aacf84e | 8838 | else if (SCM_REALP (z)) |
c8ae173e KR |
8839 | { |
8840 | if (SCM_REAL_VALUE (z) >= 0) | |
e7efe8e7 | 8841 | return flo0; |
c8ae173e | 8842 | else |
55f26379 | 8843 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 8844 | } |
0aacf84e | 8845 | else if (SCM_COMPLEXP (z)) |
55f26379 | 8846 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
8847 | else if (SCM_FRACTIONP (z)) |
8848 | { | |
73e4de09 | 8849 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
e7efe8e7 | 8850 | return flo0; |
55f26379 | 8851 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 8852 | } |
0aacf84e | 8853 | else |
2519490c | 8854 | SCM_WTA_DISPATCH_1 (g_scm_angle, z, SCM_ARG1, s_scm_angle); |
0f2d19dd | 8855 | } |
2519490c | 8856 | #undef FUNC_NAME |
0f2d19dd JB |
8857 | |
8858 | ||
2519490c MW |
8859 | SCM_PRIMITIVE_GENERIC (scm_exact_to_inexact, "exact->inexact", 1, 0, 0, |
8860 | (SCM z), | |
8861 | "Convert the number @var{z} to its inexact representation.\n") | |
8862 | #define FUNC_NAME s_scm_exact_to_inexact | |
3c9a524f | 8863 | { |
e11e83f3 | 8864 | if (SCM_I_INUMP (z)) |
55f26379 | 8865 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 8866 | else if (SCM_BIGP (z)) |
55f26379 | 8867 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 8868 | else if (SCM_FRACTIONP (z)) |
55f26379 | 8869 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
8870 | else if (SCM_INEXACTP (z)) |
8871 | return z; | |
8872 | else | |
2519490c | 8873 | SCM_WTA_DISPATCH_1 (g_scm_exact_to_inexact, z, 1, s_scm_exact_to_inexact); |
3c9a524f | 8874 | } |
2519490c | 8875 | #undef FUNC_NAME |
3c9a524f DH |
8876 | |
8877 | ||
2519490c MW |
8878 | SCM_PRIMITIVE_GENERIC (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
8879 | (SCM z), | |
8880 | "Return an exact number that is numerically closest to @var{z}.") | |
1bbd0b84 | 8881 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 8882 | { |
c7218482 | 8883 | if (SCM_I_INUMP (z) || SCM_BIGP (z) || SCM_FRACTIONP (z)) |
f872b822 | 8884 | return z; |
c7218482 | 8885 | else |
0aacf84e | 8886 | { |
c7218482 MW |
8887 | double val; |
8888 | ||
8889 | if (SCM_REALP (z)) | |
8890 | val = SCM_REAL_VALUE (z); | |
8891 | else if (SCM_COMPLEXP (z) && SCM_COMPLEX_IMAG (z) == 0.0) | |
8892 | val = SCM_COMPLEX_REAL (z); | |
8893 | else | |
8894 | SCM_WTA_DISPATCH_1 (g_scm_inexact_to_exact, z, 1, s_scm_inexact_to_exact); | |
8895 | ||
8896 | if (!SCM_LIKELY (DOUBLE_IS_FINITE (val))) | |
f92e85f7 | 8897 | SCM_OUT_OF_RANGE (1, z); |
2be24db4 | 8898 | else |
f92e85f7 MV |
8899 | { |
8900 | mpq_t frac; | |
8901 | SCM q; | |
8902 | ||
8903 | mpq_init (frac); | |
c7218482 | 8904 | mpq_set_d (frac, val); |
cba42c93 | 8905 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
c7218482 | 8906 | scm_i_mpz2num (mpq_denref (frac))); |
f92e85f7 | 8907 | |
cba42c93 | 8908 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
8909 | for frac... |
8910 | */ | |
8911 | mpq_clear (frac); | |
8912 | return q; | |
8913 | } | |
c2ff8ab0 | 8914 | } |
0f2d19dd | 8915 | } |
1bbd0b84 | 8916 | #undef FUNC_NAME |
0f2d19dd | 8917 | |
f92e85f7 | 8918 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
8919 | (SCM x, SCM eps), |
8920 | "Returns the @emph{simplest} rational number differing\n" | |
8921 | "from @var{x} by no more than @var{eps}.\n" | |
8922 | "\n" | |
8923 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
8924 | "exact result when both its arguments are exact. Thus, you might need\n" | |
8925 | "to use @code{inexact->exact} on the arguments.\n" | |
8926 | "\n" | |
8927 | "@lisp\n" | |
8928 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
8929 | "@result{} 6/5\n" | |
8930 | "@end lisp") | |
f92e85f7 MV |
8931 | #define FUNC_NAME s_scm_rationalize |
8932 | { | |
605f6980 MW |
8933 | SCM_ASSERT_TYPE (scm_is_real (x), x, SCM_ARG1, FUNC_NAME, "real"); |
8934 | SCM_ASSERT_TYPE (scm_is_real (eps), eps, SCM_ARG2, FUNC_NAME, "real"); | |
8935 | eps = scm_abs (eps); | |
8936 | if (scm_is_false (scm_positive_p (eps))) | |
8937 | { | |
8938 | /* eps is either zero or a NaN */ | |
8939 | if (scm_is_true (scm_nan_p (eps))) | |
8940 | return scm_nan (); | |
8941 | else if (SCM_INEXACTP (eps)) | |
8942 | return scm_exact_to_inexact (x); | |
8943 | else | |
8944 | return x; | |
8945 | } | |
8946 | else if (scm_is_false (scm_finite_p (eps))) | |
8947 | { | |
8948 | if (scm_is_true (scm_finite_p (x))) | |
8949 | return flo0; | |
8950 | else | |
8951 | return scm_nan (); | |
8952 | } | |
8953 | else if (scm_is_false (scm_finite_p (x))) /* checks for both inf and nan */ | |
f92e85f7 | 8954 | return x; |
605f6980 MW |
8955 | else if (scm_is_false (scm_less_p (scm_floor (scm_sum (x, eps)), |
8956 | scm_ceiling (scm_difference (x, eps))))) | |
8957 | { | |
8958 | /* There's an integer within range; we want the one closest to zero */ | |
8959 | if (scm_is_false (scm_less_p (eps, scm_abs (x)))) | |
8960 | { | |
8961 | /* zero is within range */ | |
8962 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) | |
8963 | return flo0; | |
8964 | else | |
8965 | return SCM_INUM0; | |
8966 | } | |
8967 | else if (scm_is_true (scm_positive_p (x))) | |
8968 | return scm_ceiling (scm_difference (x, eps)); | |
8969 | else | |
8970 | return scm_floor (scm_sum (x, eps)); | |
8971 | } | |
8972 | else | |
f92e85f7 MV |
8973 | { |
8974 | /* Use continued fractions to find closest ratio. All | |
8975 | arithmetic is done with exact numbers. | |
8976 | */ | |
8977 | ||
8978 | SCM ex = scm_inexact_to_exact (x); | |
8979 | SCM int_part = scm_floor (ex); | |
cff5fa33 MW |
8980 | SCM tt = SCM_INUM1; |
8981 | SCM a1 = SCM_INUM0, a2 = SCM_INUM1, a = SCM_INUM0; | |
8982 | SCM b1 = SCM_INUM1, b2 = SCM_INUM0, b = SCM_INUM0; | |
f92e85f7 MV |
8983 | SCM rx; |
8984 | int i = 0; | |
8985 | ||
f92e85f7 MV |
8986 | ex = scm_difference (ex, int_part); /* x = x-int_part */ |
8987 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
8988 | ||
8989 | /* We stop after a million iterations just to be absolutely sure | |
8990 | that we don't go into an infinite loop. The process normally | |
8991 | converges after less than a dozen iterations. | |
8992 | */ | |
8993 | ||
f92e85f7 MV |
8994 | while (++i < 1000000) |
8995 | { | |
8996 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
8997 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
8998 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
8999 | scm_is_false | |
f92e85f7 | 9000 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 9001 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
9002 | { |
9003 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
605f6980 | 9004 | if (SCM_INEXACTP (x) || SCM_INEXACTP (eps)) |
02164269 MV |
9005 | return scm_exact_to_inexact (res); |
9006 | else | |
9007 | return res; | |
9008 | } | |
f92e85f7 MV |
9009 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
9010 | SCM_UNDEFINED); | |
9011 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
9012 | a2 = a1; | |
9013 | b2 = b1; | |
9014 | a1 = a; | |
9015 | b1 = b; | |
9016 | } | |
9017 | scm_num_overflow (s_scm_rationalize); | |
9018 | } | |
f92e85f7 MV |
9019 | } |
9020 | #undef FUNC_NAME | |
9021 | ||
73e4de09 MV |
9022 | /* conversion functions */ |
9023 | ||
9024 | int | |
9025 | scm_is_integer (SCM val) | |
9026 | { | |
9027 | return scm_is_true (scm_integer_p (val)); | |
9028 | } | |
9029 | ||
9030 | int | |
9031 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
9032 | { | |
e11e83f3 | 9033 | if (SCM_I_INUMP (val)) |
73e4de09 | 9034 | { |
e11e83f3 | 9035 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9036 | return n >= min && n <= max; |
9037 | } | |
9038 | else if (SCM_BIGP (val)) | |
9039 | { | |
9040 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
9041 | return 0; | |
9042 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
9043 | { |
9044 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
9045 | { | |
9046 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
9047 | return n >= min && n <= max; | |
9048 | } | |
9049 | else | |
9050 | return 0; | |
9051 | } | |
73e4de09 MV |
9052 | else |
9053 | { | |
d956fa6f MV |
9054 | scm_t_intmax n; |
9055 | size_t count; | |
73e4de09 | 9056 | |
d956fa6f MV |
9057 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9058 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
9059 | return 0; | |
9060 | ||
9061 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9062 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9063 | |
d956fa6f | 9064 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 9065 | { |
d956fa6f MV |
9066 | if (n < 0) |
9067 | return 0; | |
73e4de09 | 9068 | } |
73e4de09 MV |
9069 | else |
9070 | { | |
d956fa6f MV |
9071 | n = -n; |
9072 | if (n >= 0) | |
9073 | return 0; | |
73e4de09 | 9074 | } |
d956fa6f MV |
9075 | |
9076 | return n >= min && n <= max; | |
73e4de09 MV |
9077 | } |
9078 | } | |
73e4de09 MV |
9079 | else |
9080 | return 0; | |
9081 | } | |
9082 | ||
9083 | int | |
9084 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
9085 | { | |
e11e83f3 | 9086 | if (SCM_I_INUMP (val)) |
73e4de09 | 9087 | { |
e11e83f3 | 9088 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
9089 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
9090 | } | |
9091 | else if (SCM_BIGP (val)) | |
9092 | { | |
9093 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
9094 | return 0; | |
9095 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
9096 | { |
9097 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
9098 | { | |
9099 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
9100 | return n >= min && n <= max; | |
9101 | } | |
9102 | else | |
9103 | return 0; | |
9104 | } | |
73e4de09 MV |
9105 | else |
9106 | { | |
d956fa6f MV |
9107 | scm_t_uintmax n; |
9108 | size_t count; | |
73e4de09 | 9109 | |
d956fa6f MV |
9110 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
9111 | return 0; | |
73e4de09 | 9112 | |
d956fa6f MV |
9113 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
9114 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 9115 | return 0; |
d956fa6f MV |
9116 | |
9117 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
9118 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 9119 | |
d956fa6f | 9120 | return n >= min && n <= max; |
73e4de09 MV |
9121 | } |
9122 | } | |
73e4de09 MV |
9123 | else |
9124 | return 0; | |
9125 | } | |
9126 | ||
1713d319 MV |
9127 | static void |
9128 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
9129 | { | |
9130 | scm_error (scm_out_of_range_key, | |
9131 | NULL, | |
9132 | "Value out of range ~S to ~S: ~S", | |
9133 | scm_list_3 (min, max, bad_val), | |
9134 | scm_list_1 (bad_val)); | |
9135 | } | |
9136 | ||
bfd7932e MV |
9137 | #define TYPE scm_t_intmax |
9138 | #define TYPE_MIN min | |
9139 | #define TYPE_MAX max | |
9140 | #define SIZEOF_TYPE 0 | |
9141 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
9142 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
9143 | #include "libguile/conv-integer.i.c" | |
9144 | ||
9145 | #define TYPE scm_t_uintmax | |
9146 | #define TYPE_MIN min | |
9147 | #define TYPE_MAX max | |
9148 | #define SIZEOF_TYPE 0 | |
9149 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
9150 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
9151 | #include "libguile/conv-uinteger.i.c" | |
9152 | ||
9153 | #define TYPE scm_t_int8 | |
9154 | #define TYPE_MIN SCM_T_INT8_MIN | |
9155 | #define TYPE_MAX SCM_T_INT8_MAX | |
9156 | #define SIZEOF_TYPE 1 | |
9157 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
9158 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
9159 | #include "libguile/conv-integer.i.c" | |
9160 | ||
9161 | #define TYPE scm_t_uint8 | |
9162 | #define TYPE_MIN 0 | |
9163 | #define TYPE_MAX SCM_T_UINT8_MAX | |
9164 | #define SIZEOF_TYPE 1 | |
9165 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
9166 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
9167 | #include "libguile/conv-uinteger.i.c" | |
9168 | ||
9169 | #define TYPE scm_t_int16 | |
9170 | #define TYPE_MIN SCM_T_INT16_MIN | |
9171 | #define TYPE_MAX SCM_T_INT16_MAX | |
9172 | #define SIZEOF_TYPE 2 | |
9173 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
9174 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
9175 | #include "libguile/conv-integer.i.c" | |
9176 | ||
9177 | #define TYPE scm_t_uint16 | |
9178 | #define TYPE_MIN 0 | |
9179 | #define TYPE_MAX SCM_T_UINT16_MAX | |
9180 | #define SIZEOF_TYPE 2 | |
9181 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
9182 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
9183 | #include "libguile/conv-uinteger.i.c" | |
9184 | ||
9185 | #define TYPE scm_t_int32 | |
9186 | #define TYPE_MIN SCM_T_INT32_MIN | |
9187 | #define TYPE_MAX SCM_T_INT32_MAX | |
9188 | #define SIZEOF_TYPE 4 | |
9189 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
9190 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
9191 | #include "libguile/conv-integer.i.c" | |
9192 | ||
9193 | #define TYPE scm_t_uint32 | |
9194 | #define TYPE_MIN 0 | |
9195 | #define TYPE_MAX SCM_T_UINT32_MAX | |
9196 | #define SIZEOF_TYPE 4 | |
9197 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
9198 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
9199 | #include "libguile/conv-uinteger.i.c" | |
9200 | ||
904a78f1 MG |
9201 | #define TYPE scm_t_wchar |
9202 | #define TYPE_MIN (scm_t_int32)-1 | |
9203 | #define TYPE_MAX (scm_t_int32)0x10ffff | |
9204 | #define SIZEOF_TYPE 4 | |
9205 | #define SCM_TO_TYPE_PROTO(arg) scm_to_wchar (arg) | |
9206 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_wchar (arg) | |
9207 | #include "libguile/conv-integer.i.c" | |
9208 | ||
bfd7932e MV |
9209 | #define TYPE scm_t_int64 |
9210 | #define TYPE_MIN SCM_T_INT64_MIN | |
9211 | #define TYPE_MAX SCM_T_INT64_MAX | |
9212 | #define SIZEOF_TYPE 8 | |
9213 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
9214 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
9215 | #include "libguile/conv-integer.i.c" | |
9216 | ||
9217 | #define TYPE scm_t_uint64 | |
9218 | #define TYPE_MIN 0 | |
9219 | #define TYPE_MAX SCM_T_UINT64_MAX | |
9220 | #define SIZEOF_TYPE 8 | |
9221 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
9222 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
9223 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 9224 | |
cd036260 MV |
9225 | void |
9226 | scm_to_mpz (SCM val, mpz_t rop) | |
9227 | { | |
9228 | if (SCM_I_INUMP (val)) | |
9229 | mpz_set_si (rop, SCM_I_INUM (val)); | |
9230 | else if (SCM_BIGP (val)) | |
9231 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
9232 | else | |
9233 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
9234 | } | |
9235 | ||
9236 | SCM | |
9237 | scm_from_mpz (mpz_t val) | |
9238 | { | |
9239 | return scm_i_mpz2num (val); | |
9240 | } | |
9241 | ||
73e4de09 MV |
9242 | int |
9243 | scm_is_real (SCM val) | |
9244 | { | |
9245 | return scm_is_true (scm_real_p (val)); | |
9246 | } | |
9247 | ||
55f26379 MV |
9248 | int |
9249 | scm_is_rational (SCM val) | |
9250 | { | |
9251 | return scm_is_true (scm_rational_p (val)); | |
9252 | } | |
9253 | ||
73e4de09 MV |
9254 | double |
9255 | scm_to_double (SCM val) | |
9256 | { | |
55f26379 MV |
9257 | if (SCM_I_INUMP (val)) |
9258 | return SCM_I_INUM (val); | |
9259 | else if (SCM_BIGP (val)) | |
9260 | return scm_i_big2dbl (val); | |
9261 | else if (SCM_FRACTIONP (val)) | |
9262 | return scm_i_fraction2double (val); | |
9263 | else if (SCM_REALP (val)) | |
9264 | return SCM_REAL_VALUE (val); | |
9265 | else | |
7a1aba42 | 9266 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
9267 | } |
9268 | ||
9269 | SCM | |
9270 | scm_from_double (double val) | |
9271 | { | |
978c52d1 LC |
9272 | SCM z; |
9273 | ||
9274 | z = PTR2SCM (scm_gc_malloc_pointerless (sizeof (scm_t_double), "real")); | |
9275 | ||
9276 | SCM_SET_CELL_TYPE (z, scm_tc16_real); | |
55f26379 | 9277 | SCM_REAL_VALUE (z) = val; |
978c52d1 | 9278 | |
55f26379 | 9279 | return z; |
73e4de09 MV |
9280 | } |
9281 | ||
220058a8 | 9282 | #if SCM_ENABLE_DEPRECATED == 1 |
55f26379 MV |
9283 | |
9284 | float | |
e25f3727 | 9285 | scm_num2float (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9286 | { |
220058a8 AW |
9287 | scm_c_issue_deprecation_warning |
9288 | ("`scm_num2float' is deprecated. Use scm_to_double instead."); | |
9289 | ||
55f26379 MV |
9290 | if (SCM_BIGP (num)) |
9291 | { | |
9292 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9293 | if (!isinf (res)) |
55f26379 MV |
9294 | return res; |
9295 | else | |
9296 | scm_out_of_range (NULL, num); | |
9297 | } | |
9298 | else | |
9299 | return scm_to_double (num); | |
9300 | } | |
9301 | ||
9302 | double | |
e25f3727 | 9303 | scm_num2double (SCM num, unsigned long pos, const char *s_caller) |
55f26379 | 9304 | { |
220058a8 AW |
9305 | scm_c_issue_deprecation_warning |
9306 | ("`scm_num2double' is deprecated. Use scm_to_double instead."); | |
9307 | ||
55f26379 MV |
9308 | if (SCM_BIGP (num)) |
9309 | { | |
9310 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
2e65b52f | 9311 | if (!isinf (res)) |
55f26379 MV |
9312 | return res; |
9313 | else | |
9314 | scm_out_of_range (NULL, num); | |
9315 | } | |
9316 | else | |
9317 | return scm_to_double (num); | |
9318 | } | |
9319 | ||
9320 | #endif | |
9321 | ||
8507ec80 MV |
9322 | int |
9323 | scm_is_complex (SCM val) | |
9324 | { | |
9325 | return scm_is_true (scm_complex_p (val)); | |
9326 | } | |
9327 | ||
9328 | double | |
9329 | scm_c_real_part (SCM z) | |
9330 | { | |
9331 | if (SCM_COMPLEXP (z)) | |
9332 | return SCM_COMPLEX_REAL (z); | |
9333 | else | |
9334 | { | |
9335 | /* Use the scm_real_part to get proper error checking and | |
9336 | dispatching. | |
9337 | */ | |
9338 | return scm_to_double (scm_real_part (z)); | |
9339 | } | |
9340 | } | |
9341 | ||
9342 | double | |
9343 | scm_c_imag_part (SCM z) | |
9344 | { | |
9345 | if (SCM_COMPLEXP (z)) | |
9346 | return SCM_COMPLEX_IMAG (z); | |
9347 | else | |
9348 | { | |
9349 | /* Use the scm_imag_part to get proper error checking and | |
9350 | dispatching. The result will almost always be 0.0, but not | |
9351 | always. | |
9352 | */ | |
9353 | return scm_to_double (scm_imag_part (z)); | |
9354 | } | |
9355 | } | |
9356 | ||
9357 | double | |
9358 | scm_c_magnitude (SCM z) | |
9359 | { | |
9360 | return scm_to_double (scm_magnitude (z)); | |
9361 | } | |
9362 | ||
9363 | double | |
9364 | scm_c_angle (SCM z) | |
9365 | { | |
9366 | return scm_to_double (scm_angle (z)); | |
9367 | } | |
9368 | ||
9369 | int | |
9370 | scm_is_number (SCM z) | |
9371 | { | |
9372 | return scm_is_true (scm_number_p (z)); | |
9373 | } | |
9374 | ||
8ab3d8a0 | 9375 | |
a5f6b751 MW |
9376 | /* Returns log(x * 2^shift) */ |
9377 | static SCM | |
9378 | log_of_shifted_double (double x, long shift) | |
9379 | { | |
9380 | double ans = log (fabs (x)) + shift * M_LN2; | |
9381 | ||
9382 | if (x > 0.0 || double_is_non_negative_zero (x)) | |
9383 | return scm_from_double (ans); | |
9384 | else | |
9385 | return scm_c_make_rectangular (ans, M_PI); | |
9386 | } | |
9387 | ||
9388 | /* Returns log(n), for exact integer n of integer-length size */ | |
9389 | static SCM | |
9390 | log_of_exact_integer_with_size (SCM n, long size) | |
9391 | { | |
9392 | long shift = size - 2 * scm_dblprec[0]; | |
9393 | ||
9394 | if (shift > 0) | |
9395 | return log_of_shifted_double | |
9396 | (scm_to_double (scm_ash (n, scm_from_long(-shift))), | |
9397 | shift); | |
9398 | else | |
9399 | return log_of_shifted_double (scm_to_double (n), 0); | |
9400 | } | |
9401 | ||
9402 | /* Returns log(n), for exact integer n of integer-length size */ | |
9403 | static SCM | |
9404 | log_of_exact_integer (SCM n) | |
9405 | { | |
9406 | return log_of_exact_integer_with_size | |
9407 | (n, scm_to_long (scm_integer_length (n))); | |
9408 | } | |
9409 | ||
9410 | /* Returns log(n/d), for exact non-zero integers n and d */ | |
9411 | static SCM | |
9412 | log_of_fraction (SCM n, SCM d) | |
9413 | { | |
9414 | long n_size = scm_to_long (scm_integer_length (n)); | |
9415 | long d_size = scm_to_long (scm_integer_length (d)); | |
9416 | ||
9417 | if (abs (n_size - d_size) > 1) | |
9418 | return (scm_difference (log_of_exact_integer_with_size (n, n_size), | |
9419 | log_of_exact_integer_with_size (d, d_size))); | |
9420 | else if (scm_is_false (scm_negative_p (n))) | |
9421 | return scm_from_double | |
9422 | (log1p (scm_to_double (scm_divide2real (scm_difference (n, d), d)))); | |
9423 | else | |
9424 | return scm_c_make_rectangular | |
9425 | (log1p (scm_to_double (scm_divide2real | |
9426 | (scm_difference (scm_abs (n), d), | |
9427 | d))), | |
9428 | M_PI); | |
9429 | } | |
9430 | ||
9431 | ||
8ab3d8a0 KR |
9432 | /* In the following functions we dispatch to the real-arg funcs like log() |
9433 | when we know the arg is real, instead of just handing everything to | |
9434 | clog() for instance. This is in case clog() doesn't optimize for a | |
9435 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
9436 | well use it to go straight to the applicable C func. */ | |
9437 | ||
2519490c MW |
9438 | SCM_PRIMITIVE_GENERIC (scm_log, "log", 1, 0, 0, |
9439 | (SCM z), | |
9440 | "Return the natural logarithm of @var{z}.") | |
8ab3d8a0 KR |
9441 | #define FUNC_NAME s_scm_log |
9442 | { | |
9443 | if (SCM_COMPLEXP (z)) | |
9444 | { | |
4b26c03e | 9445 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
9446 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
9447 | #else | |
9448 | double re = SCM_COMPLEX_REAL (z); | |
9449 | double im = SCM_COMPLEX_IMAG (z); | |
9450 | return scm_c_make_rectangular (log (hypot (re, im)), | |
9451 | atan2 (im, re)); | |
9452 | #endif | |
9453 | } | |
a5f6b751 MW |
9454 | else if (SCM_REALP (z)) |
9455 | return log_of_shifted_double (SCM_REAL_VALUE (z), 0); | |
9456 | else if (SCM_I_INUMP (z)) | |
8ab3d8a0 | 9457 | { |
a5f6b751 MW |
9458 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9459 | if (scm_is_eq (z, SCM_INUM0)) | |
9460 | scm_num_overflow (s_scm_log); | |
9461 | #endif | |
9462 | return log_of_shifted_double (SCM_I_INUM (z), 0); | |
8ab3d8a0 | 9463 | } |
a5f6b751 MW |
9464 | else if (SCM_BIGP (z)) |
9465 | return log_of_exact_integer (z); | |
9466 | else if (SCM_FRACTIONP (z)) | |
9467 | return log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9468 | SCM_FRACTION_DENOMINATOR (z)); | |
2519490c MW |
9469 | else |
9470 | SCM_WTA_DISPATCH_1 (g_scm_log, z, 1, s_scm_log); | |
8ab3d8a0 KR |
9471 | } |
9472 | #undef FUNC_NAME | |
9473 | ||
9474 | ||
2519490c MW |
9475 | SCM_PRIMITIVE_GENERIC (scm_log10, "log10", 1, 0, 0, |
9476 | (SCM z), | |
9477 | "Return the base 10 logarithm of @var{z}.") | |
8ab3d8a0 KR |
9478 | #define FUNC_NAME s_scm_log10 |
9479 | { | |
9480 | if (SCM_COMPLEXP (z)) | |
9481 | { | |
9482 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
9483 | clog() and a multiply by M_LOG10E, rather than the fallback | |
9484 | log10+hypot+atan2.) */ | |
f328f862 LC |
9485 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_CLOG10 \ |
9486 | && defined SCM_COMPLEX_VALUE | |
8ab3d8a0 KR |
9487 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
9488 | #else | |
9489 | double re = SCM_COMPLEX_REAL (z); | |
9490 | double im = SCM_COMPLEX_IMAG (z); | |
9491 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
9492 | M_LOG10E * atan2 (im, re)); | |
9493 | #endif | |
9494 | } | |
a5f6b751 | 9495 | else if (SCM_REALP (z) || SCM_I_INUMP (z)) |
8ab3d8a0 | 9496 | { |
a5f6b751 MW |
9497 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
9498 | if (scm_is_eq (z, SCM_INUM0)) | |
9499 | scm_num_overflow (s_scm_log10); | |
9500 | #endif | |
9501 | { | |
9502 | double re = scm_to_double (z); | |
9503 | double l = log10 (fabs (re)); | |
9504 | if (re > 0.0 || double_is_non_negative_zero (re)) | |
9505 | return scm_from_double (l); | |
9506 | else | |
9507 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
9508 | } | |
8ab3d8a0 | 9509 | } |
a5f6b751 MW |
9510 | else if (SCM_BIGP (z)) |
9511 | return scm_product (flo_log10e, log_of_exact_integer (z)); | |
9512 | else if (SCM_FRACTIONP (z)) | |
9513 | return scm_product (flo_log10e, | |
9514 | log_of_fraction (SCM_FRACTION_NUMERATOR (z), | |
9515 | SCM_FRACTION_DENOMINATOR (z))); | |
2519490c MW |
9516 | else |
9517 | SCM_WTA_DISPATCH_1 (g_scm_log10, z, 1, s_scm_log10); | |
8ab3d8a0 KR |
9518 | } |
9519 | #undef FUNC_NAME | |
9520 | ||
9521 | ||
2519490c MW |
9522 | SCM_PRIMITIVE_GENERIC (scm_exp, "exp", 1, 0, 0, |
9523 | (SCM z), | |
9524 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
9525 | "base of natural logarithms (2.71828@dots{}).") | |
8ab3d8a0 KR |
9526 | #define FUNC_NAME s_scm_exp |
9527 | { | |
9528 | if (SCM_COMPLEXP (z)) | |
9529 | { | |
4b26c03e | 9530 | #if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
9531 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
9532 | #else | |
9533 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
9534 | SCM_COMPLEX_IMAG (z)); | |
9535 | #endif | |
9536 | } | |
2519490c | 9537 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 KR |
9538 | { |
9539 | /* When z is a negative bignum the conversion to double overflows, | |
9540 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
9541 | return scm_from_double (exp (scm_to_double (z))); | |
9542 | } | |
2519490c MW |
9543 | else |
9544 | SCM_WTA_DISPATCH_1 (g_scm_exp, z, 1, s_scm_exp); | |
8ab3d8a0 KR |
9545 | } |
9546 | #undef FUNC_NAME | |
9547 | ||
9548 | ||
2519490c MW |
9549 | SCM_PRIMITIVE_GENERIC (scm_sqrt, "sqrt", 1, 0, 0, |
9550 | (SCM z), | |
9551 | "Return the square root of @var{z}. Of the two possible roots\n" | |
ffb62a43 | 9552 | "(positive and negative), the one with positive real part\n" |
2519490c MW |
9553 | "is returned, or if that's zero then a positive imaginary part.\n" |
9554 | "Thus,\n" | |
9555 | "\n" | |
9556 | "@example\n" | |
9557 | "(sqrt 9.0) @result{} 3.0\n" | |
9558 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
9559 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
9560 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
9561 | "@end example") | |
8ab3d8a0 KR |
9562 | #define FUNC_NAME s_scm_sqrt |
9563 | { | |
2519490c | 9564 | if (SCM_COMPLEXP (z)) |
8ab3d8a0 | 9565 | { |
f328f862 LC |
9566 | #if defined HAVE_COMPLEX_DOUBLE && defined HAVE_USABLE_CSQRT \ |
9567 | && defined SCM_COMPLEX_VALUE | |
2519490c | 9568 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (z))); |
8ab3d8a0 | 9569 | #else |
2519490c MW |
9570 | double re = SCM_COMPLEX_REAL (z); |
9571 | double im = SCM_COMPLEX_IMAG (z); | |
8ab3d8a0 KR |
9572 | return scm_c_make_polar (sqrt (hypot (re, im)), |
9573 | 0.5 * atan2 (im, re)); | |
9574 | #endif | |
9575 | } | |
2519490c | 9576 | else if (SCM_NUMBERP (z)) |
8ab3d8a0 | 9577 | { |
2519490c | 9578 | double xx = scm_to_double (z); |
8ab3d8a0 KR |
9579 | if (xx < 0) |
9580 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
9581 | else | |
9582 | return scm_from_double (sqrt (xx)); | |
9583 | } | |
2519490c MW |
9584 | else |
9585 | SCM_WTA_DISPATCH_1 (g_scm_sqrt, z, 1, s_scm_sqrt); | |
8ab3d8a0 KR |
9586 | } |
9587 | #undef FUNC_NAME | |
9588 | ||
9589 | ||
9590 | ||
0f2d19dd JB |
9591 | void |
9592 | scm_init_numbers () | |
0f2d19dd | 9593 | { |
0b799eea MV |
9594 | int i; |
9595 | ||
713a4259 KR |
9596 | mpz_init_set_si (z_negative_one, -1); |
9597 | ||
a261c0e9 DH |
9598 | /* It may be possible to tune the performance of some algorithms by using |
9599 | * the following constants to avoid the creation of bignums. Please, before | |
9600 | * using these values, remember the two rules of program optimization: | |
9601 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 9602 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 9603 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 9604 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 9605 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 9606 | |
f3ae5d60 MD |
9607 | scm_add_feature ("complex"); |
9608 | scm_add_feature ("inexact"); | |
e7efe8e7 | 9609 | flo0 = scm_from_double (0.0); |
a5f6b751 | 9610 | flo_log10e = scm_from_double (M_LOG10E); |
0b799eea MV |
9611 | |
9612 | /* determine floating point precision */ | |
55f26379 | 9613 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
9614 | { |
9615 | init_dblprec(&scm_dblprec[i-2],i); | |
9616 | init_fx_radix(fx_per_radix[i-2],i); | |
9617 | } | |
f872b822 | 9618 | #ifdef DBL_DIG |
0b799eea | 9619 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
f39448c5 | 9620 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; |
0b799eea | 9621 | #endif |
1be6b49c | 9622 | |
cff5fa33 | 9623 | exactly_one_half = scm_divide (SCM_INUM1, SCM_I_MAKINUM (2)); |
a0599745 | 9624 | #include "libguile/numbers.x" |
0f2d19dd | 9625 | } |
89e00824 ML |
9626 | |
9627 | /* | |
9628 | Local Variables: | |
9629 | c-file-style: "gnu" | |
9630 | End: | |
9631 | */ |