Commit | Line | Data |
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189171c5 | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006, 2007, 2008 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 MV |
7 | * This library is free software; you can redistribute it and/or |
8 | * modify it under the terms of the GNU Lesser General Public | |
9 | * License as published by the Free Software Foundation; either | |
10 | * version 2.1 of the License, or (at your option) any later version. | |
0f2d19dd | 11 | * |
73be1d9e MV |
12 | * This library is distributed in the hope that it will be useful, |
13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
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 | |
92205699 | 19 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA |
73be1d9e | 20 | */ |
1bbd0b84 | 21 | |
0f2d19dd | 22 | \f |
ca46fb90 RB |
23 | /* General assumptions: |
24 | * All objects satisfying SCM_COMPLEXP() have a non-zero complex component. | |
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. | |
f92e85f7 | 28 | * All objects satisfying SCM_FRACTIONP are never an integer. |
ca46fb90 RB |
29 | */ |
30 | ||
31 | /* TODO: | |
32 | ||
33 | - see if special casing bignums and reals in integer-exponent when | |
34 | possible (to use mpz_pow and mpf_pow_ui) is faster. | |
35 | ||
36 | - look in to better short-circuiting of common cases in | |
37 | integer-expt and elsewhere. | |
38 | ||
39 | - see if direct mpz operations can help in ash and elsewhere. | |
40 | ||
41 | */ | |
0f2d19dd | 42 | |
dbb605f5 | 43 | #ifdef HAVE_CONFIG_H |
ee33d62a RB |
44 | # include <config.h> |
45 | #endif | |
46 | ||
0f2d19dd | 47 | #include <math.h> |
3c9a524f | 48 | #include <ctype.h> |
fc194577 | 49 | #include <string.h> |
f92e85f7 | 50 | |
8ab3d8a0 KR |
51 | #if HAVE_COMPLEX_H |
52 | #include <complex.h> | |
53 | #endif | |
54 | ||
a0599745 | 55 | #include "libguile/_scm.h" |
a0599745 MD |
56 | #include "libguile/feature.h" |
57 | #include "libguile/ports.h" | |
58 | #include "libguile/root.h" | |
59 | #include "libguile/smob.h" | |
60 | #include "libguile/strings.h" | |
a0599745 MD |
61 | |
62 | #include "libguile/validate.h" | |
63 | #include "libguile/numbers.h" | |
1be6b49c | 64 | #include "libguile/deprecation.h" |
f4c627b3 | 65 | |
f92e85f7 MV |
66 | #include "libguile/eq.h" |
67 | ||
55f26379 MV |
68 | #include "libguile/discouraged.h" |
69 | ||
8ab3d8a0 KR |
70 | /* values per glibc, if not already defined */ |
71 | #ifndef M_LOG10E | |
72 | #define M_LOG10E 0.43429448190325182765 | |
73 | #endif | |
74 | #ifndef M_PI | |
75 | #define M_PI 3.14159265358979323846 | |
76 | #endif | |
77 | ||
0f2d19dd | 78 | \f |
f4c627b3 | 79 | |
ca46fb90 RB |
80 | /* |
81 | Wonder if this might be faster for some of our code? A switch on | |
82 | the numtag would jump directly to the right case, and the | |
83 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
84 | ||
85 | #define SCM_I_NUMTAG_NOTNUM 0 | |
86 | #define SCM_I_NUMTAG_INUM 1 | |
87 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
88 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
89 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
90 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 91 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 92 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 93 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
94 | : SCM_I_NUMTAG_NOTNUM))) |
95 | */ | |
f92e85f7 | 96 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
97 | |
98 | ||
34d19ef6 | 99 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 100 | |
56e55ac7 | 101 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
102 | * printed or scm_string representation of an inexact number. |
103 | */ | |
0b799eea | 104 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 105 | |
7351e207 MV |
106 | #if defined (SCO) |
107 | #if ! defined (HAVE_ISNAN) | |
108 | #define HAVE_ISNAN | |
109 | static int | |
110 | isnan (double x) | |
111 | { | |
112 | return (IsNANorINF (x) && NaN (x) && ! IsINF (x)) ? 1 : 0; | |
113 | } | |
0f2d19dd | 114 | #endif |
7351e207 MV |
115 | #if ! defined (HAVE_ISINF) |
116 | #define HAVE_ISINF | |
117 | static int | |
118 | isinf (double x) | |
119 | { | |
120 | return (IsNANorINF (x) && IsINF (x)) ? 1 : 0; | |
121 | } | |
0f2d19dd | 122 | |
7351e207 | 123 | #endif |
e6f3ef58 MD |
124 | #endif |
125 | ||
b127c712 | 126 | |
f8a8200b KR |
127 | /* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses |
128 | an explicit check. In some future gmp (don't know what version number), | |
129 | mpz_cmp_d is supposed to do this itself. */ | |
130 | #if 1 | |
b127c712 KR |
131 | #define xmpz_cmp_d(z, d) \ |
132 | (xisinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) | |
133 | #else | |
134 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
135 | #endif | |
136 | ||
a98ce907 KR |
137 | /* For reference, sparc solaris 7 has infinities (IEEE) but doesn't have |
138 | isinf. It does have finite and isnan though, hence the use of those. | |
139 | fpclass would be a possibility on that system too. */ | |
f92e85f7 MV |
140 | static int |
141 | xisinf (double x) | |
142 | { | |
143 | #if defined (HAVE_ISINF) | |
144 | return isinf (x); | |
145 | #elif defined (HAVE_FINITE) && defined (HAVE_ISNAN) | |
146 | return (! (finite (x) || isnan (x))); | |
147 | #else | |
148 | return 0; | |
149 | #endif | |
150 | } | |
151 | ||
152 | static int | |
153 | xisnan (double x) | |
154 | { | |
155 | #if defined (HAVE_ISNAN) | |
156 | return isnan (x); | |
157 | #else | |
158 | return 0; | |
159 | #endif | |
160 | } | |
161 | ||
4b26c03e | 162 | #if defined (GUILE_I) |
bca69a9f NJ |
163 | #if HAVE_COMPLEX_DOUBLE |
164 | ||
8ab3d8a0 KR |
165 | /* For an SCM object Z which is a complex number (ie. satisfies |
166 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
167 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 168 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 | 169 | |
7a35784c LC |
170 | static inline SCM scm_from_complex_double (complex double z) SCM_UNUSED; |
171 | ||
8ab3d8a0 | 172 | /* Convert a C "complex double" to an SCM value. */ |
7a35784c | 173 | static inline SCM |
8ab3d8a0 KR |
174 | scm_from_complex_double (complex double z) |
175 | { | |
176 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
177 | } | |
bca69a9f | 178 | |
8ab3d8a0 | 179 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 180 | #endif /* GUILE_I */ |
8ab3d8a0 | 181 | |
0f2d19dd JB |
182 | \f |
183 | ||
713a4259 | 184 | static mpz_t z_negative_one; |
ac0c002c DH |
185 | |
186 | \f | |
187 | ||
189171c5 | 188 | SCM |
ca46fb90 RB |
189 | scm_i_mkbig () |
190 | { | |
191 | /* Return a newly created bignum. */ | |
192 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
193 | mpz_init (SCM_I_BIG_MPZ (z)); | |
194 | return z; | |
195 | } | |
196 | ||
189171c5 | 197 | SCM |
c71b0706 MV |
198 | scm_i_long2big (long x) |
199 | { | |
200 | /* Return a newly created bignum initialized to X. */ | |
201 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
202 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
203 | return z; | |
204 | } | |
205 | ||
189171c5 | 206 | SCM |
c71b0706 MV |
207 | scm_i_ulong2big (unsigned long x) |
208 | { | |
209 | /* Return a newly created bignum initialized to X. */ | |
210 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
211 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); | |
212 | return z; | |
213 | } | |
214 | ||
189171c5 | 215 | SCM |
ca46fb90 RB |
216 | scm_i_clonebig (SCM src_big, int same_sign_p) |
217 | { | |
218 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
219 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
220 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); | |
0aacf84e MD |
221 | if (!same_sign_p) |
222 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
223 | return z; |
224 | } | |
225 | ||
189171c5 | 226 | int |
ca46fb90 RB |
227 | scm_i_bigcmp (SCM x, SCM y) |
228 | { | |
229 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
230 | /* presume we already know x and y are bignums */ | |
231 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
232 | scm_remember_upto_here_2 (x, y); | |
233 | return result; | |
234 | } | |
235 | ||
189171c5 | 236 | SCM |
ca46fb90 RB |
237 | scm_i_dbl2big (double d) |
238 | { | |
239 | /* results are only defined if d is an integer */ | |
240 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
241 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); | |
242 | return z; | |
243 | } | |
244 | ||
f92e85f7 MV |
245 | /* Convert a integer in double representation to a SCM number. */ |
246 | ||
189171c5 | 247 | SCM |
f92e85f7 MV |
248 | scm_i_dbl2num (double u) |
249 | { | |
250 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
251 | powers of 2, so there's no rounding when making "double" values | |
252 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
253 | get rounded on a 64-bit machine, hence the "+1". | |
254 | ||
255 | The use of floor() to force to an integer value ensures we get a | |
256 | "numerically closest" value without depending on how a | |
257 | double->long cast or how mpz_set_d will round. For reference, | |
258 | double->long probably follows the hardware rounding mode, | |
259 | mpz_set_d truncates towards zero. */ | |
260 | ||
261 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
262 | representable as a double? */ | |
263 | ||
264 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
265 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
d956fa6f | 266 | return SCM_I_MAKINUM ((long) u); |
f92e85f7 MV |
267 | else |
268 | return scm_i_dbl2big (u); | |
269 | } | |
270 | ||
089c9a59 KR |
271 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
272 | with R5RS exact->inexact. | |
273 | ||
274 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
275 | (ie. truncate towards zero), then adjust to get the closest double by |
276 | examining the next lower bit and adding 1 (to the absolute value) if | |
277 | necessary. | |
278 | ||
279 | Bignums exactly half way between representable doubles are rounded to the | |
280 | next higher absolute value (ie. away from zero). This seems like an | |
281 | adequate interpretation of R5RS "numerically closest", and it's easier | |
282 | and faster than a full "nearest-even" style. | |
283 | ||
284 | The bit test must be done on the absolute value of the mpz_t, which means | |
285 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
286 | negatives as twos complement. | |
287 | ||
288 | In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up | |
289 | following the hardware rounding mode, but applied to the absolute value | |
290 | of the mpz_t operand. This is not what we want so we put the high | |
291 | DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when, | |
292 | mpz_get_d is supposed to always truncate towards zero. | |
293 | ||
294 | ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3 | |
295 | is a slowdown. It'd be faster to pick out the relevant high bits with | |
296 | mpz_getlimbn if we could be bothered coding that, and if the new | |
297 | truncating gmp doesn't come out. */ | |
089c9a59 KR |
298 | |
299 | double | |
ca46fb90 RB |
300 | scm_i_big2dbl (SCM b) |
301 | { | |
089c9a59 KR |
302 | double result; |
303 | size_t bits; | |
304 | ||
305 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
306 | ||
f8a8200b | 307 | #if 1 |
089c9a59 | 308 | { |
f8a8200b | 309 | /* Current GMP, eg. 4.1.3, force truncation towards zero */ |
089c9a59 KR |
310 | mpz_t tmp; |
311 | if (bits > DBL_MANT_DIG) | |
312 | { | |
313 | size_t shift = bits - DBL_MANT_DIG; | |
314 | mpz_init2 (tmp, DBL_MANT_DIG); | |
315 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
316 | result = ldexp (mpz_get_d (tmp), shift); | |
317 | mpz_clear (tmp); | |
318 | } | |
319 | else | |
320 | { | |
321 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
322 | } | |
323 | } | |
324 | #else | |
f8a8200b | 325 | /* Future GMP */ |
089c9a59 KR |
326 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
327 | #endif | |
328 | ||
329 | if (bits > DBL_MANT_DIG) | |
330 | { | |
331 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
332 | /* test bit number "pos" in absolute value */ | |
333 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
334 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
335 | { | |
336 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
337 | } | |
338 | } | |
339 | ||
ca46fb90 RB |
340 | scm_remember_upto_here_1 (b); |
341 | return result; | |
342 | } | |
343 | ||
189171c5 | 344 | SCM |
ca46fb90 RB |
345 | scm_i_normbig (SCM b) |
346 | { | |
347 | /* convert a big back to a fixnum if it'll fit */ | |
348 | /* presume b is a bignum */ | |
349 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
350 | { | |
351 | long val = mpz_get_si (SCM_I_BIG_MPZ (b)); | |
352 | if (SCM_FIXABLE (val)) | |
d956fa6f | 353 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
354 | } |
355 | return b; | |
356 | } | |
f872b822 | 357 | |
f92e85f7 MV |
358 | static SCM_C_INLINE_KEYWORD SCM |
359 | scm_i_mpz2num (mpz_t b) | |
360 | { | |
361 | /* convert a mpz number to a SCM number. */ | |
362 | if (mpz_fits_slong_p (b)) | |
363 | { | |
364 | long val = mpz_get_si (b); | |
365 | if (SCM_FIXABLE (val)) | |
d956fa6f | 366 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
367 | } |
368 | ||
369 | { | |
370 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
371 | mpz_init_set (SCM_I_BIG_MPZ (z), b); | |
372 | return z; | |
373 | } | |
374 | } | |
375 | ||
376 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
377 | static SCM scm_divide2real (SCM x, SCM y); | |
378 | ||
cba42c93 MV |
379 | static SCM |
380 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 381 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 382 | { |
c60e130c MV |
383 | /* First make sure the arguments are proper. |
384 | */ | |
e11e83f3 | 385 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 386 | { |
bc36d050 | 387 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 388 | scm_num_overflow ("make-ratio"); |
bc36d050 | 389 | if (scm_is_eq (denominator, SCM_I_MAKINUM(1))) |
f92e85f7 MV |
390 | return numerator; |
391 | } | |
392 | else | |
393 | { | |
394 | if (!(SCM_BIGP(denominator))) | |
395 | SCM_WRONG_TYPE_ARG (2, denominator); | |
396 | } | |
e11e83f3 | 397 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
398 | SCM_WRONG_TYPE_ARG (1, numerator); |
399 | ||
400 | /* Then flip signs so that the denominator is positive. | |
401 | */ | |
73e4de09 | 402 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
403 | { |
404 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
405 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
406 | } | |
407 | ||
408 | /* Now consider for each of the four fixnum/bignum combinations | |
409 | whether the rational number is really an integer. | |
410 | */ | |
e11e83f3 | 411 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 412 | { |
e11e83f3 | 413 | long x = SCM_I_INUM (numerator); |
bc36d050 | 414 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 415 | return SCM_INUM0; |
e11e83f3 | 416 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 417 | { |
dd5130ca | 418 | long y; |
e11e83f3 | 419 | y = SCM_I_INUM (denominator); |
f92e85f7 | 420 | if (x == y) |
d956fa6f | 421 | return SCM_I_MAKINUM(1); |
f92e85f7 | 422 | if ((x % y) == 0) |
d956fa6f | 423 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 424 | } |
dd5130ca KR |
425 | else |
426 | { | |
427 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
428 | of that value for the denominator, as a bignum. Apart from |
429 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
430 | integer. */ | |
431 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
432 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
433 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 434 | return SCM_I_MAKINUM(-1); |
dd5130ca | 435 | } |
f92e85f7 | 436 | } |
c60e130c | 437 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 438 | { |
e11e83f3 | 439 | if (SCM_I_INUMP (denominator)) |
c60e130c | 440 | { |
e11e83f3 | 441 | long yy = SCM_I_INUM (denominator); |
c60e130c MV |
442 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
443 | return scm_divide (numerator, denominator); | |
444 | } | |
445 | else | |
f92e85f7 | 446 | { |
bc36d050 | 447 | if (scm_is_eq (numerator, denominator)) |
d956fa6f | 448 | return SCM_I_MAKINUM(1); |
c60e130c MV |
449 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
450 | SCM_I_BIG_MPZ (denominator))) | |
451 | return scm_divide(numerator, denominator); | |
f92e85f7 | 452 | } |
f92e85f7 | 453 | } |
c60e130c MV |
454 | |
455 | /* No, it's a proper fraction. | |
456 | */ | |
e2bf3b19 HWN |
457 | { |
458 | SCM divisor = scm_gcd (numerator, denominator); | |
459 | if (!(scm_is_eq (divisor, SCM_I_MAKINUM(1)))) | |
460 | { | |
461 | numerator = scm_divide (numerator, divisor); | |
462 | denominator = scm_divide (denominator, divisor); | |
463 | } | |
464 | ||
465 | return scm_double_cell (scm_tc16_fraction, | |
466 | SCM_UNPACK (numerator), | |
467 | SCM_UNPACK (denominator), 0); | |
468 | } | |
f92e85f7 | 469 | } |
c60e130c | 470 | #undef FUNC_NAME |
f92e85f7 | 471 | |
f92e85f7 MV |
472 | double |
473 | scm_i_fraction2double (SCM z) | |
474 | { | |
55f26379 MV |
475 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
476 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
477 | } |
478 | ||
a1ec6916 | 479 | SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0, |
1bbd0b84 | 480 | (SCM x), |
942e5b91 MG |
481 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
482 | "otherwise.") | |
1bbd0b84 | 483 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 484 | { |
e11e83f3 | 485 | if (SCM_I_INUMP (x)) |
0aacf84e MD |
486 | return SCM_BOOL_T; |
487 | if (SCM_BIGP (x)) | |
488 | return SCM_BOOL_T; | |
f92e85f7 MV |
489 | if (SCM_FRACTIONP (x)) |
490 | return SCM_BOOL_T; | |
eb927cb9 MV |
491 | if (SCM_NUMBERP (x)) |
492 | return SCM_BOOL_F; | |
493 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 494 | } |
1bbd0b84 | 495 | #undef FUNC_NAME |
0f2d19dd | 496 | |
4219f20d | 497 | |
a1ec6916 | 498 | SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 499 | (SCM n), |
942e5b91 MG |
500 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
501 | "otherwise.") | |
1bbd0b84 | 502 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 503 | { |
e11e83f3 | 504 | if (SCM_I_INUMP (n)) |
0aacf84e | 505 | { |
e11e83f3 | 506 | long val = SCM_I_INUM (n); |
73e4de09 | 507 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
508 | } |
509 | else if (SCM_BIGP (n)) | |
510 | { | |
511 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
512 | scm_remember_upto_here_1 (n); | |
73e4de09 | 513 | return scm_from_bool (odd_p); |
0aacf84e | 514 | } |
73e4de09 | 515 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 516 | return SCM_BOOL_T; |
f92e85f7 MV |
517 | else if (SCM_REALP (n)) |
518 | { | |
519 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
520 | if (rem == 1.0) | |
521 | return SCM_BOOL_T; | |
522 | else if (rem == 0.0) | |
523 | return SCM_BOOL_F; | |
524 | else | |
525 | SCM_WRONG_TYPE_ARG (1, n); | |
526 | } | |
0aacf84e | 527 | else |
a1a33b0f | 528 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 529 | } |
1bbd0b84 | 530 | #undef FUNC_NAME |
0f2d19dd | 531 | |
4219f20d | 532 | |
a1ec6916 | 533 | SCM_DEFINE (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 534 | (SCM n), |
942e5b91 MG |
535 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
536 | "otherwise.") | |
1bbd0b84 | 537 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 538 | { |
e11e83f3 | 539 | if (SCM_I_INUMP (n)) |
0aacf84e | 540 | { |
e11e83f3 | 541 | long val = SCM_I_INUM (n); |
73e4de09 | 542 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
543 | } |
544 | else if (SCM_BIGP (n)) | |
545 | { | |
546 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
547 | scm_remember_upto_here_1 (n); | |
73e4de09 | 548 | return scm_from_bool (even_p); |
0aacf84e | 549 | } |
73e4de09 | 550 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 551 | return SCM_BOOL_T; |
f92e85f7 MV |
552 | else if (SCM_REALP (n)) |
553 | { | |
554 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
555 | if (rem == 1.0) | |
556 | return SCM_BOOL_F; | |
557 | else if (rem == 0.0) | |
558 | return SCM_BOOL_T; | |
559 | else | |
560 | SCM_WRONG_TYPE_ARG (1, n); | |
561 | } | |
0aacf84e | 562 | else |
a1a33b0f | 563 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 564 | } |
1bbd0b84 | 565 | #undef FUNC_NAME |
0f2d19dd | 566 | |
7351e207 | 567 | SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0, |
b1092b3a MV |
568 | (SCM x), |
569 | "Return @code{#t} if @var{x} is either @samp{+inf.0}\n" | |
570 | "or @samp{-inf.0}, @code{#f} otherwise.") | |
7351e207 MV |
571 | #define FUNC_NAME s_scm_inf_p |
572 | { | |
b1092b3a MV |
573 | if (SCM_REALP (x)) |
574 | return scm_from_bool (xisinf (SCM_REAL_VALUE (x))); | |
575 | else if (SCM_COMPLEXP (x)) | |
576 | return scm_from_bool (xisinf (SCM_COMPLEX_REAL (x)) | |
577 | || xisinf (SCM_COMPLEX_IMAG (x))); | |
0aacf84e | 578 | else |
7351e207 | 579 | return SCM_BOOL_F; |
7351e207 MV |
580 | } |
581 | #undef FUNC_NAME | |
582 | ||
583 | SCM_DEFINE (scm_nan_p, "nan?", 1, 0, 0, | |
584 | (SCM n), | |
585 | "Return @code{#t} if @var{n} is a NaN, @code{#f}\n" | |
586 | "otherwise.") | |
587 | #define FUNC_NAME s_scm_nan_p | |
588 | { | |
0aacf84e | 589 | if (SCM_REALP (n)) |
73e4de09 | 590 | return scm_from_bool (xisnan (SCM_REAL_VALUE (n))); |
0aacf84e | 591 | else if (SCM_COMPLEXP (n)) |
73e4de09 | 592 | return scm_from_bool (xisnan (SCM_COMPLEX_REAL (n)) |
7351e207 | 593 | || xisnan (SCM_COMPLEX_IMAG (n))); |
0aacf84e | 594 | else |
7351e207 | 595 | return SCM_BOOL_F; |
7351e207 MV |
596 | } |
597 | #undef FUNC_NAME | |
598 | ||
599 | /* Guile's idea of infinity. */ | |
600 | static double guile_Inf; | |
601 | ||
602 | /* Guile's idea of not a number. */ | |
603 | static double guile_NaN; | |
604 | ||
605 | static void | |
606 | guile_ieee_init (void) | |
607 | { | |
608 | #if defined (HAVE_ISINF) || defined (HAVE_FINITE) | |
609 | ||
610 | /* Some version of gcc on some old version of Linux used to crash when | |
611 | trying to make Inf and NaN. */ | |
612 | ||
240a27d2 KR |
613 | #ifdef INFINITY |
614 | /* C99 INFINITY, when available. | |
615 | FIXME: The standard allows for INFINITY to be something that overflows | |
616 | at compile time. We ought to have a configure test to check for that | |
617 | before trying to use it. (But in practice we believe this is not a | |
618 | problem on any system guile is likely to target.) */ | |
619 | guile_Inf = INFINITY; | |
620 | #elif HAVE_DINFINITY | |
621 | /* OSF */ | |
7351e207 | 622 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 623 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
624 | #else |
625 | double tmp = 1e+10; | |
626 | guile_Inf = tmp; | |
627 | for (;;) | |
628 | { | |
629 | guile_Inf *= 1e+10; | |
630 | if (guile_Inf == tmp) | |
631 | break; | |
632 | tmp = guile_Inf; | |
633 | } | |
634 | #endif | |
635 | ||
636 | #endif | |
637 | ||
638 | #if defined (HAVE_ISNAN) | |
639 | ||
240a27d2 KR |
640 | #ifdef NAN |
641 | /* C99 NAN, when available */ | |
642 | guile_NaN = NAN; | |
643 | #elif HAVE_DQNAN | |
eaa94eaa LC |
644 | { |
645 | /* OSF */ | |
646 | extern unsigned int DQNAN[2]; | |
647 | guile_NaN = (*((double *)(DQNAN))); | |
648 | } | |
7351e207 MV |
649 | #else |
650 | guile_NaN = guile_Inf / guile_Inf; | |
651 | #endif | |
652 | ||
653 | #endif | |
654 | } | |
655 | ||
656 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
657 | (void), | |
658 | "Return Inf.") | |
659 | #define FUNC_NAME s_scm_inf | |
660 | { | |
661 | static int initialized = 0; | |
662 | if (! initialized) | |
663 | { | |
664 | guile_ieee_init (); | |
665 | initialized = 1; | |
666 | } | |
55f26379 | 667 | return scm_from_double (guile_Inf); |
7351e207 MV |
668 | } |
669 | #undef FUNC_NAME | |
670 | ||
671 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
672 | (void), | |
673 | "Return NaN.") | |
674 | #define FUNC_NAME s_scm_nan | |
675 | { | |
676 | static int initialized = 0; | |
0aacf84e | 677 | if (!initialized) |
7351e207 MV |
678 | { |
679 | guile_ieee_init (); | |
680 | initialized = 1; | |
681 | } | |
55f26379 | 682 | return scm_from_double (guile_NaN); |
7351e207 MV |
683 | } |
684 | #undef FUNC_NAME | |
685 | ||
4219f20d | 686 | |
a48d60b1 MD |
687 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
688 | (SCM x), | |
689 | "Return the absolute value of @var{x}.") | |
690 | #define FUNC_NAME | |
0f2d19dd | 691 | { |
e11e83f3 | 692 | if (SCM_I_INUMP (x)) |
0aacf84e | 693 | { |
e11e83f3 | 694 | long int xx = SCM_I_INUM (x); |
0aacf84e MD |
695 | if (xx >= 0) |
696 | return x; | |
697 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 698 | return SCM_I_MAKINUM (-xx); |
0aacf84e MD |
699 | else |
700 | return scm_i_long2big (-xx); | |
4219f20d | 701 | } |
0aacf84e MD |
702 | else if (SCM_BIGP (x)) |
703 | { | |
704 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
705 | if (sgn < 0) | |
706 | return scm_i_clonebig (x, 0); | |
707 | else | |
708 | return x; | |
4219f20d | 709 | } |
0aacf84e | 710 | else if (SCM_REALP (x)) |
ae38324d KR |
711 | { |
712 | /* note that if x is a NaN then xx<0 is false so we return x unchanged */ | |
713 | double xx = SCM_REAL_VALUE (x); | |
714 | if (xx < 0.0) | |
55f26379 | 715 | return scm_from_double (-xx); |
ae38324d KR |
716 | else |
717 | return x; | |
718 | } | |
f92e85f7 MV |
719 | else if (SCM_FRACTIONP (x)) |
720 | { | |
73e4de09 | 721 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 722 | return x; |
cba42c93 | 723 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
724 | SCM_FRACTION_DENOMINATOR (x)); |
725 | } | |
0aacf84e | 726 | else |
a48d60b1 | 727 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 728 | } |
a48d60b1 | 729 | #undef FUNC_NAME |
0f2d19dd | 730 | |
4219f20d | 731 | |
9de33deb | 732 | SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); |
942e5b91 MG |
733 | /* "Return the quotient of the numbers @var{x} and @var{y}." |
734 | */ | |
0f2d19dd | 735 | SCM |
6e8d25a6 | 736 | scm_quotient (SCM x, SCM y) |
0f2d19dd | 737 | { |
e11e83f3 | 738 | if (SCM_I_INUMP (x)) |
0aacf84e | 739 | { |
e11e83f3 MV |
740 | long xx = SCM_I_INUM (x); |
741 | if (SCM_I_INUMP (y)) | |
0aacf84e | 742 | { |
e11e83f3 | 743 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
744 | if (yy == 0) |
745 | scm_num_overflow (s_quotient); | |
746 | else | |
747 | { | |
748 | long z = xx / yy; | |
749 | if (SCM_FIXABLE (z)) | |
d956fa6f | 750 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
751 | else |
752 | return scm_i_long2big (z); | |
753 | } | |
828865c3 | 754 | } |
0aacf84e | 755 | else if (SCM_BIGP (y)) |
ac0c002c | 756 | { |
e11e83f3 | 757 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
758 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
759 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
760 | { | |
761 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
762 | scm_remember_upto_here_1 (y); | |
d956fa6f | 763 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 764 | } |
0aacf84e | 765 | else |
d956fa6f | 766 | return SCM_I_MAKINUM (0); |
ac0c002c DH |
767 | } |
768 | else | |
0aacf84e | 769 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); |
828865c3 | 770 | } |
0aacf84e MD |
771 | else if (SCM_BIGP (x)) |
772 | { | |
e11e83f3 | 773 | if (SCM_I_INUMP (y)) |
0aacf84e | 774 | { |
e11e83f3 | 775 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
776 | if (yy == 0) |
777 | scm_num_overflow (s_quotient); | |
778 | else if (yy == 1) | |
779 | return x; | |
780 | else | |
781 | { | |
782 | SCM result = scm_i_mkbig (); | |
783 | if (yy < 0) | |
784 | { | |
785 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
786 | SCM_I_BIG_MPZ (x), | |
787 | - yy); | |
788 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
789 | } | |
790 | else | |
791 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
792 | scm_remember_upto_here_1 (x); | |
793 | return scm_i_normbig (result); | |
794 | } | |
795 | } | |
796 | else if (SCM_BIGP (y)) | |
797 | { | |
798 | SCM result = scm_i_mkbig (); | |
799 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
800 | SCM_I_BIG_MPZ (x), | |
801 | SCM_I_BIG_MPZ (y)); | |
802 | scm_remember_upto_here_2 (x, y); | |
803 | return scm_i_normbig (result); | |
804 | } | |
805 | else | |
806 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); | |
f872b822 | 807 | } |
0aacf84e | 808 | else |
89a7e495 | 809 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient); |
0f2d19dd JB |
810 | } |
811 | ||
9de33deb | 812 | SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); |
942e5b91 MG |
813 | /* "Return the remainder of the numbers @var{x} and @var{y}.\n" |
814 | * "@lisp\n" | |
815 | * "(remainder 13 4) @result{} 1\n" | |
816 | * "(remainder -13 4) @result{} -1\n" | |
817 | * "@end lisp" | |
818 | */ | |
0f2d19dd | 819 | SCM |
6e8d25a6 | 820 | scm_remainder (SCM x, SCM y) |
0f2d19dd | 821 | { |
e11e83f3 | 822 | if (SCM_I_INUMP (x)) |
0aacf84e | 823 | { |
e11e83f3 | 824 | if (SCM_I_INUMP (y)) |
0aacf84e | 825 | { |
e11e83f3 | 826 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
827 | if (yy == 0) |
828 | scm_num_overflow (s_remainder); | |
829 | else | |
830 | { | |
e11e83f3 | 831 | long z = SCM_I_INUM (x) % yy; |
d956fa6f | 832 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
833 | } |
834 | } | |
835 | else if (SCM_BIGP (y)) | |
ac0c002c | 836 | { |
e11e83f3 | 837 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
838 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
839 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
840 | { | |
841 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
842 | scm_remember_upto_here_1 (y); | |
d956fa6f | 843 | return SCM_I_MAKINUM (0); |
4dc09ee4 | 844 | } |
0aacf84e MD |
845 | else |
846 | return x; | |
ac0c002c DH |
847 | } |
848 | else | |
0aacf84e | 849 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); |
89a7e495 | 850 | } |
0aacf84e MD |
851 | else if (SCM_BIGP (x)) |
852 | { | |
e11e83f3 | 853 | if (SCM_I_INUMP (y)) |
0aacf84e | 854 | { |
e11e83f3 | 855 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
856 | if (yy == 0) |
857 | scm_num_overflow (s_remainder); | |
858 | else | |
859 | { | |
860 | SCM result = scm_i_mkbig (); | |
861 | if (yy < 0) | |
862 | yy = - yy; | |
863 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
864 | scm_remember_upto_here_1 (x); | |
865 | return scm_i_normbig (result); | |
866 | } | |
867 | } | |
868 | else if (SCM_BIGP (y)) | |
869 | { | |
870 | SCM result = scm_i_mkbig (); | |
871 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
872 | SCM_I_BIG_MPZ (x), | |
873 | SCM_I_BIG_MPZ (y)); | |
874 | scm_remember_upto_here_2 (x, y); | |
875 | return scm_i_normbig (result); | |
876 | } | |
877 | else | |
878 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); | |
f872b822 | 879 | } |
0aacf84e | 880 | else |
89a7e495 | 881 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder); |
0f2d19dd JB |
882 | } |
883 | ||
89a7e495 | 884 | |
9de33deb | 885 | SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); |
942e5b91 MG |
886 | /* "Return the modulo of the numbers @var{x} and @var{y}.\n" |
887 | * "@lisp\n" | |
888 | * "(modulo 13 4) @result{} 1\n" | |
889 | * "(modulo -13 4) @result{} 3\n" | |
890 | * "@end lisp" | |
891 | */ | |
0f2d19dd | 892 | SCM |
6e8d25a6 | 893 | scm_modulo (SCM x, SCM y) |
0f2d19dd | 894 | { |
e11e83f3 | 895 | if (SCM_I_INUMP (x)) |
0aacf84e | 896 | { |
e11e83f3 MV |
897 | long xx = SCM_I_INUM (x); |
898 | if (SCM_I_INUMP (y)) | |
0aacf84e | 899 | { |
e11e83f3 | 900 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
901 | if (yy == 0) |
902 | scm_num_overflow (s_modulo); | |
903 | else | |
904 | { | |
66b1c775 KR |
905 | /* C99 specifies that "%" is the remainder corresponding to a |
906 | quotient rounded towards zero, and that's also traditional | |
907 | for machine division, so z here should be well defined. */ | |
0aacf84e MD |
908 | long z = xx % yy; |
909 | long result; | |
910 | ||
911 | if (yy < 0) | |
912 | { | |
913 | if (z > 0) | |
914 | result = z + yy; | |
915 | else | |
916 | result = z; | |
917 | } | |
918 | else | |
919 | { | |
920 | if (z < 0) | |
921 | result = z + yy; | |
922 | else | |
923 | result = z; | |
924 | } | |
d956fa6f | 925 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
926 | } |
927 | } | |
928 | else if (SCM_BIGP (y)) | |
929 | { | |
930 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
931 | { |
932 | mpz_t z_x; | |
933 | SCM result; | |
934 | ||
935 | if (sgn_y < 0) | |
936 | { | |
937 | SCM pos_y = scm_i_clonebig (y, 0); | |
938 | /* do this after the last scm_op */ | |
939 | mpz_init_set_si (z_x, xx); | |
940 | result = pos_y; /* re-use this bignum */ | |
941 | mpz_mod (SCM_I_BIG_MPZ (result), | |
942 | z_x, | |
943 | SCM_I_BIG_MPZ (pos_y)); | |
944 | scm_remember_upto_here_1 (pos_y); | |
945 | } | |
946 | else | |
947 | { | |
948 | result = scm_i_mkbig (); | |
949 | /* do this after the last scm_op */ | |
950 | mpz_init_set_si (z_x, xx); | |
951 | mpz_mod (SCM_I_BIG_MPZ (result), | |
952 | z_x, | |
953 | SCM_I_BIG_MPZ (y)); | |
954 | scm_remember_upto_here_1 (y); | |
955 | } | |
ca46fb90 | 956 | |
0aacf84e MD |
957 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
958 | mpz_add (SCM_I_BIG_MPZ (result), | |
959 | SCM_I_BIG_MPZ (y), | |
960 | SCM_I_BIG_MPZ (result)); | |
961 | scm_remember_upto_here_1 (y); | |
962 | /* and do this before the next one */ | |
963 | mpz_clear (z_x); | |
964 | return scm_i_normbig (result); | |
965 | } | |
966 | } | |
967 | else | |
968 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
f872b822 | 969 | } |
0aacf84e MD |
970 | else if (SCM_BIGP (x)) |
971 | { | |
e11e83f3 | 972 | if (SCM_I_INUMP (y)) |
0aacf84e | 973 | { |
e11e83f3 | 974 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
975 | if (yy == 0) |
976 | scm_num_overflow (s_modulo); | |
977 | else | |
978 | { | |
979 | SCM result = scm_i_mkbig (); | |
980 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
981 | SCM_I_BIG_MPZ (x), | |
982 | (yy < 0) ? - yy : yy); | |
983 | scm_remember_upto_here_1 (x); | |
984 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
985 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
986 | SCM_I_BIG_MPZ (result), | |
987 | - yy); | |
988 | return scm_i_normbig (result); | |
989 | } | |
990 | } | |
991 | else if (SCM_BIGP (y)) | |
992 | { | |
0aacf84e MD |
993 | { |
994 | SCM result = scm_i_mkbig (); | |
995 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
996 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
997 | mpz_mod (SCM_I_BIG_MPZ (result), | |
998 | SCM_I_BIG_MPZ (x), | |
999 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 1000 | |
0aacf84e MD |
1001 | scm_remember_upto_here_1 (x); |
1002 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1003 | mpz_add (SCM_I_BIG_MPZ (result), | |
1004 | SCM_I_BIG_MPZ (y), | |
1005 | SCM_I_BIG_MPZ (result)); | |
1006 | scm_remember_upto_here_2 (y, pos_y); | |
1007 | return scm_i_normbig (result); | |
1008 | } | |
1009 | } | |
1010 | else | |
1011 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
828865c3 | 1012 | } |
0aacf84e | 1013 | else |
09fb7599 | 1014 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); |
0f2d19dd JB |
1015 | } |
1016 | ||
9de33deb | 1017 | SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd); |
942e5b91 MG |
1018 | /* "Return the greatest common divisor of all arguments.\n" |
1019 | * "If called without arguments, 0 is returned." | |
1020 | */ | |
0f2d19dd | 1021 | SCM |
6e8d25a6 | 1022 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 1023 | { |
ca46fb90 | 1024 | if (SCM_UNBNDP (y)) |
0aacf84e | 1025 | return SCM_UNBNDP (x) ? SCM_INUM0 : x; |
ca46fb90 | 1026 | |
e11e83f3 | 1027 | if (SCM_I_INUMP (x)) |
ca46fb90 | 1028 | { |
e11e83f3 | 1029 | if (SCM_I_INUMP (y)) |
ca46fb90 | 1030 | { |
e11e83f3 MV |
1031 | long xx = SCM_I_INUM (x); |
1032 | long yy = SCM_I_INUM (y); | |
ca46fb90 RB |
1033 | long u = xx < 0 ? -xx : xx; |
1034 | long v = yy < 0 ? -yy : yy; | |
1035 | long result; | |
0aacf84e MD |
1036 | if (xx == 0) |
1037 | result = v; | |
1038 | else if (yy == 0) | |
1039 | result = u; | |
1040 | else | |
1041 | { | |
1042 | long k = 1; | |
1043 | long t; | |
1044 | /* Determine a common factor 2^k */ | |
1045 | while (!(1 & (u | v))) | |
1046 | { | |
1047 | k <<= 1; | |
1048 | u >>= 1; | |
1049 | v >>= 1; | |
1050 | } | |
1051 | /* Now, any factor 2^n can be eliminated */ | |
1052 | if (u & 1) | |
1053 | t = -v; | |
1054 | else | |
1055 | { | |
1056 | t = u; | |
1057 | b3: | |
1058 | t = SCM_SRS (t, 1); | |
1059 | } | |
1060 | if (!(1 & t)) | |
1061 | goto b3; | |
1062 | if (t > 0) | |
1063 | u = t; | |
1064 | else | |
1065 | v = -t; | |
1066 | t = u - v; | |
1067 | if (t != 0) | |
1068 | goto b3; | |
1069 | result = u * k; | |
1070 | } | |
1071 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 1072 | ? SCM_I_MAKINUM (result) |
0aacf84e | 1073 | : scm_i_long2big (result)); |
ca46fb90 RB |
1074 | } |
1075 | else if (SCM_BIGP (y)) | |
1076 | { | |
0bff4dce KR |
1077 | SCM_SWAP (x, y); |
1078 | goto big_inum; | |
ca46fb90 RB |
1079 | } |
1080 | else | |
1081 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 1082 | } |
ca46fb90 RB |
1083 | else if (SCM_BIGP (x)) |
1084 | { | |
e11e83f3 | 1085 | if (SCM_I_INUMP (y)) |
ca46fb90 RB |
1086 | { |
1087 | unsigned long result; | |
0bff4dce KR |
1088 | long yy; |
1089 | big_inum: | |
e11e83f3 | 1090 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
1091 | if (yy == 0) |
1092 | return scm_abs (x); | |
0aacf84e MD |
1093 | if (yy < 0) |
1094 | yy = -yy; | |
ca46fb90 RB |
1095 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
1096 | scm_remember_upto_here_1 (x); | |
0aacf84e | 1097 | return (SCM_POSFIXABLE (result) |
d956fa6f | 1098 | ? SCM_I_MAKINUM (result) |
c71b0706 | 1099 | : scm_from_ulong (result)); |
ca46fb90 RB |
1100 | } |
1101 | else if (SCM_BIGP (y)) | |
1102 | { | |
1103 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
1104 | mpz_gcd (SCM_I_BIG_MPZ (result), |
1105 | SCM_I_BIG_MPZ (x), | |
1106 | SCM_I_BIG_MPZ (y)); | |
1107 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
1108 | return scm_i_normbig (result); |
1109 | } | |
1110 | else | |
1111 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 1112 | } |
ca46fb90 | 1113 | else |
09fb7599 | 1114 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
1115 | } |
1116 | ||
9de33deb | 1117 | SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm); |
942e5b91 MG |
1118 | /* "Return the least common multiple of the arguments.\n" |
1119 | * "If called without arguments, 1 is returned." | |
1120 | */ | |
0f2d19dd | 1121 | SCM |
6e8d25a6 | 1122 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 1123 | { |
ca46fb90 RB |
1124 | if (SCM_UNBNDP (n2)) |
1125 | { | |
1126 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
1127 | return SCM_I_MAKINUM (1L); |
1128 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 1129 | } |
09fb7599 | 1130 | |
e11e83f3 | 1131 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 1132 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 1133 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 1134 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 1135 | |
e11e83f3 | 1136 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 1137 | { |
e11e83f3 | 1138 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1139 | { |
1140 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 1141 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
1142 | return d; |
1143 | else | |
1144 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
1145 | } | |
1146 | else | |
1147 | { | |
1148 | /* inum n1, big n2 */ | |
1149 | inumbig: | |
1150 | { | |
1151 | SCM result = scm_i_mkbig (); | |
e11e83f3 | 1152 | long nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
1153 | if (nn1 == 0) return SCM_INUM0; |
1154 | if (nn1 < 0) nn1 = - nn1; | |
1155 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
1156 | scm_remember_upto_here_1 (n2); | |
1157 | return result; | |
1158 | } | |
1159 | } | |
1160 | } | |
1161 | else | |
1162 | { | |
1163 | /* big n1 */ | |
e11e83f3 | 1164 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1165 | { |
1166 | SCM_SWAP (n1, n2); | |
1167 | goto inumbig; | |
1168 | } | |
1169 | else | |
1170 | { | |
1171 | SCM result = scm_i_mkbig (); | |
1172 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
1173 | SCM_I_BIG_MPZ (n1), | |
1174 | SCM_I_BIG_MPZ (n2)); | |
1175 | scm_remember_upto_here_2(n1, n2); | |
1176 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
1177 | return result; | |
1178 | } | |
f872b822 | 1179 | } |
0f2d19dd JB |
1180 | } |
1181 | ||
8a525303 GB |
1182 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
1183 | ||
1184 | Logand: | |
1185 | X Y Result Method: | |
1186 | (len) | |
1187 | + + + x (map digit:logand X Y) | |
1188 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
1189 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
1190 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
1191 | ||
1192 | Logior: | |
1193 | X Y Result Method: | |
1194 | ||
1195 | + + + (map digit:logior X Y) | |
1196 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
1197 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
1198 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
1199 | ||
1200 | Logxor: | |
1201 | X Y Result Method: | |
1202 | ||
1203 | + + + (map digit:logxor X Y) | |
1204 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
1205 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
1206 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
1207 | ||
1208 | Logtest: | |
1209 | X Y Result | |
1210 | ||
1211 | + + (any digit:logand X Y) | |
1212 | + - (any digit:logand X (lognot (+ -1 Y))) | |
1213 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
1214 | - - #t | |
1215 | ||
1216 | */ | |
1217 | ||
c3ee7520 | 1218 | SCM_DEFINE1 (scm_logand, "logand", scm_tc7_asubr, |
1bbd0b84 | 1219 | (SCM n1, SCM n2), |
3c3db128 GH |
1220 | "Return the bitwise AND of the integer arguments.\n\n" |
1221 | "@lisp\n" | |
1222 | "(logand) @result{} -1\n" | |
1223 | "(logand 7) @result{} 7\n" | |
535f2a51 | 1224 | "(logand #b111 #b011 #b001) @result{} 1\n" |
3c3db128 | 1225 | "@end lisp") |
1bbd0b84 | 1226 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 1227 | { |
9a00c9fc DH |
1228 | long int nn1; |
1229 | ||
0aacf84e MD |
1230 | if (SCM_UNBNDP (n2)) |
1231 | { | |
1232 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 1233 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
1234 | else if (!SCM_NUMBERP (n1)) |
1235 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1236 | else if (SCM_NUMBERP (n1)) | |
1237 | return n1; | |
1238 | else | |
1239 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1240 | } |
09fb7599 | 1241 | |
e11e83f3 | 1242 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1243 | { |
e11e83f3 MV |
1244 | nn1 = SCM_I_INUM (n1); |
1245 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1246 | { |
e11e83f3 | 1247 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1248 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
1249 | } |
1250 | else if SCM_BIGP (n2) | |
1251 | { | |
1252 | intbig: | |
1253 | if (n1 == 0) | |
1254 | return SCM_INUM0; | |
1255 | { | |
1256 | SCM result_z = scm_i_mkbig (); | |
1257 | mpz_t nn1_z; | |
1258 | mpz_init_set_si (nn1_z, nn1); | |
1259 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1260 | scm_remember_upto_here_1 (n2); | |
1261 | mpz_clear (nn1_z); | |
1262 | return scm_i_normbig (result_z); | |
1263 | } | |
1264 | } | |
1265 | else | |
1266 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1267 | } | |
1268 | else if (SCM_BIGP (n1)) | |
1269 | { | |
e11e83f3 | 1270 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1271 | { |
1272 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1273 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1274 | goto intbig; |
1275 | } | |
1276 | else if (SCM_BIGP (n2)) | |
1277 | { | |
1278 | SCM result_z = scm_i_mkbig (); | |
1279 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
1280 | SCM_I_BIG_MPZ (n1), | |
1281 | SCM_I_BIG_MPZ (n2)); | |
1282 | scm_remember_upto_here_2 (n1, n2); | |
1283 | return scm_i_normbig (result_z); | |
1284 | } | |
1285 | else | |
1286 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1287 | } |
0aacf84e | 1288 | else |
09fb7599 | 1289 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1290 | } |
1bbd0b84 | 1291 | #undef FUNC_NAME |
0f2d19dd | 1292 | |
09fb7599 | 1293 | |
c3ee7520 | 1294 | SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr, |
1bbd0b84 | 1295 | (SCM n1, SCM n2), |
3c3db128 GH |
1296 | "Return the bitwise OR of the integer arguments.\n\n" |
1297 | "@lisp\n" | |
1298 | "(logior) @result{} 0\n" | |
1299 | "(logior 7) @result{} 7\n" | |
1300 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1e6808ea | 1301 | "@end lisp") |
1bbd0b84 | 1302 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 1303 | { |
9a00c9fc DH |
1304 | long int nn1; |
1305 | ||
0aacf84e MD |
1306 | if (SCM_UNBNDP (n2)) |
1307 | { | |
1308 | if (SCM_UNBNDP (n1)) | |
1309 | return SCM_INUM0; | |
1310 | else if (SCM_NUMBERP (n1)) | |
1311 | return n1; | |
1312 | else | |
1313 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1314 | } |
09fb7599 | 1315 | |
e11e83f3 | 1316 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1317 | { |
e11e83f3 MV |
1318 | nn1 = SCM_I_INUM (n1); |
1319 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1320 | { |
e11e83f3 | 1321 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1322 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
1323 | } |
1324 | else if (SCM_BIGP (n2)) | |
1325 | { | |
1326 | intbig: | |
1327 | if (nn1 == 0) | |
1328 | return n2; | |
1329 | { | |
1330 | SCM result_z = scm_i_mkbig (); | |
1331 | mpz_t nn1_z; | |
1332 | mpz_init_set_si (nn1_z, nn1); | |
1333 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1334 | scm_remember_upto_here_1 (n2); | |
1335 | mpz_clear (nn1_z); | |
9806de0d | 1336 | return scm_i_normbig (result_z); |
0aacf84e MD |
1337 | } |
1338 | } | |
1339 | else | |
1340 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1341 | } | |
1342 | else if (SCM_BIGP (n1)) | |
1343 | { | |
e11e83f3 | 1344 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1345 | { |
1346 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1347 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1348 | goto intbig; |
1349 | } | |
1350 | else if (SCM_BIGP (n2)) | |
1351 | { | |
1352 | SCM result_z = scm_i_mkbig (); | |
1353 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
1354 | SCM_I_BIG_MPZ (n1), | |
1355 | SCM_I_BIG_MPZ (n2)); | |
1356 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 1357 | return scm_i_normbig (result_z); |
0aacf84e MD |
1358 | } |
1359 | else | |
1360 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1361 | } |
0aacf84e | 1362 | else |
09fb7599 | 1363 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1364 | } |
1bbd0b84 | 1365 | #undef FUNC_NAME |
0f2d19dd | 1366 | |
09fb7599 | 1367 | |
c3ee7520 | 1368 | SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr, |
1bbd0b84 | 1369 | (SCM n1, SCM n2), |
3c3db128 GH |
1370 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1371 | "set in the result if it is set in an odd number of arguments.\n" | |
1372 | "@lisp\n" | |
1373 | "(logxor) @result{} 0\n" | |
1374 | "(logxor 7) @result{} 7\n" | |
1375 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1376 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1377 | "@end lisp") |
1bbd0b84 | 1378 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1379 | { |
9a00c9fc DH |
1380 | long int nn1; |
1381 | ||
0aacf84e MD |
1382 | if (SCM_UNBNDP (n2)) |
1383 | { | |
1384 | if (SCM_UNBNDP (n1)) | |
1385 | return SCM_INUM0; | |
1386 | else if (SCM_NUMBERP (n1)) | |
1387 | return n1; | |
1388 | else | |
1389 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1390 | } |
09fb7599 | 1391 | |
e11e83f3 | 1392 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1393 | { |
e11e83f3 MV |
1394 | nn1 = SCM_I_INUM (n1); |
1395 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1396 | { |
e11e83f3 | 1397 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1398 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
1399 | } |
1400 | else if (SCM_BIGP (n2)) | |
1401 | { | |
1402 | intbig: | |
1403 | { | |
1404 | SCM result_z = scm_i_mkbig (); | |
1405 | mpz_t nn1_z; | |
1406 | mpz_init_set_si (nn1_z, nn1); | |
1407 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1408 | scm_remember_upto_here_1 (n2); | |
1409 | mpz_clear (nn1_z); | |
1410 | return scm_i_normbig (result_z); | |
1411 | } | |
1412 | } | |
1413 | else | |
1414 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1415 | } | |
1416 | else if (SCM_BIGP (n1)) | |
1417 | { | |
e11e83f3 | 1418 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1419 | { |
1420 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1421 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1422 | goto intbig; |
1423 | } | |
1424 | else if (SCM_BIGP (n2)) | |
1425 | { | |
1426 | SCM result_z = scm_i_mkbig (); | |
1427 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
1428 | SCM_I_BIG_MPZ (n1), | |
1429 | SCM_I_BIG_MPZ (n2)); | |
1430 | scm_remember_upto_here_2 (n1, n2); | |
1431 | return scm_i_normbig (result_z); | |
1432 | } | |
1433 | else | |
1434 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1435 | } |
0aacf84e | 1436 | else |
09fb7599 | 1437 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1438 | } |
1bbd0b84 | 1439 | #undef FUNC_NAME |
0f2d19dd | 1440 | |
09fb7599 | 1441 | |
a1ec6916 | 1442 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 1443 | (SCM j, SCM k), |
ba6e7231 KR |
1444 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
1445 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
1446 | "without actually calculating the @code{logand}, just testing\n" | |
1447 | "for non-zero.\n" | |
1448 | "\n" | |
1e6808ea | 1449 | "@lisp\n" |
b380b885 MD |
1450 | "(logtest #b0100 #b1011) @result{} #f\n" |
1451 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1452 | "@end lisp") |
1bbd0b84 | 1453 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1454 | { |
1e6808ea | 1455 | long int nj; |
9a00c9fc | 1456 | |
e11e83f3 | 1457 | if (SCM_I_INUMP (j)) |
0aacf84e | 1458 | { |
e11e83f3 MV |
1459 | nj = SCM_I_INUM (j); |
1460 | if (SCM_I_INUMP (k)) | |
0aacf84e | 1461 | { |
e11e83f3 | 1462 | long nk = SCM_I_INUM (k); |
73e4de09 | 1463 | return scm_from_bool (nj & nk); |
0aacf84e MD |
1464 | } |
1465 | else if (SCM_BIGP (k)) | |
1466 | { | |
1467 | intbig: | |
1468 | if (nj == 0) | |
1469 | return SCM_BOOL_F; | |
1470 | { | |
1471 | SCM result; | |
1472 | mpz_t nj_z; | |
1473 | mpz_init_set_si (nj_z, nj); | |
1474 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
1475 | scm_remember_upto_here_1 (k); | |
73e4de09 | 1476 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
1477 | mpz_clear (nj_z); |
1478 | return result; | |
1479 | } | |
1480 | } | |
1481 | else | |
1482 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1483 | } | |
1484 | else if (SCM_BIGP (j)) | |
1485 | { | |
e11e83f3 | 1486 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
1487 | { |
1488 | SCM_SWAP (j, k); | |
e11e83f3 | 1489 | nj = SCM_I_INUM (j); |
0aacf84e MD |
1490 | goto intbig; |
1491 | } | |
1492 | else if (SCM_BIGP (k)) | |
1493 | { | |
1494 | SCM result; | |
1495 | mpz_t result_z; | |
1496 | mpz_init (result_z); | |
1497 | mpz_and (result_z, | |
1498 | SCM_I_BIG_MPZ (j), | |
1499 | SCM_I_BIG_MPZ (k)); | |
1500 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 1501 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
1502 | mpz_clear (result_z); |
1503 | return result; | |
1504 | } | |
1505 | else | |
1506 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1507 | } | |
1508 | else | |
1509 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 1510 | } |
1bbd0b84 | 1511 | #undef FUNC_NAME |
0f2d19dd | 1512 | |
c1bfcf60 | 1513 | |
a1ec6916 | 1514 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1515 | (SCM index, SCM j), |
ba6e7231 KR |
1516 | "Test whether bit number @var{index} in @var{j} is set.\n" |
1517 | "@var{index} starts from 0 for the least significant bit.\n" | |
1518 | "\n" | |
1e6808ea | 1519 | "@lisp\n" |
b380b885 MD |
1520 | "(logbit? 0 #b1101) @result{} #t\n" |
1521 | "(logbit? 1 #b1101) @result{} #f\n" | |
1522 | "(logbit? 2 #b1101) @result{} #t\n" | |
1523 | "(logbit? 3 #b1101) @result{} #t\n" | |
1524 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1525 | "@end lisp") |
1bbd0b84 | 1526 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1527 | { |
78166ad5 | 1528 | unsigned long int iindex; |
5efd3c7d | 1529 | iindex = scm_to_ulong (index); |
78166ad5 | 1530 | |
e11e83f3 | 1531 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
1532 | { |
1533 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 1534 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 1535 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 1536 | } |
0aacf84e MD |
1537 | else if (SCM_BIGP (j)) |
1538 | { | |
1539 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
1540 | scm_remember_upto_here_1 (j); | |
73e4de09 | 1541 | return scm_from_bool (val); |
0aacf84e MD |
1542 | } |
1543 | else | |
78166ad5 | 1544 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 1545 | } |
1bbd0b84 | 1546 | #undef FUNC_NAME |
0f2d19dd | 1547 | |
78166ad5 | 1548 | |
a1ec6916 | 1549 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1550 | (SCM n), |
4d814788 | 1551 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
1552 | "argument.\n" |
1553 | "\n" | |
b380b885 MD |
1554 | "@lisp\n" |
1555 | "(number->string (lognot #b10000000) 2)\n" | |
1556 | " @result{} \"-10000001\"\n" | |
1557 | "(number->string (lognot #b0) 2)\n" | |
1558 | " @result{} \"-1\"\n" | |
1e6808ea | 1559 | "@end lisp") |
1bbd0b84 | 1560 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1561 | { |
e11e83f3 | 1562 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
1563 | /* No overflow here, just need to toggle all the bits making up the inum. |
1564 | Enhancement: No need to strip the tag and add it back, could just xor | |
1565 | a block of 1 bits, if that worked with the various debug versions of | |
1566 | the SCM typedef. */ | |
e11e83f3 | 1567 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
1568 | |
1569 | } else if (SCM_BIGP (n)) { | |
1570 | SCM result = scm_i_mkbig (); | |
1571 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
1572 | scm_remember_upto_here_1 (n); | |
1573 | return result; | |
1574 | ||
1575 | } else { | |
1576 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1577 | } | |
0f2d19dd | 1578 | } |
1bbd0b84 | 1579 | #undef FUNC_NAME |
0f2d19dd | 1580 | |
518b7508 KR |
1581 | /* returns 0 if IN is not an integer. OUT must already be |
1582 | initialized. */ | |
1583 | static int | |
1584 | coerce_to_big (SCM in, mpz_t out) | |
1585 | { | |
1586 | if (SCM_BIGP (in)) | |
1587 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
1588 | else if (SCM_I_INUMP (in)) |
1589 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
1590 | else |
1591 | return 0; | |
1592 | ||
1593 | return 1; | |
1594 | } | |
1595 | ||
d885e204 | 1596 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
1597 | (SCM n, SCM k, SCM m), |
1598 | "Return @var{n} raised to the integer exponent\n" | |
1599 | "@var{k}, modulo @var{m}.\n" | |
1600 | "\n" | |
1601 | "@lisp\n" | |
1602 | "(modulo-expt 2 3 5)\n" | |
1603 | " @result{} 3\n" | |
1604 | "@end lisp") | |
d885e204 | 1605 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
1606 | { |
1607 | mpz_t n_tmp; | |
1608 | mpz_t k_tmp; | |
1609 | mpz_t m_tmp; | |
1610 | ||
1611 | /* There are two classes of error we might encounter -- | |
1612 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
1613 | and | |
1614 | 2) wrong-type errors, which of course we'll report by calling | |
1615 | SCM_WRONG_TYPE_ARG. | |
1616 | We don't report those errors immediately, however; instead we do | |
1617 | some cleanup first. These variables tell us which error (if | |
1618 | any) we should report after cleaning up. | |
1619 | */ | |
1620 | int report_overflow = 0; | |
1621 | ||
1622 | int position_of_wrong_type = 0; | |
1623 | SCM value_of_wrong_type = SCM_INUM0; | |
1624 | ||
1625 | SCM result = SCM_UNDEFINED; | |
1626 | ||
1627 | mpz_init (n_tmp); | |
1628 | mpz_init (k_tmp); | |
1629 | mpz_init (m_tmp); | |
1630 | ||
bc36d050 | 1631 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
1632 | { |
1633 | report_overflow = 1; | |
1634 | goto cleanup; | |
1635 | } | |
1636 | ||
1637 | if (!coerce_to_big (n, n_tmp)) | |
1638 | { | |
1639 | value_of_wrong_type = n; | |
1640 | position_of_wrong_type = 1; | |
1641 | goto cleanup; | |
1642 | } | |
1643 | ||
1644 | if (!coerce_to_big (k, k_tmp)) | |
1645 | { | |
1646 | value_of_wrong_type = k; | |
1647 | position_of_wrong_type = 2; | |
1648 | goto cleanup; | |
1649 | } | |
1650 | ||
1651 | if (!coerce_to_big (m, m_tmp)) | |
1652 | { | |
1653 | value_of_wrong_type = m; | |
1654 | position_of_wrong_type = 3; | |
1655 | goto cleanup; | |
1656 | } | |
1657 | ||
1658 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
1659 | will get a divide-by-zero exception when an inverse 1/n mod m | |
1660 | doesn't exist (or is not unique). Since exceptions are hard to | |
1661 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
1662 | a simple failure code, which is easy to handle. */ | |
1663 | ||
1664 | if (-1 == mpz_sgn (k_tmp)) | |
1665 | { | |
1666 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
1667 | { | |
1668 | report_overflow = 1; | |
1669 | goto cleanup; | |
1670 | } | |
1671 | mpz_neg (k_tmp, k_tmp); | |
1672 | } | |
1673 | ||
1674 | result = scm_i_mkbig (); | |
1675 | mpz_powm (SCM_I_BIG_MPZ (result), | |
1676 | n_tmp, | |
1677 | k_tmp, | |
1678 | m_tmp); | |
b7b8c575 KR |
1679 | |
1680 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
1681 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
1682 | ||
518b7508 KR |
1683 | cleanup: |
1684 | mpz_clear (m_tmp); | |
1685 | mpz_clear (k_tmp); | |
1686 | mpz_clear (n_tmp); | |
1687 | ||
1688 | if (report_overflow) | |
1689 | scm_num_overflow (FUNC_NAME); | |
1690 | ||
1691 | if (position_of_wrong_type) | |
1692 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
1693 | value_of_wrong_type); | |
1694 | ||
1695 | return scm_i_normbig (result); | |
1696 | } | |
1697 | #undef FUNC_NAME | |
1698 | ||
a1ec6916 | 1699 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1700 | (SCM n, SCM k), |
ba6e7231 KR |
1701 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
1702 | "exact integer, @var{n} can be any number.\n" | |
1703 | "\n" | |
1704 | "Negative @var{k} is supported, and results in @math{1/n^abs(k)}\n" | |
1705 | "in the usual way. @math{@var{n}^0} is 1, as usual, and that\n" | |
1706 | "includes @math{0^0} is 1.\n" | |
1e6808ea | 1707 | "\n" |
b380b885 | 1708 | "@lisp\n" |
ba6e7231 KR |
1709 | "(integer-expt 2 5) @result{} 32\n" |
1710 | "(integer-expt -3 3) @result{} -27\n" | |
1711 | "(integer-expt 5 -3) @result{} 1/125\n" | |
1712 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 1713 | "@end lisp") |
1bbd0b84 | 1714 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1715 | { |
1c35cb19 RB |
1716 | long i2 = 0; |
1717 | SCM z_i2 = SCM_BOOL_F; | |
1718 | int i2_is_big = 0; | |
d956fa6f | 1719 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 1720 | |
d57ed702 | 1721 | /* 0^0 == 1 according to R5RS */ |
bc36d050 | 1722 | if (scm_is_eq (n, SCM_INUM0) || scm_is_eq (n, acc)) |
73e4de09 | 1723 | return scm_is_false (scm_zero_p(k)) ? n : acc; |
bc36d050 | 1724 | else if (scm_is_eq (n, SCM_I_MAKINUM (-1L))) |
73e4de09 | 1725 | return scm_is_false (scm_even_p (k)) ? n : acc; |
ca46fb90 | 1726 | |
e11e83f3 MV |
1727 | if (SCM_I_INUMP (k)) |
1728 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
1729 | else if (SCM_BIGP (k)) |
1730 | { | |
1731 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
1732 | scm_remember_upto_here_1 (k); |
1733 | i2_is_big = 1; | |
1734 | } | |
2830fd91 | 1735 | else |
ca46fb90 RB |
1736 | SCM_WRONG_TYPE_ARG (2, k); |
1737 | ||
1738 | if (i2_is_big) | |
f872b822 | 1739 | { |
ca46fb90 RB |
1740 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
1741 | { | |
1742 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
1743 | n = scm_divide (n, SCM_UNDEFINED); | |
1744 | } | |
1745 | while (1) | |
1746 | { | |
1747 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
1748 | { | |
ca46fb90 RB |
1749 | return acc; |
1750 | } | |
1751 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
1752 | { | |
ca46fb90 RB |
1753 | return scm_product (acc, n); |
1754 | } | |
1755 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
1756 | acc = scm_product (acc, n); | |
1757 | n = scm_product (n, n); | |
1758 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
1759 | } | |
f872b822 | 1760 | } |
ca46fb90 | 1761 | else |
f872b822 | 1762 | { |
ca46fb90 RB |
1763 | if (i2 < 0) |
1764 | { | |
1765 | i2 = -i2; | |
1766 | n = scm_divide (n, SCM_UNDEFINED); | |
1767 | } | |
1768 | while (1) | |
1769 | { | |
1770 | if (0 == i2) | |
1771 | return acc; | |
1772 | if (1 == i2) | |
1773 | return scm_product (acc, n); | |
1774 | if (i2 & 1) | |
1775 | acc = scm_product (acc, n); | |
1776 | n = scm_product (n, n); | |
1777 | i2 >>= 1; | |
1778 | } | |
f872b822 | 1779 | } |
0f2d19dd | 1780 | } |
1bbd0b84 | 1781 | #undef FUNC_NAME |
0f2d19dd | 1782 | |
a1ec6916 | 1783 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1784 | (SCM n, SCM cnt), |
32f19569 KR |
1785 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
1786 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 1787 | "\n" |
e7644cb2 | 1788 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
1789 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
1790 | "infinity. (Note that this is not the same rounding as\n" | |
1791 | "@code{quotient} does.)\n" | |
1792 | "\n" | |
1793 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
1794 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
1795 | "shift dropping bits.\n" | |
1e6808ea | 1796 | "\n" |
b380b885 | 1797 | "@lisp\n" |
1e6808ea MG |
1798 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1799 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
1800 | "\n" |
1801 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
1802 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 1803 | "@end lisp") |
1bbd0b84 | 1804 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1805 | { |
3ab9f56e | 1806 | long bits_to_shift; |
5efd3c7d | 1807 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 1808 | |
788aca27 KR |
1809 | if (SCM_I_INUMP (n)) |
1810 | { | |
1811 | long nn = SCM_I_INUM (n); | |
1812 | ||
1813 | if (bits_to_shift > 0) | |
1814 | { | |
1815 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
1816 | overflow a non-zero fixnum. For smaller shifts we check the | |
1817 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
1818 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
1819 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
1820 | bits_to_shift)". */ | |
1821 | ||
1822 | if (nn == 0) | |
1823 | return n; | |
1824 | ||
1825 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
1826 | && ((unsigned long) | |
1827 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) | |
1828 | <= 1)) | |
1829 | { | |
1830 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
1831 | } | |
1832 | else | |
1833 | { | |
1834 | SCM result = scm_i_long2big (nn); | |
1835 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1836 | bits_to_shift); | |
1837 | return result; | |
1838 | } | |
1839 | } | |
1840 | else | |
1841 | { | |
1842 | bits_to_shift = -bits_to_shift; | |
1843 | if (bits_to_shift >= SCM_LONG_BIT) | |
1844 | return (nn >= 0 ? SCM_I_MAKINUM (0) : SCM_I_MAKINUM(-1)); | |
1845 | else | |
1846 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
1847 | } | |
1848 | ||
1849 | } | |
1850 | else if (SCM_BIGP (n)) | |
ca46fb90 | 1851 | { |
788aca27 KR |
1852 | SCM result; |
1853 | ||
1854 | if (bits_to_shift == 0) | |
1855 | return n; | |
1856 | ||
1857 | result = scm_i_mkbig (); | |
1858 | if (bits_to_shift >= 0) | |
1859 | { | |
1860 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1861 | bits_to_shift); | |
1862 | return result; | |
1863 | } | |
ca46fb90 | 1864 | else |
788aca27 KR |
1865 | { |
1866 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
1867 | we have to allocate a bignum even if the result is going to be a | |
1868 | fixnum. */ | |
1869 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1870 | -bits_to_shift); | |
1871 | return scm_i_normbig (result); | |
1872 | } | |
1873 | ||
ca46fb90 RB |
1874 | } |
1875 | else | |
788aca27 KR |
1876 | { |
1877 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1878 | } | |
0f2d19dd | 1879 | } |
1bbd0b84 | 1880 | #undef FUNC_NAME |
0f2d19dd | 1881 | |
3c9f20f8 | 1882 | |
a1ec6916 | 1883 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 1884 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
1885 | "Return the integer composed of the @var{start} (inclusive)\n" |
1886 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
1887 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
1888 | "\n" | |
b380b885 MD |
1889 | "@lisp\n" |
1890 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
1891 | " @result{} \"1010\"\n" | |
1892 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
1893 | " @result{} \"10110\"\n" | |
1894 | "@end lisp") | |
1bbd0b84 | 1895 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 1896 | { |
7f848242 | 1897 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
1898 | istart = scm_to_ulong (start); |
1899 | iend = scm_to_ulong (end); | |
c1bfcf60 | 1900 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 1901 | |
7f848242 KR |
1902 | /* how many bits to keep */ |
1903 | bits = iend - istart; | |
1904 | ||
e11e83f3 | 1905 | if (SCM_I_INUMP (n)) |
0aacf84e | 1906 | { |
e11e83f3 | 1907 | long int in = SCM_I_INUM (n); |
7f848242 KR |
1908 | |
1909 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 1910 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 1911 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 1912 | |
0aacf84e MD |
1913 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
1914 | { | |
1915 | /* Since we emulate two's complement encoded numbers, this | |
1916 | * special case requires us to produce a result that has | |
7f848242 | 1917 | * more bits than can be stored in a fixnum. |
0aacf84e | 1918 | */ |
7f848242 KR |
1919 | SCM result = scm_i_long2big (in); |
1920 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1921 | bits); | |
1922 | return result; | |
0aacf84e | 1923 | } |
ac0c002c | 1924 | |
7f848242 | 1925 | /* mask down to requisite bits */ |
857ae6af | 1926 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 1927 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
1928 | } |
1929 | else if (SCM_BIGP (n)) | |
ac0c002c | 1930 | { |
7f848242 KR |
1931 | SCM result; |
1932 | if (bits == 1) | |
1933 | { | |
d956fa6f | 1934 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
1935 | } |
1936 | else | |
1937 | { | |
1938 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
1939 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
1940 | such bits into a ulong. */ | |
1941 | result = scm_i_mkbig (); | |
1942 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
1943 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
1944 | result = scm_i_normbig (result); | |
1945 | } | |
1946 | scm_remember_upto_here_1 (n); | |
1947 | return result; | |
ac0c002c | 1948 | } |
0aacf84e | 1949 | else |
78166ad5 | 1950 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 1951 | } |
1bbd0b84 | 1952 | #undef FUNC_NAME |
0f2d19dd | 1953 | |
7f848242 | 1954 | |
e4755e5c JB |
1955 | static const char scm_logtab[] = { |
1956 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
1957 | }; | |
1cc91f1b | 1958 | |
a1ec6916 | 1959 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 1960 | (SCM n), |
1e6808ea MG |
1961 | "Return the number of bits in integer @var{n}. If integer is\n" |
1962 | "positive, the 1-bits in its binary representation are counted.\n" | |
1963 | "If negative, the 0-bits in its two's-complement binary\n" | |
1964 | "representation are counted. If 0, 0 is returned.\n" | |
1965 | "\n" | |
b380b885 MD |
1966 | "@lisp\n" |
1967 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
1968 | " @result{} 4\n" |
1969 | "(logcount 0)\n" | |
1970 | " @result{} 0\n" | |
1971 | "(logcount -2)\n" | |
1972 | " @result{} 1\n" | |
1973 | "@end lisp") | |
1974 | #define FUNC_NAME s_scm_logcount | |
1975 | { | |
e11e83f3 | 1976 | if (SCM_I_INUMP (n)) |
f872b822 | 1977 | { |
ca46fb90 | 1978 | unsigned long int c = 0; |
e11e83f3 | 1979 | long int nn = SCM_I_INUM (n); |
ca46fb90 RB |
1980 | if (nn < 0) |
1981 | nn = -1 - nn; | |
1982 | while (nn) | |
1983 | { | |
1984 | c += scm_logtab[15 & nn]; | |
1985 | nn >>= 4; | |
1986 | } | |
d956fa6f | 1987 | return SCM_I_MAKINUM (c); |
f872b822 | 1988 | } |
ca46fb90 | 1989 | else if (SCM_BIGP (n)) |
f872b822 | 1990 | { |
ca46fb90 | 1991 | unsigned long count; |
713a4259 KR |
1992 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
1993 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 1994 | else |
713a4259 KR |
1995 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
1996 | scm_remember_upto_here_1 (n); | |
d956fa6f | 1997 | return SCM_I_MAKINUM (count); |
f872b822 | 1998 | } |
ca46fb90 RB |
1999 | else |
2000 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 2001 | } |
ca46fb90 | 2002 | #undef FUNC_NAME |
0f2d19dd JB |
2003 | |
2004 | ||
ca46fb90 RB |
2005 | static const char scm_ilentab[] = { |
2006 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
2007 | }; | |
2008 | ||
0f2d19dd | 2009 | |
ca46fb90 RB |
2010 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
2011 | (SCM n), | |
2012 | "Return the number of bits necessary to represent @var{n}.\n" | |
2013 | "\n" | |
2014 | "@lisp\n" | |
2015 | "(integer-length #b10101010)\n" | |
2016 | " @result{} 8\n" | |
2017 | "(integer-length 0)\n" | |
2018 | " @result{} 0\n" | |
2019 | "(integer-length #b1111)\n" | |
2020 | " @result{} 4\n" | |
2021 | "@end lisp") | |
2022 | #define FUNC_NAME s_scm_integer_length | |
2023 | { | |
e11e83f3 | 2024 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2025 | { |
2026 | unsigned long int c = 0; | |
2027 | unsigned int l = 4; | |
e11e83f3 | 2028 | long int nn = SCM_I_INUM (n); |
0aacf84e MD |
2029 | if (nn < 0) |
2030 | nn = -1 - nn; | |
2031 | while (nn) | |
2032 | { | |
2033 | c += 4; | |
2034 | l = scm_ilentab [15 & nn]; | |
2035 | nn >>= 4; | |
2036 | } | |
d956fa6f | 2037 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
2038 | } |
2039 | else if (SCM_BIGP (n)) | |
2040 | { | |
2041 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
2042 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
2043 | 1 too big, so check for that and adjust. */ | |
2044 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
2045 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
2046 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
2047 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
2048 | size--; | |
2049 | scm_remember_upto_here_1 (n); | |
d956fa6f | 2050 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
2051 | } |
2052 | else | |
ca46fb90 | 2053 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
2054 | } |
2055 | #undef FUNC_NAME | |
0f2d19dd JB |
2056 | |
2057 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
2058 | #define SCM_MAX_DBL_PREC 60 |
2059 | #define SCM_MAX_DBL_RADIX 36 | |
2060 | ||
2061 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
2062 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
2063 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
2064 | ||
2065 | static | |
2066 | void init_dblprec(int *prec, int radix) { | |
2067 | /* determine floating point precision by adding successively | |
2068 | smaller increments to 1.0 until it is considered == 1.0 */ | |
2069 | double f = ((double)1.0)/radix; | |
2070 | double fsum = 1.0 + f; | |
2071 | ||
2072 | *prec = 0; | |
2073 | while (fsum != 1.0) | |
2074 | { | |
2075 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
2076 | fsum = 1.0; | |
2077 | else | |
2078 | { | |
2079 | f /= radix; | |
2080 | fsum = f + 1.0; | |
2081 | } | |
2082 | } | |
2083 | (*prec) -= 1; | |
2084 | } | |
2085 | ||
2086 | static | |
2087 | void init_fx_radix(double *fx_list, int radix) | |
2088 | { | |
2089 | /* initialize a per-radix list of tolerances. When added | |
2090 | to a number < 1.0, we can determine if we should raund | |
2091 | up and quit converting a number to a string. */ | |
2092 | int i; | |
2093 | fx_list[0] = 0.0; | |
2094 | fx_list[1] = 0.5; | |
2095 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
2096 | fx_list[i] = (fx_list[i-1] / radix); | |
2097 | } | |
2098 | ||
2099 | /* use this array as a way to generate a single digit */ | |
2100 | static const char*number_chars="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; | |
0f2d19dd | 2101 | |
1be6b49c | 2102 | static size_t |
0b799eea | 2103 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 2104 | { |
0b799eea MV |
2105 | int efmt, dpt, d, i, wp; |
2106 | double *fx; | |
2107 | #ifdef DBL_MIN_10_EXP | |
2108 | double f_cpy; | |
2109 | int exp_cpy; | |
2110 | #endif /* DBL_MIN_10_EXP */ | |
2111 | size_t ch = 0; | |
2112 | int exp = 0; | |
2113 | ||
2114 | if(radix < 2 || | |
2115 | radix > SCM_MAX_DBL_RADIX) | |
2116 | { | |
2117 | /* revert to existing behavior */ | |
2118 | radix = 10; | |
2119 | } | |
2120 | ||
2121 | wp = scm_dblprec[radix-2]; | |
2122 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 2123 | |
f872b822 | 2124 | if (f == 0.0) |
abb7e44d MV |
2125 | { |
2126 | #ifdef HAVE_COPYSIGN | |
2127 | double sgn = copysign (1.0, f); | |
2128 | ||
2129 | if (sgn < 0.0) | |
2130 | a[ch++] = '-'; | |
2131 | #endif | |
abb7e44d MV |
2132 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
2133 | } | |
7351e207 MV |
2134 | |
2135 | if (xisinf (f)) | |
2136 | { | |
2137 | if (f < 0) | |
2138 | strcpy (a, "-inf.0"); | |
2139 | else | |
2140 | strcpy (a, "+inf.0"); | |
2141 | return ch+6; | |
2142 | } | |
2143 | else if (xisnan (f)) | |
2144 | { | |
2145 | strcpy (a, "+nan.0"); | |
2146 | return ch+6; | |
2147 | } | |
2148 | ||
f872b822 MD |
2149 | if (f < 0.0) |
2150 | { | |
2151 | f = -f; | |
2152 | a[ch++] = '-'; | |
2153 | } | |
7351e207 | 2154 | |
f872b822 MD |
2155 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
2156 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
2157 | /* just do the checking...if it passes, we do the conversion for our |
2158 | radix again below */ | |
2159 | f_cpy = f; | |
2160 | exp_cpy = exp; | |
2161 | ||
2162 | while (f_cpy < 1.0) | |
f872b822 | 2163 | { |
0b799eea MV |
2164 | f_cpy *= 10.0; |
2165 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
2166 | { |
2167 | a[ch++] = '#'; | |
2168 | a[ch++] = '.'; | |
2169 | a[ch++] = '#'; | |
2170 | return ch; | |
2171 | } | |
f872b822 | 2172 | } |
0b799eea | 2173 | while (f_cpy > 10.0) |
f872b822 | 2174 | { |
0b799eea MV |
2175 | f_cpy *= 0.10; |
2176 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
2177 | { |
2178 | a[ch++] = '#'; | |
2179 | a[ch++] = '.'; | |
2180 | a[ch++] = '#'; | |
2181 | return ch; | |
2182 | } | |
f872b822 | 2183 | } |
0b799eea MV |
2184 | #endif |
2185 | ||
f872b822 MD |
2186 | while (f < 1.0) |
2187 | { | |
0b799eea | 2188 | f *= radix; |
f872b822 MD |
2189 | exp--; |
2190 | } | |
0b799eea | 2191 | while (f > radix) |
f872b822 | 2192 | { |
0b799eea | 2193 | f /= radix; |
f872b822 MD |
2194 | exp++; |
2195 | } | |
0b799eea MV |
2196 | |
2197 | if (f + fx[wp] >= radix) | |
f872b822 MD |
2198 | { |
2199 | f = 1.0; | |
2200 | exp++; | |
2201 | } | |
0f2d19dd | 2202 | zero: |
0b799eea MV |
2203 | #ifdef ENGNOT |
2204 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 2205 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
2206 | exp -= dpt++; |
2207 | efmt = 1; | |
f872b822 MD |
2208 | #else |
2209 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 2210 | if (!efmt) |
cda139a7 MD |
2211 | { |
2212 | if (exp < 0) | |
2213 | { | |
2214 | a[ch++] = '0'; | |
2215 | a[ch++] = '.'; | |
2216 | dpt = exp; | |
f872b822 MD |
2217 | while (++dpt) |
2218 | a[ch++] = '0'; | |
cda139a7 MD |
2219 | } |
2220 | else | |
f872b822 | 2221 | dpt = exp + 1; |
cda139a7 | 2222 | } |
0f2d19dd JB |
2223 | else |
2224 | dpt = 1; | |
f872b822 MD |
2225 | #endif |
2226 | ||
2227 | do | |
2228 | { | |
2229 | d = f; | |
2230 | f -= d; | |
0b799eea | 2231 | a[ch++] = number_chars[d]; |
f872b822 MD |
2232 | if (f < fx[wp]) |
2233 | break; | |
2234 | if (f + fx[wp] >= 1.0) | |
2235 | { | |
0b799eea | 2236 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
2237 | break; |
2238 | } | |
0b799eea | 2239 | f *= radix; |
f872b822 MD |
2240 | if (!(--dpt)) |
2241 | a[ch++] = '.'; | |
0f2d19dd | 2242 | } |
f872b822 | 2243 | while (wp--); |
0f2d19dd JB |
2244 | |
2245 | if (dpt > 0) | |
cda139a7 | 2246 | { |
f872b822 | 2247 | #ifndef ENGNOT |
cda139a7 MD |
2248 | if ((dpt > 4) && (exp > 6)) |
2249 | { | |
f872b822 | 2250 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 2251 | for (i = ch++; i > d; i--) |
f872b822 | 2252 | a[i] = a[i - 1]; |
cda139a7 MD |
2253 | a[d] = '.'; |
2254 | efmt = 1; | |
2255 | } | |
2256 | else | |
f872b822 | 2257 | #endif |
cda139a7 | 2258 | { |
f872b822 MD |
2259 | while (--dpt) |
2260 | a[ch++] = '0'; | |
cda139a7 MD |
2261 | a[ch++] = '.'; |
2262 | } | |
2263 | } | |
f872b822 MD |
2264 | if (a[ch - 1] == '.') |
2265 | a[ch++] = '0'; /* trailing zero */ | |
2266 | if (efmt && exp) | |
2267 | { | |
2268 | a[ch++] = 'e'; | |
2269 | if (exp < 0) | |
2270 | { | |
2271 | exp = -exp; | |
2272 | a[ch++] = '-'; | |
2273 | } | |
0b799eea MV |
2274 | for (i = radix; i <= exp; i *= radix); |
2275 | for (i /= radix; i; i /= radix) | |
f872b822 | 2276 | { |
0b799eea | 2277 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
2278 | exp %= i; |
2279 | } | |
0f2d19dd | 2280 | } |
0f2d19dd JB |
2281 | return ch; |
2282 | } | |
2283 | ||
7a1aba42 MV |
2284 | |
2285 | static size_t | |
2286 | icmplx2str (double real, double imag, char *str, int radix) | |
2287 | { | |
2288 | size_t i; | |
2289 | ||
2290 | i = idbl2str (real, str, radix); | |
2291 | if (imag != 0.0) | |
2292 | { | |
2293 | /* Don't output a '+' for negative numbers or for Inf and | |
2294 | NaN. They will provide their own sign. */ | |
2295 | if (0 <= imag && !xisinf (imag) && !xisnan (imag)) | |
2296 | str[i++] = '+'; | |
2297 | i += idbl2str (imag, &str[i], radix); | |
2298 | str[i++] = 'i'; | |
2299 | } | |
2300 | return i; | |
2301 | } | |
2302 | ||
1be6b49c | 2303 | static size_t |
0b799eea | 2304 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 2305 | { |
1be6b49c | 2306 | size_t i; |
3c9a524f | 2307 | if (SCM_REALP (flt)) |
0b799eea | 2308 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 2309 | else |
7a1aba42 MV |
2310 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
2311 | str, radix); | |
0f2d19dd JB |
2312 | return i; |
2313 | } | |
0f2d19dd | 2314 | |
2881e77b | 2315 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
2316 | characters in the result. |
2317 | rad is output base | |
2318 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2319 | size_t |
2881e77b MV |
2320 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
2321 | { | |
2322 | if (num < 0) | |
2323 | { | |
2324 | *p++ = '-'; | |
2325 | return scm_iuint2str (-num, rad, p) + 1; | |
2326 | } | |
2327 | else | |
2328 | return scm_iuint2str (num, rad, p); | |
2329 | } | |
2330 | ||
2331 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
2332 | characters in the result. | |
2333 | rad is output base | |
2334 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
2335 | size_t | |
2336 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 2337 | { |
1be6b49c ML |
2338 | size_t j = 1; |
2339 | size_t i; | |
2881e77b | 2340 | scm_t_uintmax n = num; |
5c11cc9d | 2341 | |
f872b822 | 2342 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2343 | j++; |
2344 | ||
2345 | i = j; | |
2881e77b | 2346 | n = num; |
f872b822 MD |
2347 | while (i--) |
2348 | { | |
5c11cc9d GH |
2349 | int d = n % rad; |
2350 | ||
f872b822 MD |
2351 | n /= rad; |
2352 | p[i] = d + ((d < 10) ? '0' : 'a' - 10); | |
2353 | } | |
0f2d19dd JB |
2354 | return j; |
2355 | } | |
2356 | ||
a1ec6916 | 2357 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2358 | (SCM n, SCM radix), |
2359 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2360 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2361 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2362 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2363 | { |
1bbd0b84 | 2364 | int base; |
98cb6e75 | 2365 | |
0aacf84e | 2366 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 2367 | base = 10; |
0aacf84e | 2368 | else |
5efd3c7d | 2369 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 2370 | |
e11e83f3 | 2371 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2372 | { |
2373 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 2374 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 2375 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
2376 | } |
2377 | else if (SCM_BIGP (n)) | |
2378 | { | |
2379 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
2380 | scm_remember_upto_here_1 (n); | |
cc95e00a | 2381 | return scm_take_locale_string (str); |
0aacf84e | 2382 | } |
f92e85f7 MV |
2383 | else if (SCM_FRACTIONP (n)) |
2384 | { | |
f92e85f7 | 2385 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 2386 | scm_from_locale_string ("/"), |
f92e85f7 MV |
2387 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
2388 | } | |
0aacf84e MD |
2389 | else if (SCM_INEXACTP (n)) |
2390 | { | |
2391 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 2392 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
2393 | } |
2394 | else | |
bb628794 | 2395 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 2396 | } |
1bbd0b84 | 2397 | #undef FUNC_NAME |
0f2d19dd JB |
2398 | |
2399 | ||
ca46fb90 RB |
2400 | /* These print routines used to be stubbed here so that scm_repl.c |
2401 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 2402 | |
0f2d19dd | 2403 | int |
e81d98ec | 2404 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2405 | { |
56e55ac7 | 2406 | char num_buf[FLOBUFLEN]; |
0b799eea | 2407 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
2408 | return !0; |
2409 | } | |
2410 | ||
b479fe9a MV |
2411 | void |
2412 | scm_i_print_double (double val, SCM port) | |
2413 | { | |
2414 | char num_buf[FLOBUFLEN]; | |
2415 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
2416 | } | |
2417 | ||
f3ae5d60 | 2418 | int |
e81d98ec | 2419 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 2420 | |
f3ae5d60 | 2421 | { |
56e55ac7 | 2422 | char num_buf[FLOBUFLEN]; |
0b799eea | 2423 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
2424 | return !0; |
2425 | } | |
1cc91f1b | 2426 | |
7a1aba42 MV |
2427 | void |
2428 | scm_i_print_complex (double real, double imag, SCM port) | |
2429 | { | |
2430 | char num_buf[FLOBUFLEN]; | |
2431 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
2432 | } | |
2433 | ||
f92e85f7 MV |
2434 | int |
2435 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
2436 | { | |
2437 | SCM str; | |
f92e85f7 | 2438 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
cc95e00a | 2439 | scm_lfwrite (scm_i_string_chars (str), scm_i_string_length (str), port); |
f92e85f7 MV |
2440 | scm_remember_upto_here_1 (str); |
2441 | return !0; | |
2442 | } | |
2443 | ||
0f2d19dd | 2444 | int |
e81d98ec | 2445 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2446 | { |
ca46fb90 RB |
2447 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
2448 | scm_remember_upto_here_1 (exp); | |
2449 | scm_lfwrite (str, (size_t) strlen (str), port); | |
2450 | free (str); | |
0f2d19dd JB |
2451 | return !0; |
2452 | } | |
2453 | /*** END nums->strs ***/ | |
2454 | ||
3c9a524f | 2455 | |
0f2d19dd | 2456 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2457 | |
3c9a524f DH |
2458 | /* The following functions implement the conversion from strings to numbers. |
2459 | * The implementation somehow follows the grammar for numbers as it is given | |
2460 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2461 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2462 | * points should be noted about the implementation: | |
2463 | * * Each function keeps a local index variable 'idx' that points at the | |
2464 | * current position within the parsed string. The global index is only | |
2465 | * updated if the function could parse the corresponding syntactic unit | |
2466 | * successfully. | |
2467 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2468 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2469 | * global exactness information is only updated after each part has been | |
2470 | * successfully parsed. | |
2471 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2472 | * Only if these fixnums would overflow, the result variables are updated | |
2473 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2474 | * the temporary variables holding the fixnums are cleared, and the process | |
2475 | * starts over again. If for example fixnums were able to store five decimal | |
2476 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2477 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2478 | * only every five digits two bignum operations were performed. | |
2479 | */ | |
2480 | ||
2481 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2482 | ||
2483 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2484 | ||
2485 | /* In non ASCII-style encodings the following macro might not work. */ | |
71df73ac KR |
2486 | #define XDIGIT2UINT(d) \ |
2487 | (isdigit ((int) (unsigned char) d) \ | |
2488 | ? (d) - '0' \ | |
2489 | : tolower ((int) (unsigned char) d) - 'a' + 10) | |
3c9a524f | 2490 | |
2a8fecee | 2491 | static SCM |
3c9a524f DH |
2492 | mem2uinteger (const char* mem, size_t len, unsigned int *p_idx, |
2493 | unsigned int radix, enum t_exactness *p_exactness) | |
2a8fecee | 2494 | { |
3c9a524f DH |
2495 | unsigned int idx = *p_idx; |
2496 | unsigned int hash_seen = 0; | |
2497 | scm_t_bits shift = 1; | |
2498 | scm_t_bits add = 0; | |
2499 | unsigned int digit_value; | |
2500 | SCM result; | |
2501 | char c; | |
2502 | ||
2503 | if (idx == len) | |
2504 | return SCM_BOOL_F; | |
2a8fecee | 2505 | |
3c9a524f | 2506 | c = mem[idx]; |
71df73ac | 2507 | if (!isxdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2508 | return SCM_BOOL_F; |
2509 | digit_value = XDIGIT2UINT (c); | |
2510 | if (digit_value >= radix) | |
2511 | return SCM_BOOL_F; | |
2512 | ||
2513 | idx++; | |
d956fa6f | 2514 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 2515 | while (idx != len) |
f872b822 | 2516 | { |
3c9a524f | 2517 | char c = mem[idx]; |
71df73ac | 2518 | if (isxdigit ((int) (unsigned char) c)) |
f872b822 | 2519 | { |
3c9a524f | 2520 | if (hash_seen) |
1fe5e088 | 2521 | break; |
3c9a524f DH |
2522 | digit_value = XDIGIT2UINT (c); |
2523 | if (digit_value >= radix) | |
1fe5e088 | 2524 | break; |
f872b822 | 2525 | } |
3c9a524f DH |
2526 | else if (c == '#') |
2527 | { | |
2528 | hash_seen = 1; | |
2529 | digit_value = 0; | |
2530 | } | |
2531 | else | |
2532 | break; | |
2533 | ||
2534 | idx++; | |
2535 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2536 | { | |
d956fa6f | 2537 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2538 | if (add > 0) |
d956fa6f | 2539 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2540 | |
2541 | shift = radix; | |
2542 | add = digit_value; | |
2543 | } | |
2544 | else | |
2545 | { | |
2546 | shift = shift * radix; | |
2547 | add = add * radix + digit_value; | |
2548 | } | |
2549 | }; | |
2550 | ||
2551 | if (shift > 1) | |
d956fa6f | 2552 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2553 | if (add > 0) |
d956fa6f | 2554 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2555 | |
2556 | *p_idx = idx; | |
2557 | if (hash_seen) | |
2558 | *p_exactness = INEXACT; | |
2559 | ||
2560 | return result; | |
2a8fecee JB |
2561 | } |
2562 | ||
2563 | ||
3c9a524f DH |
2564 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2565 | * covers the parts of the rules that start at a potential point. The value | |
2566 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2567 | * in variable result. The content of *p_exactness indicates, whether a hash |
2568 | * has already been seen in the digits before the point. | |
3c9a524f | 2569 | */ |
1cc91f1b | 2570 | |
3c9a524f DH |
2571 | /* In non ASCII-style encodings the following macro might not work. */ |
2572 | #define DIGIT2UINT(d) ((d) - '0') | |
2573 | ||
2574 | static SCM | |
79d34f68 | 2575 | mem2decimal_from_point (SCM result, const char* mem, size_t len, |
3c9a524f | 2576 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2577 | { |
3c9a524f DH |
2578 | unsigned int idx = *p_idx; |
2579 | enum t_exactness x = *p_exactness; | |
3c9a524f DH |
2580 | |
2581 | if (idx == len) | |
79d34f68 | 2582 | return result; |
3c9a524f DH |
2583 | |
2584 | if (mem[idx] == '.') | |
2585 | { | |
2586 | scm_t_bits shift = 1; | |
2587 | scm_t_bits add = 0; | |
2588 | unsigned int digit_value; | |
d956fa6f | 2589 | SCM big_shift = SCM_I_MAKINUM (1); |
3c9a524f DH |
2590 | |
2591 | idx++; | |
2592 | while (idx != len) | |
2593 | { | |
2594 | char c = mem[idx]; | |
71df73ac | 2595 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2596 | { |
2597 | if (x == INEXACT) | |
2598 | return SCM_BOOL_F; | |
2599 | else | |
2600 | digit_value = DIGIT2UINT (c); | |
2601 | } | |
2602 | else if (c == '#') | |
2603 | { | |
2604 | x = INEXACT; | |
2605 | digit_value = 0; | |
2606 | } | |
2607 | else | |
2608 | break; | |
2609 | ||
2610 | idx++; | |
2611 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2612 | { | |
d956fa6f MV |
2613 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2614 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 2615 | if (add > 0) |
d956fa6f | 2616 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2617 | |
2618 | shift = 10; | |
2619 | add = digit_value; | |
2620 | } | |
2621 | else | |
2622 | { | |
2623 | shift = shift * 10; | |
2624 | add = add * 10 + digit_value; | |
2625 | } | |
2626 | }; | |
2627 | ||
2628 | if (add > 0) | |
2629 | { | |
d956fa6f MV |
2630 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2631 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
2632 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
2633 | } |
2634 | ||
d8592269 | 2635 | result = scm_divide (result, big_shift); |
79d34f68 | 2636 | |
3c9a524f DH |
2637 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2638 | x = INEXACT; | |
f872b822 | 2639 | } |
3c9a524f | 2640 | |
3c9a524f | 2641 | if (idx != len) |
f872b822 | 2642 | { |
3c9a524f DH |
2643 | int sign = 1; |
2644 | unsigned int start; | |
2645 | char c; | |
2646 | int exponent; | |
2647 | SCM e; | |
2648 | ||
2649 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2650 | ||
2651 | switch (mem[idx]) | |
f872b822 | 2652 | { |
3c9a524f DH |
2653 | case 'd': case 'D': |
2654 | case 'e': case 'E': | |
2655 | case 'f': case 'F': | |
2656 | case 'l': case 'L': | |
2657 | case 's': case 'S': | |
2658 | idx++; | |
2659 | start = idx; | |
2660 | c = mem[idx]; | |
2661 | if (c == '-') | |
2662 | { | |
2663 | idx++; | |
2664 | sign = -1; | |
2665 | c = mem[idx]; | |
2666 | } | |
2667 | else if (c == '+') | |
2668 | { | |
2669 | idx++; | |
2670 | sign = 1; | |
2671 | c = mem[idx]; | |
2672 | } | |
2673 | else | |
2674 | sign = 1; | |
2675 | ||
71df73ac | 2676 | if (!isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2677 | return SCM_BOOL_F; |
2678 | ||
2679 | idx++; | |
2680 | exponent = DIGIT2UINT (c); | |
2681 | while (idx != len) | |
f872b822 | 2682 | { |
3c9a524f | 2683 | char c = mem[idx]; |
71df73ac | 2684 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2685 | { |
2686 | idx++; | |
2687 | if (exponent <= SCM_MAXEXP) | |
2688 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2689 | } | |
2690 | else | |
2691 | break; | |
f872b822 | 2692 | } |
3c9a524f DH |
2693 | |
2694 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2695 | { |
3c9a524f | 2696 | size_t exp_len = idx - start; |
cc95e00a | 2697 | SCM exp_string = scm_from_locale_stringn (&mem[start], exp_len); |
3c9a524f DH |
2698 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
2699 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2700 | } |
3c9a524f | 2701 | |
d956fa6f | 2702 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
2703 | if (sign == 1) |
2704 | result = scm_product (result, e); | |
2705 | else | |
f92e85f7 | 2706 | result = scm_divide2real (result, e); |
3c9a524f DH |
2707 | |
2708 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2709 | x = INEXACT; | |
2710 | ||
f872b822 | 2711 | break; |
3c9a524f | 2712 | |
f872b822 | 2713 | default: |
3c9a524f | 2714 | break; |
f872b822 | 2715 | } |
0f2d19dd | 2716 | } |
3c9a524f DH |
2717 | |
2718 | *p_idx = idx; | |
2719 | if (x == INEXACT) | |
2720 | *p_exactness = x; | |
2721 | ||
2722 | return result; | |
0f2d19dd | 2723 | } |
0f2d19dd | 2724 | |
3c9a524f DH |
2725 | |
2726 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2727 | ||
2728 | static SCM | |
2729 | mem2ureal (const char* mem, size_t len, unsigned int *p_idx, | |
2730 | unsigned int radix, enum t_exactness *p_exactness) | |
0f2d19dd | 2731 | { |
3c9a524f | 2732 | unsigned int idx = *p_idx; |
164d2481 | 2733 | SCM result; |
3c9a524f DH |
2734 | |
2735 | if (idx == len) | |
2736 | return SCM_BOOL_F; | |
2737 | ||
7351e207 MV |
2738 | if (idx+5 <= len && !strncmp (mem+idx, "inf.0", 5)) |
2739 | { | |
2740 | *p_idx = idx+5; | |
2741 | return scm_inf (); | |
2742 | } | |
2743 | ||
2744 | if (idx+4 < len && !strncmp (mem+idx, "nan.", 4)) | |
2745 | { | |
2746 | enum t_exactness x = EXACT; | |
2747 | ||
d8592269 MV |
2748 | /* Cobble up the fractional part. We might want to set the |
2749 | NaN's mantissa from it. */ | |
7351e207 MV |
2750 | idx += 4; |
2751 | mem2uinteger (mem, len, &idx, 10, &x); | |
2752 | *p_idx = idx; | |
2753 | return scm_nan (); | |
2754 | } | |
2755 | ||
3c9a524f DH |
2756 | if (mem[idx] == '.') |
2757 | { | |
2758 | if (radix != 10) | |
2759 | return SCM_BOOL_F; | |
2760 | else if (idx + 1 == len) | |
2761 | return SCM_BOOL_F; | |
71df73ac | 2762 | else if (!isdigit ((int) (unsigned char) mem[idx + 1])) |
3c9a524f DH |
2763 | return SCM_BOOL_F; |
2764 | else | |
d956fa6f | 2765 | result = mem2decimal_from_point (SCM_I_MAKINUM (0), mem, len, |
164d2481 | 2766 | p_idx, p_exactness); |
f872b822 | 2767 | } |
3c9a524f DH |
2768 | else |
2769 | { | |
2770 | enum t_exactness x = EXACT; | |
2771 | SCM uinteger; | |
3c9a524f DH |
2772 | |
2773 | uinteger = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2774 | if (scm_is_false (uinteger)) |
3c9a524f DH |
2775 | return SCM_BOOL_F; |
2776 | ||
2777 | if (idx == len) | |
2778 | result = uinteger; | |
2779 | else if (mem[idx] == '/') | |
f872b822 | 2780 | { |
3c9a524f DH |
2781 | SCM divisor; |
2782 | ||
2783 | idx++; | |
2784 | ||
2785 | divisor = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2786 | if (scm_is_false (divisor)) |
3c9a524f DH |
2787 | return SCM_BOOL_F; |
2788 | ||
f92e85f7 | 2789 | /* both are int/big here, I assume */ |
cba42c93 | 2790 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 2791 | } |
3c9a524f DH |
2792 | else if (radix == 10) |
2793 | { | |
2794 | result = mem2decimal_from_point (uinteger, mem, len, &idx, &x); | |
73e4de09 | 2795 | if (scm_is_false (result)) |
3c9a524f DH |
2796 | return SCM_BOOL_F; |
2797 | } | |
2798 | else | |
2799 | result = uinteger; | |
2800 | ||
2801 | *p_idx = idx; | |
2802 | if (x == INEXACT) | |
2803 | *p_exactness = x; | |
f872b822 | 2804 | } |
164d2481 MV |
2805 | |
2806 | /* When returning an inexact zero, make sure it is represented as a | |
2807 | floating point value so that we can change its sign. | |
2808 | */ | |
bc36d050 | 2809 | if (scm_is_eq (result, SCM_I_MAKINUM(0)) && *p_exactness == INEXACT) |
55f26379 | 2810 | result = scm_from_double (0.0); |
164d2481 MV |
2811 | |
2812 | return result; | |
3c9a524f | 2813 | } |
0f2d19dd | 2814 | |
0f2d19dd | 2815 | |
3c9a524f | 2816 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2817 | |
3c9a524f DH |
2818 | static SCM |
2819 | mem2complex (const char* mem, size_t len, unsigned int idx, | |
2820 | unsigned int radix, enum t_exactness *p_exactness) | |
2821 | { | |
2822 | char c; | |
2823 | int sign = 0; | |
2824 | SCM ureal; | |
2825 | ||
2826 | if (idx == len) | |
2827 | return SCM_BOOL_F; | |
2828 | ||
2829 | c = mem[idx]; | |
2830 | if (c == '+') | |
2831 | { | |
2832 | idx++; | |
2833 | sign = 1; | |
2834 | } | |
2835 | else if (c == '-') | |
2836 | { | |
2837 | idx++; | |
2838 | sign = -1; | |
0f2d19dd | 2839 | } |
0f2d19dd | 2840 | |
3c9a524f DH |
2841 | if (idx == len) |
2842 | return SCM_BOOL_F; | |
2843 | ||
2844 | ureal = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2845 | if (scm_is_false (ureal)) |
f872b822 | 2846 | { |
3c9a524f DH |
2847 | /* input must be either +i or -i */ |
2848 | ||
2849 | if (sign == 0) | |
2850 | return SCM_BOOL_F; | |
2851 | ||
2852 | if (mem[idx] == 'i' || mem[idx] == 'I') | |
f872b822 | 2853 | { |
3c9a524f DH |
2854 | idx++; |
2855 | if (idx != len) | |
2856 | return SCM_BOOL_F; | |
2857 | ||
d956fa6f | 2858 | return scm_make_rectangular (SCM_I_MAKINUM (0), SCM_I_MAKINUM (sign)); |
f872b822 | 2859 | } |
3c9a524f DH |
2860 | else |
2861 | return SCM_BOOL_F; | |
0f2d19dd | 2862 | } |
3c9a524f DH |
2863 | else |
2864 | { | |
73e4de09 | 2865 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 2866 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 2867 | |
3c9a524f DH |
2868 | if (idx == len) |
2869 | return ureal; | |
2870 | ||
2871 | c = mem[idx]; | |
2872 | switch (c) | |
f872b822 | 2873 | { |
3c9a524f DH |
2874 | case 'i': case 'I': |
2875 | /* either +<ureal>i or -<ureal>i */ | |
2876 | ||
2877 | idx++; | |
2878 | if (sign == 0) | |
2879 | return SCM_BOOL_F; | |
2880 | if (idx != len) | |
2881 | return SCM_BOOL_F; | |
d956fa6f | 2882 | return scm_make_rectangular (SCM_I_MAKINUM (0), ureal); |
3c9a524f DH |
2883 | |
2884 | case '@': | |
2885 | /* polar input: <real>@<real>. */ | |
2886 | ||
2887 | idx++; | |
2888 | if (idx == len) | |
2889 | return SCM_BOOL_F; | |
2890 | else | |
f872b822 | 2891 | { |
3c9a524f DH |
2892 | int sign; |
2893 | SCM angle; | |
2894 | SCM result; | |
2895 | ||
2896 | c = mem[idx]; | |
2897 | if (c == '+') | |
2898 | { | |
2899 | idx++; | |
2900 | sign = 1; | |
2901 | } | |
2902 | else if (c == '-') | |
2903 | { | |
2904 | idx++; | |
2905 | sign = -1; | |
2906 | } | |
2907 | else | |
2908 | sign = 1; | |
2909 | ||
2910 | angle = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2911 | if (scm_is_false (angle)) |
3c9a524f DH |
2912 | return SCM_BOOL_F; |
2913 | if (idx != len) | |
2914 | return SCM_BOOL_F; | |
2915 | ||
73e4de09 | 2916 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
2917 | angle = scm_difference (angle, SCM_UNDEFINED); |
2918 | ||
2919 | result = scm_make_polar (ureal, angle); | |
2920 | return result; | |
f872b822 | 2921 | } |
3c9a524f DH |
2922 | case '+': |
2923 | case '-': | |
2924 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 2925 | |
3c9a524f DH |
2926 | idx++; |
2927 | if (idx == len) | |
2928 | return SCM_BOOL_F; | |
2929 | else | |
2930 | { | |
2931 | int sign = (c == '+') ? 1 : -1; | |
2932 | SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness); | |
0f2d19dd | 2933 | |
73e4de09 | 2934 | if (scm_is_false (imag)) |
d956fa6f | 2935 | imag = SCM_I_MAKINUM (sign); |
73e4de09 | 2936 | else if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
1fe5e088 | 2937 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 2938 | |
3c9a524f DH |
2939 | if (idx == len) |
2940 | return SCM_BOOL_F; | |
2941 | if (mem[idx] != 'i' && mem[idx] != 'I') | |
2942 | return SCM_BOOL_F; | |
0f2d19dd | 2943 | |
3c9a524f DH |
2944 | idx++; |
2945 | if (idx != len) | |
2946 | return SCM_BOOL_F; | |
0f2d19dd | 2947 | |
1fe5e088 | 2948 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
2949 | } |
2950 | default: | |
2951 | return SCM_BOOL_F; | |
2952 | } | |
2953 | } | |
0f2d19dd | 2954 | } |
0f2d19dd JB |
2955 | |
2956 | ||
3c9a524f DH |
2957 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
2958 | ||
2959 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 2960 | |
0f2d19dd | 2961 | SCM |
2b829bbb KR |
2962 | scm_c_locale_stringn_to_number (const char* mem, size_t len, |
2963 | unsigned int default_radix) | |
0f2d19dd | 2964 | { |
3c9a524f DH |
2965 | unsigned int idx = 0; |
2966 | unsigned int radix = NO_RADIX; | |
2967 | enum t_exactness forced_x = NO_EXACTNESS; | |
2968 | enum t_exactness implicit_x = EXACT; | |
2969 | SCM result; | |
2970 | ||
2971 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
2972 | while (idx + 2 < len && mem[idx] == '#') | |
2973 | { | |
2974 | switch (mem[idx + 1]) | |
2975 | { | |
2976 | case 'b': case 'B': | |
2977 | if (radix != NO_RADIX) | |
2978 | return SCM_BOOL_F; | |
2979 | radix = DUAL; | |
2980 | break; | |
2981 | case 'd': case 'D': | |
2982 | if (radix != NO_RADIX) | |
2983 | return SCM_BOOL_F; | |
2984 | radix = DEC; | |
2985 | break; | |
2986 | case 'i': case 'I': | |
2987 | if (forced_x != NO_EXACTNESS) | |
2988 | return SCM_BOOL_F; | |
2989 | forced_x = INEXACT; | |
2990 | break; | |
2991 | case 'e': case 'E': | |
2992 | if (forced_x != NO_EXACTNESS) | |
2993 | return SCM_BOOL_F; | |
2994 | forced_x = EXACT; | |
2995 | break; | |
2996 | case 'o': case 'O': | |
2997 | if (radix != NO_RADIX) | |
2998 | return SCM_BOOL_F; | |
2999 | radix = OCT; | |
3000 | break; | |
3001 | case 'x': case 'X': | |
3002 | if (radix != NO_RADIX) | |
3003 | return SCM_BOOL_F; | |
3004 | radix = HEX; | |
3005 | break; | |
3006 | default: | |
f872b822 | 3007 | return SCM_BOOL_F; |
3c9a524f DH |
3008 | } |
3009 | idx += 2; | |
3010 | } | |
3011 | ||
3012 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
3013 | if (radix == NO_RADIX) | |
3014 | result = mem2complex (mem, len, idx, default_radix, &implicit_x); | |
3015 | else | |
3016 | result = mem2complex (mem, len, idx, (unsigned int) radix, &implicit_x); | |
3017 | ||
73e4de09 | 3018 | if (scm_is_false (result)) |
3c9a524f | 3019 | return SCM_BOOL_F; |
f872b822 | 3020 | |
3c9a524f | 3021 | switch (forced_x) |
f872b822 | 3022 | { |
3c9a524f DH |
3023 | case EXACT: |
3024 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
3025 | return scm_inexact_to_exact (result); |
3026 | else | |
3027 | return result; | |
3028 | case INEXACT: | |
3029 | if (SCM_INEXACTP (result)) | |
3030 | return result; | |
3031 | else | |
3032 | return scm_exact_to_inexact (result); | |
3033 | case NO_EXACTNESS: | |
3034 | default: | |
3035 | if (implicit_x == INEXACT) | |
3036 | { | |
3037 | if (SCM_INEXACTP (result)) | |
3038 | return result; | |
3039 | else | |
3040 | return scm_exact_to_inexact (result); | |
3041 | } | |
3042 | else | |
3043 | return result; | |
f872b822 | 3044 | } |
0f2d19dd JB |
3045 | } |
3046 | ||
3047 | ||
a1ec6916 | 3048 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 3049 | (SCM string, SCM radix), |
1e6808ea | 3050 | "Return a number of the maximally precise representation\n" |
942e5b91 | 3051 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
3052 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
3053 | "is a default radix that may be overridden by an explicit radix\n" | |
3054 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
3055 | "supplied, then the default radix is 10. If string is not a\n" | |
3056 | "syntactically valid notation for a number, then\n" | |
3057 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 3058 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
3059 | { |
3060 | SCM answer; | |
5efd3c7d | 3061 | unsigned int base; |
a6d9e5ab | 3062 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
3063 | |
3064 | if (SCM_UNBNDP (radix)) | |
3065 | base = 10; | |
3066 | else | |
3067 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
3068 | ||
2b829bbb KR |
3069 | answer = scm_c_locale_stringn_to_number (scm_i_string_chars (string), |
3070 | scm_i_string_length (string), | |
3071 | base); | |
8824ac88 MV |
3072 | scm_remember_upto_here_1 (string); |
3073 | return answer; | |
0f2d19dd | 3074 | } |
1bbd0b84 | 3075 | #undef FUNC_NAME |
3c9a524f DH |
3076 | |
3077 | ||
0f2d19dd JB |
3078 | /*** END strs->nums ***/ |
3079 | ||
5986c47d | 3080 | |
0f2d19dd | 3081 | SCM |
1bbd0b84 | 3082 | scm_bigequal (SCM x, SCM y) |
0f2d19dd | 3083 | { |
47ae1f0e | 3084 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
ca46fb90 | 3085 | scm_remember_upto_here_2 (x, y); |
73e4de09 | 3086 | return scm_from_bool (0 == result); |
0f2d19dd JB |
3087 | } |
3088 | ||
0f2d19dd | 3089 | SCM |
f3ae5d60 | 3090 | scm_real_equalp (SCM x, SCM y) |
0f2d19dd | 3091 | { |
73e4de09 | 3092 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0f2d19dd JB |
3093 | } |
3094 | ||
f3ae5d60 MD |
3095 | SCM |
3096 | scm_complex_equalp (SCM x, SCM y) | |
3097 | { | |
73e4de09 | 3098 | return scm_from_bool (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) |
f3ae5d60 MD |
3099 | && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); |
3100 | } | |
0f2d19dd | 3101 | |
f92e85f7 MV |
3102 | SCM |
3103 | scm_i_fraction_equalp (SCM x, SCM y) | |
3104 | { | |
73e4de09 | 3105 | if (scm_is_false (scm_equal_p (SCM_FRACTION_NUMERATOR (x), |
02164269 | 3106 | SCM_FRACTION_NUMERATOR (y))) |
73e4de09 | 3107 | || scm_is_false (scm_equal_p (SCM_FRACTION_DENOMINATOR (x), |
02164269 MV |
3108 | SCM_FRACTION_DENOMINATOR (y)))) |
3109 | return SCM_BOOL_F; | |
3110 | else | |
3111 | return SCM_BOOL_T; | |
f92e85f7 | 3112 | } |
0f2d19dd JB |
3113 | |
3114 | ||
8507ec80 MV |
3115 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
3116 | (SCM x), | |
3117 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
3118 | "otherwise.") | |
3119 | #define FUNC_NAME s_scm_number_p | |
3120 | { | |
3121 | return scm_from_bool (SCM_NUMBERP (x)); | |
3122 | } | |
3123 | #undef FUNC_NAME | |
3124 | ||
3125 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 3126 | (SCM x), |
942e5b91 | 3127 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 3128 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
3129 | "values form subsets of the set of complex numbers, i. e. the\n" |
3130 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
3131 | "rational or integer number.") | |
8507ec80 | 3132 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 3133 | { |
8507ec80 MV |
3134 | /* all numbers are complex. */ |
3135 | return scm_number_p (x); | |
0f2d19dd | 3136 | } |
1bbd0b84 | 3137 | #undef FUNC_NAME |
0f2d19dd | 3138 | |
f92e85f7 MV |
3139 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
3140 | (SCM x), | |
3141 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
3142 | "otherwise. Note that the set of integer values forms a subset of\n" | |
3143 | "the set of real numbers, i. e. the predicate will also be\n" | |
3144 | "fulfilled if @var{x} is an integer number.") | |
3145 | #define FUNC_NAME s_scm_real_p | |
3146 | { | |
3147 | /* we can't represent irrational numbers. */ | |
3148 | return scm_rational_p (x); | |
3149 | } | |
3150 | #undef FUNC_NAME | |
3151 | ||
3152 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 3153 | (SCM x), |
942e5b91 | 3154 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 3155 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 3156 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
3157 | "fulfilled if @var{x} is an integer number.") |
3158 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 3159 | { |
e11e83f3 | 3160 | if (SCM_I_INUMP (x)) |
0f2d19dd | 3161 | return SCM_BOOL_T; |
0aacf84e | 3162 | else if (SCM_IMP (x)) |
0f2d19dd | 3163 | return SCM_BOOL_F; |
0aacf84e | 3164 | else if (SCM_BIGP (x)) |
0f2d19dd | 3165 | return SCM_BOOL_T; |
f92e85f7 MV |
3166 | else if (SCM_FRACTIONP (x)) |
3167 | return SCM_BOOL_T; | |
3168 | else if (SCM_REALP (x)) | |
3169 | /* due to their limited precision, all floating point numbers are | |
3170 | rational as well. */ | |
3171 | return SCM_BOOL_T; | |
0aacf84e | 3172 | else |
bb628794 | 3173 | return SCM_BOOL_F; |
0f2d19dd | 3174 | } |
1bbd0b84 | 3175 | #undef FUNC_NAME |
0f2d19dd | 3176 | |
a1ec6916 | 3177 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 3178 | (SCM x), |
942e5b91 MG |
3179 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
3180 | "else.") | |
1bbd0b84 | 3181 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd JB |
3182 | { |
3183 | double r; | |
e11e83f3 | 3184 | if (SCM_I_INUMP (x)) |
f872b822 MD |
3185 | return SCM_BOOL_T; |
3186 | if (SCM_IMP (x)) | |
3187 | return SCM_BOOL_F; | |
f872b822 MD |
3188 | if (SCM_BIGP (x)) |
3189 | return SCM_BOOL_T; | |
3c9a524f | 3190 | if (!SCM_INEXACTP (x)) |
f872b822 | 3191 | return SCM_BOOL_F; |
3c9a524f | 3192 | if (SCM_COMPLEXP (x)) |
f872b822 | 3193 | return SCM_BOOL_F; |
5986c47d | 3194 | r = SCM_REAL_VALUE (x); |
1e35a229 | 3195 | /* +/-inf passes r==floor(r), making those #t */ |
f872b822 MD |
3196 | if (r == floor (r)) |
3197 | return SCM_BOOL_T; | |
0f2d19dd JB |
3198 | return SCM_BOOL_F; |
3199 | } | |
1bbd0b84 | 3200 | #undef FUNC_NAME |
0f2d19dd JB |
3201 | |
3202 | ||
a1ec6916 | 3203 | SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, |
1bbd0b84 | 3204 | (SCM x), |
942e5b91 MG |
3205 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" |
3206 | "else.") | |
1bbd0b84 | 3207 | #define FUNC_NAME s_scm_inexact_p |
0f2d19dd | 3208 | { |
eb927cb9 MV |
3209 | if (SCM_INEXACTP (x)) |
3210 | return SCM_BOOL_T; | |
3211 | if (SCM_NUMBERP (x)) | |
3212 | return SCM_BOOL_F; | |
3213 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 3214 | } |
1bbd0b84 | 3215 | #undef FUNC_NAME |
0f2d19dd JB |
3216 | |
3217 | ||
152f82bf | 3218 | SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p); |
942e5b91 | 3219 | /* "Return @code{#t} if all parameters are numerically equal." */ |
0f2d19dd | 3220 | SCM |
6e8d25a6 | 3221 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 3222 | { |
d8b95e27 | 3223 | again: |
e11e83f3 | 3224 | if (SCM_I_INUMP (x)) |
0aacf84e | 3225 | { |
e11e83f3 MV |
3226 | long xx = SCM_I_INUM (x); |
3227 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3228 | { |
e11e83f3 | 3229 | long yy = SCM_I_INUM (y); |
73e4de09 | 3230 | return scm_from_bool (xx == yy); |
0aacf84e MD |
3231 | } |
3232 | else if (SCM_BIGP (y)) | |
3233 | return SCM_BOOL_F; | |
3234 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
3235 | { |
3236 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
3237 | to a double and compare. | |
3238 | ||
3239 | But on a 64-bit system an inum is bigger than a double and | |
3240 | casting it to a double (call that dxx) will round. dxx is at | |
3241 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
3242 | an integer and fits a long. So we cast yy to a long and | |
3243 | compare with plain xx. | |
3244 | ||
3245 | An alternative (for any size system actually) would be to check | |
3246 | yy is an integer (with floor) and is in range of an inum | |
3247 | (compare against appropriate powers of 2) then test | |
3248 | xx==(long)yy. It's just a matter of which casts/comparisons | |
3249 | might be fastest or easiest for the cpu. */ | |
3250 | ||
3251 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
3252 | return scm_from_bool ((double) xx == yy |
3253 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
3254 | || xx == (long) yy)); | |
e8c5b1f2 | 3255 | } |
0aacf84e | 3256 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3257 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3258 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
3259 | else if (SCM_FRACTIONP (y)) |
3260 | return SCM_BOOL_F; | |
0aacf84e MD |
3261 | else |
3262 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3263 | } |
0aacf84e MD |
3264 | else if (SCM_BIGP (x)) |
3265 | { | |
e11e83f3 | 3266 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3267 | return SCM_BOOL_F; |
3268 | else if (SCM_BIGP (y)) | |
3269 | { | |
3270 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3271 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3272 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3273 | } |
3274 | else if (SCM_REALP (y)) | |
3275 | { | |
3276 | int cmp; | |
3277 | if (xisnan (SCM_REAL_VALUE (y))) | |
3278 | return SCM_BOOL_F; | |
3279 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3280 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3281 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3282 | } |
3283 | else if (SCM_COMPLEXP (y)) | |
3284 | { | |
3285 | int cmp; | |
3286 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
3287 | return SCM_BOOL_F; | |
3288 | if (xisnan (SCM_COMPLEX_REAL (y))) | |
3289 | return SCM_BOOL_F; | |
3290 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
3291 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3292 | return scm_from_bool (0 == cmp); |
0aacf84e | 3293 | } |
f92e85f7 MV |
3294 | else if (SCM_FRACTIONP (y)) |
3295 | return SCM_BOOL_F; | |
0aacf84e MD |
3296 | else |
3297 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3298 | } |
0aacf84e MD |
3299 | else if (SCM_REALP (x)) |
3300 | { | |
e8c5b1f2 | 3301 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 3302 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
3303 | { |
3304 | /* see comments with inum/real above */ | |
3305 | long yy = SCM_I_INUM (y); | |
3a1b45fd MV |
3306 | return scm_from_bool (xx == (double) yy |
3307 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
3308 | || (long) xx == yy)); | |
e8c5b1f2 | 3309 | } |
0aacf84e MD |
3310 | else if (SCM_BIGP (y)) |
3311 | { | |
3312 | int cmp; | |
3313 | if (xisnan (SCM_REAL_VALUE (x))) | |
3314 | return SCM_BOOL_F; | |
3315 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3316 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3317 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3318 | } |
3319 | else if (SCM_REALP (y)) | |
73e4de09 | 3320 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 3321 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3322 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3323 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3324 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3325 | { |
3326 | double xx = SCM_REAL_VALUE (x); | |
3327 | if (xisnan (xx)) | |
3328 | return SCM_BOOL_F; | |
3329 | if (xisinf (xx)) | |
73e4de09 | 3330 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3331 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3332 | goto again; | |
3333 | } | |
0aacf84e MD |
3334 | else |
3335 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3336 | } |
0aacf84e MD |
3337 | else if (SCM_COMPLEXP (x)) |
3338 | { | |
e11e83f3 MV |
3339 | if (SCM_I_INUMP (y)) |
3340 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
3341 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3342 | else if (SCM_BIGP (y)) | |
3343 | { | |
3344 | int cmp; | |
3345 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
3346 | return SCM_BOOL_F; | |
3347 | if (xisnan (SCM_COMPLEX_REAL (x))) | |
3348 | return SCM_BOOL_F; | |
3349 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
3350 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3351 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3352 | } |
3353 | else if (SCM_REALP (y)) | |
73e4de09 | 3354 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
3355 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3356 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 3357 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3358 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3359 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3360 | { |
3361 | double xx; | |
3362 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
3363 | return SCM_BOOL_F; | |
3364 | xx = SCM_COMPLEX_REAL (x); | |
3365 | if (xisnan (xx)) | |
3366 | return SCM_BOOL_F; | |
3367 | if (xisinf (xx)) | |
73e4de09 | 3368 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3369 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3370 | goto again; | |
3371 | } | |
f92e85f7 MV |
3372 | else |
3373 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
3374 | } | |
3375 | else if (SCM_FRACTIONP (x)) | |
3376 | { | |
e11e83f3 | 3377 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
3378 | return SCM_BOOL_F; |
3379 | else if (SCM_BIGP (y)) | |
3380 | return SCM_BOOL_F; | |
3381 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
3382 | { |
3383 | double yy = SCM_REAL_VALUE (y); | |
3384 | if (xisnan (yy)) | |
3385 | return SCM_BOOL_F; | |
3386 | if (xisinf (yy)) | |
73e4de09 | 3387 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3388 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3389 | goto again; | |
3390 | } | |
f92e85f7 | 3391 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
3392 | { |
3393 | double yy; | |
3394 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
3395 | return SCM_BOOL_F; | |
3396 | yy = SCM_COMPLEX_REAL (y); | |
3397 | if (xisnan (yy)) | |
3398 | return SCM_BOOL_F; | |
3399 | if (xisinf (yy)) | |
73e4de09 | 3400 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3401 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3402 | goto again; | |
3403 | } | |
f92e85f7 MV |
3404 | else if (SCM_FRACTIONP (y)) |
3405 | return scm_i_fraction_equalp (x, y); | |
0aacf84e MD |
3406 | else |
3407 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3408 | } |
0aacf84e | 3409 | else |
f4c627b3 | 3410 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p); |
0f2d19dd JB |
3411 | } |
3412 | ||
3413 | ||
a5f0b599 KR |
3414 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
3415 | done are good for inums, but for bignums an answer can almost always be | |
3416 | had by just examining a few high bits of the operands, as done by GMP in | |
3417 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
3418 | of the float exponent to take into account. */ | |
3419 | ||
152f82bf | 3420 | SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p); |
942e5b91 MG |
3421 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3422 | * "increasing." | |
3423 | */ | |
0f2d19dd | 3424 | SCM |
6e8d25a6 | 3425 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3426 | { |
a5f0b599 | 3427 | again: |
e11e83f3 | 3428 | if (SCM_I_INUMP (x)) |
0aacf84e | 3429 | { |
e11e83f3 MV |
3430 | long xx = SCM_I_INUM (x); |
3431 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3432 | { |
e11e83f3 | 3433 | long yy = SCM_I_INUM (y); |
73e4de09 | 3434 | return scm_from_bool (xx < yy); |
0aacf84e MD |
3435 | } |
3436 | else if (SCM_BIGP (y)) | |
3437 | { | |
3438 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3439 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3440 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3441 | } |
3442 | else if (SCM_REALP (y)) | |
73e4de09 | 3443 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 3444 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3445 | { |
3446 | /* "x < a/b" becomes "x*b < a" */ | |
3447 | int_frac: | |
3448 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
3449 | y = SCM_FRACTION_NUMERATOR (y); | |
3450 | goto again; | |
3451 | } | |
0aacf84e MD |
3452 | else |
3453 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3454 | } |
0aacf84e MD |
3455 | else if (SCM_BIGP (x)) |
3456 | { | |
e11e83f3 | 3457 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3458 | { |
3459 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3460 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3461 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3462 | } |
3463 | else if (SCM_BIGP (y)) | |
3464 | { | |
3465 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3466 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3467 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
3468 | } |
3469 | else if (SCM_REALP (y)) | |
3470 | { | |
3471 | int cmp; | |
3472 | if (xisnan (SCM_REAL_VALUE (y))) | |
3473 | return SCM_BOOL_F; | |
3474 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3475 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3476 | return scm_from_bool (cmp < 0); |
0aacf84e | 3477 | } |
f92e85f7 | 3478 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 3479 | goto int_frac; |
0aacf84e MD |
3480 | else |
3481 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f4c627b3 | 3482 | } |
0aacf84e MD |
3483 | else if (SCM_REALP (x)) |
3484 | { | |
e11e83f3 MV |
3485 | if (SCM_I_INUMP (y)) |
3486 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3487 | else if (SCM_BIGP (y)) |
3488 | { | |
3489 | int cmp; | |
3490 | if (xisnan (SCM_REAL_VALUE (x))) | |
3491 | return SCM_BOOL_F; | |
3492 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3493 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3494 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
3495 | } |
3496 | else if (SCM_REALP (y)) | |
73e4de09 | 3497 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 3498 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3499 | { |
3500 | double xx = SCM_REAL_VALUE (x); | |
3501 | if (xisnan (xx)) | |
3502 | return SCM_BOOL_F; | |
3503 | if (xisinf (xx)) | |
73e4de09 | 3504 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
3505 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3506 | goto again; | |
3507 | } | |
f92e85f7 MV |
3508 | else |
3509 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
3510 | } | |
3511 | else if (SCM_FRACTIONP (x)) | |
3512 | { | |
e11e83f3 | 3513 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
3514 | { |
3515 | /* "a/b < y" becomes "a < y*b" */ | |
3516 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
3517 | x = SCM_FRACTION_NUMERATOR (x); | |
3518 | goto again; | |
3519 | } | |
f92e85f7 | 3520 | else if (SCM_REALP (y)) |
a5f0b599 KR |
3521 | { |
3522 | double yy = SCM_REAL_VALUE (y); | |
3523 | if (xisnan (yy)) | |
3524 | return SCM_BOOL_F; | |
3525 | if (xisinf (yy)) | |
73e4de09 | 3526 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
3527 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3528 | goto again; | |
3529 | } | |
f92e85f7 | 3530 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3531 | { |
3532 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
3533 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
3534 | SCM_FRACTION_DENOMINATOR (y)); | |
3535 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
3536 | SCM_FRACTION_DENOMINATOR (x)); | |
3537 | x = new_x; | |
3538 | y = new_y; | |
3539 | goto again; | |
3540 | } | |
0aacf84e MD |
3541 | else |
3542 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3543 | } |
0aacf84e | 3544 | else |
f4c627b3 | 3545 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p); |
0f2d19dd JB |
3546 | } |
3547 | ||
3548 | ||
c76b1eaf | 3549 | SCM_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p); |
942e5b91 MG |
3550 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3551 | * "decreasing." | |
c76b1eaf | 3552 | */ |
1bbd0b84 | 3553 | #define FUNC_NAME s_scm_gr_p |
c76b1eaf MD |
3554 | SCM |
3555 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3556 | { |
c76b1eaf MD |
3557 | if (!SCM_NUMBERP (x)) |
3558 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME); | |
3559 | else if (!SCM_NUMBERP (y)) | |
3560 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME); | |
3561 | else | |
3562 | return scm_less_p (y, x); | |
0f2d19dd | 3563 | } |
1bbd0b84 | 3564 | #undef FUNC_NAME |
0f2d19dd JB |
3565 | |
3566 | ||
c76b1eaf | 3567 | SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p); |
942e5b91 | 3568 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3569 | * "non-decreasing." |
3570 | */ | |
1bbd0b84 | 3571 | #define FUNC_NAME s_scm_leq_p |
c76b1eaf MD |
3572 | SCM |
3573 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3574 | { |
c76b1eaf MD |
3575 | if (!SCM_NUMBERP (x)) |
3576 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3577 | else if (!SCM_NUMBERP (y)) | |
3578 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3579 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3580 | return SCM_BOOL_F; |
c76b1eaf | 3581 | else |
73e4de09 | 3582 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 3583 | } |
1bbd0b84 | 3584 | #undef FUNC_NAME |
0f2d19dd JB |
3585 | |
3586 | ||
c76b1eaf | 3587 | SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p); |
942e5b91 | 3588 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3589 | * "non-increasing." |
3590 | */ | |
1bbd0b84 | 3591 | #define FUNC_NAME s_scm_geq_p |
c76b1eaf MD |
3592 | SCM |
3593 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3594 | { |
c76b1eaf MD |
3595 | if (!SCM_NUMBERP (x)) |
3596 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3597 | else if (!SCM_NUMBERP (y)) | |
3598 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3599 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3600 | return SCM_BOOL_F; |
c76b1eaf | 3601 | else |
73e4de09 | 3602 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 3603 | } |
1bbd0b84 | 3604 | #undef FUNC_NAME |
0f2d19dd JB |
3605 | |
3606 | ||
152f82bf | 3607 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3608 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3609 | * "zero." | |
3610 | */ | |
0f2d19dd | 3611 | SCM |
6e8d25a6 | 3612 | scm_zero_p (SCM z) |
0f2d19dd | 3613 | { |
e11e83f3 | 3614 | if (SCM_I_INUMP (z)) |
bc36d050 | 3615 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 3616 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 3617 | return SCM_BOOL_F; |
0aacf84e | 3618 | else if (SCM_REALP (z)) |
73e4de09 | 3619 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 3620 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 3621 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 3622 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
3623 | else if (SCM_FRACTIONP (z)) |
3624 | return SCM_BOOL_F; | |
0aacf84e | 3625 | else |
c2ff8ab0 | 3626 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); |
0f2d19dd JB |
3627 | } |
3628 | ||
3629 | ||
152f82bf | 3630 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3631 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3632 | * "zero." | |
3633 | */ | |
0f2d19dd | 3634 | SCM |
6e8d25a6 | 3635 | scm_positive_p (SCM x) |
0f2d19dd | 3636 | { |
e11e83f3 MV |
3637 | if (SCM_I_INUMP (x)) |
3638 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
3639 | else if (SCM_BIGP (x)) |
3640 | { | |
3641 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3642 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3643 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3644 | } |
3645 | else if (SCM_REALP (x)) | |
73e4de09 | 3646 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
3647 | else if (SCM_FRACTIONP (x)) |
3648 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3649 | else |
c2ff8ab0 | 3650 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); |
0f2d19dd JB |
3651 | } |
3652 | ||
3653 | ||
152f82bf | 3654 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3655 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3656 | * "zero." | |
3657 | */ | |
0f2d19dd | 3658 | SCM |
6e8d25a6 | 3659 | scm_negative_p (SCM x) |
0f2d19dd | 3660 | { |
e11e83f3 MV |
3661 | if (SCM_I_INUMP (x)) |
3662 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
3663 | else if (SCM_BIGP (x)) |
3664 | { | |
3665 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3666 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3667 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3668 | } |
3669 | else if (SCM_REALP (x)) | |
73e4de09 | 3670 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
3671 | else if (SCM_FRACTIONP (x)) |
3672 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3673 | else |
c2ff8ab0 | 3674 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); |
0f2d19dd JB |
3675 | } |
3676 | ||
3677 | ||
2a06f791 KR |
3678 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
3679 | required by r5rs. On that basis, for exact/inexact combinations the | |
3680 | exact is converted to inexact to compare and possibly return. This is | |
3681 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
3682 | its test, such trouble is not required for min and max. */ | |
3683 | ||
9de33deb | 3684 | SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max); |
942e5b91 MG |
3685 | /* "Return the maximum of all parameter values." |
3686 | */ | |
0f2d19dd | 3687 | SCM |
6e8d25a6 | 3688 | scm_max (SCM x, SCM y) |
0f2d19dd | 3689 | { |
0aacf84e MD |
3690 | if (SCM_UNBNDP (y)) |
3691 | { | |
3692 | if (SCM_UNBNDP (x)) | |
3693 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 3694 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3695 | return x; |
3696 | else | |
3697 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3698 | } |
f4c627b3 | 3699 | |
e11e83f3 | 3700 | if (SCM_I_INUMP (x)) |
0aacf84e | 3701 | { |
e11e83f3 MV |
3702 | long xx = SCM_I_INUM (x); |
3703 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3704 | { |
e11e83f3 | 3705 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3706 | return (xx < yy) ? y : x; |
3707 | } | |
3708 | else if (SCM_BIGP (y)) | |
3709 | { | |
3710 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3711 | scm_remember_upto_here_1 (y); | |
3712 | return (sgn < 0) ? x : y; | |
3713 | } | |
3714 | else if (SCM_REALP (y)) | |
3715 | { | |
3716 | double z = xx; | |
3717 | /* if y==NaN then ">" is false and we return NaN */ | |
55f26379 | 3718 | return (z > SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3719 | } |
f92e85f7 MV |
3720 | else if (SCM_FRACTIONP (y)) |
3721 | { | |
e4bc5d6c | 3722 | use_less: |
73e4de09 | 3723 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 3724 | } |
0aacf84e MD |
3725 | else |
3726 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3727 | } |
0aacf84e MD |
3728 | else if (SCM_BIGP (x)) |
3729 | { | |
e11e83f3 | 3730 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3731 | { |
3732 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3733 | scm_remember_upto_here_1 (x); | |
3734 | return (sgn < 0) ? y : x; | |
3735 | } | |
3736 | else if (SCM_BIGP (y)) | |
3737 | { | |
3738 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3739 | scm_remember_upto_here_2 (x, y); | |
3740 | return (cmp > 0) ? x : y; | |
3741 | } | |
3742 | else if (SCM_REALP (y)) | |
3743 | { | |
2a06f791 KR |
3744 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
3745 | double xx, yy; | |
3746 | big_real: | |
3747 | xx = scm_i_big2dbl (x); | |
3748 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3749 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 3750 | } |
f92e85f7 MV |
3751 | else if (SCM_FRACTIONP (y)) |
3752 | { | |
e4bc5d6c | 3753 | goto use_less; |
f92e85f7 | 3754 | } |
0aacf84e MD |
3755 | else |
3756 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 3757 | } |
0aacf84e MD |
3758 | else if (SCM_REALP (x)) |
3759 | { | |
e11e83f3 | 3760 | if (SCM_I_INUMP (y)) |
0aacf84e | 3761 | { |
e11e83f3 | 3762 | double z = SCM_I_INUM (y); |
0aacf84e | 3763 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3764 | return (SCM_REAL_VALUE (x) < z) ? scm_from_double (z) : x; |
0aacf84e MD |
3765 | } |
3766 | else if (SCM_BIGP (y)) | |
3767 | { | |
b6f8f763 | 3768 | SCM_SWAP (x, y); |
2a06f791 | 3769 | goto big_real; |
0aacf84e MD |
3770 | } |
3771 | else if (SCM_REALP (y)) | |
3772 | { | |
3773 | /* if x==NaN then our explicit check means we return NaN | |
3774 | if y==NaN then ">" is false and we return NaN | |
3775 | calling isnan is unavoidable, since it's the only way to know | |
3776 | which of x or y causes any compares to be false */ | |
3777 | double xx = SCM_REAL_VALUE (x); | |
3778 | return (xisnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y; | |
3779 | } | |
f92e85f7 MV |
3780 | else if (SCM_FRACTIONP (y)) |
3781 | { | |
3782 | double yy = scm_i_fraction2double (y); | |
3783 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3784 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
3785 | } |
3786 | else | |
3787 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3788 | } | |
3789 | else if (SCM_FRACTIONP (x)) | |
3790 | { | |
e11e83f3 | 3791 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3792 | { |
e4bc5d6c | 3793 | goto use_less; |
f92e85f7 MV |
3794 | } |
3795 | else if (SCM_BIGP (y)) | |
3796 | { | |
e4bc5d6c | 3797 | goto use_less; |
f92e85f7 MV |
3798 | } |
3799 | else if (SCM_REALP (y)) | |
3800 | { | |
3801 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3802 | return (xx < SCM_REAL_VALUE (y)) ? y : scm_from_double (xx); |
f92e85f7 MV |
3803 | } |
3804 | else if (SCM_FRACTIONP (y)) | |
3805 | { | |
e4bc5d6c | 3806 | goto use_less; |
f92e85f7 | 3807 | } |
0aacf84e MD |
3808 | else |
3809 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3810 | } |
0aacf84e | 3811 | else |
f4c627b3 | 3812 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
3813 | } |
3814 | ||
3815 | ||
9de33deb | 3816 | SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min); |
942e5b91 MG |
3817 | /* "Return the minium of all parameter values." |
3818 | */ | |
0f2d19dd | 3819 | SCM |
6e8d25a6 | 3820 | scm_min (SCM x, SCM y) |
0f2d19dd | 3821 | { |
0aacf84e MD |
3822 | if (SCM_UNBNDP (y)) |
3823 | { | |
3824 | if (SCM_UNBNDP (x)) | |
3825 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 3826 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3827 | return x; |
3828 | else | |
3829 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 3830 | } |
f4c627b3 | 3831 | |
e11e83f3 | 3832 | if (SCM_I_INUMP (x)) |
0aacf84e | 3833 | { |
e11e83f3 MV |
3834 | long xx = SCM_I_INUM (x); |
3835 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3836 | { |
e11e83f3 | 3837 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3838 | return (xx < yy) ? x : y; |
3839 | } | |
3840 | else if (SCM_BIGP (y)) | |
3841 | { | |
3842 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3843 | scm_remember_upto_here_1 (y); | |
3844 | return (sgn < 0) ? y : x; | |
3845 | } | |
3846 | else if (SCM_REALP (y)) | |
3847 | { | |
3848 | double z = xx; | |
3849 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 3850 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3851 | } |
f92e85f7 MV |
3852 | else if (SCM_FRACTIONP (y)) |
3853 | { | |
e4bc5d6c | 3854 | use_less: |
73e4de09 | 3855 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 3856 | } |
0aacf84e MD |
3857 | else |
3858 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3859 | } |
0aacf84e MD |
3860 | else if (SCM_BIGP (x)) |
3861 | { | |
e11e83f3 | 3862 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3863 | { |
3864 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3865 | scm_remember_upto_here_1 (x); | |
3866 | return (sgn < 0) ? x : y; | |
3867 | } | |
3868 | else if (SCM_BIGP (y)) | |
3869 | { | |
3870 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3871 | scm_remember_upto_here_2 (x, y); | |
3872 | return (cmp > 0) ? y : x; | |
3873 | } | |
3874 | else if (SCM_REALP (y)) | |
3875 | { | |
2a06f791 KR |
3876 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
3877 | double xx, yy; | |
3878 | big_real: | |
3879 | xx = scm_i_big2dbl (x); | |
3880 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3881 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 3882 | } |
f92e85f7 MV |
3883 | else if (SCM_FRACTIONP (y)) |
3884 | { | |
e4bc5d6c | 3885 | goto use_less; |
f92e85f7 | 3886 | } |
0aacf84e MD |
3887 | else |
3888 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 3889 | } |
0aacf84e MD |
3890 | else if (SCM_REALP (x)) |
3891 | { | |
e11e83f3 | 3892 | if (SCM_I_INUMP (y)) |
0aacf84e | 3893 | { |
e11e83f3 | 3894 | double z = SCM_I_INUM (y); |
0aacf84e | 3895 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3896 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
3897 | } |
3898 | else if (SCM_BIGP (y)) | |
3899 | { | |
b6f8f763 | 3900 | SCM_SWAP (x, y); |
2a06f791 | 3901 | goto big_real; |
0aacf84e MD |
3902 | } |
3903 | else if (SCM_REALP (y)) | |
3904 | { | |
3905 | /* if x==NaN then our explicit check means we return NaN | |
3906 | if y==NaN then "<" is false and we return NaN | |
3907 | calling isnan is unavoidable, since it's the only way to know | |
3908 | which of x or y causes any compares to be false */ | |
3909 | double xx = SCM_REAL_VALUE (x); | |
3910 | return (xisnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y; | |
3911 | } | |
f92e85f7 MV |
3912 | else if (SCM_FRACTIONP (y)) |
3913 | { | |
3914 | double yy = scm_i_fraction2double (y); | |
3915 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3916 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 3917 | } |
0aacf84e MD |
3918 | else |
3919 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3920 | } |
f92e85f7 MV |
3921 | else if (SCM_FRACTIONP (x)) |
3922 | { | |
e11e83f3 | 3923 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3924 | { |
e4bc5d6c | 3925 | goto use_less; |
f92e85f7 MV |
3926 | } |
3927 | else if (SCM_BIGP (y)) | |
3928 | { | |
e4bc5d6c | 3929 | goto use_less; |
f92e85f7 MV |
3930 | } |
3931 | else if (SCM_REALP (y)) | |
3932 | { | |
3933 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3934 | return (SCM_REAL_VALUE (y) < xx) ? y : scm_from_double (xx); |
f92e85f7 MV |
3935 | } |
3936 | else if (SCM_FRACTIONP (y)) | |
3937 | { | |
e4bc5d6c | 3938 | goto use_less; |
f92e85f7 MV |
3939 | } |
3940 | else | |
3941 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3942 | } | |
0aacf84e | 3943 | else |
f4c627b3 | 3944 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
3945 | } |
3946 | ||
3947 | ||
9de33deb | 3948 | SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum); |
942e5b91 MG |
3949 | /* "Return the sum of all parameter values. Return 0 if called without\n" |
3950 | * "any parameters." | |
3951 | */ | |
0f2d19dd | 3952 | SCM |
6e8d25a6 | 3953 | scm_sum (SCM x, SCM y) |
0f2d19dd | 3954 | { |
9cc37597 | 3955 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
3956 | { |
3957 | if (SCM_NUMBERP (x)) return x; | |
3958 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 3959 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 3960 | } |
c209c88e | 3961 | |
9cc37597 | 3962 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 3963 | { |
9cc37597 | 3964 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 3965 | { |
e11e83f3 MV |
3966 | long xx = SCM_I_INUM (x); |
3967 | long yy = SCM_I_INUM (y); | |
ca46fb90 | 3968 | long int z = xx + yy; |
d956fa6f | 3969 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_long2big (z); |
ca46fb90 RB |
3970 | } |
3971 | else if (SCM_BIGP (y)) | |
3972 | { | |
3973 | SCM_SWAP (x, y); | |
3974 | goto add_big_inum; | |
3975 | } | |
3976 | else if (SCM_REALP (y)) | |
3977 | { | |
e11e83f3 | 3978 | long int xx = SCM_I_INUM (x); |
55f26379 | 3979 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
3980 | } |
3981 | else if (SCM_COMPLEXP (y)) | |
3982 | { | |
e11e83f3 | 3983 | long int xx = SCM_I_INUM (x); |
8507ec80 | 3984 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
3985 | SCM_COMPLEX_IMAG (y)); |
3986 | } | |
f92e85f7 | 3987 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 3988 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
3989 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
3990 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
3991 | else |
3992 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
3993 | } else if (SCM_BIGP (x)) |
3994 | { | |
e11e83f3 | 3995 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3996 | { |
3997 | long int inum; | |
3998 | int bigsgn; | |
3999 | add_big_inum: | |
e11e83f3 | 4000 | inum = SCM_I_INUM (y); |
0aacf84e MD |
4001 | if (inum == 0) |
4002 | return x; | |
4003 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4004 | if (inum < 0) | |
4005 | { | |
4006 | SCM result = scm_i_mkbig (); | |
4007 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
4008 | scm_remember_upto_here_1 (x); | |
4009 | /* we know the result will have to be a bignum */ | |
4010 | if (bigsgn == -1) | |
4011 | return result; | |
4012 | return scm_i_normbig (result); | |
4013 | } | |
4014 | else | |
4015 | { | |
4016 | SCM result = scm_i_mkbig (); | |
4017 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
4018 | scm_remember_upto_here_1 (x); | |
4019 | /* we know the result will have to be a bignum */ | |
4020 | if (bigsgn == 1) | |
4021 | return result; | |
4022 | return scm_i_normbig (result); | |
4023 | } | |
4024 | } | |
4025 | else if (SCM_BIGP (y)) | |
4026 | { | |
4027 | SCM result = scm_i_mkbig (); | |
4028 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4029 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4030 | mpz_add (SCM_I_BIG_MPZ (result), | |
4031 | SCM_I_BIG_MPZ (x), | |
4032 | SCM_I_BIG_MPZ (y)); | |
4033 | scm_remember_upto_here_2 (x, y); | |
4034 | /* we know the result will have to be a bignum */ | |
4035 | if (sgn_x == sgn_y) | |
4036 | return result; | |
4037 | return scm_i_normbig (result); | |
4038 | } | |
4039 | else if (SCM_REALP (y)) | |
4040 | { | |
4041 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
4042 | scm_remember_upto_here_1 (x); | |
55f26379 | 4043 | return scm_from_double (result); |
0aacf84e MD |
4044 | } |
4045 | else if (SCM_COMPLEXP (y)) | |
4046 | { | |
4047 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4048 | + SCM_COMPLEX_REAL (y)); | |
4049 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4050 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4051 | } |
f92e85f7 | 4052 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4053 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
4054 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
4055 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4056 | else |
4057 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 4058 | } |
0aacf84e MD |
4059 | else if (SCM_REALP (x)) |
4060 | { | |
e11e83f3 | 4061 | if (SCM_I_INUMP (y)) |
55f26379 | 4062 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
4063 | else if (SCM_BIGP (y)) |
4064 | { | |
4065 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
4066 | scm_remember_upto_here_1 (y); | |
55f26379 | 4067 | return scm_from_double (result); |
0aacf84e MD |
4068 | } |
4069 | else if (SCM_REALP (y)) | |
55f26379 | 4070 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 4071 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4072 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4073 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4074 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4075 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
4076 | else |
4077 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 4078 | } |
0aacf84e MD |
4079 | else if (SCM_COMPLEXP (x)) |
4080 | { | |
e11e83f3 | 4081 | if (SCM_I_INUMP (y)) |
8507ec80 | 4082 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
4083 | SCM_COMPLEX_IMAG (x)); |
4084 | else if (SCM_BIGP (y)) | |
4085 | { | |
4086 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
4087 | + SCM_COMPLEX_REAL (x)); | |
4088 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4089 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4090 | } |
4091 | else if (SCM_REALP (y)) | |
8507ec80 | 4092 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
4093 | SCM_COMPLEX_IMAG (x)); |
4094 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4095 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4096 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4097 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4098 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
4099 | SCM_COMPLEX_IMAG (x)); |
4100 | else | |
4101 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
4102 | } | |
4103 | else if (SCM_FRACTIONP (x)) | |
4104 | { | |
e11e83f3 | 4105 | if (SCM_I_INUMP (y)) |
cba42c93 | 4106 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4107 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4108 | SCM_FRACTION_DENOMINATOR (x)); | |
4109 | else if (SCM_BIGP (y)) | |
cba42c93 | 4110 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4111 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4112 | SCM_FRACTION_DENOMINATOR (x)); | |
4113 | else if (SCM_REALP (y)) | |
55f26379 | 4114 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 4115 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4116 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
4117 | SCM_COMPLEX_IMAG (y)); |
4118 | else if (SCM_FRACTIONP (y)) | |
4119 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 4120 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4121 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4122 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4123 | else |
4124 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 4125 | } |
0aacf84e | 4126 | else |
98cb6e75 | 4127 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
4128 | } |
4129 | ||
4130 | ||
40882e3d KR |
4131 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
4132 | (SCM x), | |
4133 | "Return @math{@var{x}+1}.") | |
4134 | #define FUNC_NAME s_scm_oneplus | |
4135 | { | |
4136 | return scm_sum (x, SCM_I_MAKINUM (1)); | |
4137 | } | |
4138 | #undef FUNC_NAME | |
4139 | ||
4140 | ||
9de33deb | 4141 | SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference); |
609c3d30 MG |
4142 | /* If called with one argument @var{z1}, -@var{z1} returned. Otherwise |
4143 | * the sum of all but the first argument are subtracted from the first | |
4144 | * argument. */ | |
c05e97b7 | 4145 | #define FUNC_NAME s_difference |
0f2d19dd | 4146 | SCM |
6e8d25a6 | 4147 | scm_difference (SCM x, SCM y) |
0f2d19dd | 4148 | { |
9cc37597 | 4149 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
4150 | { |
4151 | if (SCM_UNBNDP (x)) | |
4152 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
4153 | else | |
e11e83f3 | 4154 | if (SCM_I_INUMP (x)) |
ca46fb90 | 4155 | { |
e11e83f3 | 4156 | long xx = -SCM_I_INUM (x); |
ca46fb90 | 4157 | if (SCM_FIXABLE (xx)) |
d956fa6f | 4158 | return SCM_I_MAKINUM (xx); |
ca46fb90 RB |
4159 | else |
4160 | return scm_i_long2big (xx); | |
4161 | } | |
4162 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
4163 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
4164 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
4165 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
4166 | else if (SCM_REALP (x)) | |
55f26379 | 4167 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 4168 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 4169 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 4170 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 4171 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4172 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 4173 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
4174 | else |
4175 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 4176 | } |
ca46fb90 | 4177 | |
9cc37597 | 4178 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 4179 | { |
9cc37597 | 4180 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4181 | { |
e11e83f3 MV |
4182 | long int xx = SCM_I_INUM (x); |
4183 | long int yy = SCM_I_INUM (y); | |
0aacf84e MD |
4184 | long int z = xx - yy; |
4185 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4186 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4187 | else |
4188 | return scm_i_long2big (z); | |
4189 | } | |
4190 | else if (SCM_BIGP (y)) | |
4191 | { | |
4192 | /* inum-x - big-y */ | |
e11e83f3 | 4193 | long xx = SCM_I_INUM (x); |
ca46fb90 | 4194 | |
0aacf84e MD |
4195 | if (xx == 0) |
4196 | return scm_i_clonebig (y, 0); | |
4197 | else | |
4198 | { | |
4199 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4200 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4201 | |
0aacf84e MD |
4202 | if (xx >= 0) |
4203 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
4204 | else | |
4205 | { | |
4206 | /* x - y == -(y + -x) */ | |
4207 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
4208 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4209 | } | |
4210 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 4211 | |
0aacf84e MD |
4212 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
4213 | /* we know the result will have to be a bignum */ | |
4214 | return result; | |
4215 | else | |
4216 | return scm_i_normbig (result); | |
4217 | } | |
4218 | } | |
4219 | else if (SCM_REALP (y)) | |
4220 | { | |
e11e83f3 | 4221 | long int xx = SCM_I_INUM (x); |
55f26379 | 4222 | return scm_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
4223 | } |
4224 | else if (SCM_COMPLEXP (y)) | |
4225 | { | |
e11e83f3 | 4226 | long int xx = SCM_I_INUM (x); |
8507ec80 | 4227 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4228 | - SCM_COMPLEX_IMAG (y)); |
4229 | } | |
f92e85f7 MV |
4230 | else if (SCM_FRACTIONP (y)) |
4231 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 4232 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4233 | SCM_FRACTION_NUMERATOR (y)), |
4234 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4235 | else |
4236 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 4237 | } |
0aacf84e MD |
4238 | else if (SCM_BIGP (x)) |
4239 | { | |
e11e83f3 | 4240 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4241 | { |
4242 | /* big-x - inum-y */ | |
e11e83f3 | 4243 | long yy = SCM_I_INUM (y); |
0aacf84e | 4244 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 4245 | |
0aacf84e MD |
4246 | scm_remember_upto_here_1 (x); |
4247 | if (sgn_x == 0) | |
c71b0706 MV |
4248 | return (SCM_FIXABLE (-yy) ? |
4249 | SCM_I_MAKINUM (-yy) : scm_from_long (-yy)); | |
0aacf84e MD |
4250 | else |
4251 | { | |
4252 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4253 | |
708f22c6 KR |
4254 | if (yy >= 0) |
4255 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
4256 | else | |
4257 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 4258 | scm_remember_upto_here_1 (x); |
ca46fb90 | 4259 | |
0aacf84e MD |
4260 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
4261 | /* we know the result will have to be a bignum */ | |
4262 | return result; | |
4263 | else | |
4264 | return scm_i_normbig (result); | |
4265 | } | |
4266 | } | |
4267 | else if (SCM_BIGP (y)) | |
4268 | { | |
4269 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4270 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4271 | SCM result = scm_i_mkbig (); | |
4272 | mpz_sub (SCM_I_BIG_MPZ (result), | |
4273 | SCM_I_BIG_MPZ (x), | |
4274 | SCM_I_BIG_MPZ (y)); | |
4275 | scm_remember_upto_here_2 (x, y); | |
4276 | /* we know the result will have to be a bignum */ | |
4277 | if ((sgn_x == 1) && (sgn_y == -1)) | |
4278 | return result; | |
4279 | if ((sgn_x == -1) && (sgn_y == 1)) | |
4280 | return result; | |
4281 | return scm_i_normbig (result); | |
4282 | } | |
4283 | else if (SCM_REALP (y)) | |
4284 | { | |
4285 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
4286 | scm_remember_upto_here_1 (x); | |
55f26379 | 4287 | return scm_from_double (result); |
0aacf84e MD |
4288 | } |
4289 | else if (SCM_COMPLEXP (y)) | |
4290 | { | |
4291 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4292 | - SCM_COMPLEX_REAL (y)); | |
4293 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4294 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4295 | } |
f92e85f7 | 4296 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4297 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4298 | SCM_FRACTION_NUMERATOR (y)), |
4299 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 4300 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 4301 | } |
0aacf84e MD |
4302 | else if (SCM_REALP (x)) |
4303 | { | |
e11e83f3 | 4304 | if (SCM_I_INUMP (y)) |
55f26379 | 4305 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
4306 | else if (SCM_BIGP (y)) |
4307 | { | |
4308 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4309 | scm_remember_upto_here_1 (x); | |
55f26379 | 4310 | return scm_from_double (result); |
0aacf84e MD |
4311 | } |
4312 | else if (SCM_REALP (y)) | |
55f26379 | 4313 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 4314 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4315 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4316 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4317 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4318 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
4319 | else |
4320 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4321 | } |
0aacf84e MD |
4322 | else if (SCM_COMPLEXP (x)) |
4323 | { | |
e11e83f3 | 4324 | if (SCM_I_INUMP (y)) |
8507ec80 | 4325 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
4326 | SCM_COMPLEX_IMAG (x)); |
4327 | else if (SCM_BIGP (y)) | |
4328 | { | |
4329 | double real_part = (SCM_COMPLEX_REAL (x) | |
4330 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
4331 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4332 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
4333 | } |
4334 | else if (SCM_REALP (y)) | |
8507ec80 | 4335 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
4336 | SCM_COMPLEX_IMAG (x)); |
4337 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4338 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4339 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4340 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4341 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
4342 | SCM_COMPLEX_IMAG (x)); |
4343 | else | |
4344 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
4345 | } | |
4346 | else if (SCM_FRACTIONP (x)) | |
4347 | { | |
e11e83f3 | 4348 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4349 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 4350 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4351 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4352 | SCM_FRACTION_DENOMINATOR (x)); | |
4353 | else if (SCM_BIGP (y)) | |
cba42c93 | 4354 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4355 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4356 | SCM_FRACTION_DENOMINATOR (x)); | |
4357 | else if (SCM_REALP (y)) | |
55f26379 | 4358 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 4359 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4360 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4361 | -SCM_COMPLEX_IMAG (y)); |
4362 | else if (SCM_FRACTIONP (y)) | |
4363 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 4364 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4365 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4366 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4367 | else |
4368 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4369 | } |
0aacf84e | 4370 | else |
98cb6e75 | 4371 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 4372 | } |
c05e97b7 | 4373 | #undef FUNC_NAME |
0f2d19dd | 4374 | |
ca46fb90 | 4375 | |
40882e3d KR |
4376 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
4377 | (SCM x), | |
4378 | "Return @math{@var{x}-1}.") | |
4379 | #define FUNC_NAME s_scm_oneminus | |
4380 | { | |
4381 | return scm_difference (x, SCM_I_MAKINUM (1)); | |
4382 | } | |
4383 | #undef FUNC_NAME | |
4384 | ||
4385 | ||
9de33deb | 4386 | SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product); |
942e5b91 MG |
4387 | /* "Return the product of all arguments. If called without arguments,\n" |
4388 | * "1 is returned." | |
4389 | */ | |
0f2d19dd | 4390 | SCM |
6e8d25a6 | 4391 | scm_product (SCM x, SCM y) |
0f2d19dd | 4392 | { |
9cc37597 | 4393 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
4394 | { |
4395 | if (SCM_UNBNDP (x)) | |
d956fa6f | 4396 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
4397 | else if (SCM_NUMBERP (x)) |
4398 | return x; | |
4399 | else | |
4400 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 4401 | } |
ca46fb90 | 4402 | |
9cc37597 | 4403 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e MD |
4404 | { |
4405 | long xx; | |
f4c627b3 | 4406 | |
0aacf84e | 4407 | intbig: |
e11e83f3 | 4408 | xx = SCM_I_INUM (x); |
f4c627b3 | 4409 | |
0aacf84e MD |
4410 | switch (xx) |
4411 | { | |
ca46fb90 RB |
4412 | case 0: return x; break; |
4413 | case 1: return y; break; | |
0aacf84e | 4414 | } |
f4c627b3 | 4415 | |
9cc37597 | 4416 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4417 | { |
e11e83f3 | 4418 | long yy = SCM_I_INUM (y); |
0aacf84e | 4419 | long kk = xx * yy; |
d956fa6f | 4420 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 4421 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
4422 | return k; |
4423 | else | |
4424 | { | |
4425 | SCM result = scm_i_long2big (xx); | |
4426 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); | |
4427 | return scm_i_normbig (result); | |
4428 | } | |
4429 | } | |
4430 | else if (SCM_BIGP (y)) | |
4431 | { | |
4432 | SCM result = scm_i_mkbig (); | |
4433 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
4434 | scm_remember_upto_here_1 (y); | |
4435 | return result; | |
4436 | } | |
4437 | else if (SCM_REALP (y)) | |
55f26379 | 4438 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 4439 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4440 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 4441 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4442 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4443 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4444 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4445 | else |
4446 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4447 | } |
0aacf84e MD |
4448 | else if (SCM_BIGP (x)) |
4449 | { | |
e11e83f3 | 4450 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4451 | { |
4452 | SCM_SWAP (x, y); | |
4453 | goto intbig; | |
4454 | } | |
4455 | else if (SCM_BIGP (y)) | |
4456 | { | |
4457 | SCM result = scm_i_mkbig (); | |
4458 | mpz_mul (SCM_I_BIG_MPZ (result), | |
4459 | SCM_I_BIG_MPZ (x), | |
4460 | SCM_I_BIG_MPZ (y)); | |
4461 | scm_remember_upto_here_2 (x, y); | |
4462 | return result; | |
4463 | } | |
4464 | else if (SCM_REALP (y)) | |
4465 | { | |
4466 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
4467 | scm_remember_upto_here_1 (x); | |
55f26379 | 4468 | return scm_from_double (result); |
0aacf84e MD |
4469 | } |
4470 | else if (SCM_COMPLEXP (y)) | |
4471 | { | |
4472 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4473 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4474 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4475 | z * SCM_COMPLEX_IMAG (y)); |
4476 | } | |
f92e85f7 | 4477 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4478 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4479 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4480 | else |
4481 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4482 | } |
0aacf84e MD |
4483 | else if (SCM_REALP (x)) |
4484 | { | |
e11e83f3 | 4485 | if (SCM_I_INUMP (y)) |
23d72566 KR |
4486 | { |
4487 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
4488 | if (scm_is_eq (y, SCM_INUM0)) | |
4489 | return y; | |
4490 | return scm_from_double (SCM_I_INUM (y) * SCM_REAL_VALUE (x)); | |
4491 | } | |
0aacf84e MD |
4492 | else if (SCM_BIGP (y)) |
4493 | { | |
4494 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
4495 | scm_remember_upto_here_1 (y); | |
55f26379 | 4496 | return scm_from_double (result); |
0aacf84e MD |
4497 | } |
4498 | else if (SCM_REALP (y)) | |
55f26379 | 4499 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 4500 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4501 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 4502 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4503 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4504 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
4505 | else |
4506 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4507 | } |
0aacf84e MD |
4508 | else if (SCM_COMPLEXP (x)) |
4509 | { | |
e11e83f3 | 4510 | if (SCM_I_INUMP (y)) |
23d72566 KR |
4511 | { |
4512 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
4513 | if (scm_is_eq (y, SCM_INUM0)) | |
4514 | return y; | |
4515 | return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x), | |
4516 | SCM_I_INUM (y) * SCM_COMPLEX_IMAG (x)); | |
4517 | } | |
0aacf84e MD |
4518 | else if (SCM_BIGP (y)) |
4519 | { | |
4520 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4521 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4522 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 4523 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4524 | } |
4525 | else if (SCM_REALP (y)) | |
8507ec80 | 4526 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
4527 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
4528 | else if (SCM_COMPLEXP (y)) | |
4529 | { | |
8507ec80 | 4530 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
4531 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
4532 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
4533 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
4534 | } | |
f92e85f7 MV |
4535 | else if (SCM_FRACTIONP (y)) |
4536 | { | |
4537 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4538 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
4539 | yy * SCM_COMPLEX_IMAG (x)); |
4540 | } | |
4541 | else | |
4542 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
4543 | } | |
4544 | else if (SCM_FRACTIONP (x)) | |
4545 | { | |
e11e83f3 | 4546 | if (SCM_I_INUMP (y)) |
cba42c93 | 4547 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4548 | SCM_FRACTION_DENOMINATOR (x)); |
4549 | else if (SCM_BIGP (y)) | |
cba42c93 | 4550 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4551 | SCM_FRACTION_DENOMINATOR (x)); |
4552 | else if (SCM_REALP (y)) | |
55f26379 | 4553 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
4554 | else if (SCM_COMPLEXP (y)) |
4555 | { | |
4556 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 4557 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4558 | xx * SCM_COMPLEX_IMAG (y)); |
4559 | } | |
4560 | else if (SCM_FRACTIONP (y)) | |
4561 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 4562 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4563 | SCM_FRACTION_NUMERATOR (y)), |
4564 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
4565 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4566 | else |
4567 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4568 | } |
0aacf84e | 4569 | else |
f4c627b3 | 4570 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
4571 | } |
4572 | ||
7351e207 MV |
4573 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
4574 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
4575 | #define ALLOW_DIVIDE_BY_ZERO | |
4576 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
4577 | #endif | |
0f2d19dd | 4578 | |
ba74ef4e MV |
4579 | /* The code below for complex division is adapted from the GNU |
4580 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
4581 | this copyright: */ | |
4582 | ||
4583 | /**************************************************************** | |
4584 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
4585 | ||
4586 | Permission to use, copy, modify, and distribute this software | |
4587 | and its documentation for any purpose and without fee is hereby | |
4588 | granted, provided that the above copyright notice appear in all | |
4589 | copies and that both that the copyright notice and this | |
4590 | permission notice and warranty disclaimer appear in supporting | |
4591 | documentation, and that the names of AT&T Bell Laboratories or | |
4592 | Bellcore or any of their entities not be used in advertising or | |
4593 | publicity pertaining to distribution of the software without | |
4594 | specific, written prior permission. | |
4595 | ||
4596 | AT&T and Bellcore disclaim all warranties with regard to this | |
4597 | software, including all implied warranties of merchantability | |
4598 | and fitness. In no event shall AT&T or Bellcore be liable for | |
4599 | any special, indirect or consequential damages or any damages | |
4600 | whatsoever resulting from loss of use, data or profits, whether | |
4601 | in an action of contract, negligence or other tortious action, | |
4602 | arising out of or in connection with the use or performance of | |
4603 | this software. | |
4604 | ****************************************************************/ | |
4605 | ||
9de33deb | 4606 | SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide); |
609c3d30 MG |
4607 | /* Divide the first argument by the product of the remaining |
4608 | arguments. If called with one argument @var{z1}, 1/@var{z1} is | |
4609 | returned. */ | |
c05e97b7 | 4610 | #define FUNC_NAME s_divide |
f92e85f7 MV |
4611 | static SCM |
4612 | scm_i_divide (SCM x, SCM y, int inexact) | |
0f2d19dd | 4613 | { |
f8de44c1 DH |
4614 | double a; |
4615 | ||
9cc37597 | 4616 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
4617 | { |
4618 | if (SCM_UNBNDP (x)) | |
4619 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 4620 | else if (SCM_I_INUMP (x)) |
0aacf84e | 4621 | { |
e11e83f3 | 4622 | long xx = SCM_I_INUM (x); |
0aacf84e MD |
4623 | if (xx == 1 || xx == -1) |
4624 | return x; | |
7351e207 | 4625 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4626 | else if (xx == 0) |
4627 | scm_num_overflow (s_divide); | |
7351e207 | 4628 | #endif |
0aacf84e | 4629 | else |
f92e85f7 MV |
4630 | { |
4631 | if (inexact) | |
55f26379 | 4632 | return scm_from_double (1.0 / (double) xx); |
cba42c93 | 4633 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4634 | } |
0aacf84e MD |
4635 | } |
4636 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
4637 | { |
4638 | if (inexact) | |
55f26379 | 4639 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cba42c93 | 4640 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4641 | } |
0aacf84e MD |
4642 | else if (SCM_REALP (x)) |
4643 | { | |
4644 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 4645 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4646 | if (xx == 0.0) |
4647 | scm_num_overflow (s_divide); | |
4648 | else | |
7351e207 | 4649 | #endif |
55f26379 | 4650 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
4651 | } |
4652 | else if (SCM_COMPLEXP (x)) | |
4653 | { | |
4654 | double r = SCM_COMPLEX_REAL (x); | |
4655 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 4656 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
4657 | { |
4658 | double t = r / i; | |
4659 | double d = i * (1.0 + t * t); | |
8507ec80 | 4660 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
4661 | } |
4662 | else | |
4663 | { | |
4664 | double t = i / r; | |
4665 | double d = r * (1.0 + t * t); | |
8507ec80 | 4666 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
4667 | } |
4668 | } | |
f92e85f7 | 4669 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4670 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 4671 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
4672 | else |
4673 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 4674 | } |
f8de44c1 | 4675 | |
9cc37597 | 4676 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 4677 | { |
e11e83f3 | 4678 | long xx = SCM_I_INUM (x); |
9cc37597 | 4679 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4680 | { |
e11e83f3 | 4681 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
4682 | if (yy == 0) |
4683 | { | |
7351e207 | 4684 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4685 | scm_num_overflow (s_divide); |
7351e207 | 4686 | #else |
55f26379 | 4687 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 4688 | #endif |
0aacf84e MD |
4689 | } |
4690 | else if (xx % yy != 0) | |
f92e85f7 MV |
4691 | { |
4692 | if (inexact) | |
55f26379 | 4693 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 4694 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4695 | } |
0aacf84e MD |
4696 | else |
4697 | { | |
4698 | long z = xx / yy; | |
4699 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4700 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4701 | else |
4702 | return scm_i_long2big (z); | |
4703 | } | |
f872b822 | 4704 | } |
0aacf84e | 4705 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
4706 | { |
4707 | if (inexact) | |
55f26379 | 4708 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 4709 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4710 | } |
0aacf84e MD |
4711 | else if (SCM_REALP (y)) |
4712 | { | |
4713 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4714 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4715 | if (yy == 0.0) |
4716 | scm_num_overflow (s_divide); | |
4717 | else | |
7351e207 | 4718 | #endif |
55f26379 | 4719 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 4720 | } |
0aacf84e MD |
4721 | else if (SCM_COMPLEXP (y)) |
4722 | { | |
4723 | a = xx; | |
4724 | complex_div: /* y _must_ be a complex number */ | |
4725 | { | |
4726 | double r = SCM_COMPLEX_REAL (y); | |
4727 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 4728 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
4729 | { |
4730 | double t = r / i; | |
4731 | double d = i * (1.0 + t * t); | |
8507ec80 | 4732 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
4733 | } |
4734 | else | |
4735 | { | |
4736 | double t = i / r; | |
4737 | double d = r * (1.0 + t * t); | |
8507ec80 | 4738 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
4739 | } |
4740 | } | |
4741 | } | |
f92e85f7 MV |
4742 | else if (SCM_FRACTIONP (y)) |
4743 | /* a / b/c = ac / b */ | |
cba42c93 | 4744 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4745 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4746 | else |
4747 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4748 | } |
0aacf84e MD |
4749 | else if (SCM_BIGP (x)) |
4750 | { | |
e11e83f3 | 4751 | if (SCM_I_INUMP (y)) |
0aacf84e | 4752 | { |
e11e83f3 | 4753 | long int yy = SCM_I_INUM (y); |
0aacf84e MD |
4754 | if (yy == 0) |
4755 | { | |
7351e207 | 4756 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4757 | scm_num_overflow (s_divide); |
7351e207 | 4758 | #else |
0aacf84e MD |
4759 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4760 | scm_remember_upto_here_1 (x); | |
4761 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 4762 | #endif |
0aacf84e MD |
4763 | } |
4764 | else if (yy == 1) | |
4765 | return x; | |
4766 | else | |
4767 | { | |
4768 | /* FIXME: HMM, what are the relative performance issues here? | |
4769 | We need to test. Is it faster on average to test | |
4770 | divisible_p, then perform whichever operation, or is it | |
4771 | faster to perform the integer div opportunistically and | |
4772 | switch to real if there's a remainder? For now we take the | |
4773 | middle ground: test, then if divisible, use the faster div | |
4774 | func. */ | |
4775 | ||
4776 | long abs_yy = yy < 0 ? -yy : yy; | |
4777 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); | |
4778 | ||
4779 | if (divisible_p) | |
4780 | { | |
4781 | SCM result = scm_i_mkbig (); | |
4782 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
4783 | scm_remember_upto_here_1 (x); | |
4784 | if (yy < 0) | |
4785 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4786 | return scm_i_normbig (result); | |
4787 | } | |
4788 | else | |
f92e85f7 MV |
4789 | { |
4790 | if (inexact) | |
55f26379 | 4791 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 4792 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4793 | } |
0aacf84e MD |
4794 | } |
4795 | } | |
4796 | else if (SCM_BIGP (y)) | |
4797 | { | |
4798 | int y_is_zero = (mpz_sgn (SCM_I_BIG_MPZ (y)) == 0); | |
4799 | if (y_is_zero) | |
4800 | { | |
ca46fb90 | 4801 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4802 | scm_num_overflow (s_divide); |
f872b822 | 4803 | #else |
0aacf84e MD |
4804 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4805 | scm_remember_upto_here_1 (x); | |
4806 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
f872b822 | 4807 | #endif |
0aacf84e MD |
4808 | } |
4809 | else | |
4810 | { | |
4811 | /* big_x / big_y */ | |
23f2b9a3 KR |
4812 | if (inexact) |
4813 | { | |
4814 | /* It's easily possible for the ratio x/y to fit a double | |
4815 | but one or both x and y be too big to fit a double, | |
4816 | hence the use of mpq_get_d rather than converting and | |
4817 | dividing. */ | |
4818 | mpq_t q; | |
4819 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
4820 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
4821 | return scm_from_double (mpq_get_d (q)); | |
4822 | } | |
4823 | else | |
4824 | { | |
4825 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), | |
4826 | SCM_I_BIG_MPZ (y)); | |
4827 | if (divisible_p) | |
4828 | { | |
4829 | SCM result = scm_i_mkbig (); | |
4830 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
4831 | SCM_I_BIG_MPZ (x), | |
4832 | SCM_I_BIG_MPZ (y)); | |
4833 | scm_remember_upto_here_2 (x, y); | |
4834 | return scm_i_normbig (result); | |
4835 | } | |
4836 | else | |
4837 | return scm_i_make_ratio (x, y); | |
4838 | } | |
0aacf84e MD |
4839 | } |
4840 | } | |
4841 | else if (SCM_REALP (y)) | |
4842 | { | |
4843 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4844 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4845 | if (yy == 0.0) |
4846 | scm_num_overflow (s_divide); | |
4847 | else | |
7351e207 | 4848 | #endif |
55f26379 | 4849 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
4850 | } |
4851 | else if (SCM_COMPLEXP (y)) | |
4852 | { | |
4853 | a = scm_i_big2dbl (x); | |
4854 | goto complex_div; | |
4855 | } | |
f92e85f7 | 4856 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4857 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4858 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4859 | else |
4860 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4861 | } |
0aacf84e MD |
4862 | else if (SCM_REALP (x)) |
4863 | { | |
4864 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 4865 | if (SCM_I_INUMP (y)) |
0aacf84e | 4866 | { |
e11e83f3 | 4867 | long int yy = SCM_I_INUM (y); |
7351e207 | 4868 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4869 | if (yy == 0) |
4870 | scm_num_overflow (s_divide); | |
4871 | else | |
7351e207 | 4872 | #endif |
55f26379 | 4873 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
4874 | } |
4875 | else if (SCM_BIGP (y)) | |
4876 | { | |
4877 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4878 | scm_remember_upto_here_1 (y); | |
55f26379 | 4879 | return scm_from_double (rx / dby); |
0aacf84e MD |
4880 | } |
4881 | else if (SCM_REALP (y)) | |
4882 | { | |
4883 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4884 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4885 | if (yy == 0.0) |
4886 | scm_num_overflow (s_divide); | |
4887 | else | |
7351e207 | 4888 | #endif |
55f26379 | 4889 | return scm_from_double (rx / yy); |
0aacf84e MD |
4890 | } |
4891 | else if (SCM_COMPLEXP (y)) | |
4892 | { | |
4893 | a = rx; | |
4894 | goto complex_div; | |
4895 | } | |
f92e85f7 | 4896 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4897 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
4898 | else |
4899 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4900 | } |
0aacf84e MD |
4901 | else if (SCM_COMPLEXP (x)) |
4902 | { | |
4903 | double rx = SCM_COMPLEX_REAL (x); | |
4904 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 4905 | if (SCM_I_INUMP (y)) |
0aacf84e | 4906 | { |
e11e83f3 | 4907 | long int yy = SCM_I_INUM (y); |
7351e207 | 4908 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4909 | if (yy == 0) |
4910 | scm_num_overflow (s_divide); | |
4911 | else | |
7351e207 | 4912 | #endif |
0aacf84e MD |
4913 | { |
4914 | double d = yy; | |
8507ec80 | 4915 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
4916 | } |
4917 | } | |
4918 | else if (SCM_BIGP (y)) | |
4919 | { | |
4920 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4921 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4922 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
4923 | } |
4924 | else if (SCM_REALP (y)) | |
4925 | { | |
4926 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4927 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4928 | if (yy == 0.0) |
4929 | scm_num_overflow (s_divide); | |
4930 | else | |
7351e207 | 4931 | #endif |
8507ec80 | 4932 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
4933 | } |
4934 | else if (SCM_COMPLEXP (y)) | |
4935 | { | |
4936 | double ry = SCM_COMPLEX_REAL (y); | |
4937 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 4938 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
4939 | { |
4940 | double t = ry / iy; | |
4941 | double d = iy * (1.0 + t * t); | |
8507ec80 | 4942 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
4943 | } |
4944 | else | |
4945 | { | |
4946 | double t = iy / ry; | |
4947 | double d = ry * (1.0 + t * t); | |
8507ec80 | 4948 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
4949 | } |
4950 | } | |
f92e85f7 MV |
4951 | else if (SCM_FRACTIONP (y)) |
4952 | { | |
4953 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4954 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 4955 | } |
0aacf84e MD |
4956 | else |
4957 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4958 | } |
f92e85f7 MV |
4959 | else if (SCM_FRACTIONP (x)) |
4960 | { | |
e11e83f3 | 4961 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4962 | { |
e11e83f3 | 4963 | long int yy = SCM_I_INUM (y); |
f92e85f7 MV |
4964 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
4965 | if (yy == 0) | |
4966 | scm_num_overflow (s_divide); | |
4967 | else | |
4968 | #endif | |
cba42c93 | 4969 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4970 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4971 | } | |
4972 | else if (SCM_BIGP (y)) | |
4973 | { | |
cba42c93 | 4974 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4975 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4976 | } | |
4977 | else if (SCM_REALP (y)) | |
4978 | { | |
4979 | double yy = SCM_REAL_VALUE (y); | |
4980 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
4981 | if (yy == 0.0) | |
4982 | scm_num_overflow (s_divide); | |
4983 | else | |
4984 | #endif | |
55f26379 | 4985 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
4986 | } |
4987 | else if (SCM_COMPLEXP (y)) | |
4988 | { | |
4989 | a = scm_i_fraction2double (x); | |
4990 | goto complex_div; | |
4991 | } | |
4992 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 4993 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4994 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
4995 | else | |
4996 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
4997 | } | |
0aacf84e | 4998 | else |
f8de44c1 | 4999 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 5000 | } |
f92e85f7 MV |
5001 | |
5002 | SCM | |
5003 | scm_divide (SCM x, SCM y) | |
5004 | { | |
5005 | return scm_i_divide (x, y, 0); | |
5006 | } | |
5007 | ||
5008 | static SCM scm_divide2real (SCM x, SCM y) | |
5009 | { | |
5010 | return scm_i_divide (x, y, 1); | |
5011 | } | |
c05e97b7 | 5012 | #undef FUNC_NAME |
0f2d19dd | 5013 | |
fa605590 | 5014 | |
0f2d19dd | 5015 | double |
6e8d25a6 | 5016 | scm_asinh (double x) |
0f2d19dd | 5017 | { |
fa605590 KR |
5018 | #if HAVE_ASINH |
5019 | return asinh (x); | |
5020 | #else | |
5021 | #define asinh scm_asinh | |
f872b822 | 5022 | return log (x + sqrt (x * x + 1)); |
fa605590 | 5023 | #endif |
0f2d19dd | 5024 | } |
fa605590 KR |
5025 | SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_dsubr, (SCM (*)()) asinh, g_asinh); |
5026 | /* "Return the inverse hyperbolic sine of @var{x}." | |
5027 | */ | |
0f2d19dd JB |
5028 | |
5029 | ||
0f2d19dd | 5030 | double |
6e8d25a6 | 5031 | scm_acosh (double x) |
0f2d19dd | 5032 | { |
fa605590 KR |
5033 | #if HAVE_ACOSH |
5034 | return acosh (x); | |
5035 | #else | |
5036 | #define acosh scm_acosh | |
f872b822 | 5037 | return log (x + sqrt (x * x - 1)); |
fa605590 | 5038 | #endif |
0f2d19dd | 5039 | } |
fa605590 KR |
5040 | SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_dsubr, (SCM (*)()) acosh, g_acosh); |
5041 | /* "Return the inverse hyperbolic cosine of @var{x}." | |
5042 | */ | |
0f2d19dd JB |
5043 | |
5044 | ||
0f2d19dd | 5045 | double |
6e8d25a6 | 5046 | scm_atanh (double x) |
0f2d19dd | 5047 | { |
fa605590 KR |
5048 | #if HAVE_ATANH |
5049 | return atanh (x); | |
5050 | #else | |
5051 | #define atanh scm_atanh | |
f872b822 | 5052 | return 0.5 * log ((1 + x) / (1 - x)); |
fa605590 | 5053 | #endif |
0f2d19dd | 5054 | } |
fa605590 KR |
5055 | SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_dsubr, (SCM (*)()) atanh, g_atanh); |
5056 | /* "Return the inverse hyperbolic tangent of @var{x}." | |
5057 | */ | |
0f2d19dd JB |
5058 | |
5059 | ||
0f2d19dd | 5060 | double |
3101f40f | 5061 | scm_c_truncate (double x) |
0f2d19dd | 5062 | { |
fa605590 KR |
5063 | #if HAVE_TRUNC |
5064 | return trunc (x); | |
5065 | #else | |
f872b822 MD |
5066 | if (x < 0.0) |
5067 | return -floor (-x); | |
5068 | return floor (x); | |
fa605590 | 5069 | #endif |
0f2d19dd | 5070 | } |
0f2d19dd | 5071 | |
3101f40f MV |
5072 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
5073 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
5074 | Then half-way cases are identified and adjusted down if the | |
5075 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
5076 | |
5077 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
5078 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
5079 | ||
5080 | An odd "result" value is identified with result/2 != floor(result/2). | |
5081 | This is done with plus_half, since that value is ready for use sooner in | |
5082 | a pipelined cpu, and we're already requiring plus_half == result. | |
5083 | ||
5084 | Note however that we need to be careful when x is big and already an | |
5085 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
5086 | us to return such a value, incorrectly. For instance if the hardware is | |
5087 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
5088 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
5089 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
5090 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
5091 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
5092 | ||
5093 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
5094 | x is already an integer. If it is then clearly that's the desired result | |
5095 | already. And if it's not then the exponent must be small enough to allow | |
5096 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
5097 | ||
0f2d19dd | 5098 | double |
3101f40f | 5099 | scm_c_round (double x) |
0f2d19dd | 5100 | { |
6187f48b KR |
5101 | double plus_half, result; |
5102 | ||
5103 | if (x == floor (x)) | |
5104 | return x; | |
5105 | ||
5106 | plus_half = x + 0.5; | |
5107 | result = floor (plus_half); | |
3101f40f | 5108 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
5109 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
5110 | ? result - 1 | |
5111 | : result); | |
0f2d19dd JB |
5112 | } |
5113 | ||
f92e85f7 MV |
5114 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
5115 | (SCM x), | |
5116 | "Round the number @var{x} towards zero.") | |
5117 | #define FUNC_NAME s_scm_truncate_number | |
5118 | { | |
73e4de09 | 5119 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5120 | return scm_floor (x); |
5121 | else | |
5122 | return scm_ceiling (x); | |
5123 | } | |
5124 | #undef FUNC_NAME | |
5125 | ||
5126 | static SCM exactly_one_half; | |
5127 | ||
5128 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, | |
5129 | (SCM x), | |
5130 | "Round the number @var{x} towards the nearest integer. " | |
5131 | "When it is exactly halfway between two integers, " | |
5132 | "round towards the even one.") | |
5133 | #define FUNC_NAME s_scm_round_number | |
5134 | { | |
e11e83f3 | 5135 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
5136 | return x; |
5137 | else if (SCM_REALP (x)) | |
3101f40f | 5138 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 5139 | else |
bae30667 KR |
5140 | { |
5141 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
5142 | single quotient+remainder division then examining to see which way | |
5143 | the rounding should go. */ | |
5144 | SCM plus_half = scm_sum (x, exactly_one_half); | |
5145 | SCM result = scm_floor (plus_half); | |
3101f40f | 5146 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
5147 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
5148 | && scm_is_true (scm_odd_p (result))) | |
d956fa6f | 5149 | return scm_difference (result, SCM_I_MAKINUM (1)); |
bae30667 KR |
5150 | else |
5151 | return result; | |
5152 | } | |
f92e85f7 MV |
5153 | } |
5154 | #undef FUNC_NAME | |
5155 | ||
5156 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
5157 | (SCM x), | |
5158 | "Round the number @var{x} towards minus infinity.") | |
5159 | #define FUNC_NAME s_scm_floor | |
5160 | { | |
e11e83f3 | 5161 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5162 | return x; |
5163 | else if (SCM_REALP (x)) | |
55f26379 | 5164 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5165 | else if (SCM_FRACTIONP (x)) |
5166 | { | |
5167 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5168 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5169 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5170 | { |
5171 | /* For positive x, rounding towards zero is correct. */ | |
5172 | return q; | |
5173 | } | |
5174 | else | |
5175 | { | |
5176 | /* For negative x, we need to return q-1 unless x is an | |
5177 | integer. But fractions are never integer, per our | |
5178 | assumptions. */ | |
d956fa6f | 5179 | return scm_difference (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5180 | } |
5181 | } | |
5182 | else | |
5183 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
5184 | } | |
5185 | #undef FUNC_NAME | |
5186 | ||
5187 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
5188 | (SCM x), | |
5189 | "Round the number @var{x} towards infinity.") | |
5190 | #define FUNC_NAME s_scm_ceiling | |
5191 | { | |
e11e83f3 | 5192 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5193 | return x; |
5194 | else if (SCM_REALP (x)) | |
55f26379 | 5195 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5196 | else if (SCM_FRACTIONP (x)) |
5197 | { | |
5198 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5199 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5200 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
5201 | { |
5202 | /* For negative x, rounding towards zero is correct. */ | |
5203 | return q; | |
5204 | } | |
5205 | else | |
5206 | { | |
5207 | /* For positive x, we need to return q+1 unless x is an | |
5208 | integer. But fractions are never integer, per our | |
5209 | assumptions. */ | |
d956fa6f | 5210 | return scm_sum (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5211 | } |
5212 | } | |
5213 | else | |
5214 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
5215 | } | |
5216 | #undef FUNC_NAME | |
0f2d19dd | 5217 | |
14b18ed6 | 5218 | SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_dsubr, (SCM (*)()) sqrt, g_i_sqrt); |
942e5b91 MG |
5219 | /* "Return the square root of the real number @var{x}." |
5220 | */ | |
14b18ed6 | 5221 | SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_dsubr, (SCM (*)()) fabs, g_i_abs); |
942e5b91 MG |
5222 | /* "Return the absolute value of the real number @var{x}." |
5223 | */ | |
14b18ed6 | 5224 | SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_dsubr, (SCM (*)()) exp, g_i_exp); |
942e5b91 MG |
5225 | /* "Return the @var{x}th power of e." |
5226 | */ | |
14b18ed6 | 5227 | SCM_GPROC1 (s_i_log, "$log", scm_tc7_dsubr, (SCM (*)()) log, g_i_log); |
b3fcac34 | 5228 | /* "Return the natural logarithm of the real number @var{x}." |
942e5b91 | 5229 | */ |
14b18ed6 | 5230 | SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_dsubr, (SCM (*)()) sin, g_i_sin); |
942e5b91 MG |
5231 | /* "Return the sine of the real number @var{x}." |
5232 | */ | |
14b18ed6 | 5233 | SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_dsubr, (SCM (*)()) cos, g_i_cos); |
942e5b91 MG |
5234 | /* "Return the cosine of the real number @var{x}." |
5235 | */ | |
14b18ed6 | 5236 | SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_dsubr, (SCM (*)()) tan, g_i_tan); |
942e5b91 MG |
5237 | /* "Return the tangent of the real number @var{x}." |
5238 | */ | |
14b18ed6 | 5239 | SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_dsubr, (SCM (*)()) asin, g_i_asin); |
942e5b91 MG |
5240 | /* "Return the arc sine of the real number @var{x}." |
5241 | */ | |
14b18ed6 | 5242 | SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_dsubr, (SCM (*)()) acos, g_i_acos); |
942e5b91 MG |
5243 | /* "Return the arc cosine of the real number @var{x}." |
5244 | */ | |
14b18ed6 | 5245 | SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_dsubr, (SCM (*)()) atan, g_i_atan); |
942e5b91 MG |
5246 | /* "Return the arc tangent of the real number @var{x}." |
5247 | */ | |
14b18ed6 | 5248 | SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_dsubr, (SCM (*)()) sinh, g_i_sinh); |
942e5b91 MG |
5249 | /* "Return the hyperbolic sine of the real number @var{x}." |
5250 | */ | |
14b18ed6 | 5251 | SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_dsubr, (SCM (*)()) cosh, g_i_cosh); |
942e5b91 MG |
5252 | /* "Return the hyperbolic cosine of the real number @var{x}." |
5253 | */ | |
14b18ed6 | 5254 | SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_dsubr, (SCM (*)()) tanh, g_i_tanh); |
942e5b91 MG |
5255 | /* "Return the hyperbolic tangent of the real number @var{x}." |
5256 | */ | |
f872b822 MD |
5257 | |
5258 | struct dpair | |
5259 | { | |
5260 | double x, y; | |
5261 | }; | |
5262 | ||
27c37006 NJ |
5263 | static void scm_two_doubles (SCM x, |
5264 | SCM y, | |
3eeba8d4 JB |
5265 | const char *sstring, |
5266 | struct dpair * xy); | |
f872b822 MD |
5267 | |
5268 | static void | |
27c37006 NJ |
5269 | scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy) |
5270 | { | |
e11e83f3 MV |
5271 | if (SCM_I_INUMP (x)) |
5272 | xy->x = SCM_I_INUM (x); | |
0aacf84e | 5273 | else if (SCM_BIGP (x)) |
1be6b49c | 5274 | xy->x = scm_i_big2dbl (x); |
0aacf84e | 5275 | else if (SCM_REALP (x)) |
27c37006 | 5276 | xy->x = SCM_REAL_VALUE (x); |
f92e85f7 MV |
5277 | else if (SCM_FRACTIONP (x)) |
5278 | xy->x = scm_i_fraction2double (x); | |
0aacf84e | 5279 | else |
27c37006 | 5280 | scm_wrong_type_arg (sstring, SCM_ARG1, x); |
98cb6e75 | 5281 | |
e11e83f3 MV |
5282 | if (SCM_I_INUMP (y)) |
5283 | xy->y = SCM_I_INUM (y); | |
0aacf84e | 5284 | else if (SCM_BIGP (y)) |
1be6b49c | 5285 | xy->y = scm_i_big2dbl (y); |
0aacf84e | 5286 | else if (SCM_REALP (y)) |
27c37006 | 5287 | xy->y = SCM_REAL_VALUE (y); |
f92e85f7 MV |
5288 | else if (SCM_FRACTIONP (y)) |
5289 | xy->y = scm_i_fraction2double (y); | |
0aacf84e | 5290 | else |
27c37006 | 5291 | scm_wrong_type_arg (sstring, SCM_ARG2, y); |
0f2d19dd JB |
5292 | } |
5293 | ||
5294 | ||
a1ec6916 | 5295 | SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0, |
27c37006 NJ |
5296 | (SCM x, SCM y), |
5297 | "Return @var{x} raised to the power of @var{y}. This\n" | |
0137a31b | 5298 | "procedure does not accept complex arguments.") |
1bbd0b84 | 5299 | #define FUNC_NAME s_scm_sys_expt |
0f2d19dd JB |
5300 | { |
5301 | struct dpair xy; | |
27c37006 | 5302 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5303 | return scm_from_double (pow (xy.x, xy.y)); |
0f2d19dd | 5304 | } |
1bbd0b84 | 5305 | #undef FUNC_NAME |
0f2d19dd JB |
5306 | |
5307 | ||
a1ec6916 | 5308 | SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0, |
27c37006 NJ |
5309 | (SCM x, SCM y), |
5310 | "Return the arc tangent of the two arguments @var{x} and\n" | |
5311 | "@var{y}. This is similar to calculating the arc tangent of\n" | |
5312 | "@var{x} / @var{y}, except that the signs of both arguments\n" | |
0137a31b MG |
5313 | "are used to determine the quadrant of the result. This\n" |
5314 | "procedure does not accept complex arguments.") | |
1bbd0b84 | 5315 | #define FUNC_NAME s_scm_sys_atan2 |
0f2d19dd JB |
5316 | { |
5317 | struct dpair xy; | |
27c37006 | 5318 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5319 | return scm_from_double (atan2 (xy.x, xy.y)); |
0f2d19dd | 5320 | } |
1bbd0b84 | 5321 | #undef FUNC_NAME |
0f2d19dd | 5322 | |
8507ec80 MV |
5323 | SCM |
5324 | scm_c_make_rectangular (double re, double im) | |
5325 | { | |
5326 | if (im == 0.0) | |
5327 | return scm_from_double (re); | |
5328 | else | |
5329 | { | |
5330 | SCM z; | |
5331 | SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (sizeof (scm_t_complex), | |
5332 | "complex")); | |
5333 | SCM_COMPLEX_REAL (z) = re; | |
5334 | SCM_COMPLEX_IMAG (z) = im; | |
5335 | return z; | |
5336 | } | |
5337 | } | |
0f2d19dd | 5338 | |
a1ec6916 | 5339 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
5340 | (SCM real_part, SCM imaginary_part), |
5341 | "Return a complex number constructed of the given @var{real-part} " | |
5342 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 5343 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd JB |
5344 | { |
5345 | struct dpair xy; | |
a2c25234 | 5346 | scm_two_doubles (real_part, imaginary_part, FUNC_NAME, &xy); |
8507ec80 | 5347 | return scm_c_make_rectangular (xy.x, xy.y); |
0f2d19dd | 5348 | } |
1bbd0b84 | 5349 | #undef FUNC_NAME |
0f2d19dd | 5350 | |
8507ec80 MV |
5351 | SCM |
5352 | scm_c_make_polar (double mag, double ang) | |
5353 | { | |
5354 | double s, c; | |
5355 | #if HAVE_SINCOS | |
5356 | sincos (ang, &s, &c); | |
5357 | #else | |
5358 | s = sin (ang); | |
5359 | c = cos (ang); | |
5360 | #endif | |
5361 | return scm_c_make_rectangular (mag * c, mag * s); | |
5362 | } | |
0f2d19dd | 5363 | |
a1ec6916 | 5364 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 5365 | (SCM x, SCM y), |
942e5b91 | 5366 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 5367 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd JB |
5368 | { |
5369 | struct dpair xy; | |
27c37006 | 5370 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
8507ec80 | 5371 | return scm_c_make_polar (xy.x, xy.y); |
0f2d19dd | 5372 | } |
1bbd0b84 | 5373 | #undef FUNC_NAME |
0f2d19dd JB |
5374 | |
5375 | ||
152f82bf | 5376 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
5377 | /* "Return the real part of the number @var{z}." |
5378 | */ | |
0f2d19dd | 5379 | SCM |
6e8d25a6 | 5380 | scm_real_part (SCM z) |
0f2d19dd | 5381 | { |
e11e83f3 | 5382 | if (SCM_I_INUMP (z)) |
c2ff8ab0 | 5383 | return z; |
0aacf84e | 5384 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5385 | return z; |
0aacf84e | 5386 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5387 | return z; |
0aacf84e | 5388 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5389 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
f92e85f7 | 5390 | else if (SCM_FRACTIONP (z)) |
2fa2d879 | 5391 | return z; |
0aacf84e | 5392 | else |
c2ff8ab0 | 5393 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); |
0f2d19dd JB |
5394 | } |
5395 | ||
5396 | ||
152f82bf | 5397 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
5398 | /* "Return the imaginary part of the number @var{z}." |
5399 | */ | |
0f2d19dd | 5400 | SCM |
6e8d25a6 | 5401 | scm_imag_part (SCM z) |
0f2d19dd | 5402 | { |
e11e83f3 | 5403 | if (SCM_I_INUMP (z)) |
f872b822 | 5404 | return SCM_INUM0; |
0aacf84e | 5405 | else if (SCM_BIGP (z)) |
f872b822 | 5406 | return SCM_INUM0; |
0aacf84e | 5407 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5408 | return scm_flo0; |
0aacf84e | 5409 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5410 | return scm_from_double (SCM_COMPLEX_IMAG (z)); |
f92e85f7 MV |
5411 | else if (SCM_FRACTIONP (z)) |
5412 | return SCM_INUM0; | |
0aacf84e | 5413 | else |
c2ff8ab0 | 5414 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); |
0f2d19dd JB |
5415 | } |
5416 | ||
f92e85f7 MV |
5417 | SCM_GPROC (s_numerator, "numerator", 1, 0, 0, scm_numerator, g_numerator); |
5418 | /* "Return the numerator of the number @var{z}." | |
5419 | */ | |
5420 | SCM | |
5421 | scm_numerator (SCM z) | |
5422 | { | |
e11e83f3 | 5423 | if (SCM_I_INUMP (z)) |
f92e85f7 MV |
5424 | return z; |
5425 | else if (SCM_BIGP (z)) | |
5426 | return z; | |
5427 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 5428 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
5429 | else if (SCM_REALP (z)) |
5430 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
5431 | else | |
5432 | SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator); | |
5433 | } | |
5434 | ||
5435 | ||
5436 | SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator); | |
5437 | /* "Return the denominator of the number @var{z}." | |
5438 | */ | |
5439 | SCM | |
5440 | scm_denominator (SCM z) | |
5441 | { | |
e11e83f3 | 5442 | if (SCM_I_INUMP (z)) |
d956fa6f | 5443 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5444 | else if (SCM_BIGP (z)) |
d956fa6f | 5445 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5446 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 5447 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
5448 | else if (SCM_REALP (z)) |
5449 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
5450 | else | |
5451 | SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator); | |
5452 | } | |
0f2d19dd | 5453 | |
9de33deb | 5454 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
5455 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
5456 | * "@code{abs} for real arguments, but also allows complex numbers." | |
5457 | */ | |
0f2d19dd | 5458 | SCM |
6e8d25a6 | 5459 | scm_magnitude (SCM z) |
0f2d19dd | 5460 | { |
e11e83f3 | 5461 | if (SCM_I_INUMP (z)) |
0aacf84e | 5462 | { |
e11e83f3 | 5463 | long int zz = SCM_I_INUM (z); |
0aacf84e MD |
5464 | if (zz >= 0) |
5465 | return z; | |
5466 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 5467 | return SCM_I_MAKINUM (-zz); |
0aacf84e MD |
5468 | else |
5469 | return scm_i_long2big (-zz); | |
5986c47d | 5470 | } |
0aacf84e MD |
5471 | else if (SCM_BIGP (z)) |
5472 | { | |
5473 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5474 | scm_remember_upto_here_1 (z); | |
5475 | if (sgn < 0) | |
5476 | return scm_i_clonebig (z, 0); | |
5477 | else | |
5478 | return z; | |
5986c47d | 5479 | } |
0aacf84e | 5480 | else if (SCM_REALP (z)) |
55f26379 | 5481 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 5482 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5483 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
5484 | else if (SCM_FRACTIONP (z)) |
5485 | { | |
73e4de09 | 5486 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5487 | return z; |
cba42c93 | 5488 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
5489 | SCM_FRACTION_DENOMINATOR (z)); |
5490 | } | |
0aacf84e | 5491 | else |
c2ff8ab0 | 5492 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); |
0f2d19dd JB |
5493 | } |
5494 | ||
5495 | ||
9de33deb | 5496 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
5497 | /* "Return the angle of the complex number @var{z}." |
5498 | */ | |
0f2d19dd | 5499 | SCM |
6e8d25a6 | 5500 | scm_angle (SCM z) |
0f2d19dd | 5501 | { |
c8ae173e | 5502 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
55f26379 | 5503 | scm_flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
5504 | But if atan2 follows the floating point rounding mode, then the value |
5505 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 5506 | if (SCM_I_INUMP (z)) |
0aacf84e | 5507 | { |
e11e83f3 | 5508 | if (SCM_I_INUM (z) >= 0) |
c8ae173e | 5509 | return scm_flo0; |
0aacf84e | 5510 | else |
55f26379 | 5511 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 5512 | } |
0aacf84e MD |
5513 | else if (SCM_BIGP (z)) |
5514 | { | |
5515 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5516 | scm_remember_upto_here_1 (z); | |
5517 | if (sgn < 0) | |
55f26379 | 5518 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 5519 | else |
c8ae173e | 5520 | return scm_flo0; |
0f2d19dd | 5521 | } |
0aacf84e | 5522 | else if (SCM_REALP (z)) |
c8ae173e KR |
5523 | { |
5524 | if (SCM_REAL_VALUE (z) >= 0) | |
5525 | return scm_flo0; | |
5526 | else | |
55f26379 | 5527 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 5528 | } |
0aacf84e | 5529 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5530 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
5531 | else if (SCM_FRACTIONP (z)) |
5532 | { | |
73e4de09 | 5533 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5534 | return scm_flo0; |
55f26379 | 5535 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 5536 | } |
0aacf84e | 5537 | else |
f4c627b3 | 5538 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); |
0f2d19dd JB |
5539 | } |
5540 | ||
5541 | ||
3c9a524f DH |
5542 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
5543 | /* Convert the number @var{x} to its inexact representation.\n" | |
5544 | */ | |
5545 | SCM | |
5546 | scm_exact_to_inexact (SCM z) | |
5547 | { | |
e11e83f3 | 5548 | if (SCM_I_INUMP (z)) |
55f26379 | 5549 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 5550 | else if (SCM_BIGP (z)) |
55f26379 | 5551 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 5552 | else if (SCM_FRACTIONP (z)) |
55f26379 | 5553 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
5554 | else if (SCM_INEXACTP (z)) |
5555 | return z; | |
5556 | else | |
5557 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
5558 | } | |
5559 | ||
5560 | ||
a1ec6916 | 5561 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 5562 | (SCM z), |
1e6808ea | 5563 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 5564 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 5565 | { |
e11e83f3 | 5566 | if (SCM_I_INUMP (z)) |
f872b822 | 5567 | return z; |
0aacf84e | 5568 | else if (SCM_BIGP (z)) |
f872b822 | 5569 | return z; |
0aacf84e MD |
5570 | else if (SCM_REALP (z)) |
5571 | { | |
f92e85f7 MV |
5572 | if (xisinf (SCM_REAL_VALUE (z)) || xisnan (SCM_REAL_VALUE (z))) |
5573 | SCM_OUT_OF_RANGE (1, z); | |
2be24db4 | 5574 | else |
f92e85f7 MV |
5575 | { |
5576 | mpq_t frac; | |
5577 | SCM q; | |
5578 | ||
5579 | mpq_init (frac); | |
5580 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 5581 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
5582 | scm_i_mpz2num (mpq_denref (frac))); |
5583 | ||
cba42c93 | 5584 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
5585 | for frac... |
5586 | */ | |
5587 | mpq_clear (frac); | |
5588 | return q; | |
5589 | } | |
c2ff8ab0 | 5590 | } |
f92e85f7 MV |
5591 | else if (SCM_FRACTIONP (z)) |
5592 | return z; | |
0aacf84e | 5593 | else |
c2ff8ab0 | 5594 | SCM_WRONG_TYPE_ARG (1, z); |
0f2d19dd | 5595 | } |
1bbd0b84 | 5596 | #undef FUNC_NAME |
0f2d19dd | 5597 | |
f92e85f7 | 5598 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
76dae881 NJ |
5599 | (SCM x, SCM eps), |
5600 | "Returns the @emph{simplest} rational number differing\n" | |
5601 | "from @var{x} by no more than @var{eps}.\n" | |
5602 | "\n" | |
5603 | "As required by @acronym{R5RS}, @code{rationalize} only returns an\n" | |
5604 | "exact result when both its arguments are exact. Thus, you might need\n" | |
5605 | "to use @code{inexact->exact} on the arguments.\n" | |
5606 | "\n" | |
5607 | "@lisp\n" | |
5608 | "(rationalize (inexact->exact 1.2) 1/100)\n" | |
5609 | "@result{} 6/5\n" | |
5610 | "@end lisp") | |
f92e85f7 MV |
5611 | #define FUNC_NAME s_scm_rationalize |
5612 | { | |
e11e83f3 | 5613 | if (SCM_I_INUMP (x)) |
f92e85f7 MV |
5614 | return x; |
5615 | else if (SCM_BIGP (x)) | |
5616 | return x; | |
5617 | else if ((SCM_REALP (x)) || SCM_FRACTIONP (x)) | |
5618 | { | |
5619 | /* Use continued fractions to find closest ratio. All | |
5620 | arithmetic is done with exact numbers. | |
5621 | */ | |
5622 | ||
5623 | SCM ex = scm_inexact_to_exact (x); | |
5624 | SCM int_part = scm_floor (ex); | |
d956fa6f MV |
5625 | SCM tt = SCM_I_MAKINUM (1); |
5626 | SCM a1 = SCM_I_MAKINUM (0), a2 = SCM_I_MAKINUM (1), a = SCM_I_MAKINUM (0); | |
5627 | SCM b1 = SCM_I_MAKINUM (1), b2 = SCM_I_MAKINUM (0), b = SCM_I_MAKINUM (0); | |
f92e85f7 MV |
5628 | SCM rx; |
5629 | int i = 0; | |
5630 | ||
73e4de09 | 5631 | if (scm_is_true (scm_num_eq_p (ex, int_part))) |
f92e85f7 MV |
5632 | return ex; |
5633 | ||
5634 | ex = scm_difference (ex, int_part); /* x = x-int_part */ | |
5635 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
5636 | ||
5637 | /* We stop after a million iterations just to be absolutely sure | |
5638 | that we don't go into an infinite loop. The process normally | |
5639 | converges after less than a dozen iterations. | |
5640 | */ | |
5641 | ||
76dae881 | 5642 | eps = scm_abs (eps); |
f92e85f7 MV |
5643 | while (++i < 1000000) |
5644 | { | |
5645 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
5646 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
5647 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
5648 | scm_is_false | |
f92e85f7 | 5649 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
76dae881 | 5650 | eps))) /* abs(x-a/b) <= eps */ |
02164269 MV |
5651 | { |
5652 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
73e4de09 | 5653 | if (scm_is_false (scm_exact_p (x)) |
76dae881 | 5654 | || scm_is_false (scm_exact_p (eps))) |
02164269 MV |
5655 | return scm_exact_to_inexact (res); |
5656 | else | |
5657 | return res; | |
5658 | } | |
f92e85f7 MV |
5659 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
5660 | SCM_UNDEFINED); | |
5661 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
5662 | a2 = a1; | |
5663 | b2 = b1; | |
5664 | a1 = a; | |
5665 | b1 = b; | |
5666 | } | |
5667 | scm_num_overflow (s_scm_rationalize); | |
5668 | } | |
5669 | else | |
5670 | SCM_WRONG_TYPE_ARG (1, x); | |
5671 | } | |
5672 | #undef FUNC_NAME | |
5673 | ||
73e4de09 MV |
5674 | /* conversion functions */ |
5675 | ||
5676 | int | |
5677 | scm_is_integer (SCM val) | |
5678 | { | |
5679 | return scm_is_true (scm_integer_p (val)); | |
5680 | } | |
5681 | ||
5682 | int | |
5683 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
5684 | { | |
e11e83f3 | 5685 | if (SCM_I_INUMP (val)) |
73e4de09 | 5686 | { |
e11e83f3 | 5687 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5688 | return n >= min && n <= max; |
5689 | } | |
5690 | else if (SCM_BIGP (val)) | |
5691 | { | |
5692 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
5693 | return 0; | |
5694 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
5695 | { |
5696 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
5697 | { | |
5698 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
5699 | return n >= min && n <= max; | |
5700 | } | |
5701 | else | |
5702 | return 0; | |
5703 | } | |
73e4de09 MV |
5704 | else |
5705 | { | |
d956fa6f MV |
5706 | scm_t_intmax n; |
5707 | size_t count; | |
73e4de09 | 5708 | |
d956fa6f MV |
5709 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5710 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
5711 | return 0; | |
5712 | ||
5713 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5714 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5715 | |
d956fa6f | 5716 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 5717 | { |
d956fa6f MV |
5718 | if (n < 0) |
5719 | return 0; | |
73e4de09 | 5720 | } |
73e4de09 MV |
5721 | else |
5722 | { | |
d956fa6f MV |
5723 | n = -n; |
5724 | if (n >= 0) | |
5725 | return 0; | |
73e4de09 | 5726 | } |
d956fa6f MV |
5727 | |
5728 | return n >= min && n <= max; | |
73e4de09 MV |
5729 | } |
5730 | } | |
73e4de09 MV |
5731 | else |
5732 | return 0; | |
5733 | } | |
5734 | ||
5735 | int | |
5736 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
5737 | { | |
e11e83f3 | 5738 | if (SCM_I_INUMP (val)) |
73e4de09 | 5739 | { |
e11e83f3 | 5740 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5741 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
5742 | } | |
5743 | else if (SCM_BIGP (val)) | |
5744 | { | |
5745 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
5746 | return 0; | |
5747 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
5748 | { |
5749 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
5750 | { | |
5751 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
5752 | return n >= min && n <= max; | |
5753 | } | |
5754 | else | |
5755 | return 0; | |
5756 | } | |
73e4de09 MV |
5757 | else |
5758 | { | |
d956fa6f MV |
5759 | scm_t_uintmax n; |
5760 | size_t count; | |
73e4de09 | 5761 | |
d956fa6f MV |
5762 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
5763 | return 0; | |
73e4de09 | 5764 | |
d956fa6f MV |
5765 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5766 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 5767 | return 0; |
d956fa6f MV |
5768 | |
5769 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5770 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5771 | |
d956fa6f | 5772 | return n >= min && n <= max; |
73e4de09 MV |
5773 | } |
5774 | } | |
73e4de09 MV |
5775 | else |
5776 | return 0; | |
5777 | } | |
5778 | ||
1713d319 MV |
5779 | static void |
5780 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
5781 | { | |
5782 | scm_error (scm_out_of_range_key, | |
5783 | NULL, | |
5784 | "Value out of range ~S to ~S: ~S", | |
5785 | scm_list_3 (min, max, bad_val), | |
5786 | scm_list_1 (bad_val)); | |
5787 | } | |
5788 | ||
bfd7932e MV |
5789 | #define TYPE scm_t_intmax |
5790 | #define TYPE_MIN min | |
5791 | #define TYPE_MAX max | |
5792 | #define SIZEOF_TYPE 0 | |
5793 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
5794 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
5795 | #include "libguile/conv-integer.i.c" | |
5796 | ||
5797 | #define TYPE scm_t_uintmax | |
5798 | #define TYPE_MIN min | |
5799 | #define TYPE_MAX max | |
5800 | #define SIZEOF_TYPE 0 | |
5801 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
5802 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
5803 | #include "libguile/conv-uinteger.i.c" | |
5804 | ||
5805 | #define TYPE scm_t_int8 | |
5806 | #define TYPE_MIN SCM_T_INT8_MIN | |
5807 | #define TYPE_MAX SCM_T_INT8_MAX | |
5808 | #define SIZEOF_TYPE 1 | |
5809 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
5810 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
5811 | #include "libguile/conv-integer.i.c" | |
5812 | ||
5813 | #define TYPE scm_t_uint8 | |
5814 | #define TYPE_MIN 0 | |
5815 | #define TYPE_MAX SCM_T_UINT8_MAX | |
5816 | #define SIZEOF_TYPE 1 | |
5817 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
5818 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
5819 | #include "libguile/conv-uinteger.i.c" | |
5820 | ||
5821 | #define TYPE scm_t_int16 | |
5822 | #define TYPE_MIN SCM_T_INT16_MIN | |
5823 | #define TYPE_MAX SCM_T_INT16_MAX | |
5824 | #define SIZEOF_TYPE 2 | |
5825 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
5826 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
5827 | #include "libguile/conv-integer.i.c" | |
5828 | ||
5829 | #define TYPE scm_t_uint16 | |
5830 | #define TYPE_MIN 0 | |
5831 | #define TYPE_MAX SCM_T_UINT16_MAX | |
5832 | #define SIZEOF_TYPE 2 | |
5833 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
5834 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
5835 | #include "libguile/conv-uinteger.i.c" | |
5836 | ||
5837 | #define TYPE scm_t_int32 | |
5838 | #define TYPE_MIN SCM_T_INT32_MIN | |
5839 | #define TYPE_MAX SCM_T_INT32_MAX | |
5840 | #define SIZEOF_TYPE 4 | |
5841 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
5842 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
5843 | #include "libguile/conv-integer.i.c" | |
5844 | ||
5845 | #define TYPE scm_t_uint32 | |
5846 | #define TYPE_MIN 0 | |
5847 | #define TYPE_MAX SCM_T_UINT32_MAX | |
5848 | #define SIZEOF_TYPE 4 | |
5849 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
5850 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
5851 | #include "libguile/conv-uinteger.i.c" | |
5852 | ||
5853 | #if SCM_HAVE_T_INT64 | |
5854 | ||
5855 | #define TYPE scm_t_int64 | |
5856 | #define TYPE_MIN SCM_T_INT64_MIN | |
5857 | #define TYPE_MAX SCM_T_INT64_MAX | |
5858 | #define SIZEOF_TYPE 8 | |
5859 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
5860 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
5861 | #include "libguile/conv-integer.i.c" | |
5862 | ||
5863 | #define TYPE scm_t_uint64 | |
5864 | #define TYPE_MIN 0 | |
5865 | #define TYPE_MAX SCM_T_UINT64_MAX | |
5866 | #define SIZEOF_TYPE 8 | |
5867 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
5868 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
5869 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 5870 | |
bfd7932e | 5871 | #endif |
73e4de09 | 5872 | |
cd036260 MV |
5873 | void |
5874 | scm_to_mpz (SCM val, mpz_t rop) | |
5875 | { | |
5876 | if (SCM_I_INUMP (val)) | |
5877 | mpz_set_si (rop, SCM_I_INUM (val)); | |
5878 | else if (SCM_BIGP (val)) | |
5879 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
5880 | else | |
5881 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
5882 | } | |
5883 | ||
5884 | SCM | |
5885 | scm_from_mpz (mpz_t val) | |
5886 | { | |
5887 | return scm_i_mpz2num (val); | |
5888 | } | |
5889 | ||
73e4de09 MV |
5890 | int |
5891 | scm_is_real (SCM val) | |
5892 | { | |
5893 | return scm_is_true (scm_real_p (val)); | |
5894 | } | |
5895 | ||
55f26379 MV |
5896 | int |
5897 | scm_is_rational (SCM val) | |
5898 | { | |
5899 | return scm_is_true (scm_rational_p (val)); | |
5900 | } | |
5901 | ||
73e4de09 MV |
5902 | double |
5903 | scm_to_double (SCM val) | |
5904 | { | |
55f26379 MV |
5905 | if (SCM_I_INUMP (val)) |
5906 | return SCM_I_INUM (val); | |
5907 | else if (SCM_BIGP (val)) | |
5908 | return scm_i_big2dbl (val); | |
5909 | else if (SCM_FRACTIONP (val)) | |
5910 | return scm_i_fraction2double (val); | |
5911 | else if (SCM_REALP (val)) | |
5912 | return SCM_REAL_VALUE (val); | |
5913 | else | |
7a1aba42 | 5914 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
5915 | } |
5916 | ||
5917 | SCM | |
5918 | scm_from_double (double val) | |
5919 | { | |
55f26379 MV |
5920 | SCM z = scm_double_cell (scm_tc16_real, 0, 0, 0); |
5921 | SCM_REAL_VALUE (z) = val; | |
5922 | return z; | |
73e4de09 MV |
5923 | } |
5924 | ||
55f26379 MV |
5925 | #if SCM_ENABLE_DISCOURAGED == 1 |
5926 | ||
5927 | float | |
5928 | scm_num2float (SCM num, unsigned long int pos, const char *s_caller) | |
5929 | { | |
5930 | if (SCM_BIGP (num)) | |
5931 | { | |
5932 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5933 | if (!xisinf (res)) | |
5934 | return res; | |
5935 | else | |
5936 | scm_out_of_range (NULL, num); | |
5937 | } | |
5938 | else | |
5939 | return scm_to_double (num); | |
5940 | } | |
5941 | ||
5942 | double | |
5943 | scm_num2double (SCM num, unsigned long int pos, const char *s_caller) | |
5944 | { | |
5945 | if (SCM_BIGP (num)) | |
5946 | { | |
5947 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5948 | if (!xisinf (res)) | |
5949 | return res; | |
5950 | else | |
5951 | scm_out_of_range (NULL, num); | |
5952 | } | |
5953 | else | |
5954 | return scm_to_double (num); | |
5955 | } | |
5956 | ||
5957 | #endif | |
5958 | ||
8507ec80 MV |
5959 | int |
5960 | scm_is_complex (SCM val) | |
5961 | { | |
5962 | return scm_is_true (scm_complex_p (val)); | |
5963 | } | |
5964 | ||
5965 | double | |
5966 | scm_c_real_part (SCM z) | |
5967 | { | |
5968 | if (SCM_COMPLEXP (z)) | |
5969 | return SCM_COMPLEX_REAL (z); | |
5970 | else | |
5971 | { | |
5972 | /* Use the scm_real_part to get proper error checking and | |
5973 | dispatching. | |
5974 | */ | |
5975 | return scm_to_double (scm_real_part (z)); | |
5976 | } | |
5977 | } | |
5978 | ||
5979 | double | |
5980 | scm_c_imag_part (SCM z) | |
5981 | { | |
5982 | if (SCM_COMPLEXP (z)) | |
5983 | return SCM_COMPLEX_IMAG (z); | |
5984 | else | |
5985 | { | |
5986 | /* Use the scm_imag_part to get proper error checking and | |
5987 | dispatching. The result will almost always be 0.0, but not | |
5988 | always. | |
5989 | */ | |
5990 | return scm_to_double (scm_imag_part (z)); | |
5991 | } | |
5992 | } | |
5993 | ||
5994 | double | |
5995 | scm_c_magnitude (SCM z) | |
5996 | { | |
5997 | return scm_to_double (scm_magnitude (z)); | |
5998 | } | |
5999 | ||
6000 | double | |
6001 | scm_c_angle (SCM z) | |
6002 | { | |
6003 | return scm_to_double (scm_angle (z)); | |
6004 | } | |
6005 | ||
6006 | int | |
6007 | scm_is_number (SCM z) | |
6008 | { | |
6009 | return scm_is_true (scm_number_p (z)); | |
6010 | } | |
6011 | ||
8ab3d8a0 KR |
6012 | |
6013 | /* In the following functions we dispatch to the real-arg funcs like log() | |
6014 | when we know the arg is real, instead of just handing everything to | |
6015 | clog() for instance. This is in case clog() doesn't optimize for a | |
6016 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
6017 | well use it to go straight to the applicable C func. */ | |
6018 | ||
6019 | SCM_DEFINE (scm_log, "log", 1, 0, 0, | |
6020 | (SCM z), | |
6021 | "Return the natural logarithm of @var{z}.") | |
6022 | #define FUNC_NAME s_scm_log | |
6023 | { | |
6024 | if (SCM_COMPLEXP (z)) | |
6025 | { | |
4b26c03e | 6026 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6027 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
6028 | #else | |
6029 | double re = SCM_COMPLEX_REAL (z); | |
6030 | double im = SCM_COMPLEX_IMAG (z); | |
6031 | return scm_c_make_rectangular (log (hypot (re, im)), | |
6032 | atan2 (im, re)); | |
6033 | #endif | |
6034 | } | |
6035 | else | |
6036 | { | |
6037 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6038 | although the value itself overflows. */ | |
6039 | double re = scm_to_double (z); | |
6040 | double l = log (fabs (re)); | |
6041 | if (re >= 0.0) | |
6042 | return scm_from_double (l); | |
6043 | else | |
6044 | return scm_c_make_rectangular (l, M_PI); | |
6045 | } | |
6046 | } | |
6047 | #undef FUNC_NAME | |
6048 | ||
6049 | ||
6050 | SCM_DEFINE (scm_log10, "log10", 1, 0, 0, | |
6051 | (SCM z), | |
6052 | "Return the base 10 logarithm of @var{z}.") | |
6053 | #define FUNC_NAME s_scm_log10 | |
6054 | { | |
6055 | if (SCM_COMPLEXP (z)) | |
6056 | { | |
6057 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
6058 | clog() and a multiply by M_LOG10E, rather than the fallback | |
6059 | log10+hypot+atan2.) */ | |
4b26c03e | 6060 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG10 && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6061 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
6062 | #else | |
6063 | double re = SCM_COMPLEX_REAL (z); | |
6064 | double im = SCM_COMPLEX_IMAG (z); | |
6065 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
6066 | M_LOG10E * atan2 (im, re)); | |
6067 | #endif | |
6068 | } | |
6069 | else | |
6070 | { | |
6071 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6072 | although the value itself overflows. */ | |
6073 | double re = scm_to_double (z); | |
6074 | double l = log10 (fabs (re)); | |
6075 | if (re >= 0.0) | |
6076 | return scm_from_double (l); | |
6077 | else | |
6078 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
6079 | } | |
6080 | } | |
6081 | #undef FUNC_NAME | |
6082 | ||
6083 | ||
6084 | SCM_DEFINE (scm_exp, "exp", 1, 0, 0, | |
6085 | (SCM z), | |
6086 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
6087 | "base of natural logarithms (2.71828@dots{}).") | |
6088 | #define FUNC_NAME s_scm_exp | |
6089 | { | |
6090 | if (SCM_COMPLEXP (z)) | |
6091 | { | |
4b26c03e | 6092 | #if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6093 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
6094 | #else | |
6095 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
6096 | SCM_COMPLEX_IMAG (z)); | |
6097 | #endif | |
6098 | } | |
6099 | else | |
6100 | { | |
6101 | /* When z is a negative bignum the conversion to double overflows, | |
6102 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
6103 | return scm_from_double (exp (scm_to_double (z))); | |
6104 | } | |
6105 | } | |
6106 | #undef FUNC_NAME | |
6107 | ||
6108 | ||
6109 | SCM_DEFINE (scm_sqrt, "sqrt", 1, 0, 0, | |
6110 | (SCM x), | |
6111 | "Return the square root of @var{z}. Of the two possible roots\n" | |
6112 | "(positive and negative), the one with the a positive real part\n" | |
6113 | "is returned, or if that's zero then a positive imaginary part.\n" | |
6114 | "Thus,\n" | |
6115 | "\n" | |
6116 | "@example\n" | |
6117 | "(sqrt 9.0) @result{} 3.0\n" | |
6118 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
6119 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
6120 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
6121 | "@end example") | |
6122 | #define FUNC_NAME s_scm_sqrt | |
6123 | { | |
6124 | if (SCM_COMPLEXP (x)) | |
6125 | { | |
4b26c03e | 6126 | #if HAVE_COMPLEX_DOUBLE && HAVE_USABLE_CSQRT && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6127 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (x))); |
6128 | #else | |
6129 | double re = SCM_COMPLEX_REAL (x); | |
6130 | double im = SCM_COMPLEX_IMAG (x); | |
6131 | return scm_c_make_polar (sqrt (hypot (re, im)), | |
6132 | 0.5 * atan2 (im, re)); | |
6133 | #endif | |
6134 | } | |
6135 | else | |
6136 | { | |
6137 | double xx = scm_to_double (x); | |
6138 | if (xx < 0) | |
6139 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
6140 | else | |
6141 | return scm_from_double (sqrt (xx)); | |
6142 | } | |
6143 | } | |
6144 | #undef FUNC_NAME | |
6145 | ||
6146 | ||
6147 | ||
0f2d19dd JB |
6148 | void |
6149 | scm_init_numbers () | |
0f2d19dd | 6150 | { |
0b799eea MV |
6151 | int i; |
6152 | ||
713a4259 KR |
6153 | mpz_init_set_si (z_negative_one, -1); |
6154 | ||
a261c0e9 DH |
6155 | /* It may be possible to tune the performance of some algorithms by using |
6156 | * the following constants to avoid the creation of bignums. Please, before | |
6157 | * using these values, remember the two rules of program optimization: | |
6158 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 6159 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 6160 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 6161 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 6162 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 6163 | |
f3ae5d60 MD |
6164 | scm_add_feature ("complex"); |
6165 | scm_add_feature ("inexact"); | |
55f26379 | 6166 | scm_flo0 = scm_from_double (0.0); |
0b799eea MV |
6167 | |
6168 | /* determine floating point precision */ | |
55f26379 | 6169 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
6170 | { |
6171 | init_dblprec(&scm_dblprec[i-2],i); | |
6172 | init_fx_radix(fx_per_radix[i-2],i); | |
6173 | } | |
f872b822 | 6174 | #ifdef DBL_DIG |
0b799eea MV |
6175 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
6176 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; | |
6177 | #endif | |
1be6b49c | 6178 | |
d956fa6f MV |
6179 | exactly_one_half = scm_permanent_object (scm_divide (SCM_I_MAKINUM (1), |
6180 | SCM_I_MAKINUM (2))); | |
a0599745 | 6181 | #include "libguile/numbers.x" |
0f2d19dd | 6182 | } |
89e00824 ML |
6183 | |
6184 | /* | |
6185 | Local Variables: | |
6186 | c-file-style: "gnu" | |
6187 | End: | |
6188 | */ |