Commit | Line | Data |
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238ebcef | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004 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 | |
19 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA | |
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 | |
fa605590 KR |
43 | /* tell glibc (2.3) to give prototype for C99 trunc() */ |
44 | #define _GNU_SOURCE | |
45 | ||
ee33d62a RB |
46 | #if HAVE_CONFIG_H |
47 | # include <config.h> | |
48 | #endif | |
49 | ||
0f2d19dd | 50 | #include <math.h> |
3c9a524f | 51 | #include <ctype.h> |
fc194577 | 52 | #include <string.h> |
ca46fb90 | 53 | #include <gmp.h> |
f92e85f7 | 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 | ||
0f2d19dd | 70 | \f |
f4c627b3 | 71 | |
ca46fb90 RB |
72 | /* |
73 | Wonder if this might be faster for some of our code? A switch on | |
74 | the numtag would jump directly to the right case, and the | |
75 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
76 | ||
77 | #define SCM_I_NUMTAG_NOTNUM 0 | |
78 | #define SCM_I_NUMTAG_INUM 1 | |
79 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
80 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
81 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
82 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 83 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 84 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 85 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
86 | : SCM_I_NUMTAG_NOTNUM))) |
87 | */ | |
f92e85f7 | 88 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
89 | |
90 | ||
34d19ef6 | 91 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 92 | |
56e55ac7 | 93 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
94 | * printed or scm_string representation of an inexact number. |
95 | */ | |
0b799eea | 96 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 97 | |
7351e207 MV |
98 | #if defined (SCO) |
99 | #if ! defined (HAVE_ISNAN) | |
100 | #define HAVE_ISNAN | |
101 | static int | |
102 | isnan (double x) | |
103 | { | |
104 | return (IsNANorINF (x) && NaN (x) && ! IsINF (x)) ? 1 : 0; | |
105 | } | |
0f2d19dd | 106 | #endif |
7351e207 MV |
107 | #if ! defined (HAVE_ISINF) |
108 | #define HAVE_ISINF | |
109 | static int | |
110 | isinf (double x) | |
111 | { | |
112 | return (IsNANorINF (x) && IsINF (x)) ? 1 : 0; | |
113 | } | |
0f2d19dd | 114 | |
7351e207 | 115 | #endif |
e6f3ef58 MD |
116 | #endif |
117 | ||
b127c712 | 118 | |
f8a8200b KR |
119 | /* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses |
120 | an explicit check. In some future gmp (don't know what version number), | |
121 | mpz_cmp_d is supposed to do this itself. */ | |
122 | #if 1 | |
b127c712 KR |
123 | #define xmpz_cmp_d(z, d) \ |
124 | (xisinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) | |
125 | #else | |
126 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
127 | #endif | |
128 | ||
a98ce907 KR |
129 | /* For reference, sparc solaris 7 has infinities (IEEE) but doesn't have |
130 | isinf. It does have finite and isnan though, hence the use of those. | |
131 | fpclass would be a possibility on that system too. */ | |
f92e85f7 MV |
132 | static int |
133 | xisinf (double x) | |
134 | { | |
135 | #if defined (HAVE_ISINF) | |
136 | return isinf (x); | |
137 | #elif defined (HAVE_FINITE) && defined (HAVE_ISNAN) | |
138 | return (! (finite (x) || isnan (x))); | |
139 | #else | |
140 | return 0; | |
141 | #endif | |
142 | } | |
143 | ||
144 | static int | |
145 | xisnan (double x) | |
146 | { | |
147 | #if defined (HAVE_ISNAN) | |
148 | return isnan (x); | |
149 | #else | |
150 | return 0; | |
151 | #endif | |
152 | } | |
153 | ||
0f2d19dd JB |
154 | \f |
155 | ||
713a4259 | 156 | static mpz_t z_negative_one; |
ac0c002c DH |
157 | |
158 | \f | |
159 | ||
570b6821 | 160 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
161 | scm_i_mkbig () |
162 | { | |
163 | /* Return a newly created bignum. */ | |
164 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
165 | mpz_init (SCM_I_BIG_MPZ (z)); | |
166 | return z; | |
167 | } | |
168 | ||
c71b0706 MV |
169 | SCM_C_INLINE_KEYWORD SCM |
170 | scm_i_long2big (long x) | |
171 | { | |
172 | /* Return a newly created bignum initialized to X. */ | |
173 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
174 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
175 | return z; | |
176 | } | |
177 | ||
178 | SCM_C_INLINE_KEYWORD SCM | |
179 | scm_i_ulong2big (unsigned long x) | |
180 | { | |
181 | /* Return a newly created bignum initialized to X. */ | |
182 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
183 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); | |
184 | return z; | |
185 | } | |
186 | ||
570b6821 | 187 | SCM_C_INLINE_KEYWORD static SCM |
ca46fb90 RB |
188 | scm_i_clonebig (SCM src_big, int same_sign_p) |
189 | { | |
190 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
191 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
192 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); | |
0aacf84e MD |
193 | if (!same_sign_p) |
194 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
195 | return z; |
196 | } | |
197 | ||
570b6821 | 198 | SCM_C_INLINE_KEYWORD int |
ca46fb90 RB |
199 | scm_i_bigcmp (SCM x, SCM y) |
200 | { | |
201 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
202 | /* presume we already know x and y are bignums */ | |
203 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
204 | scm_remember_upto_here_2 (x, y); | |
205 | return result; | |
206 | } | |
207 | ||
570b6821 | 208 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
209 | scm_i_dbl2big (double d) |
210 | { | |
211 | /* results are only defined if d is an integer */ | |
212 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
213 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); | |
214 | return z; | |
215 | } | |
216 | ||
f92e85f7 MV |
217 | /* Convert a integer in double representation to a SCM number. */ |
218 | ||
219 | SCM_C_INLINE_KEYWORD SCM | |
220 | scm_i_dbl2num (double u) | |
221 | { | |
222 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
223 | powers of 2, so there's no rounding when making "double" values | |
224 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
225 | get rounded on a 64-bit machine, hence the "+1". | |
226 | ||
227 | The use of floor() to force to an integer value ensures we get a | |
228 | "numerically closest" value without depending on how a | |
229 | double->long cast or how mpz_set_d will round. For reference, | |
230 | double->long probably follows the hardware rounding mode, | |
231 | mpz_set_d truncates towards zero. */ | |
232 | ||
233 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
234 | representable as a double? */ | |
235 | ||
236 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
237 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
d956fa6f | 238 | return SCM_I_MAKINUM ((long) u); |
f92e85f7 MV |
239 | else |
240 | return scm_i_dbl2big (u); | |
241 | } | |
242 | ||
089c9a59 KR |
243 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
244 | with R5RS exact->inexact. | |
245 | ||
246 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
247 | (ie. truncate towards zero), then adjust to get the closest double by |
248 | examining the next lower bit and adding 1 (to the absolute value) if | |
249 | necessary. | |
250 | ||
251 | Bignums exactly half way between representable doubles are rounded to the | |
252 | next higher absolute value (ie. away from zero). This seems like an | |
253 | adequate interpretation of R5RS "numerically closest", and it's easier | |
254 | and faster than a full "nearest-even" style. | |
255 | ||
256 | The bit test must be done on the absolute value of the mpz_t, which means | |
257 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
258 | negatives as twos complement. | |
259 | ||
260 | In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up | |
261 | following the hardware rounding mode, but applied to the absolute value | |
262 | of the mpz_t operand. This is not what we want so we put the high | |
263 | DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when, | |
264 | mpz_get_d is supposed to always truncate towards zero. | |
265 | ||
266 | ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3 | |
267 | is a slowdown. It'd be faster to pick out the relevant high bits with | |
268 | mpz_getlimbn if we could be bothered coding that, and if the new | |
269 | truncating gmp doesn't come out. */ | |
089c9a59 KR |
270 | |
271 | double | |
ca46fb90 RB |
272 | scm_i_big2dbl (SCM b) |
273 | { | |
089c9a59 KR |
274 | double result; |
275 | size_t bits; | |
276 | ||
277 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
278 | ||
f8a8200b | 279 | #if 1 |
089c9a59 | 280 | { |
f8a8200b | 281 | /* Current GMP, eg. 4.1.3, force truncation towards zero */ |
089c9a59 KR |
282 | mpz_t tmp; |
283 | if (bits > DBL_MANT_DIG) | |
284 | { | |
285 | size_t shift = bits - DBL_MANT_DIG; | |
286 | mpz_init2 (tmp, DBL_MANT_DIG); | |
287 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
288 | result = ldexp (mpz_get_d (tmp), shift); | |
289 | mpz_clear (tmp); | |
290 | } | |
291 | else | |
292 | { | |
293 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
294 | } | |
295 | } | |
296 | #else | |
f8a8200b | 297 | /* Future GMP */ |
089c9a59 KR |
298 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
299 | #endif | |
300 | ||
301 | if (bits > DBL_MANT_DIG) | |
302 | { | |
303 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
304 | /* test bit number "pos" in absolute value */ | |
305 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
306 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
307 | { | |
308 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
309 | } | |
310 | } | |
311 | ||
ca46fb90 RB |
312 | scm_remember_upto_here_1 (b); |
313 | return result; | |
314 | } | |
315 | ||
570b6821 | 316 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
317 | scm_i_normbig (SCM b) |
318 | { | |
319 | /* convert a big back to a fixnum if it'll fit */ | |
320 | /* presume b is a bignum */ | |
321 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
322 | { | |
323 | long val = mpz_get_si (SCM_I_BIG_MPZ (b)); | |
324 | if (SCM_FIXABLE (val)) | |
d956fa6f | 325 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
326 | } |
327 | return b; | |
328 | } | |
f872b822 | 329 | |
f92e85f7 MV |
330 | static SCM_C_INLINE_KEYWORD SCM |
331 | scm_i_mpz2num (mpz_t b) | |
332 | { | |
333 | /* convert a mpz number to a SCM number. */ | |
334 | if (mpz_fits_slong_p (b)) | |
335 | { | |
336 | long val = mpz_get_si (b); | |
337 | if (SCM_FIXABLE (val)) | |
d956fa6f | 338 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
339 | } |
340 | ||
341 | { | |
342 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
343 | mpz_init_set (SCM_I_BIG_MPZ (z), b); | |
344 | return z; | |
345 | } | |
346 | } | |
347 | ||
348 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
349 | static SCM scm_divide2real (SCM x, SCM y); | |
350 | ||
cba42c93 MV |
351 | static SCM |
352 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 353 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 354 | { |
c60e130c MV |
355 | /* First make sure the arguments are proper. |
356 | */ | |
e11e83f3 | 357 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 358 | { |
bc36d050 | 359 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 360 | scm_num_overflow ("make-ratio"); |
bc36d050 | 361 | if (scm_is_eq (denominator, SCM_I_MAKINUM(1))) |
f92e85f7 MV |
362 | return numerator; |
363 | } | |
364 | else | |
365 | { | |
366 | if (!(SCM_BIGP(denominator))) | |
367 | SCM_WRONG_TYPE_ARG (2, denominator); | |
368 | } | |
e11e83f3 | 369 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
370 | SCM_WRONG_TYPE_ARG (1, numerator); |
371 | ||
372 | /* Then flip signs so that the denominator is positive. | |
373 | */ | |
73e4de09 | 374 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
375 | { |
376 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
377 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
378 | } | |
379 | ||
380 | /* Now consider for each of the four fixnum/bignum combinations | |
381 | whether the rational number is really an integer. | |
382 | */ | |
e11e83f3 | 383 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 384 | { |
e11e83f3 | 385 | long x = SCM_I_INUM (numerator); |
bc36d050 | 386 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 387 | return SCM_INUM0; |
e11e83f3 | 388 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 389 | { |
dd5130ca | 390 | long y; |
e11e83f3 | 391 | y = SCM_I_INUM (denominator); |
f92e85f7 | 392 | if (x == y) |
d956fa6f | 393 | return SCM_I_MAKINUM(1); |
f92e85f7 | 394 | if ((x % y) == 0) |
d956fa6f | 395 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 396 | } |
dd5130ca KR |
397 | else |
398 | { | |
399 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
400 | of that value for the denominator, as a bignum. Apart from |
401 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
402 | integer. */ | |
403 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
404 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
405 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 406 | return SCM_I_MAKINUM(-1); |
dd5130ca | 407 | } |
f92e85f7 | 408 | } |
c60e130c | 409 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 410 | { |
e11e83f3 | 411 | if (SCM_I_INUMP (denominator)) |
c60e130c | 412 | { |
e11e83f3 | 413 | long yy = SCM_I_INUM (denominator); |
c60e130c MV |
414 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
415 | return scm_divide (numerator, denominator); | |
416 | } | |
417 | else | |
f92e85f7 | 418 | { |
bc36d050 | 419 | if (scm_is_eq (numerator, denominator)) |
d956fa6f | 420 | return SCM_I_MAKINUM(1); |
c60e130c MV |
421 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
422 | SCM_I_BIG_MPZ (denominator))) | |
423 | return scm_divide(numerator, denominator); | |
f92e85f7 | 424 | } |
f92e85f7 | 425 | } |
c60e130c MV |
426 | |
427 | /* No, it's a proper fraction. | |
428 | */ | |
429 | return scm_double_cell (scm_tc16_fraction, | |
430 | SCM_UNPACK (numerator), | |
431 | SCM_UNPACK (denominator), 0); | |
f92e85f7 | 432 | } |
c60e130c | 433 | #undef FUNC_NAME |
f92e85f7 MV |
434 | |
435 | static void scm_i_fraction_reduce (SCM z) | |
436 | { | |
437 | if (!(SCM_FRACTION_REDUCED (z))) | |
438 | { | |
439 | SCM divisor; | |
440 | divisor = scm_gcd (SCM_FRACTION_NUMERATOR (z), SCM_FRACTION_DENOMINATOR (z)); | |
bc36d050 | 441 | if (!(scm_is_eq (divisor, SCM_I_MAKINUM(1)))) |
f92e85f7 MV |
442 | { |
443 | /* is this safe? */ | |
444 | SCM_FRACTION_SET_NUMERATOR (z, scm_divide (SCM_FRACTION_NUMERATOR (z), divisor)); | |
445 | SCM_FRACTION_SET_DENOMINATOR (z, scm_divide (SCM_FRACTION_DENOMINATOR (z), divisor)); | |
446 | } | |
447 | SCM_FRACTION_REDUCED_SET (z); | |
448 | } | |
449 | } | |
450 | ||
451 | double | |
452 | scm_i_fraction2double (SCM z) | |
453 | { | |
55f26379 MV |
454 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
455 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
456 | } |
457 | ||
a1ec6916 | 458 | SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0, |
1bbd0b84 | 459 | (SCM x), |
942e5b91 MG |
460 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
461 | "otherwise.") | |
1bbd0b84 | 462 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 463 | { |
e11e83f3 | 464 | if (SCM_I_INUMP (x)) |
0aacf84e MD |
465 | return SCM_BOOL_T; |
466 | if (SCM_BIGP (x)) | |
467 | return SCM_BOOL_T; | |
f92e85f7 MV |
468 | if (SCM_FRACTIONP (x)) |
469 | return SCM_BOOL_T; | |
eb927cb9 MV |
470 | if (SCM_NUMBERP (x)) |
471 | return SCM_BOOL_F; | |
472 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 473 | } |
1bbd0b84 | 474 | #undef FUNC_NAME |
0f2d19dd | 475 | |
4219f20d | 476 | |
a1ec6916 | 477 | SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 478 | (SCM n), |
942e5b91 MG |
479 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
480 | "otherwise.") | |
1bbd0b84 | 481 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 482 | { |
e11e83f3 | 483 | if (SCM_I_INUMP (n)) |
0aacf84e | 484 | { |
e11e83f3 | 485 | long val = SCM_I_INUM (n); |
73e4de09 | 486 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
487 | } |
488 | else if (SCM_BIGP (n)) | |
489 | { | |
490 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
491 | scm_remember_upto_here_1 (n); | |
73e4de09 | 492 | return scm_from_bool (odd_p); |
0aacf84e | 493 | } |
73e4de09 | 494 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 495 | return SCM_BOOL_T; |
f92e85f7 MV |
496 | else if (SCM_REALP (n)) |
497 | { | |
498 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
499 | if (rem == 1.0) | |
500 | return SCM_BOOL_T; | |
501 | else if (rem == 0.0) | |
502 | return SCM_BOOL_F; | |
503 | else | |
504 | SCM_WRONG_TYPE_ARG (1, n); | |
505 | } | |
0aacf84e | 506 | else |
a1a33b0f | 507 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 508 | } |
1bbd0b84 | 509 | #undef FUNC_NAME |
0f2d19dd | 510 | |
4219f20d | 511 | |
a1ec6916 | 512 | SCM_DEFINE (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 513 | (SCM n), |
942e5b91 MG |
514 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
515 | "otherwise.") | |
1bbd0b84 | 516 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 517 | { |
e11e83f3 | 518 | if (SCM_I_INUMP (n)) |
0aacf84e | 519 | { |
e11e83f3 | 520 | long val = SCM_I_INUM (n); |
73e4de09 | 521 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
522 | } |
523 | else if (SCM_BIGP (n)) | |
524 | { | |
525 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
526 | scm_remember_upto_here_1 (n); | |
73e4de09 | 527 | return scm_from_bool (even_p); |
0aacf84e | 528 | } |
73e4de09 | 529 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 530 | return SCM_BOOL_T; |
f92e85f7 MV |
531 | else if (SCM_REALP (n)) |
532 | { | |
533 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
534 | if (rem == 1.0) | |
535 | return SCM_BOOL_F; | |
536 | else if (rem == 0.0) | |
537 | return SCM_BOOL_T; | |
538 | else | |
539 | SCM_WRONG_TYPE_ARG (1, n); | |
540 | } | |
0aacf84e | 541 | else |
a1a33b0f | 542 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 543 | } |
1bbd0b84 | 544 | #undef FUNC_NAME |
0f2d19dd | 545 | |
7351e207 MV |
546 | SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0, |
547 | (SCM n), | |
548 | "Return @code{#t} if @var{n} is infinite, @code{#f}\n" | |
549 | "otherwise.") | |
550 | #define FUNC_NAME s_scm_inf_p | |
551 | { | |
0aacf84e | 552 | if (SCM_REALP (n)) |
73e4de09 | 553 | return scm_from_bool (xisinf (SCM_REAL_VALUE (n))); |
0aacf84e | 554 | else if (SCM_COMPLEXP (n)) |
73e4de09 | 555 | return scm_from_bool (xisinf (SCM_COMPLEX_REAL (n)) |
7351e207 | 556 | || xisinf (SCM_COMPLEX_IMAG (n))); |
0aacf84e | 557 | else |
7351e207 | 558 | return SCM_BOOL_F; |
7351e207 MV |
559 | } |
560 | #undef FUNC_NAME | |
561 | ||
562 | SCM_DEFINE (scm_nan_p, "nan?", 1, 0, 0, | |
563 | (SCM n), | |
564 | "Return @code{#t} if @var{n} is a NaN, @code{#f}\n" | |
565 | "otherwise.") | |
566 | #define FUNC_NAME s_scm_nan_p | |
567 | { | |
0aacf84e | 568 | if (SCM_REALP (n)) |
73e4de09 | 569 | return scm_from_bool (xisnan (SCM_REAL_VALUE (n))); |
0aacf84e | 570 | else if (SCM_COMPLEXP (n)) |
73e4de09 | 571 | return scm_from_bool (xisnan (SCM_COMPLEX_REAL (n)) |
7351e207 | 572 | || xisnan (SCM_COMPLEX_IMAG (n))); |
0aacf84e | 573 | else |
7351e207 | 574 | return SCM_BOOL_F; |
7351e207 MV |
575 | } |
576 | #undef FUNC_NAME | |
577 | ||
578 | /* Guile's idea of infinity. */ | |
579 | static double guile_Inf; | |
580 | ||
581 | /* Guile's idea of not a number. */ | |
582 | static double guile_NaN; | |
583 | ||
584 | static void | |
585 | guile_ieee_init (void) | |
586 | { | |
587 | #if defined (HAVE_ISINF) || defined (HAVE_FINITE) | |
588 | ||
589 | /* Some version of gcc on some old version of Linux used to crash when | |
590 | trying to make Inf and NaN. */ | |
591 | ||
240a27d2 KR |
592 | #ifdef INFINITY |
593 | /* C99 INFINITY, when available. | |
594 | FIXME: The standard allows for INFINITY to be something that overflows | |
595 | at compile time. We ought to have a configure test to check for that | |
596 | before trying to use it. (But in practice we believe this is not a | |
597 | problem on any system guile is likely to target.) */ | |
598 | guile_Inf = INFINITY; | |
599 | #elif HAVE_DINFINITY | |
600 | /* OSF */ | |
7351e207 MV |
601 | extern unsigned int DINFINITY[2]; |
602 | guile_Inf = (*(X_CAST(double *, DINFINITY))); | |
603 | #else | |
604 | double tmp = 1e+10; | |
605 | guile_Inf = tmp; | |
606 | for (;;) | |
607 | { | |
608 | guile_Inf *= 1e+10; | |
609 | if (guile_Inf == tmp) | |
610 | break; | |
611 | tmp = guile_Inf; | |
612 | } | |
613 | #endif | |
614 | ||
615 | #endif | |
616 | ||
617 | #if defined (HAVE_ISNAN) | |
618 | ||
240a27d2 KR |
619 | #ifdef NAN |
620 | /* C99 NAN, when available */ | |
621 | guile_NaN = NAN; | |
622 | #elif HAVE_DQNAN | |
623 | /* OSF */ | |
7351e207 MV |
624 | extern unsigned int DQNAN[2]; |
625 | guile_NaN = (*(X_CAST(double *, DQNAN))); | |
626 | #else | |
627 | guile_NaN = guile_Inf / guile_Inf; | |
628 | #endif | |
629 | ||
630 | #endif | |
631 | } | |
632 | ||
633 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
634 | (void), | |
635 | "Return Inf.") | |
636 | #define FUNC_NAME s_scm_inf | |
637 | { | |
638 | static int initialized = 0; | |
639 | if (! initialized) | |
640 | { | |
641 | guile_ieee_init (); | |
642 | initialized = 1; | |
643 | } | |
55f26379 | 644 | return scm_from_double (guile_Inf); |
7351e207 MV |
645 | } |
646 | #undef FUNC_NAME | |
647 | ||
648 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
649 | (void), | |
650 | "Return NaN.") | |
651 | #define FUNC_NAME s_scm_nan | |
652 | { | |
653 | static int initialized = 0; | |
0aacf84e | 654 | if (!initialized) |
7351e207 MV |
655 | { |
656 | guile_ieee_init (); | |
657 | initialized = 1; | |
658 | } | |
55f26379 | 659 | return scm_from_double (guile_NaN); |
7351e207 MV |
660 | } |
661 | #undef FUNC_NAME | |
662 | ||
4219f20d | 663 | |
a48d60b1 MD |
664 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
665 | (SCM x), | |
666 | "Return the absolute value of @var{x}.") | |
667 | #define FUNC_NAME | |
0f2d19dd | 668 | { |
e11e83f3 | 669 | if (SCM_I_INUMP (x)) |
0aacf84e | 670 | { |
e11e83f3 | 671 | long int xx = SCM_I_INUM (x); |
0aacf84e MD |
672 | if (xx >= 0) |
673 | return x; | |
674 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 675 | return SCM_I_MAKINUM (-xx); |
0aacf84e MD |
676 | else |
677 | return scm_i_long2big (-xx); | |
4219f20d | 678 | } |
0aacf84e MD |
679 | else if (SCM_BIGP (x)) |
680 | { | |
681 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
682 | if (sgn < 0) | |
683 | return scm_i_clonebig (x, 0); | |
684 | else | |
685 | return x; | |
4219f20d | 686 | } |
0aacf84e | 687 | else if (SCM_REALP (x)) |
ae38324d KR |
688 | { |
689 | /* note that if x is a NaN then xx<0 is false so we return x unchanged */ | |
690 | double xx = SCM_REAL_VALUE (x); | |
691 | if (xx < 0.0) | |
55f26379 | 692 | return scm_from_double (-xx); |
ae38324d KR |
693 | else |
694 | return x; | |
695 | } | |
f92e85f7 MV |
696 | else if (SCM_FRACTIONP (x)) |
697 | { | |
73e4de09 | 698 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 699 | return x; |
cba42c93 | 700 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
701 | SCM_FRACTION_DENOMINATOR (x)); |
702 | } | |
0aacf84e | 703 | else |
a48d60b1 | 704 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 705 | } |
a48d60b1 | 706 | #undef FUNC_NAME |
0f2d19dd | 707 | |
4219f20d | 708 | |
9de33deb | 709 | SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); |
942e5b91 MG |
710 | /* "Return the quotient of the numbers @var{x} and @var{y}." |
711 | */ | |
0f2d19dd | 712 | SCM |
6e8d25a6 | 713 | scm_quotient (SCM x, SCM y) |
0f2d19dd | 714 | { |
e11e83f3 | 715 | if (SCM_I_INUMP (x)) |
0aacf84e | 716 | { |
e11e83f3 MV |
717 | long xx = SCM_I_INUM (x); |
718 | if (SCM_I_INUMP (y)) | |
0aacf84e | 719 | { |
e11e83f3 | 720 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
721 | if (yy == 0) |
722 | scm_num_overflow (s_quotient); | |
723 | else | |
724 | { | |
725 | long z = xx / yy; | |
726 | if (SCM_FIXABLE (z)) | |
d956fa6f | 727 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
728 | else |
729 | return scm_i_long2big (z); | |
730 | } | |
828865c3 | 731 | } |
0aacf84e | 732 | else if (SCM_BIGP (y)) |
ac0c002c | 733 | { |
e11e83f3 | 734 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
735 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
736 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
737 | { | |
738 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
739 | scm_remember_upto_here_1 (y); | |
d956fa6f | 740 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 741 | } |
0aacf84e | 742 | else |
d956fa6f | 743 | return SCM_I_MAKINUM (0); |
ac0c002c DH |
744 | } |
745 | else | |
0aacf84e | 746 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); |
828865c3 | 747 | } |
0aacf84e MD |
748 | else if (SCM_BIGP (x)) |
749 | { | |
e11e83f3 | 750 | if (SCM_I_INUMP (y)) |
0aacf84e | 751 | { |
e11e83f3 | 752 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
753 | if (yy == 0) |
754 | scm_num_overflow (s_quotient); | |
755 | else if (yy == 1) | |
756 | return x; | |
757 | else | |
758 | { | |
759 | SCM result = scm_i_mkbig (); | |
760 | if (yy < 0) | |
761 | { | |
762 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
763 | SCM_I_BIG_MPZ (x), | |
764 | - yy); | |
765 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
766 | } | |
767 | else | |
768 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
769 | scm_remember_upto_here_1 (x); | |
770 | return scm_i_normbig (result); | |
771 | } | |
772 | } | |
773 | else if (SCM_BIGP (y)) | |
774 | { | |
775 | SCM result = scm_i_mkbig (); | |
776 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
777 | SCM_I_BIG_MPZ (x), | |
778 | SCM_I_BIG_MPZ (y)); | |
779 | scm_remember_upto_here_2 (x, y); | |
780 | return scm_i_normbig (result); | |
781 | } | |
782 | else | |
783 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); | |
f872b822 | 784 | } |
0aacf84e | 785 | else |
89a7e495 | 786 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient); |
0f2d19dd JB |
787 | } |
788 | ||
9de33deb | 789 | SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); |
942e5b91 MG |
790 | /* "Return the remainder of the numbers @var{x} and @var{y}.\n" |
791 | * "@lisp\n" | |
792 | * "(remainder 13 4) @result{} 1\n" | |
793 | * "(remainder -13 4) @result{} -1\n" | |
794 | * "@end lisp" | |
795 | */ | |
0f2d19dd | 796 | SCM |
6e8d25a6 | 797 | scm_remainder (SCM x, SCM y) |
0f2d19dd | 798 | { |
e11e83f3 | 799 | if (SCM_I_INUMP (x)) |
0aacf84e | 800 | { |
e11e83f3 | 801 | if (SCM_I_INUMP (y)) |
0aacf84e | 802 | { |
e11e83f3 | 803 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
804 | if (yy == 0) |
805 | scm_num_overflow (s_remainder); | |
806 | else | |
807 | { | |
e11e83f3 | 808 | long z = SCM_I_INUM (x) % yy; |
d956fa6f | 809 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
810 | } |
811 | } | |
812 | else if (SCM_BIGP (y)) | |
ac0c002c | 813 | { |
e11e83f3 | 814 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
815 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
816 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
817 | { | |
818 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
819 | scm_remember_upto_here_1 (y); | |
d956fa6f | 820 | return SCM_I_MAKINUM (0); |
4dc09ee4 | 821 | } |
0aacf84e MD |
822 | else |
823 | return x; | |
ac0c002c DH |
824 | } |
825 | else | |
0aacf84e | 826 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); |
89a7e495 | 827 | } |
0aacf84e MD |
828 | else if (SCM_BIGP (x)) |
829 | { | |
e11e83f3 | 830 | if (SCM_I_INUMP (y)) |
0aacf84e | 831 | { |
e11e83f3 | 832 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
833 | if (yy == 0) |
834 | scm_num_overflow (s_remainder); | |
835 | else | |
836 | { | |
837 | SCM result = scm_i_mkbig (); | |
838 | if (yy < 0) | |
839 | yy = - yy; | |
840 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
841 | scm_remember_upto_here_1 (x); | |
842 | return scm_i_normbig (result); | |
843 | } | |
844 | } | |
845 | else if (SCM_BIGP (y)) | |
846 | { | |
847 | SCM result = scm_i_mkbig (); | |
848 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
849 | SCM_I_BIG_MPZ (x), | |
850 | SCM_I_BIG_MPZ (y)); | |
851 | scm_remember_upto_here_2 (x, y); | |
852 | return scm_i_normbig (result); | |
853 | } | |
854 | else | |
855 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); | |
f872b822 | 856 | } |
0aacf84e | 857 | else |
89a7e495 | 858 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder); |
0f2d19dd JB |
859 | } |
860 | ||
89a7e495 | 861 | |
9de33deb | 862 | SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); |
942e5b91 MG |
863 | /* "Return the modulo of the numbers @var{x} and @var{y}.\n" |
864 | * "@lisp\n" | |
865 | * "(modulo 13 4) @result{} 1\n" | |
866 | * "(modulo -13 4) @result{} 3\n" | |
867 | * "@end lisp" | |
868 | */ | |
0f2d19dd | 869 | SCM |
6e8d25a6 | 870 | scm_modulo (SCM x, SCM y) |
0f2d19dd | 871 | { |
e11e83f3 | 872 | if (SCM_I_INUMP (x)) |
0aacf84e | 873 | { |
e11e83f3 MV |
874 | long xx = SCM_I_INUM (x); |
875 | if (SCM_I_INUMP (y)) | |
0aacf84e | 876 | { |
e11e83f3 | 877 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
878 | if (yy == 0) |
879 | scm_num_overflow (s_modulo); | |
880 | else | |
881 | { | |
882 | /* FIXME: I think this may be a bug on some arches -- results | |
883 | of % with negative second arg are undefined... */ | |
884 | long z = xx % yy; | |
885 | long result; | |
886 | ||
887 | if (yy < 0) | |
888 | { | |
889 | if (z > 0) | |
890 | result = z + yy; | |
891 | else | |
892 | result = z; | |
893 | } | |
894 | else | |
895 | { | |
896 | if (z < 0) | |
897 | result = z + yy; | |
898 | else | |
899 | result = z; | |
900 | } | |
d956fa6f | 901 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
902 | } |
903 | } | |
904 | else if (SCM_BIGP (y)) | |
905 | { | |
906 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
907 | { |
908 | mpz_t z_x; | |
909 | SCM result; | |
910 | ||
911 | if (sgn_y < 0) | |
912 | { | |
913 | SCM pos_y = scm_i_clonebig (y, 0); | |
914 | /* do this after the last scm_op */ | |
915 | mpz_init_set_si (z_x, xx); | |
916 | result = pos_y; /* re-use this bignum */ | |
917 | mpz_mod (SCM_I_BIG_MPZ (result), | |
918 | z_x, | |
919 | SCM_I_BIG_MPZ (pos_y)); | |
920 | scm_remember_upto_here_1 (pos_y); | |
921 | } | |
922 | else | |
923 | { | |
924 | result = scm_i_mkbig (); | |
925 | /* do this after the last scm_op */ | |
926 | mpz_init_set_si (z_x, xx); | |
927 | mpz_mod (SCM_I_BIG_MPZ (result), | |
928 | z_x, | |
929 | SCM_I_BIG_MPZ (y)); | |
930 | scm_remember_upto_here_1 (y); | |
931 | } | |
ca46fb90 | 932 | |
0aacf84e MD |
933 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
934 | mpz_add (SCM_I_BIG_MPZ (result), | |
935 | SCM_I_BIG_MPZ (y), | |
936 | SCM_I_BIG_MPZ (result)); | |
937 | scm_remember_upto_here_1 (y); | |
938 | /* and do this before the next one */ | |
939 | mpz_clear (z_x); | |
940 | return scm_i_normbig (result); | |
941 | } | |
942 | } | |
943 | else | |
944 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
f872b822 | 945 | } |
0aacf84e MD |
946 | else if (SCM_BIGP (x)) |
947 | { | |
e11e83f3 | 948 | if (SCM_I_INUMP (y)) |
0aacf84e | 949 | { |
e11e83f3 | 950 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
951 | if (yy == 0) |
952 | scm_num_overflow (s_modulo); | |
953 | else | |
954 | { | |
955 | SCM result = scm_i_mkbig (); | |
956 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
957 | SCM_I_BIG_MPZ (x), | |
958 | (yy < 0) ? - yy : yy); | |
959 | scm_remember_upto_here_1 (x); | |
960 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
961 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
962 | SCM_I_BIG_MPZ (result), | |
963 | - yy); | |
964 | return scm_i_normbig (result); | |
965 | } | |
966 | } | |
967 | else if (SCM_BIGP (y)) | |
968 | { | |
0aacf84e MD |
969 | { |
970 | SCM result = scm_i_mkbig (); | |
971 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
972 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
973 | mpz_mod (SCM_I_BIG_MPZ (result), | |
974 | SCM_I_BIG_MPZ (x), | |
975 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 976 | |
0aacf84e MD |
977 | scm_remember_upto_here_1 (x); |
978 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
979 | mpz_add (SCM_I_BIG_MPZ (result), | |
980 | SCM_I_BIG_MPZ (y), | |
981 | SCM_I_BIG_MPZ (result)); | |
982 | scm_remember_upto_here_2 (y, pos_y); | |
983 | return scm_i_normbig (result); | |
984 | } | |
985 | } | |
986 | else | |
987 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
828865c3 | 988 | } |
0aacf84e | 989 | else |
09fb7599 | 990 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); |
0f2d19dd JB |
991 | } |
992 | ||
9de33deb | 993 | SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd); |
942e5b91 MG |
994 | /* "Return the greatest common divisor of all arguments.\n" |
995 | * "If called without arguments, 0 is returned." | |
996 | */ | |
0f2d19dd | 997 | SCM |
6e8d25a6 | 998 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 999 | { |
ca46fb90 | 1000 | if (SCM_UNBNDP (y)) |
0aacf84e | 1001 | return SCM_UNBNDP (x) ? SCM_INUM0 : x; |
ca46fb90 | 1002 | |
e11e83f3 | 1003 | if (SCM_I_INUMP (x)) |
ca46fb90 | 1004 | { |
e11e83f3 | 1005 | if (SCM_I_INUMP (y)) |
ca46fb90 | 1006 | { |
e11e83f3 MV |
1007 | long xx = SCM_I_INUM (x); |
1008 | long yy = SCM_I_INUM (y); | |
ca46fb90 RB |
1009 | long u = xx < 0 ? -xx : xx; |
1010 | long v = yy < 0 ? -yy : yy; | |
1011 | long result; | |
0aacf84e MD |
1012 | if (xx == 0) |
1013 | result = v; | |
1014 | else if (yy == 0) | |
1015 | result = u; | |
1016 | else | |
1017 | { | |
1018 | long k = 1; | |
1019 | long t; | |
1020 | /* Determine a common factor 2^k */ | |
1021 | while (!(1 & (u | v))) | |
1022 | { | |
1023 | k <<= 1; | |
1024 | u >>= 1; | |
1025 | v >>= 1; | |
1026 | } | |
1027 | /* Now, any factor 2^n can be eliminated */ | |
1028 | if (u & 1) | |
1029 | t = -v; | |
1030 | else | |
1031 | { | |
1032 | t = u; | |
1033 | b3: | |
1034 | t = SCM_SRS (t, 1); | |
1035 | } | |
1036 | if (!(1 & t)) | |
1037 | goto b3; | |
1038 | if (t > 0) | |
1039 | u = t; | |
1040 | else | |
1041 | v = -t; | |
1042 | t = u - v; | |
1043 | if (t != 0) | |
1044 | goto b3; | |
1045 | result = u * k; | |
1046 | } | |
1047 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 1048 | ? SCM_I_MAKINUM (result) |
0aacf84e | 1049 | : scm_i_long2big (result)); |
ca46fb90 RB |
1050 | } |
1051 | else if (SCM_BIGP (y)) | |
1052 | { | |
0bff4dce KR |
1053 | SCM_SWAP (x, y); |
1054 | goto big_inum; | |
ca46fb90 RB |
1055 | } |
1056 | else | |
1057 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 1058 | } |
ca46fb90 RB |
1059 | else if (SCM_BIGP (x)) |
1060 | { | |
e11e83f3 | 1061 | if (SCM_I_INUMP (y)) |
ca46fb90 RB |
1062 | { |
1063 | unsigned long result; | |
0bff4dce KR |
1064 | long yy; |
1065 | big_inum: | |
e11e83f3 | 1066 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
1067 | if (yy == 0) |
1068 | return scm_abs (x); | |
0aacf84e MD |
1069 | if (yy < 0) |
1070 | yy = -yy; | |
ca46fb90 RB |
1071 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
1072 | scm_remember_upto_here_1 (x); | |
0aacf84e | 1073 | return (SCM_POSFIXABLE (result) |
d956fa6f | 1074 | ? SCM_I_MAKINUM (result) |
c71b0706 | 1075 | : scm_from_ulong (result)); |
ca46fb90 RB |
1076 | } |
1077 | else if (SCM_BIGP (y)) | |
1078 | { | |
1079 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
1080 | mpz_gcd (SCM_I_BIG_MPZ (result), |
1081 | SCM_I_BIG_MPZ (x), | |
1082 | SCM_I_BIG_MPZ (y)); | |
1083 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
1084 | return scm_i_normbig (result); |
1085 | } | |
1086 | else | |
1087 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 1088 | } |
ca46fb90 | 1089 | else |
09fb7599 | 1090 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
1091 | } |
1092 | ||
9de33deb | 1093 | SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm); |
942e5b91 MG |
1094 | /* "Return the least common multiple of the arguments.\n" |
1095 | * "If called without arguments, 1 is returned." | |
1096 | */ | |
0f2d19dd | 1097 | SCM |
6e8d25a6 | 1098 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 1099 | { |
ca46fb90 RB |
1100 | if (SCM_UNBNDP (n2)) |
1101 | { | |
1102 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
1103 | return SCM_I_MAKINUM (1L); |
1104 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 1105 | } |
09fb7599 | 1106 | |
e11e83f3 | 1107 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 1108 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 1109 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 1110 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 1111 | |
e11e83f3 | 1112 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 1113 | { |
e11e83f3 | 1114 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1115 | { |
1116 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 1117 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
1118 | return d; |
1119 | else | |
1120 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
1121 | } | |
1122 | else | |
1123 | { | |
1124 | /* inum n1, big n2 */ | |
1125 | inumbig: | |
1126 | { | |
1127 | SCM result = scm_i_mkbig (); | |
e11e83f3 | 1128 | long nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
1129 | if (nn1 == 0) return SCM_INUM0; |
1130 | if (nn1 < 0) nn1 = - nn1; | |
1131 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
1132 | scm_remember_upto_here_1 (n2); | |
1133 | return result; | |
1134 | } | |
1135 | } | |
1136 | } | |
1137 | else | |
1138 | { | |
1139 | /* big n1 */ | |
e11e83f3 | 1140 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1141 | { |
1142 | SCM_SWAP (n1, n2); | |
1143 | goto inumbig; | |
1144 | } | |
1145 | else | |
1146 | { | |
1147 | SCM result = scm_i_mkbig (); | |
1148 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
1149 | SCM_I_BIG_MPZ (n1), | |
1150 | SCM_I_BIG_MPZ (n2)); | |
1151 | scm_remember_upto_here_2(n1, n2); | |
1152 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
1153 | return result; | |
1154 | } | |
f872b822 | 1155 | } |
0f2d19dd JB |
1156 | } |
1157 | ||
8a525303 GB |
1158 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
1159 | ||
1160 | Logand: | |
1161 | X Y Result Method: | |
1162 | (len) | |
1163 | + + + x (map digit:logand X Y) | |
1164 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
1165 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
1166 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
1167 | ||
1168 | Logior: | |
1169 | X Y Result Method: | |
1170 | ||
1171 | + + + (map digit:logior X Y) | |
1172 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
1173 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
1174 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
1175 | ||
1176 | Logxor: | |
1177 | X Y Result Method: | |
1178 | ||
1179 | + + + (map digit:logxor X Y) | |
1180 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
1181 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
1182 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
1183 | ||
1184 | Logtest: | |
1185 | X Y Result | |
1186 | ||
1187 | + + (any digit:logand X Y) | |
1188 | + - (any digit:logand X (lognot (+ -1 Y))) | |
1189 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
1190 | - - #t | |
1191 | ||
1192 | */ | |
1193 | ||
c3ee7520 | 1194 | SCM_DEFINE1 (scm_logand, "logand", scm_tc7_asubr, |
1bbd0b84 | 1195 | (SCM n1, SCM n2), |
3c3db128 GH |
1196 | "Return the bitwise AND of the integer arguments.\n\n" |
1197 | "@lisp\n" | |
1198 | "(logand) @result{} -1\n" | |
1199 | "(logand 7) @result{} 7\n" | |
535f2a51 | 1200 | "(logand #b111 #b011 #b001) @result{} 1\n" |
3c3db128 | 1201 | "@end lisp") |
1bbd0b84 | 1202 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 1203 | { |
9a00c9fc DH |
1204 | long int nn1; |
1205 | ||
0aacf84e MD |
1206 | if (SCM_UNBNDP (n2)) |
1207 | { | |
1208 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 1209 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
1210 | else if (!SCM_NUMBERP (n1)) |
1211 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1212 | else if (SCM_NUMBERP (n1)) | |
1213 | return n1; | |
1214 | else | |
1215 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1216 | } |
09fb7599 | 1217 | |
e11e83f3 | 1218 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1219 | { |
e11e83f3 MV |
1220 | nn1 = SCM_I_INUM (n1); |
1221 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1222 | { |
e11e83f3 | 1223 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1224 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
1225 | } |
1226 | else if SCM_BIGP (n2) | |
1227 | { | |
1228 | intbig: | |
1229 | if (n1 == 0) | |
1230 | return SCM_INUM0; | |
1231 | { | |
1232 | SCM result_z = scm_i_mkbig (); | |
1233 | mpz_t nn1_z; | |
1234 | mpz_init_set_si (nn1_z, nn1); | |
1235 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1236 | scm_remember_upto_here_1 (n2); | |
1237 | mpz_clear (nn1_z); | |
1238 | return scm_i_normbig (result_z); | |
1239 | } | |
1240 | } | |
1241 | else | |
1242 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1243 | } | |
1244 | else if (SCM_BIGP (n1)) | |
1245 | { | |
e11e83f3 | 1246 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1247 | { |
1248 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1249 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1250 | goto intbig; |
1251 | } | |
1252 | else if (SCM_BIGP (n2)) | |
1253 | { | |
1254 | SCM result_z = scm_i_mkbig (); | |
1255 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
1256 | SCM_I_BIG_MPZ (n1), | |
1257 | SCM_I_BIG_MPZ (n2)); | |
1258 | scm_remember_upto_here_2 (n1, n2); | |
1259 | return scm_i_normbig (result_z); | |
1260 | } | |
1261 | else | |
1262 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1263 | } |
0aacf84e | 1264 | else |
09fb7599 | 1265 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1266 | } |
1bbd0b84 | 1267 | #undef FUNC_NAME |
0f2d19dd | 1268 | |
09fb7599 | 1269 | |
c3ee7520 | 1270 | SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr, |
1bbd0b84 | 1271 | (SCM n1, SCM n2), |
3c3db128 GH |
1272 | "Return the bitwise OR of the integer arguments.\n\n" |
1273 | "@lisp\n" | |
1274 | "(logior) @result{} 0\n" | |
1275 | "(logior 7) @result{} 7\n" | |
1276 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1e6808ea | 1277 | "@end lisp") |
1bbd0b84 | 1278 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 1279 | { |
9a00c9fc DH |
1280 | long int nn1; |
1281 | ||
0aacf84e MD |
1282 | if (SCM_UNBNDP (n2)) |
1283 | { | |
1284 | if (SCM_UNBNDP (n1)) | |
1285 | return SCM_INUM0; | |
1286 | else if (SCM_NUMBERP (n1)) | |
1287 | return n1; | |
1288 | else | |
1289 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1290 | } |
09fb7599 | 1291 | |
e11e83f3 | 1292 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1293 | { |
e11e83f3 MV |
1294 | nn1 = SCM_I_INUM (n1); |
1295 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1296 | { |
e11e83f3 | 1297 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1298 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
1299 | } |
1300 | else if (SCM_BIGP (n2)) | |
1301 | { | |
1302 | intbig: | |
1303 | if (nn1 == 0) | |
1304 | return n2; | |
1305 | { | |
1306 | SCM result_z = scm_i_mkbig (); | |
1307 | mpz_t nn1_z; | |
1308 | mpz_init_set_si (nn1_z, nn1); | |
1309 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1310 | scm_remember_upto_here_1 (n2); | |
1311 | mpz_clear (nn1_z); | |
1312 | return result_z; | |
1313 | } | |
1314 | } | |
1315 | else | |
1316 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1317 | } | |
1318 | else if (SCM_BIGP (n1)) | |
1319 | { | |
e11e83f3 | 1320 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1321 | { |
1322 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1323 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1324 | goto intbig; |
1325 | } | |
1326 | else if (SCM_BIGP (n2)) | |
1327 | { | |
1328 | SCM result_z = scm_i_mkbig (); | |
1329 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
1330 | SCM_I_BIG_MPZ (n1), | |
1331 | SCM_I_BIG_MPZ (n2)); | |
1332 | scm_remember_upto_here_2 (n1, n2); | |
1333 | return result_z; | |
1334 | } | |
1335 | else | |
1336 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1337 | } |
0aacf84e | 1338 | else |
09fb7599 | 1339 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1340 | } |
1bbd0b84 | 1341 | #undef FUNC_NAME |
0f2d19dd | 1342 | |
09fb7599 | 1343 | |
c3ee7520 | 1344 | SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr, |
1bbd0b84 | 1345 | (SCM n1, SCM n2), |
3c3db128 GH |
1346 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1347 | "set in the result if it is set in an odd number of arguments.\n" | |
1348 | "@lisp\n" | |
1349 | "(logxor) @result{} 0\n" | |
1350 | "(logxor 7) @result{} 7\n" | |
1351 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1352 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1353 | "@end lisp") |
1bbd0b84 | 1354 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1355 | { |
9a00c9fc DH |
1356 | long int nn1; |
1357 | ||
0aacf84e MD |
1358 | if (SCM_UNBNDP (n2)) |
1359 | { | |
1360 | if (SCM_UNBNDP (n1)) | |
1361 | return SCM_INUM0; | |
1362 | else if (SCM_NUMBERP (n1)) | |
1363 | return n1; | |
1364 | else | |
1365 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1366 | } |
09fb7599 | 1367 | |
e11e83f3 | 1368 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1369 | { |
e11e83f3 MV |
1370 | nn1 = SCM_I_INUM (n1); |
1371 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1372 | { |
e11e83f3 | 1373 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1374 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
1375 | } |
1376 | else if (SCM_BIGP (n2)) | |
1377 | { | |
1378 | intbig: | |
1379 | { | |
1380 | SCM result_z = scm_i_mkbig (); | |
1381 | mpz_t nn1_z; | |
1382 | mpz_init_set_si (nn1_z, nn1); | |
1383 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1384 | scm_remember_upto_here_1 (n2); | |
1385 | mpz_clear (nn1_z); | |
1386 | return scm_i_normbig (result_z); | |
1387 | } | |
1388 | } | |
1389 | else | |
1390 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1391 | } | |
1392 | else if (SCM_BIGP (n1)) | |
1393 | { | |
e11e83f3 | 1394 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1395 | { |
1396 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1397 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1398 | goto intbig; |
1399 | } | |
1400 | else if (SCM_BIGP (n2)) | |
1401 | { | |
1402 | SCM result_z = scm_i_mkbig (); | |
1403 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
1404 | SCM_I_BIG_MPZ (n1), | |
1405 | SCM_I_BIG_MPZ (n2)); | |
1406 | scm_remember_upto_here_2 (n1, n2); | |
1407 | return scm_i_normbig (result_z); | |
1408 | } | |
1409 | else | |
1410 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1411 | } |
0aacf84e | 1412 | else |
09fb7599 | 1413 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1414 | } |
1bbd0b84 | 1415 | #undef FUNC_NAME |
0f2d19dd | 1416 | |
09fb7599 | 1417 | |
a1ec6916 | 1418 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea MG |
1419 | (SCM j, SCM k), |
1420 | "@lisp\n" | |
b380b885 MD |
1421 | "(logtest j k) @equiv{} (not (zero? (logand j k)))\n\n" |
1422 | "(logtest #b0100 #b1011) @result{} #f\n" | |
1423 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1424 | "@end lisp") |
1bbd0b84 | 1425 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1426 | { |
1e6808ea | 1427 | long int nj; |
9a00c9fc | 1428 | |
e11e83f3 | 1429 | if (SCM_I_INUMP (j)) |
0aacf84e | 1430 | { |
e11e83f3 MV |
1431 | nj = SCM_I_INUM (j); |
1432 | if (SCM_I_INUMP (k)) | |
0aacf84e | 1433 | { |
e11e83f3 | 1434 | long nk = SCM_I_INUM (k); |
73e4de09 | 1435 | return scm_from_bool (nj & nk); |
0aacf84e MD |
1436 | } |
1437 | else if (SCM_BIGP (k)) | |
1438 | { | |
1439 | intbig: | |
1440 | if (nj == 0) | |
1441 | return SCM_BOOL_F; | |
1442 | { | |
1443 | SCM result; | |
1444 | mpz_t nj_z; | |
1445 | mpz_init_set_si (nj_z, nj); | |
1446 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
1447 | scm_remember_upto_here_1 (k); | |
73e4de09 | 1448 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
1449 | mpz_clear (nj_z); |
1450 | return result; | |
1451 | } | |
1452 | } | |
1453 | else | |
1454 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1455 | } | |
1456 | else if (SCM_BIGP (j)) | |
1457 | { | |
e11e83f3 | 1458 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
1459 | { |
1460 | SCM_SWAP (j, k); | |
e11e83f3 | 1461 | nj = SCM_I_INUM (j); |
0aacf84e MD |
1462 | goto intbig; |
1463 | } | |
1464 | else if (SCM_BIGP (k)) | |
1465 | { | |
1466 | SCM result; | |
1467 | mpz_t result_z; | |
1468 | mpz_init (result_z); | |
1469 | mpz_and (result_z, | |
1470 | SCM_I_BIG_MPZ (j), | |
1471 | SCM_I_BIG_MPZ (k)); | |
1472 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 1473 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
1474 | mpz_clear (result_z); |
1475 | return result; | |
1476 | } | |
1477 | else | |
1478 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1479 | } | |
1480 | else | |
1481 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 1482 | } |
1bbd0b84 | 1483 | #undef FUNC_NAME |
0f2d19dd | 1484 | |
c1bfcf60 | 1485 | |
a1ec6916 | 1486 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1487 | (SCM index, SCM j), |
1e6808ea | 1488 | "@lisp\n" |
b380b885 MD |
1489 | "(logbit? index j) @equiv{} (logtest (integer-expt 2 index) j)\n\n" |
1490 | "(logbit? 0 #b1101) @result{} #t\n" | |
1491 | "(logbit? 1 #b1101) @result{} #f\n" | |
1492 | "(logbit? 2 #b1101) @result{} #t\n" | |
1493 | "(logbit? 3 #b1101) @result{} #t\n" | |
1494 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1495 | "@end lisp") |
1bbd0b84 | 1496 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1497 | { |
78166ad5 | 1498 | unsigned long int iindex; |
5efd3c7d | 1499 | iindex = scm_to_ulong (index); |
78166ad5 | 1500 | |
e11e83f3 | 1501 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
1502 | { |
1503 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 1504 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 1505 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 1506 | } |
0aacf84e MD |
1507 | else if (SCM_BIGP (j)) |
1508 | { | |
1509 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
1510 | scm_remember_upto_here_1 (j); | |
73e4de09 | 1511 | return scm_from_bool (val); |
0aacf84e MD |
1512 | } |
1513 | else | |
78166ad5 | 1514 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 1515 | } |
1bbd0b84 | 1516 | #undef FUNC_NAME |
0f2d19dd | 1517 | |
78166ad5 | 1518 | |
a1ec6916 | 1519 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1520 | (SCM n), |
4d814788 | 1521 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
1522 | "argument.\n" |
1523 | "\n" | |
b380b885 MD |
1524 | "@lisp\n" |
1525 | "(number->string (lognot #b10000000) 2)\n" | |
1526 | " @result{} \"-10000001\"\n" | |
1527 | "(number->string (lognot #b0) 2)\n" | |
1528 | " @result{} \"-1\"\n" | |
1e6808ea | 1529 | "@end lisp") |
1bbd0b84 | 1530 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1531 | { |
e11e83f3 | 1532 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
1533 | /* No overflow here, just need to toggle all the bits making up the inum. |
1534 | Enhancement: No need to strip the tag and add it back, could just xor | |
1535 | a block of 1 bits, if that worked with the various debug versions of | |
1536 | the SCM typedef. */ | |
e11e83f3 | 1537 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
1538 | |
1539 | } else if (SCM_BIGP (n)) { | |
1540 | SCM result = scm_i_mkbig (); | |
1541 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
1542 | scm_remember_upto_here_1 (n); | |
1543 | return result; | |
1544 | ||
1545 | } else { | |
1546 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1547 | } | |
0f2d19dd | 1548 | } |
1bbd0b84 | 1549 | #undef FUNC_NAME |
0f2d19dd | 1550 | |
518b7508 KR |
1551 | /* returns 0 if IN is not an integer. OUT must already be |
1552 | initialized. */ | |
1553 | static int | |
1554 | coerce_to_big (SCM in, mpz_t out) | |
1555 | { | |
1556 | if (SCM_BIGP (in)) | |
1557 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
1558 | else if (SCM_I_INUMP (in)) |
1559 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
1560 | else |
1561 | return 0; | |
1562 | ||
1563 | return 1; | |
1564 | } | |
1565 | ||
d885e204 | 1566 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
1567 | (SCM n, SCM k, SCM m), |
1568 | "Return @var{n} raised to the integer exponent\n" | |
1569 | "@var{k}, modulo @var{m}.\n" | |
1570 | "\n" | |
1571 | "@lisp\n" | |
1572 | "(modulo-expt 2 3 5)\n" | |
1573 | " @result{} 3\n" | |
1574 | "@end lisp") | |
d885e204 | 1575 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
1576 | { |
1577 | mpz_t n_tmp; | |
1578 | mpz_t k_tmp; | |
1579 | mpz_t m_tmp; | |
1580 | ||
1581 | /* There are two classes of error we might encounter -- | |
1582 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
1583 | and | |
1584 | 2) wrong-type errors, which of course we'll report by calling | |
1585 | SCM_WRONG_TYPE_ARG. | |
1586 | We don't report those errors immediately, however; instead we do | |
1587 | some cleanup first. These variables tell us which error (if | |
1588 | any) we should report after cleaning up. | |
1589 | */ | |
1590 | int report_overflow = 0; | |
1591 | ||
1592 | int position_of_wrong_type = 0; | |
1593 | SCM value_of_wrong_type = SCM_INUM0; | |
1594 | ||
1595 | SCM result = SCM_UNDEFINED; | |
1596 | ||
1597 | mpz_init (n_tmp); | |
1598 | mpz_init (k_tmp); | |
1599 | mpz_init (m_tmp); | |
1600 | ||
bc36d050 | 1601 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
1602 | { |
1603 | report_overflow = 1; | |
1604 | goto cleanup; | |
1605 | } | |
1606 | ||
1607 | if (!coerce_to_big (n, n_tmp)) | |
1608 | { | |
1609 | value_of_wrong_type = n; | |
1610 | position_of_wrong_type = 1; | |
1611 | goto cleanup; | |
1612 | } | |
1613 | ||
1614 | if (!coerce_to_big (k, k_tmp)) | |
1615 | { | |
1616 | value_of_wrong_type = k; | |
1617 | position_of_wrong_type = 2; | |
1618 | goto cleanup; | |
1619 | } | |
1620 | ||
1621 | if (!coerce_to_big (m, m_tmp)) | |
1622 | { | |
1623 | value_of_wrong_type = m; | |
1624 | position_of_wrong_type = 3; | |
1625 | goto cleanup; | |
1626 | } | |
1627 | ||
1628 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
1629 | will get a divide-by-zero exception when an inverse 1/n mod m | |
1630 | doesn't exist (or is not unique). Since exceptions are hard to | |
1631 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
1632 | a simple failure code, which is easy to handle. */ | |
1633 | ||
1634 | if (-1 == mpz_sgn (k_tmp)) | |
1635 | { | |
1636 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
1637 | { | |
1638 | report_overflow = 1; | |
1639 | goto cleanup; | |
1640 | } | |
1641 | mpz_neg (k_tmp, k_tmp); | |
1642 | } | |
1643 | ||
1644 | result = scm_i_mkbig (); | |
1645 | mpz_powm (SCM_I_BIG_MPZ (result), | |
1646 | n_tmp, | |
1647 | k_tmp, | |
1648 | m_tmp); | |
b7b8c575 KR |
1649 | |
1650 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
1651 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
1652 | ||
518b7508 KR |
1653 | cleanup: |
1654 | mpz_clear (m_tmp); | |
1655 | mpz_clear (k_tmp); | |
1656 | mpz_clear (n_tmp); | |
1657 | ||
1658 | if (report_overflow) | |
1659 | scm_num_overflow (FUNC_NAME); | |
1660 | ||
1661 | if (position_of_wrong_type) | |
1662 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
1663 | value_of_wrong_type); | |
1664 | ||
1665 | return scm_i_normbig (result); | |
1666 | } | |
1667 | #undef FUNC_NAME | |
1668 | ||
a1ec6916 | 1669 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1670 | (SCM n, SCM k), |
1e6808ea MG |
1671 | "Return @var{n} raised to the non-negative integer exponent\n" |
1672 | "@var{k}.\n" | |
1673 | "\n" | |
b380b885 MD |
1674 | "@lisp\n" |
1675 | "(integer-expt 2 5)\n" | |
1676 | " @result{} 32\n" | |
1677 | "(integer-expt -3 3)\n" | |
1678 | " @result{} -27\n" | |
1679 | "@end lisp") | |
1bbd0b84 | 1680 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1681 | { |
1c35cb19 RB |
1682 | long i2 = 0; |
1683 | SCM z_i2 = SCM_BOOL_F; | |
1684 | int i2_is_big = 0; | |
d956fa6f | 1685 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 1686 | |
d57ed702 | 1687 | /* 0^0 == 1 according to R5RS */ |
bc36d050 | 1688 | if (scm_is_eq (n, SCM_INUM0) || scm_is_eq (n, acc)) |
73e4de09 | 1689 | return scm_is_false (scm_zero_p(k)) ? n : acc; |
bc36d050 | 1690 | else if (scm_is_eq (n, SCM_I_MAKINUM (-1L))) |
73e4de09 | 1691 | return scm_is_false (scm_even_p (k)) ? n : acc; |
ca46fb90 | 1692 | |
e11e83f3 MV |
1693 | if (SCM_I_INUMP (k)) |
1694 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
1695 | else if (SCM_BIGP (k)) |
1696 | { | |
1697 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
1698 | scm_remember_upto_here_1 (k); |
1699 | i2_is_big = 1; | |
1700 | } | |
1701 | else if (SCM_REALP (k)) | |
2830fd91 MD |
1702 | { |
1703 | double r = SCM_REAL_VALUE (k); | |
ca46fb90 RB |
1704 | if (floor (r) != r) |
1705 | SCM_WRONG_TYPE_ARG (2, k); | |
1706 | if ((r > SCM_MOST_POSITIVE_FIXNUM) || (r < SCM_MOST_NEGATIVE_FIXNUM)) | |
1707 | { | |
1708 | z_i2 = scm_i_mkbig (); | |
753ac1e7 | 1709 | mpz_set_d (SCM_I_BIG_MPZ (z_i2), r); |
ca46fb90 RB |
1710 | i2_is_big = 1; |
1711 | } | |
1712 | else | |
1713 | { | |
1714 | i2 = r; | |
1715 | } | |
2830fd91 MD |
1716 | } |
1717 | else | |
ca46fb90 RB |
1718 | SCM_WRONG_TYPE_ARG (2, k); |
1719 | ||
1720 | if (i2_is_big) | |
f872b822 | 1721 | { |
ca46fb90 RB |
1722 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
1723 | { | |
1724 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
1725 | n = scm_divide (n, SCM_UNDEFINED); | |
1726 | } | |
1727 | while (1) | |
1728 | { | |
1729 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
1730 | { | |
ca46fb90 RB |
1731 | return acc; |
1732 | } | |
1733 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
1734 | { | |
ca46fb90 RB |
1735 | return scm_product (acc, n); |
1736 | } | |
1737 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
1738 | acc = scm_product (acc, n); | |
1739 | n = scm_product (n, n); | |
1740 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
1741 | } | |
f872b822 | 1742 | } |
ca46fb90 | 1743 | else |
f872b822 | 1744 | { |
ca46fb90 RB |
1745 | if (i2 < 0) |
1746 | { | |
1747 | i2 = -i2; | |
1748 | n = scm_divide (n, SCM_UNDEFINED); | |
1749 | } | |
1750 | while (1) | |
1751 | { | |
1752 | if (0 == i2) | |
1753 | return acc; | |
1754 | if (1 == i2) | |
1755 | return scm_product (acc, n); | |
1756 | if (i2 & 1) | |
1757 | acc = scm_product (acc, n); | |
1758 | n = scm_product (n, n); | |
1759 | i2 >>= 1; | |
1760 | } | |
f872b822 | 1761 | } |
0f2d19dd | 1762 | } |
1bbd0b84 | 1763 | #undef FUNC_NAME |
0f2d19dd | 1764 | |
a1ec6916 | 1765 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1766 | (SCM n, SCM cnt), |
32f19569 KR |
1767 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
1768 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 1769 | "\n" |
e7644cb2 | 1770 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
1771 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
1772 | "infinity. (Note that this is not the same rounding as\n" | |
1773 | "@code{quotient} does.)\n" | |
1774 | "\n" | |
1775 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
1776 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
1777 | "shift dropping bits.\n" | |
1e6808ea | 1778 | "\n" |
b380b885 | 1779 | "@lisp\n" |
1e6808ea MG |
1780 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1781 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
1782 | "\n" |
1783 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
1784 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 1785 | "@end lisp") |
1bbd0b84 | 1786 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1787 | { |
3ab9f56e | 1788 | long bits_to_shift; |
5efd3c7d | 1789 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 RB |
1790 | |
1791 | if (bits_to_shift < 0) | |
1792 | { | |
1793 | /* Shift right by abs(cnt) bits. This is realized as a division | |
1794 | by div:=2^abs(cnt). However, to guarantee the floor | |
1795 | rounding, negative values require some special treatment. | |
1796 | */ | |
d956fa6f | 1797 | SCM div = scm_integer_expt (SCM_I_MAKINUM (2), |
5efd3c7d | 1798 | scm_from_long (-bits_to_shift)); |
f92e85f7 MV |
1799 | |
1800 | /* scm_quotient assumes its arguments are integers, but it's legal to (ash 1/2 -1) */ | |
73e4de09 | 1801 | if (scm_is_false (scm_negative_p (n))) |
ca46fb90 RB |
1802 | return scm_quotient (n, div); |
1803 | else | |
d956fa6f MV |
1804 | return scm_sum (SCM_I_MAKINUM (-1L), |
1805 | scm_quotient (scm_sum (SCM_I_MAKINUM (1L), n), div)); | |
ca46fb90 RB |
1806 | } |
1807 | else | |
3ab9f56e | 1808 | /* Shift left is done by multiplication with 2^CNT */ |
d956fa6f | 1809 | return scm_product (n, scm_integer_expt (SCM_I_MAKINUM (2), cnt)); |
0f2d19dd | 1810 | } |
1bbd0b84 | 1811 | #undef FUNC_NAME |
0f2d19dd | 1812 | |
3c9f20f8 | 1813 | |
a1ec6916 | 1814 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 1815 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
1816 | "Return the integer composed of the @var{start} (inclusive)\n" |
1817 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
1818 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
1819 | "\n" | |
b380b885 MD |
1820 | "@lisp\n" |
1821 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
1822 | " @result{} \"1010\"\n" | |
1823 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
1824 | " @result{} \"10110\"\n" | |
1825 | "@end lisp") | |
1bbd0b84 | 1826 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 1827 | { |
7f848242 | 1828 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
1829 | istart = scm_to_ulong (start); |
1830 | iend = scm_to_ulong (end); | |
c1bfcf60 | 1831 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 1832 | |
7f848242 KR |
1833 | /* how many bits to keep */ |
1834 | bits = iend - istart; | |
1835 | ||
e11e83f3 | 1836 | if (SCM_I_INUMP (n)) |
0aacf84e | 1837 | { |
e11e83f3 | 1838 | long int in = SCM_I_INUM (n); |
7f848242 KR |
1839 | |
1840 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 1841 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 1842 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 1843 | |
0aacf84e MD |
1844 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
1845 | { | |
1846 | /* Since we emulate two's complement encoded numbers, this | |
1847 | * special case requires us to produce a result that has | |
7f848242 | 1848 | * more bits than can be stored in a fixnum. |
0aacf84e | 1849 | */ |
7f848242 KR |
1850 | SCM result = scm_i_long2big (in); |
1851 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1852 | bits); | |
1853 | return result; | |
0aacf84e | 1854 | } |
ac0c002c | 1855 | |
7f848242 | 1856 | /* mask down to requisite bits */ |
857ae6af | 1857 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 1858 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
1859 | } |
1860 | else if (SCM_BIGP (n)) | |
ac0c002c | 1861 | { |
7f848242 KR |
1862 | SCM result; |
1863 | if (bits == 1) | |
1864 | { | |
d956fa6f | 1865 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
1866 | } |
1867 | else | |
1868 | { | |
1869 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
1870 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
1871 | such bits into a ulong. */ | |
1872 | result = scm_i_mkbig (); | |
1873 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
1874 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
1875 | result = scm_i_normbig (result); | |
1876 | } | |
1877 | scm_remember_upto_here_1 (n); | |
1878 | return result; | |
ac0c002c | 1879 | } |
0aacf84e | 1880 | else |
78166ad5 | 1881 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 1882 | } |
1bbd0b84 | 1883 | #undef FUNC_NAME |
0f2d19dd | 1884 | |
7f848242 | 1885 | |
e4755e5c JB |
1886 | static const char scm_logtab[] = { |
1887 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
1888 | }; | |
1cc91f1b | 1889 | |
a1ec6916 | 1890 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 1891 | (SCM n), |
1e6808ea MG |
1892 | "Return the number of bits in integer @var{n}. If integer is\n" |
1893 | "positive, the 1-bits in its binary representation are counted.\n" | |
1894 | "If negative, the 0-bits in its two's-complement binary\n" | |
1895 | "representation are counted. If 0, 0 is returned.\n" | |
1896 | "\n" | |
b380b885 MD |
1897 | "@lisp\n" |
1898 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
1899 | " @result{} 4\n" |
1900 | "(logcount 0)\n" | |
1901 | " @result{} 0\n" | |
1902 | "(logcount -2)\n" | |
1903 | " @result{} 1\n" | |
1904 | "@end lisp") | |
1905 | #define FUNC_NAME s_scm_logcount | |
1906 | { | |
e11e83f3 | 1907 | if (SCM_I_INUMP (n)) |
f872b822 | 1908 | { |
ca46fb90 | 1909 | unsigned long int c = 0; |
e11e83f3 | 1910 | long int nn = SCM_I_INUM (n); |
ca46fb90 RB |
1911 | if (nn < 0) |
1912 | nn = -1 - nn; | |
1913 | while (nn) | |
1914 | { | |
1915 | c += scm_logtab[15 & nn]; | |
1916 | nn >>= 4; | |
1917 | } | |
d956fa6f | 1918 | return SCM_I_MAKINUM (c); |
f872b822 | 1919 | } |
ca46fb90 | 1920 | else if (SCM_BIGP (n)) |
f872b822 | 1921 | { |
ca46fb90 | 1922 | unsigned long count; |
713a4259 KR |
1923 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
1924 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 1925 | else |
713a4259 KR |
1926 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
1927 | scm_remember_upto_here_1 (n); | |
d956fa6f | 1928 | return SCM_I_MAKINUM (count); |
f872b822 | 1929 | } |
ca46fb90 RB |
1930 | else |
1931 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 1932 | } |
ca46fb90 | 1933 | #undef FUNC_NAME |
0f2d19dd JB |
1934 | |
1935 | ||
ca46fb90 RB |
1936 | static const char scm_ilentab[] = { |
1937 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
1938 | }; | |
1939 | ||
0f2d19dd | 1940 | |
ca46fb90 RB |
1941 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
1942 | (SCM n), | |
1943 | "Return the number of bits necessary to represent @var{n}.\n" | |
1944 | "\n" | |
1945 | "@lisp\n" | |
1946 | "(integer-length #b10101010)\n" | |
1947 | " @result{} 8\n" | |
1948 | "(integer-length 0)\n" | |
1949 | " @result{} 0\n" | |
1950 | "(integer-length #b1111)\n" | |
1951 | " @result{} 4\n" | |
1952 | "@end lisp") | |
1953 | #define FUNC_NAME s_scm_integer_length | |
1954 | { | |
e11e83f3 | 1955 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
1956 | { |
1957 | unsigned long int c = 0; | |
1958 | unsigned int l = 4; | |
e11e83f3 | 1959 | long int nn = SCM_I_INUM (n); |
0aacf84e MD |
1960 | if (nn < 0) |
1961 | nn = -1 - nn; | |
1962 | while (nn) | |
1963 | { | |
1964 | c += 4; | |
1965 | l = scm_ilentab [15 & nn]; | |
1966 | nn >>= 4; | |
1967 | } | |
d956fa6f | 1968 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
1969 | } |
1970 | else if (SCM_BIGP (n)) | |
1971 | { | |
1972 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
1973 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
1974 | 1 too big, so check for that and adjust. */ | |
1975 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
1976 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
1977 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
1978 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
1979 | size--; | |
1980 | scm_remember_upto_here_1 (n); | |
d956fa6f | 1981 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
1982 | } |
1983 | else | |
ca46fb90 | 1984 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
1985 | } |
1986 | #undef FUNC_NAME | |
0f2d19dd JB |
1987 | |
1988 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
1989 | #define SCM_MAX_DBL_PREC 60 |
1990 | #define SCM_MAX_DBL_RADIX 36 | |
1991 | ||
1992 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
1993 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
1994 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
1995 | ||
1996 | static | |
1997 | void init_dblprec(int *prec, int radix) { | |
1998 | /* determine floating point precision by adding successively | |
1999 | smaller increments to 1.0 until it is considered == 1.0 */ | |
2000 | double f = ((double)1.0)/radix; | |
2001 | double fsum = 1.0 + f; | |
2002 | ||
2003 | *prec = 0; | |
2004 | while (fsum != 1.0) | |
2005 | { | |
2006 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
2007 | fsum = 1.0; | |
2008 | else | |
2009 | { | |
2010 | f /= radix; | |
2011 | fsum = f + 1.0; | |
2012 | } | |
2013 | } | |
2014 | (*prec) -= 1; | |
2015 | } | |
2016 | ||
2017 | static | |
2018 | void init_fx_radix(double *fx_list, int radix) | |
2019 | { | |
2020 | /* initialize a per-radix list of tolerances. When added | |
2021 | to a number < 1.0, we can determine if we should raund | |
2022 | up and quit converting a number to a string. */ | |
2023 | int i; | |
2024 | fx_list[0] = 0.0; | |
2025 | fx_list[1] = 0.5; | |
2026 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
2027 | fx_list[i] = (fx_list[i-1] / radix); | |
2028 | } | |
2029 | ||
2030 | /* use this array as a way to generate a single digit */ | |
2031 | static const char*number_chars="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; | |
0f2d19dd | 2032 | |
1be6b49c | 2033 | static size_t |
0b799eea | 2034 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 2035 | { |
0b799eea MV |
2036 | int efmt, dpt, d, i, wp; |
2037 | double *fx; | |
2038 | #ifdef DBL_MIN_10_EXP | |
2039 | double f_cpy; | |
2040 | int exp_cpy; | |
2041 | #endif /* DBL_MIN_10_EXP */ | |
2042 | size_t ch = 0; | |
2043 | int exp = 0; | |
2044 | ||
2045 | if(radix < 2 || | |
2046 | radix > SCM_MAX_DBL_RADIX) | |
2047 | { | |
2048 | /* revert to existing behavior */ | |
2049 | radix = 10; | |
2050 | } | |
2051 | ||
2052 | wp = scm_dblprec[radix-2]; | |
2053 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 2054 | |
f872b822 | 2055 | if (f == 0.0) |
abb7e44d MV |
2056 | { |
2057 | #ifdef HAVE_COPYSIGN | |
2058 | double sgn = copysign (1.0, f); | |
2059 | ||
2060 | if (sgn < 0.0) | |
2061 | a[ch++] = '-'; | |
2062 | #endif | |
abb7e44d MV |
2063 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
2064 | } | |
7351e207 MV |
2065 | |
2066 | if (xisinf (f)) | |
2067 | { | |
2068 | if (f < 0) | |
2069 | strcpy (a, "-inf.0"); | |
2070 | else | |
2071 | strcpy (a, "+inf.0"); | |
2072 | return ch+6; | |
2073 | } | |
2074 | else if (xisnan (f)) | |
2075 | { | |
2076 | strcpy (a, "+nan.0"); | |
2077 | return ch+6; | |
2078 | } | |
2079 | ||
f872b822 MD |
2080 | if (f < 0.0) |
2081 | { | |
2082 | f = -f; | |
2083 | a[ch++] = '-'; | |
2084 | } | |
7351e207 | 2085 | |
f872b822 MD |
2086 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
2087 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
2088 | /* just do the checking...if it passes, we do the conversion for our |
2089 | radix again below */ | |
2090 | f_cpy = f; | |
2091 | exp_cpy = exp; | |
2092 | ||
2093 | while (f_cpy < 1.0) | |
f872b822 | 2094 | { |
0b799eea MV |
2095 | f_cpy *= 10.0; |
2096 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
2097 | { |
2098 | a[ch++] = '#'; | |
2099 | a[ch++] = '.'; | |
2100 | a[ch++] = '#'; | |
2101 | return ch; | |
2102 | } | |
f872b822 | 2103 | } |
0b799eea | 2104 | while (f_cpy > 10.0) |
f872b822 | 2105 | { |
0b799eea MV |
2106 | f_cpy *= 0.10; |
2107 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
2108 | { |
2109 | a[ch++] = '#'; | |
2110 | a[ch++] = '.'; | |
2111 | a[ch++] = '#'; | |
2112 | return ch; | |
2113 | } | |
f872b822 | 2114 | } |
0b799eea MV |
2115 | #endif |
2116 | ||
f872b822 MD |
2117 | while (f < 1.0) |
2118 | { | |
0b799eea | 2119 | f *= radix; |
f872b822 MD |
2120 | exp--; |
2121 | } | |
0b799eea | 2122 | while (f > radix) |
f872b822 | 2123 | { |
0b799eea | 2124 | f /= radix; |
f872b822 MD |
2125 | exp++; |
2126 | } | |
0b799eea MV |
2127 | |
2128 | if (f + fx[wp] >= radix) | |
f872b822 MD |
2129 | { |
2130 | f = 1.0; | |
2131 | exp++; | |
2132 | } | |
0f2d19dd | 2133 | zero: |
0b799eea MV |
2134 | #ifdef ENGNOT |
2135 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 2136 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
2137 | exp -= dpt++; |
2138 | efmt = 1; | |
f872b822 MD |
2139 | #else |
2140 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 2141 | if (!efmt) |
cda139a7 MD |
2142 | { |
2143 | if (exp < 0) | |
2144 | { | |
2145 | a[ch++] = '0'; | |
2146 | a[ch++] = '.'; | |
2147 | dpt = exp; | |
f872b822 MD |
2148 | while (++dpt) |
2149 | a[ch++] = '0'; | |
cda139a7 MD |
2150 | } |
2151 | else | |
f872b822 | 2152 | dpt = exp + 1; |
cda139a7 | 2153 | } |
0f2d19dd JB |
2154 | else |
2155 | dpt = 1; | |
f872b822 MD |
2156 | #endif |
2157 | ||
2158 | do | |
2159 | { | |
2160 | d = f; | |
2161 | f -= d; | |
0b799eea | 2162 | a[ch++] = number_chars[d]; |
f872b822 MD |
2163 | if (f < fx[wp]) |
2164 | break; | |
2165 | if (f + fx[wp] >= 1.0) | |
2166 | { | |
0b799eea | 2167 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
2168 | break; |
2169 | } | |
0b799eea | 2170 | f *= radix; |
f872b822 MD |
2171 | if (!(--dpt)) |
2172 | a[ch++] = '.'; | |
0f2d19dd | 2173 | } |
f872b822 | 2174 | while (wp--); |
0f2d19dd JB |
2175 | |
2176 | if (dpt > 0) | |
cda139a7 | 2177 | { |
f872b822 | 2178 | #ifndef ENGNOT |
cda139a7 MD |
2179 | if ((dpt > 4) && (exp > 6)) |
2180 | { | |
f872b822 | 2181 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 2182 | for (i = ch++; i > d; i--) |
f872b822 | 2183 | a[i] = a[i - 1]; |
cda139a7 MD |
2184 | a[d] = '.'; |
2185 | efmt = 1; | |
2186 | } | |
2187 | else | |
f872b822 | 2188 | #endif |
cda139a7 | 2189 | { |
f872b822 MD |
2190 | while (--dpt) |
2191 | a[ch++] = '0'; | |
cda139a7 MD |
2192 | a[ch++] = '.'; |
2193 | } | |
2194 | } | |
f872b822 MD |
2195 | if (a[ch - 1] == '.') |
2196 | a[ch++] = '0'; /* trailing zero */ | |
2197 | if (efmt && exp) | |
2198 | { | |
2199 | a[ch++] = 'e'; | |
2200 | if (exp < 0) | |
2201 | { | |
2202 | exp = -exp; | |
2203 | a[ch++] = '-'; | |
2204 | } | |
0b799eea MV |
2205 | for (i = radix; i <= exp; i *= radix); |
2206 | for (i /= radix; i; i /= radix) | |
f872b822 | 2207 | { |
0b799eea | 2208 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
2209 | exp %= i; |
2210 | } | |
0f2d19dd | 2211 | } |
0f2d19dd JB |
2212 | return ch; |
2213 | } | |
2214 | ||
1be6b49c | 2215 | static size_t |
0b799eea | 2216 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 2217 | { |
1be6b49c | 2218 | size_t i; |
3c9a524f | 2219 | if (SCM_REALP (flt)) |
0b799eea | 2220 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 2221 | else |
f872b822 | 2222 | { |
0b799eea | 2223 | i = idbl2str (SCM_COMPLEX_REAL (flt), str, radix); |
f3ae5d60 MD |
2224 | if (SCM_COMPLEX_IMAG (flt) != 0.0) |
2225 | { | |
7351e207 MV |
2226 | double imag = SCM_COMPLEX_IMAG (flt); |
2227 | /* Don't output a '+' for negative numbers or for Inf and | |
2228 | NaN. They will provide their own sign. */ | |
2229 | if (0 <= imag && !xisinf (imag) && !xisnan (imag)) | |
f3ae5d60 | 2230 | str[i++] = '+'; |
0b799eea | 2231 | i += idbl2str (imag, &str[i], radix); |
f3ae5d60 MD |
2232 | str[i++] = 'i'; |
2233 | } | |
f872b822 | 2234 | } |
0f2d19dd JB |
2235 | return i; |
2236 | } | |
0f2d19dd | 2237 | |
5c11cc9d | 2238 | /* convert a long to a string (unterminated). returns the number of |
1bbd0b84 GB |
2239 | characters in the result. |
2240 | rad is output base | |
2241 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2242 | size_t |
1bbd0b84 | 2243 | scm_iint2str (long num, int rad, char *p) |
0f2d19dd | 2244 | { |
1be6b49c ML |
2245 | size_t j = 1; |
2246 | size_t i; | |
5c11cc9d GH |
2247 | unsigned long n = (num < 0) ? -num : num; |
2248 | ||
f872b822 | 2249 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2250 | j++; |
2251 | ||
2252 | i = j; | |
2253 | if (num < 0) | |
f872b822 | 2254 | { |
f872b822 | 2255 | *p++ = '-'; |
5c11cc9d GH |
2256 | j++; |
2257 | n = -num; | |
f872b822 | 2258 | } |
5c11cc9d GH |
2259 | else |
2260 | n = num; | |
f872b822 MD |
2261 | while (i--) |
2262 | { | |
5c11cc9d GH |
2263 | int d = n % rad; |
2264 | ||
f872b822 MD |
2265 | n /= rad; |
2266 | p[i] = d + ((d < 10) ? '0' : 'a' - 10); | |
2267 | } | |
0f2d19dd JB |
2268 | return j; |
2269 | } | |
2270 | ||
a1ec6916 | 2271 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2272 | (SCM n, SCM radix), |
2273 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2274 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2275 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2276 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2277 | { |
1bbd0b84 | 2278 | int base; |
98cb6e75 | 2279 | |
0aacf84e | 2280 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 2281 | base = 10; |
0aacf84e | 2282 | else |
5efd3c7d | 2283 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 2284 | |
e11e83f3 | 2285 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2286 | { |
2287 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 2288 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
0aacf84e MD |
2289 | return scm_mem2string (num_buf, length); |
2290 | } | |
2291 | else if (SCM_BIGP (n)) | |
2292 | { | |
2293 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
2294 | scm_remember_upto_here_1 (n); | |
2295 | return scm_take0str (str); | |
2296 | } | |
f92e85f7 MV |
2297 | else if (SCM_FRACTIONP (n)) |
2298 | { | |
2299 | scm_i_fraction_reduce (n); | |
2300 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), | |
2301 | scm_mem2string ("/", 1), | |
2302 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); | |
2303 | } | |
0aacf84e MD |
2304 | else if (SCM_INEXACTP (n)) |
2305 | { | |
2306 | char num_buf [FLOBUFLEN]; | |
0b799eea | 2307 | return scm_mem2string (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
2308 | } |
2309 | else | |
bb628794 | 2310 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 2311 | } |
1bbd0b84 | 2312 | #undef FUNC_NAME |
0f2d19dd JB |
2313 | |
2314 | ||
ca46fb90 RB |
2315 | /* These print routines used to be stubbed here so that scm_repl.c |
2316 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 2317 | |
0f2d19dd | 2318 | int |
e81d98ec | 2319 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2320 | { |
56e55ac7 | 2321 | char num_buf[FLOBUFLEN]; |
0b799eea | 2322 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
2323 | return !0; |
2324 | } | |
2325 | ||
f3ae5d60 | 2326 | int |
e81d98ec | 2327 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 2328 | |
f3ae5d60 | 2329 | { |
56e55ac7 | 2330 | char num_buf[FLOBUFLEN]; |
0b799eea | 2331 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
2332 | return !0; |
2333 | } | |
1cc91f1b | 2334 | |
f92e85f7 MV |
2335 | int |
2336 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
2337 | { | |
2338 | SCM str; | |
2339 | scm_i_fraction_reduce (sexp); | |
2340 | str = scm_number_to_string (sexp, SCM_UNDEFINED); | |
8824ac88 | 2341 | scm_lfwrite (SCM_I_STRING_CHARS (str), SCM_I_STRING_LENGTH (str), port); |
f92e85f7 MV |
2342 | scm_remember_upto_here_1 (str); |
2343 | return !0; | |
2344 | } | |
2345 | ||
0f2d19dd | 2346 | int |
e81d98ec | 2347 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2348 | { |
ca46fb90 RB |
2349 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
2350 | scm_remember_upto_here_1 (exp); | |
2351 | scm_lfwrite (str, (size_t) strlen (str), port); | |
2352 | free (str); | |
0f2d19dd JB |
2353 | return !0; |
2354 | } | |
2355 | /*** END nums->strs ***/ | |
2356 | ||
3c9a524f | 2357 | |
0f2d19dd | 2358 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2359 | |
3c9a524f DH |
2360 | /* The following functions implement the conversion from strings to numbers. |
2361 | * The implementation somehow follows the grammar for numbers as it is given | |
2362 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2363 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2364 | * points should be noted about the implementation: | |
2365 | * * Each function keeps a local index variable 'idx' that points at the | |
2366 | * current position within the parsed string. The global index is only | |
2367 | * updated if the function could parse the corresponding syntactic unit | |
2368 | * successfully. | |
2369 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2370 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2371 | * global exactness information is only updated after each part has been | |
2372 | * successfully parsed. | |
2373 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2374 | * Only if these fixnums would overflow, the result variables are updated | |
2375 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2376 | * the temporary variables holding the fixnums are cleared, and the process | |
2377 | * starts over again. If for example fixnums were able to store five decimal | |
2378 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2379 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2380 | * only every five digits two bignum operations were performed. | |
2381 | */ | |
2382 | ||
2383 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2384 | ||
2385 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2386 | ||
2387 | /* In non ASCII-style encodings the following macro might not work. */ | |
71df73ac KR |
2388 | #define XDIGIT2UINT(d) \ |
2389 | (isdigit ((int) (unsigned char) d) \ | |
2390 | ? (d) - '0' \ | |
2391 | : tolower ((int) (unsigned char) d) - 'a' + 10) | |
3c9a524f | 2392 | |
2a8fecee | 2393 | static SCM |
3c9a524f DH |
2394 | mem2uinteger (const char* mem, size_t len, unsigned int *p_idx, |
2395 | unsigned int radix, enum t_exactness *p_exactness) | |
2a8fecee | 2396 | { |
3c9a524f DH |
2397 | unsigned int idx = *p_idx; |
2398 | unsigned int hash_seen = 0; | |
2399 | scm_t_bits shift = 1; | |
2400 | scm_t_bits add = 0; | |
2401 | unsigned int digit_value; | |
2402 | SCM result; | |
2403 | char c; | |
2404 | ||
2405 | if (idx == len) | |
2406 | return SCM_BOOL_F; | |
2a8fecee | 2407 | |
3c9a524f | 2408 | c = mem[idx]; |
71df73ac | 2409 | if (!isxdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2410 | return SCM_BOOL_F; |
2411 | digit_value = XDIGIT2UINT (c); | |
2412 | if (digit_value >= radix) | |
2413 | return SCM_BOOL_F; | |
2414 | ||
2415 | idx++; | |
d956fa6f | 2416 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 2417 | while (idx != len) |
f872b822 | 2418 | { |
3c9a524f | 2419 | char c = mem[idx]; |
71df73ac | 2420 | if (isxdigit ((int) (unsigned char) c)) |
f872b822 | 2421 | { |
3c9a524f | 2422 | if (hash_seen) |
1fe5e088 | 2423 | break; |
3c9a524f DH |
2424 | digit_value = XDIGIT2UINT (c); |
2425 | if (digit_value >= radix) | |
1fe5e088 | 2426 | break; |
f872b822 | 2427 | } |
3c9a524f DH |
2428 | else if (c == '#') |
2429 | { | |
2430 | hash_seen = 1; | |
2431 | digit_value = 0; | |
2432 | } | |
2433 | else | |
2434 | break; | |
2435 | ||
2436 | idx++; | |
2437 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2438 | { | |
d956fa6f | 2439 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2440 | if (add > 0) |
d956fa6f | 2441 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2442 | |
2443 | shift = radix; | |
2444 | add = digit_value; | |
2445 | } | |
2446 | else | |
2447 | { | |
2448 | shift = shift * radix; | |
2449 | add = add * radix + digit_value; | |
2450 | } | |
2451 | }; | |
2452 | ||
2453 | if (shift > 1) | |
d956fa6f | 2454 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2455 | if (add > 0) |
d956fa6f | 2456 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2457 | |
2458 | *p_idx = idx; | |
2459 | if (hash_seen) | |
2460 | *p_exactness = INEXACT; | |
2461 | ||
2462 | return result; | |
2a8fecee JB |
2463 | } |
2464 | ||
2465 | ||
3c9a524f DH |
2466 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2467 | * covers the parts of the rules that start at a potential point. The value | |
2468 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2469 | * in variable result. The content of *p_exactness indicates, whether a hash |
2470 | * has already been seen in the digits before the point. | |
3c9a524f | 2471 | */ |
1cc91f1b | 2472 | |
3c9a524f DH |
2473 | /* In non ASCII-style encodings the following macro might not work. */ |
2474 | #define DIGIT2UINT(d) ((d) - '0') | |
2475 | ||
2476 | static SCM | |
79d34f68 | 2477 | mem2decimal_from_point (SCM result, const char* mem, size_t len, |
3c9a524f | 2478 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2479 | { |
3c9a524f DH |
2480 | unsigned int idx = *p_idx; |
2481 | enum t_exactness x = *p_exactness; | |
3c9a524f DH |
2482 | |
2483 | if (idx == len) | |
79d34f68 | 2484 | return result; |
3c9a524f DH |
2485 | |
2486 | if (mem[idx] == '.') | |
2487 | { | |
2488 | scm_t_bits shift = 1; | |
2489 | scm_t_bits add = 0; | |
2490 | unsigned int digit_value; | |
d956fa6f | 2491 | SCM big_shift = SCM_I_MAKINUM (1); |
3c9a524f DH |
2492 | |
2493 | idx++; | |
2494 | while (idx != len) | |
2495 | { | |
2496 | char c = mem[idx]; | |
71df73ac | 2497 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2498 | { |
2499 | if (x == INEXACT) | |
2500 | return SCM_BOOL_F; | |
2501 | else | |
2502 | digit_value = DIGIT2UINT (c); | |
2503 | } | |
2504 | else if (c == '#') | |
2505 | { | |
2506 | x = INEXACT; | |
2507 | digit_value = 0; | |
2508 | } | |
2509 | else | |
2510 | break; | |
2511 | ||
2512 | idx++; | |
2513 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2514 | { | |
d956fa6f MV |
2515 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2516 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 2517 | if (add > 0) |
d956fa6f | 2518 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2519 | |
2520 | shift = 10; | |
2521 | add = digit_value; | |
2522 | } | |
2523 | else | |
2524 | { | |
2525 | shift = shift * 10; | |
2526 | add = add * 10 + digit_value; | |
2527 | } | |
2528 | }; | |
2529 | ||
2530 | if (add > 0) | |
2531 | { | |
d956fa6f MV |
2532 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2533 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
2534 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
2535 | } |
2536 | ||
d8592269 | 2537 | result = scm_divide (result, big_shift); |
79d34f68 | 2538 | |
3c9a524f DH |
2539 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2540 | x = INEXACT; | |
f872b822 | 2541 | } |
3c9a524f | 2542 | |
3c9a524f | 2543 | if (idx != len) |
f872b822 | 2544 | { |
3c9a524f DH |
2545 | int sign = 1; |
2546 | unsigned int start; | |
2547 | char c; | |
2548 | int exponent; | |
2549 | SCM e; | |
2550 | ||
2551 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2552 | ||
2553 | switch (mem[idx]) | |
f872b822 | 2554 | { |
3c9a524f DH |
2555 | case 'd': case 'D': |
2556 | case 'e': case 'E': | |
2557 | case 'f': case 'F': | |
2558 | case 'l': case 'L': | |
2559 | case 's': case 'S': | |
2560 | idx++; | |
2561 | start = idx; | |
2562 | c = mem[idx]; | |
2563 | if (c == '-') | |
2564 | { | |
2565 | idx++; | |
2566 | sign = -1; | |
2567 | c = mem[idx]; | |
2568 | } | |
2569 | else if (c == '+') | |
2570 | { | |
2571 | idx++; | |
2572 | sign = 1; | |
2573 | c = mem[idx]; | |
2574 | } | |
2575 | else | |
2576 | sign = 1; | |
2577 | ||
71df73ac | 2578 | if (!isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2579 | return SCM_BOOL_F; |
2580 | ||
2581 | idx++; | |
2582 | exponent = DIGIT2UINT (c); | |
2583 | while (idx != len) | |
f872b822 | 2584 | { |
3c9a524f | 2585 | char c = mem[idx]; |
71df73ac | 2586 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2587 | { |
2588 | idx++; | |
2589 | if (exponent <= SCM_MAXEXP) | |
2590 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2591 | } | |
2592 | else | |
2593 | break; | |
f872b822 | 2594 | } |
3c9a524f DH |
2595 | |
2596 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2597 | { |
3c9a524f DH |
2598 | size_t exp_len = idx - start; |
2599 | SCM exp_string = scm_mem2string (&mem[start], exp_len); | |
2600 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); | |
2601 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2602 | } |
3c9a524f | 2603 | |
d956fa6f | 2604 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
2605 | if (sign == 1) |
2606 | result = scm_product (result, e); | |
2607 | else | |
f92e85f7 | 2608 | result = scm_divide2real (result, e); |
3c9a524f DH |
2609 | |
2610 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2611 | x = INEXACT; | |
2612 | ||
f872b822 | 2613 | break; |
3c9a524f | 2614 | |
f872b822 | 2615 | default: |
3c9a524f | 2616 | break; |
f872b822 | 2617 | } |
0f2d19dd | 2618 | } |
3c9a524f DH |
2619 | |
2620 | *p_idx = idx; | |
2621 | if (x == INEXACT) | |
2622 | *p_exactness = x; | |
2623 | ||
2624 | return result; | |
0f2d19dd | 2625 | } |
0f2d19dd | 2626 | |
3c9a524f DH |
2627 | |
2628 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2629 | ||
2630 | static SCM | |
2631 | mem2ureal (const char* mem, size_t len, unsigned int *p_idx, | |
2632 | unsigned int radix, enum t_exactness *p_exactness) | |
0f2d19dd | 2633 | { |
3c9a524f | 2634 | unsigned int idx = *p_idx; |
164d2481 | 2635 | SCM result; |
3c9a524f DH |
2636 | |
2637 | if (idx == len) | |
2638 | return SCM_BOOL_F; | |
2639 | ||
7351e207 MV |
2640 | if (idx+5 <= len && !strncmp (mem+idx, "inf.0", 5)) |
2641 | { | |
2642 | *p_idx = idx+5; | |
2643 | return scm_inf (); | |
2644 | } | |
2645 | ||
2646 | if (idx+4 < len && !strncmp (mem+idx, "nan.", 4)) | |
2647 | { | |
2648 | enum t_exactness x = EXACT; | |
2649 | ||
d8592269 MV |
2650 | /* Cobble up the fractional part. We might want to set the |
2651 | NaN's mantissa from it. */ | |
7351e207 MV |
2652 | idx += 4; |
2653 | mem2uinteger (mem, len, &idx, 10, &x); | |
2654 | *p_idx = idx; | |
2655 | return scm_nan (); | |
2656 | } | |
2657 | ||
3c9a524f DH |
2658 | if (mem[idx] == '.') |
2659 | { | |
2660 | if (radix != 10) | |
2661 | return SCM_BOOL_F; | |
2662 | else if (idx + 1 == len) | |
2663 | return SCM_BOOL_F; | |
71df73ac | 2664 | else if (!isdigit ((int) (unsigned char) mem[idx + 1])) |
3c9a524f DH |
2665 | return SCM_BOOL_F; |
2666 | else | |
d956fa6f | 2667 | result = mem2decimal_from_point (SCM_I_MAKINUM (0), mem, len, |
164d2481 | 2668 | p_idx, p_exactness); |
f872b822 | 2669 | } |
3c9a524f DH |
2670 | else |
2671 | { | |
2672 | enum t_exactness x = EXACT; | |
2673 | SCM uinteger; | |
3c9a524f DH |
2674 | |
2675 | uinteger = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2676 | if (scm_is_false (uinteger)) |
3c9a524f DH |
2677 | return SCM_BOOL_F; |
2678 | ||
2679 | if (idx == len) | |
2680 | result = uinteger; | |
2681 | else if (mem[idx] == '/') | |
f872b822 | 2682 | { |
3c9a524f DH |
2683 | SCM divisor; |
2684 | ||
2685 | idx++; | |
2686 | ||
2687 | divisor = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2688 | if (scm_is_false (divisor)) |
3c9a524f DH |
2689 | return SCM_BOOL_F; |
2690 | ||
f92e85f7 | 2691 | /* both are int/big here, I assume */ |
cba42c93 | 2692 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 2693 | } |
3c9a524f DH |
2694 | else if (radix == 10) |
2695 | { | |
2696 | result = mem2decimal_from_point (uinteger, mem, len, &idx, &x); | |
73e4de09 | 2697 | if (scm_is_false (result)) |
3c9a524f DH |
2698 | return SCM_BOOL_F; |
2699 | } | |
2700 | else | |
2701 | result = uinteger; | |
2702 | ||
2703 | *p_idx = idx; | |
2704 | if (x == INEXACT) | |
2705 | *p_exactness = x; | |
f872b822 | 2706 | } |
164d2481 MV |
2707 | |
2708 | /* When returning an inexact zero, make sure it is represented as a | |
2709 | floating point value so that we can change its sign. | |
2710 | */ | |
bc36d050 | 2711 | if (scm_is_eq (result, SCM_I_MAKINUM(0)) && *p_exactness == INEXACT) |
55f26379 | 2712 | result = scm_from_double (0.0); |
164d2481 MV |
2713 | |
2714 | return result; | |
3c9a524f | 2715 | } |
0f2d19dd | 2716 | |
0f2d19dd | 2717 | |
3c9a524f | 2718 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2719 | |
3c9a524f DH |
2720 | static SCM |
2721 | mem2complex (const char* mem, size_t len, unsigned int idx, | |
2722 | unsigned int radix, enum t_exactness *p_exactness) | |
2723 | { | |
2724 | char c; | |
2725 | int sign = 0; | |
2726 | SCM ureal; | |
2727 | ||
2728 | if (idx == len) | |
2729 | return SCM_BOOL_F; | |
2730 | ||
2731 | c = mem[idx]; | |
2732 | if (c == '+') | |
2733 | { | |
2734 | idx++; | |
2735 | sign = 1; | |
2736 | } | |
2737 | else if (c == '-') | |
2738 | { | |
2739 | idx++; | |
2740 | sign = -1; | |
0f2d19dd | 2741 | } |
0f2d19dd | 2742 | |
3c9a524f DH |
2743 | if (idx == len) |
2744 | return SCM_BOOL_F; | |
2745 | ||
2746 | ureal = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2747 | if (scm_is_false (ureal)) |
f872b822 | 2748 | { |
3c9a524f DH |
2749 | /* input must be either +i or -i */ |
2750 | ||
2751 | if (sign == 0) | |
2752 | return SCM_BOOL_F; | |
2753 | ||
2754 | if (mem[idx] == 'i' || mem[idx] == 'I') | |
f872b822 | 2755 | { |
3c9a524f DH |
2756 | idx++; |
2757 | if (idx != len) | |
2758 | return SCM_BOOL_F; | |
2759 | ||
d956fa6f | 2760 | return scm_make_rectangular (SCM_I_MAKINUM (0), SCM_I_MAKINUM (sign)); |
f872b822 | 2761 | } |
3c9a524f DH |
2762 | else |
2763 | return SCM_BOOL_F; | |
0f2d19dd | 2764 | } |
3c9a524f DH |
2765 | else |
2766 | { | |
73e4de09 | 2767 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 2768 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 2769 | |
3c9a524f DH |
2770 | if (idx == len) |
2771 | return ureal; | |
2772 | ||
2773 | c = mem[idx]; | |
2774 | switch (c) | |
f872b822 | 2775 | { |
3c9a524f DH |
2776 | case 'i': case 'I': |
2777 | /* either +<ureal>i or -<ureal>i */ | |
2778 | ||
2779 | idx++; | |
2780 | if (sign == 0) | |
2781 | return SCM_BOOL_F; | |
2782 | if (idx != len) | |
2783 | return SCM_BOOL_F; | |
d956fa6f | 2784 | return scm_make_rectangular (SCM_I_MAKINUM (0), ureal); |
3c9a524f DH |
2785 | |
2786 | case '@': | |
2787 | /* polar input: <real>@<real>. */ | |
2788 | ||
2789 | idx++; | |
2790 | if (idx == len) | |
2791 | return SCM_BOOL_F; | |
2792 | else | |
f872b822 | 2793 | { |
3c9a524f DH |
2794 | int sign; |
2795 | SCM angle; | |
2796 | SCM result; | |
2797 | ||
2798 | c = mem[idx]; | |
2799 | if (c == '+') | |
2800 | { | |
2801 | idx++; | |
2802 | sign = 1; | |
2803 | } | |
2804 | else if (c == '-') | |
2805 | { | |
2806 | idx++; | |
2807 | sign = -1; | |
2808 | } | |
2809 | else | |
2810 | sign = 1; | |
2811 | ||
2812 | angle = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2813 | if (scm_is_false (angle)) |
3c9a524f DH |
2814 | return SCM_BOOL_F; |
2815 | if (idx != len) | |
2816 | return SCM_BOOL_F; | |
2817 | ||
73e4de09 | 2818 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
2819 | angle = scm_difference (angle, SCM_UNDEFINED); |
2820 | ||
2821 | result = scm_make_polar (ureal, angle); | |
2822 | return result; | |
f872b822 | 2823 | } |
3c9a524f DH |
2824 | case '+': |
2825 | case '-': | |
2826 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 2827 | |
3c9a524f DH |
2828 | idx++; |
2829 | if (idx == len) | |
2830 | return SCM_BOOL_F; | |
2831 | else | |
2832 | { | |
2833 | int sign = (c == '+') ? 1 : -1; | |
2834 | SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness); | |
0f2d19dd | 2835 | |
73e4de09 | 2836 | if (scm_is_false (imag)) |
d956fa6f | 2837 | imag = SCM_I_MAKINUM (sign); |
73e4de09 | 2838 | else if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
1fe5e088 | 2839 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 2840 | |
3c9a524f DH |
2841 | if (idx == len) |
2842 | return SCM_BOOL_F; | |
2843 | if (mem[idx] != 'i' && mem[idx] != 'I') | |
2844 | return SCM_BOOL_F; | |
0f2d19dd | 2845 | |
3c9a524f DH |
2846 | idx++; |
2847 | if (idx != len) | |
2848 | return SCM_BOOL_F; | |
0f2d19dd | 2849 | |
1fe5e088 | 2850 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
2851 | } |
2852 | default: | |
2853 | return SCM_BOOL_F; | |
2854 | } | |
2855 | } | |
0f2d19dd | 2856 | } |
0f2d19dd JB |
2857 | |
2858 | ||
3c9a524f DH |
2859 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
2860 | ||
2861 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 2862 | |
0f2d19dd | 2863 | SCM |
3c9a524f | 2864 | scm_i_mem2number (const char* mem, size_t len, unsigned int default_radix) |
0f2d19dd | 2865 | { |
3c9a524f DH |
2866 | unsigned int idx = 0; |
2867 | unsigned int radix = NO_RADIX; | |
2868 | enum t_exactness forced_x = NO_EXACTNESS; | |
2869 | enum t_exactness implicit_x = EXACT; | |
2870 | SCM result; | |
2871 | ||
2872 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
2873 | while (idx + 2 < len && mem[idx] == '#') | |
2874 | { | |
2875 | switch (mem[idx + 1]) | |
2876 | { | |
2877 | case 'b': case 'B': | |
2878 | if (radix != NO_RADIX) | |
2879 | return SCM_BOOL_F; | |
2880 | radix = DUAL; | |
2881 | break; | |
2882 | case 'd': case 'D': | |
2883 | if (radix != NO_RADIX) | |
2884 | return SCM_BOOL_F; | |
2885 | radix = DEC; | |
2886 | break; | |
2887 | case 'i': case 'I': | |
2888 | if (forced_x != NO_EXACTNESS) | |
2889 | return SCM_BOOL_F; | |
2890 | forced_x = INEXACT; | |
2891 | break; | |
2892 | case 'e': case 'E': | |
2893 | if (forced_x != NO_EXACTNESS) | |
2894 | return SCM_BOOL_F; | |
2895 | forced_x = EXACT; | |
2896 | break; | |
2897 | case 'o': case 'O': | |
2898 | if (radix != NO_RADIX) | |
2899 | return SCM_BOOL_F; | |
2900 | radix = OCT; | |
2901 | break; | |
2902 | case 'x': case 'X': | |
2903 | if (radix != NO_RADIX) | |
2904 | return SCM_BOOL_F; | |
2905 | radix = HEX; | |
2906 | break; | |
2907 | default: | |
f872b822 | 2908 | return SCM_BOOL_F; |
3c9a524f DH |
2909 | } |
2910 | idx += 2; | |
2911 | } | |
2912 | ||
2913 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
2914 | if (radix == NO_RADIX) | |
2915 | result = mem2complex (mem, len, idx, default_radix, &implicit_x); | |
2916 | else | |
2917 | result = mem2complex (mem, len, idx, (unsigned int) radix, &implicit_x); | |
2918 | ||
73e4de09 | 2919 | if (scm_is_false (result)) |
3c9a524f | 2920 | return SCM_BOOL_F; |
f872b822 | 2921 | |
3c9a524f | 2922 | switch (forced_x) |
f872b822 | 2923 | { |
3c9a524f DH |
2924 | case EXACT: |
2925 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
2926 | return scm_inexact_to_exact (result); |
2927 | else | |
2928 | return result; | |
2929 | case INEXACT: | |
2930 | if (SCM_INEXACTP (result)) | |
2931 | return result; | |
2932 | else | |
2933 | return scm_exact_to_inexact (result); | |
2934 | case NO_EXACTNESS: | |
2935 | default: | |
2936 | if (implicit_x == INEXACT) | |
2937 | { | |
2938 | if (SCM_INEXACTP (result)) | |
2939 | return result; | |
2940 | else | |
2941 | return scm_exact_to_inexact (result); | |
2942 | } | |
2943 | else | |
2944 | return result; | |
f872b822 | 2945 | } |
0f2d19dd JB |
2946 | } |
2947 | ||
2948 | ||
a1ec6916 | 2949 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 2950 | (SCM string, SCM radix), |
1e6808ea | 2951 | "Return a number of the maximally precise representation\n" |
942e5b91 | 2952 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
2953 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
2954 | "is a default radix that may be overridden by an explicit radix\n" | |
2955 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
2956 | "supplied, then the default radix is 10. If string is not a\n" | |
2957 | "syntactically valid notation for a number, then\n" | |
2958 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 2959 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
2960 | { |
2961 | SCM answer; | |
5efd3c7d | 2962 | unsigned int base; |
a6d9e5ab | 2963 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
2964 | |
2965 | if (SCM_UNBNDP (radix)) | |
2966 | base = 10; | |
2967 | else | |
2968 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
2969 | ||
8824ac88 MV |
2970 | answer = scm_i_mem2number (SCM_I_STRING_CHARS (string), |
2971 | SCM_I_STRING_LENGTH (string), | |
d8592269 | 2972 | base); |
8824ac88 MV |
2973 | scm_remember_upto_here_1 (string); |
2974 | return answer; | |
0f2d19dd | 2975 | } |
1bbd0b84 | 2976 | #undef FUNC_NAME |
3c9a524f DH |
2977 | |
2978 | ||
0f2d19dd JB |
2979 | /*** END strs->nums ***/ |
2980 | ||
5986c47d | 2981 | |
0f2d19dd | 2982 | SCM |
1bbd0b84 | 2983 | scm_bigequal (SCM x, SCM y) |
0f2d19dd | 2984 | { |
47ae1f0e | 2985 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
ca46fb90 | 2986 | scm_remember_upto_here_2 (x, y); |
73e4de09 | 2987 | return scm_from_bool (0 == result); |
0f2d19dd JB |
2988 | } |
2989 | ||
0f2d19dd | 2990 | SCM |
f3ae5d60 | 2991 | scm_real_equalp (SCM x, SCM y) |
0f2d19dd | 2992 | { |
73e4de09 | 2993 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0f2d19dd JB |
2994 | } |
2995 | ||
f3ae5d60 MD |
2996 | SCM |
2997 | scm_complex_equalp (SCM x, SCM y) | |
2998 | { | |
73e4de09 | 2999 | return scm_from_bool (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) |
f3ae5d60 MD |
3000 | && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); |
3001 | } | |
0f2d19dd | 3002 | |
f92e85f7 MV |
3003 | SCM |
3004 | scm_i_fraction_equalp (SCM x, SCM y) | |
3005 | { | |
3006 | scm_i_fraction_reduce (x); | |
3007 | scm_i_fraction_reduce (y); | |
73e4de09 | 3008 | if (scm_is_false (scm_equal_p (SCM_FRACTION_NUMERATOR (x), |
02164269 | 3009 | SCM_FRACTION_NUMERATOR (y))) |
73e4de09 | 3010 | || scm_is_false (scm_equal_p (SCM_FRACTION_DENOMINATOR (x), |
02164269 MV |
3011 | SCM_FRACTION_DENOMINATOR (y)))) |
3012 | return SCM_BOOL_F; | |
3013 | else | |
3014 | return SCM_BOOL_T; | |
f92e85f7 | 3015 | } |
0f2d19dd JB |
3016 | |
3017 | ||
8507ec80 MV |
3018 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
3019 | (SCM x), | |
3020 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
3021 | "otherwise.") | |
3022 | #define FUNC_NAME s_scm_number_p | |
3023 | { | |
3024 | return scm_from_bool (SCM_NUMBERP (x)); | |
3025 | } | |
3026 | #undef FUNC_NAME | |
3027 | ||
3028 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 3029 | (SCM x), |
942e5b91 | 3030 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 3031 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
3032 | "values form subsets of the set of complex numbers, i. e. the\n" |
3033 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
3034 | "rational or integer number.") | |
8507ec80 | 3035 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 3036 | { |
8507ec80 MV |
3037 | /* all numbers are complex. */ |
3038 | return scm_number_p (x); | |
0f2d19dd | 3039 | } |
1bbd0b84 | 3040 | #undef FUNC_NAME |
0f2d19dd | 3041 | |
f92e85f7 MV |
3042 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
3043 | (SCM x), | |
3044 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
3045 | "otherwise. Note that the set of integer values forms a subset of\n" | |
3046 | "the set of real numbers, i. e. the predicate will also be\n" | |
3047 | "fulfilled if @var{x} is an integer number.") | |
3048 | #define FUNC_NAME s_scm_real_p | |
3049 | { | |
3050 | /* we can't represent irrational numbers. */ | |
3051 | return scm_rational_p (x); | |
3052 | } | |
3053 | #undef FUNC_NAME | |
3054 | ||
3055 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 3056 | (SCM x), |
942e5b91 | 3057 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 3058 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 3059 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
3060 | "fulfilled if @var{x} is an integer number.") |
3061 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 3062 | { |
e11e83f3 | 3063 | if (SCM_I_INUMP (x)) |
0f2d19dd | 3064 | return SCM_BOOL_T; |
0aacf84e | 3065 | else if (SCM_IMP (x)) |
0f2d19dd | 3066 | return SCM_BOOL_F; |
0aacf84e | 3067 | else if (SCM_BIGP (x)) |
0f2d19dd | 3068 | return SCM_BOOL_T; |
f92e85f7 MV |
3069 | else if (SCM_FRACTIONP (x)) |
3070 | return SCM_BOOL_T; | |
3071 | else if (SCM_REALP (x)) | |
3072 | /* due to their limited precision, all floating point numbers are | |
3073 | rational as well. */ | |
3074 | return SCM_BOOL_T; | |
0aacf84e | 3075 | else |
bb628794 | 3076 | return SCM_BOOL_F; |
0f2d19dd | 3077 | } |
1bbd0b84 | 3078 | #undef FUNC_NAME |
0f2d19dd | 3079 | |
a1ec6916 | 3080 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 3081 | (SCM x), |
942e5b91 MG |
3082 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
3083 | "else.") | |
1bbd0b84 | 3084 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd JB |
3085 | { |
3086 | double r; | |
e11e83f3 | 3087 | if (SCM_I_INUMP (x)) |
f872b822 MD |
3088 | return SCM_BOOL_T; |
3089 | if (SCM_IMP (x)) | |
3090 | return SCM_BOOL_F; | |
f872b822 MD |
3091 | if (SCM_BIGP (x)) |
3092 | return SCM_BOOL_T; | |
3c9a524f | 3093 | if (!SCM_INEXACTP (x)) |
f872b822 | 3094 | return SCM_BOOL_F; |
3c9a524f | 3095 | if (SCM_COMPLEXP (x)) |
f872b822 | 3096 | return SCM_BOOL_F; |
5986c47d | 3097 | r = SCM_REAL_VALUE (x); |
f872b822 MD |
3098 | if (r == floor (r)) |
3099 | return SCM_BOOL_T; | |
0f2d19dd JB |
3100 | return SCM_BOOL_F; |
3101 | } | |
1bbd0b84 | 3102 | #undef FUNC_NAME |
0f2d19dd JB |
3103 | |
3104 | ||
a1ec6916 | 3105 | SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, |
1bbd0b84 | 3106 | (SCM x), |
942e5b91 MG |
3107 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" |
3108 | "else.") | |
1bbd0b84 | 3109 | #define FUNC_NAME s_scm_inexact_p |
0f2d19dd | 3110 | { |
eb927cb9 MV |
3111 | if (SCM_INEXACTP (x)) |
3112 | return SCM_BOOL_T; | |
3113 | if (SCM_NUMBERP (x)) | |
3114 | return SCM_BOOL_F; | |
3115 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 3116 | } |
1bbd0b84 | 3117 | #undef FUNC_NAME |
0f2d19dd JB |
3118 | |
3119 | ||
152f82bf | 3120 | SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p); |
942e5b91 | 3121 | /* "Return @code{#t} if all parameters are numerically equal." */ |
0f2d19dd | 3122 | SCM |
6e8d25a6 | 3123 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 3124 | { |
d8b95e27 | 3125 | again: |
e11e83f3 | 3126 | if (SCM_I_INUMP (x)) |
0aacf84e | 3127 | { |
e11e83f3 MV |
3128 | long xx = SCM_I_INUM (x); |
3129 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3130 | { |
e11e83f3 | 3131 | long yy = SCM_I_INUM (y); |
73e4de09 | 3132 | return scm_from_bool (xx == yy); |
0aacf84e MD |
3133 | } |
3134 | else if (SCM_BIGP (y)) | |
3135 | return SCM_BOOL_F; | |
3136 | else if (SCM_REALP (y)) | |
73e4de09 | 3137 | return scm_from_bool ((double) xx == SCM_REAL_VALUE (y)); |
0aacf84e | 3138 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3139 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3140 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
3141 | else if (SCM_FRACTIONP (y)) |
3142 | return SCM_BOOL_F; | |
0aacf84e MD |
3143 | else |
3144 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3145 | } |
0aacf84e MD |
3146 | else if (SCM_BIGP (x)) |
3147 | { | |
e11e83f3 | 3148 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3149 | return SCM_BOOL_F; |
3150 | else if (SCM_BIGP (y)) | |
3151 | { | |
3152 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3153 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3154 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3155 | } |
3156 | else if (SCM_REALP (y)) | |
3157 | { | |
3158 | int cmp; | |
3159 | if (xisnan (SCM_REAL_VALUE (y))) | |
3160 | return SCM_BOOL_F; | |
3161 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3162 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3163 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3164 | } |
3165 | else if (SCM_COMPLEXP (y)) | |
3166 | { | |
3167 | int cmp; | |
3168 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
3169 | return SCM_BOOL_F; | |
3170 | if (xisnan (SCM_COMPLEX_REAL (y))) | |
3171 | return SCM_BOOL_F; | |
3172 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
3173 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3174 | return scm_from_bool (0 == cmp); |
0aacf84e | 3175 | } |
f92e85f7 MV |
3176 | else if (SCM_FRACTIONP (y)) |
3177 | return SCM_BOOL_F; | |
0aacf84e MD |
3178 | else |
3179 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3180 | } |
0aacf84e MD |
3181 | else if (SCM_REALP (x)) |
3182 | { | |
e11e83f3 MV |
3183 | if (SCM_I_INUMP (y)) |
3184 | return scm_from_bool (SCM_REAL_VALUE (x) == (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3185 | else if (SCM_BIGP (y)) |
3186 | { | |
3187 | int cmp; | |
3188 | if (xisnan (SCM_REAL_VALUE (x))) | |
3189 | return SCM_BOOL_F; | |
3190 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3191 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3192 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3193 | } |
3194 | else if (SCM_REALP (y)) | |
73e4de09 | 3195 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 3196 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3197 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3198 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3199 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3200 | { |
3201 | double xx = SCM_REAL_VALUE (x); | |
3202 | if (xisnan (xx)) | |
3203 | return SCM_BOOL_F; | |
3204 | if (xisinf (xx)) | |
73e4de09 | 3205 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3206 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3207 | goto again; | |
3208 | } | |
0aacf84e MD |
3209 | else |
3210 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3211 | } |
0aacf84e MD |
3212 | else if (SCM_COMPLEXP (x)) |
3213 | { | |
e11e83f3 MV |
3214 | if (SCM_I_INUMP (y)) |
3215 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
3216 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3217 | else if (SCM_BIGP (y)) | |
3218 | { | |
3219 | int cmp; | |
3220 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
3221 | return SCM_BOOL_F; | |
3222 | if (xisnan (SCM_COMPLEX_REAL (x))) | |
3223 | return SCM_BOOL_F; | |
3224 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
3225 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3226 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3227 | } |
3228 | else if (SCM_REALP (y)) | |
73e4de09 | 3229 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
3230 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3231 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 3232 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3233 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3234 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3235 | { |
3236 | double xx; | |
3237 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
3238 | return SCM_BOOL_F; | |
3239 | xx = SCM_COMPLEX_REAL (x); | |
3240 | if (xisnan (xx)) | |
3241 | return SCM_BOOL_F; | |
3242 | if (xisinf (xx)) | |
73e4de09 | 3243 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3244 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3245 | goto again; | |
3246 | } | |
f92e85f7 MV |
3247 | else |
3248 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
3249 | } | |
3250 | else if (SCM_FRACTIONP (x)) | |
3251 | { | |
e11e83f3 | 3252 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
3253 | return SCM_BOOL_F; |
3254 | else if (SCM_BIGP (y)) | |
3255 | return SCM_BOOL_F; | |
3256 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
3257 | { |
3258 | double yy = SCM_REAL_VALUE (y); | |
3259 | if (xisnan (yy)) | |
3260 | return SCM_BOOL_F; | |
3261 | if (xisinf (yy)) | |
73e4de09 | 3262 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3263 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3264 | goto again; | |
3265 | } | |
f92e85f7 | 3266 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
3267 | { |
3268 | double yy; | |
3269 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
3270 | return SCM_BOOL_F; | |
3271 | yy = SCM_COMPLEX_REAL (y); | |
3272 | if (xisnan (yy)) | |
3273 | return SCM_BOOL_F; | |
3274 | if (xisinf (yy)) | |
73e4de09 | 3275 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3276 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3277 | goto again; | |
3278 | } | |
f92e85f7 MV |
3279 | else if (SCM_FRACTIONP (y)) |
3280 | return scm_i_fraction_equalp (x, y); | |
0aacf84e MD |
3281 | else |
3282 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3283 | } |
0aacf84e | 3284 | else |
f4c627b3 | 3285 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p); |
0f2d19dd JB |
3286 | } |
3287 | ||
3288 | ||
a5f0b599 KR |
3289 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
3290 | done are good for inums, but for bignums an answer can almost always be | |
3291 | had by just examining a few high bits of the operands, as done by GMP in | |
3292 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
3293 | of the float exponent to take into account. */ | |
3294 | ||
152f82bf | 3295 | SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p); |
942e5b91 MG |
3296 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3297 | * "increasing." | |
3298 | */ | |
0f2d19dd | 3299 | SCM |
6e8d25a6 | 3300 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3301 | { |
a5f0b599 | 3302 | again: |
e11e83f3 | 3303 | if (SCM_I_INUMP (x)) |
0aacf84e | 3304 | { |
e11e83f3 MV |
3305 | long xx = SCM_I_INUM (x); |
3306 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3307 | { |
e11e83f3 | 3308 | long yy = SCM_I_INUM (y); |
73e4de09 | 3309 | return scm_from_bool (xx < yy); |
0aacf84e MD |
3310 | } |
3311 | else if (SCM_BIGP (y)) | |
3312 | { | |
3313 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3314 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3315 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3316 | } |
3317 | else if (SCM_REALP (y)) | |
73e4de09 | 3318 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 3319 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3320 | { |
3321 | /* "x < a/b" becomes "x*b < a" */ | |
3322 | int_frac: | |
3323 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
3324 | y = SCM_FRACTION_NUMERATOR (y); | |
3325 | goto again; | |
3326 | } | |
0aacf84e MD |
3327 | else |
3328 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3329 | } |
0aacf84e MD |
3330 | else if (SCM_BIGP (x)) |
3331 | { | |
e11e83f3 | 3332 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3333 | { |
3334 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3335 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3336 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3337 | } |
3338 | else if (SCM_BIGP (y)) | |
3339 | { | |
3340 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3341 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3342 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
3343 | } |
3344 | else if (SCM_REALP (y)) | |
3345 | { | |
3346 | int cmp; | |
3347 | if (xisnan (SCM_REAL_VALUE (y))) | |
3348 | return SCM_BOOL_F; | |
3349 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3350 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3351 | return scm_from_bool (cmp < 0); |
0aacf84e | 3352 | } |
f92e85f7 | 3353 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 3354 | goto int_frac; |
0aacf84e MD |
3355 | else |
3356 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f4c627b3 | 3357 | } |
0aacf84e MD |
3358 | else if (SCM_REALP (x)) |
3359 | { | |
e11e83f3 MV |
3360 | if (SCM_I_INUMP (y)) |
3361 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3362 | else if (SCM_BIGP (y)) |
3363 | { | |
3364 | int cmp; | |
3365 | if (xisnan (SCM_REAL_VALUE (x))) | |
3366 | return SCM_BOOL_F; | |
3367 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3368 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3369 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
3370 | } |
3371 | else if (SCM_REALP (y)) | |
73e4de09 | 3372 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 3373 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3374 | { |
3375 | double xx = SCM_REAL_VALUE (x); | |
3376 | if (xisnan (xx)) | |
3377 | return SCM_BOOL_F; | |
3378 | if (xisinf (xx)) | |
73e4de09 | 3379 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
3380 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3381 | goto again; | |
3382 | } | |
f92e85f7 MV |
3383 | else |
3384 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
3385 | } | |
3386 | else if (SCM_FRACTIONP (x)) | |
3387 | { | |
e11e83f3 | 3388 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
3389 | { |
3390 | /* "a/b < y" becomes "a < y*b" */ | |
3391 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
3392 | x = SCM_FRACTION_NUMERATOR (x); | |
3393 | goto again; | |
3394 | } | |
f92e85f7 | 3395 | else if (SCM_REALP (y)) |
a5f0b599 KR |
3396 | { |
3397 | double yy = SCM_REAL_VALUE (y); | |
3398 | if (xisnan (yy)) | |
3399 | return SCM_BOOL_F; | |
3400 | if (xisinf (yy)) | |
73e4de09 | 3401 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
3402 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3403 | goto again; | |
3404 | } | |
f92e85f7 | 3405 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3406 | { |
3407 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
3408 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
3409 | SCM_FRACTION_DENOMINATOR (y)); | |
3410 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
3411 | SCM_FRACTION_DENOMINATOR (x)); | |
3412 | x = new_x; | |
3413 | y = new_y; | |
3414 | goto again; | |
3415 | } | |
0aacf84e MD |
3416 | else |
3417 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3418 | } |
0aacf84e | 3419 | else |
f4c627b3 | 3420 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p); |
0f2d19dd JB |
3421 | } |
3422 | ||
3423 | ||
c76b1eaf | 3424 | SCM_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p); |
942e5b91 MG |
3425 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3426 | * "decreasing." | |
c76b1eaf | 3427 | */ |
1bbd0b84 | 3428 | #define FUNC_NAME s_scm_gr_p |
c76b1eaf MD |
3429 | SCM |
3430 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3431 | { |
c76b1eaf MD |
3432 | if (!SCM_NUMBERP (x)) |
3433 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME); | |
3434 | else if (!SCM_NUMBERP (y)) | |
3435 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME); | |
3436 | else | |
3437 | return scm_less_p (y, x); | |
0f2d19dd | 3438 | } |
1bbd0b84 | 3439 | #undef FUNC_NAME |
0f2d19dd JB |
3440 | |
3441 | ||
c76b1eaf | 3442 | SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p); |
942e5b91 | 3443 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3444 | * "non-decreasing." |
3445 | */ | |
1bbd0b84 | 3446 | #define FUNC_NAME s_scm_leq_p |
c76b1eaf MD |
3447 | SCM |
3448 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3449 | { |
c76b1eaf MD |
3450 | if (!SCM_NUMBERP (x)) |
3451 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3452 | else if (!SCM_NUMBERP (y)) | |
3453 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3454 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3455 | return SCM_BOOL_F; |
c76b1eaf | 3456 | else |
73e4de09 | 3457 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 3458 | } |
1bbd0b84 | 3459 | #undef FUNC_NAME |
0f2d19dd JB |
3460 | |
3461 | ||
c76b1eaf | 3462 | SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p); |
942e5b91 | 3463 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3464 | * "non-increasing." |
3465 | */ | |
1bbd0b84 | 3466 | #define FUNC_NAME s_scm_geq_p |
c76b1eaf MD |
3467 | SCM |
3468 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3469 | { |
c76b1eaf MD |
3470 | if (!SCM_NUMBERP (x)) |
3471 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3472 | else if (!SCM_NUMBERP (y)) | |
3473 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3474 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3475 | return SCM_BOOL_F; |
c76b1eaf | 3476 | else |
73e4de09 | 3477 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 3478 | } |
1bbd0b84 | 3479 | #undef FUNC_NAME |
0f2d19dd JB |
3480 | |
3481 | ||
152f82bf | 3482 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3483 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3484 | * "zero." | |
3485 | */ | |
0f2d19dd | 3486 | SCM |
6e8d25a6 | 3487 | scm_zero_p (SCM z) |
0f2d19dd | 3488 | { |
e11e83f3 | 3489 | if (SCM_I_INUMP (z)) |
bc36d050 | 3490 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 3491 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 3492 | return SCM_BOOL_F; |
0aacf84e | 3493 | else if (SCM_REALP (z)) |
73e4de09 | 3494 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 3495 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 3496 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 3497 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
3498 | else if (SCM_FRACTIONP (z)) |
3499 | return SCM_BOOL_F; | |
0aacf84e | 3500 | else |
c2ff8ab0 | 3501 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); |
0f2d19dd JB |
3502 | } |
3503 | ||
3504 | ||
152f82bf | 3505 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3506 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3507 | * "zero." | |
3508 | */ | |
0f2d19dd | 3509 | SCM |
6e8d25a6 | 3510 | scm_positive_p (SCM x) |
0f2d19dd | 3511 | { |
e11e83f3 MV |
3512 | if (SCM_I_INUMP (x)) |
3513 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
3514 | else if (SCM_BIGP (x)) |
3515 | { | |
3516 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3517 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3518 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3519 | } |
3520 | else if (SCM_REALP (x)) | |
73e4de09 | 3521 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
3522 | else if (SCM_FRACTIONP (x)) |
3523 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3524 | else |
c2ff8ab0 | 3525 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); |
0f2d19dd JB |
3526 | } |
3527 | ||
3528 | ||
152f82bf | 3529 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3530 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3531 | * "zero." | |
3532 | */ | |
0f2d19dd | 3533 | SCM |
6e8d25a6 | 3534 | scm_negative_p (SCM x) |
0f2d19dd | 3535 | { |
e11e83f3 MV |
3536 | if (SCM_I_INUMP (x)) |
3537 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
3538 | else if (SCM_BIGP (x)) |
3539 | { | |
3540 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3541 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3542 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3543 | } |
3544 | else if (SCM_REALP (x)) | |
73e4de09 | 3545 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
3546 | else if (SCM_FRACTIONP (x)) |
3547 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3548 | else |
c2ff8ab0 | 3549 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); |
0f2d19dd JB |
3550 | } |
3551 | ||
3552 | ||
2a06f791 KR |
3553 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
3554 | required by r5rs. On that basis, for exact/inexact combinations the | |
3555 | exact is converted to inexact to compare and possibly return. This is | |
3556 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
3557 | its test, such trouble is not required for min and max. */ | |
3558 | ||
9de33deb | 3559 | SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max); |
942e5b91 MG |
3560 | /* "Return the maximum of all parameter values." |
3561 | */ | |
0f2d19dd | 3562 | SCM |
6e8d25a6 | 3563 | scm_max (SCM x, SCM y) |
0f2d19dd | 3564 | { |
0aacf84e MD |
3565 | if (SCM_UNBNDP (y)) |
3566 | { | |
3567 | if (SCM_UNBNDP (x)) | |
3568 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 3569 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3570 | return x; |
3571 | else | |
3572 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3573 | } |
f4c627b3 | 3574 | |
e11e83f3 | 3575 | if (SCM_I_INUMP (x)) |
0aacf84e | 3576 | { |
e11e83f3 MV |
3577 | long xx = SCM_I_INUM (x); |
3578 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3579 | { |
e11e83f3 | 3580 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3581 | return (xx < yy) ? y : x; |
3582 | } | |
3583 | else if (SCM_BIGP (y)) | |
3584 | { | |
3585 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3586 | scm_remember_upto_here_1 (y); | |
3587 | return (sgn < 0) ? x : y; | |
3588 | } | |
3589 | else if (SCM_REALP (y)) | |
3590 | { | |
3591 | double z = xx; | |
3592 | /* if y==NaN then ">" is false and we return NaN */ | |
55f26379 | 3593 | return (z > SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3594 | } |
f92e85f7 MV |
3595 | else if (SCM_FRACTIONP (y)) |
3596 | { | |
e4bc5d6c | 3597 | use_less: |
73e4de09 | 3598 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 3599 | } |
0aacf84e MD |
3600 | else |
3601 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3602 | } |
0aacf84e MD |
3603 | else if (SCM_BIGP (x)) |
3604 | { | |
e11e83f3 | 3605 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3606 | { |
3607 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3608 | scm_remember_upto_here_1 (x); | |
3609 | return (sgn < 0) ? y : x; | |
3610 | } | |
3611 | else if (SCM_BIGP (y)) | |
3612 | { | |
3613 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3614 | scm_remember_upto_here_2 (x, y); | |
3615 | return (cmp > 0) ? x : y; | |
3616 | } | |
3617 | else if (SCM_REALP (y)) | |
3618 | { | |
2a06f791 KR |
3619 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
3620 | double xx, yy; | |
3621 | big_real: | |
3622 | xx = scm_i_big2dbl (x); | |
3623 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3624 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 3625 | } |
f92e85f7 MV |
3626 | else if (SCM_FRACTIONP (y)) |
3627 | { | |
e4bc5d6c | 3628 | goto use_less; |
f92e85f7 | 3629 | } |
0aacf84e MD |
3630 | else |
3631 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 3632 | } |
0aacf84e MD |
3633 | else if (SCM_REALP (x)) |
3634 | { | |
e11e83f3 | 3635 | if (SCM_I_INUMP (y)) |
0aacf84e | 3636 | { |
e11e83f3 | 3637 | double z = SCM_I_INUM (y); |
0aacf84e | 3638 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3639 | return (SCM_REAL_VALUE (x) < z) ? scm_from_double (z) : x; |
0aacf84e MD |
3640 | } |
3641 | else if (SCM_BIGP (y)) | |
3642 | { | |
b6f8f763 | 3643 | SCM_SWAP (x, y); |
2a06f791 | 3644 | goto big_real; |
0aacf84e MD |
3645 | } |
3646 | else if (SCM_REALP (y)) | |
3647 | { | |
3648 | /* if x==NaN then our explicit check means we return NaN | |
3649 | if y==NaN then ">" is false and we return NaN | |
3650 | calling isnan is unavoidable, since it's the only way to know | |
3651 | which of x or y causes any compares to be false */ | |
3652 | double xx = SCM_REAL_VALUE (x); | |
3653 | return (xisnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y; | |
3654 | } | |
f92e85f7 MV |
3655 | else if (SCM_FRACTIONP (y)) |
3656 | { | |
3657 | double yy = scm_i_fraction2double (y); | |
3658 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3659 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
3660 | } |
3661 | else | |
3662 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3663 | } | |
3664 | else if (SCM_FRACTIONP (x)) | |
3665 | { | |
e11e83f3 | 3666 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3667 | { |
e4bc5d6c | 3668 | goto use_less; |
f92e85f7 MV |
3669 | } |
3670 | else if (SCM_BIGP (y)) | |
3671 | { | |
e4bc5d6c | 3672 | goto use_less; |
f92e85f7 MV |
3673 | } |
3674 | else if (SCM_REALP (y)) | |
3675 | { | |
3676 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3677 | return (xx < SCM_REAL_VALUE (y)) ? y : scm_from_double (xx); |
f92e85f7 MV |
3678 | } |
3679 | else if (SCM_FRACTIONP (y)) | |
3680 | { | |
e4bc5d6c | 3681 | goto use_less; |
f92e85f7 | 3682 | } |
0aacf84e MD |
3683 | else |
3684 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3685 | } |
0aacf84e | 3686 | else |
f4c627b3 | 3687 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
3688 | } |
3689 | ||
3690 | ||
9de33deb | 3691 | SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min); |
942e5b91 MG |
3692 | /* "Return the minium of all parameter values." |
3693 | */ | |
0f2d19dd | 3694 | SCM |
6e8d25a6 | 3695 | scm_min (SCM x, SCM y) |
0f2d19dd | 3696 | { |
0aacf84e MD |
3697 | if (SCM_UNBNDP (y)) |
3698 | { | |
3699 | if (SCM_UNBNDP (x)) | |
3700 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 3701 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3702 | return x; |
3703 | else | |
3704 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 3705 | } |
f4c627b3 | 3706 | |
e11e83f3 | 3707 | if (SCM_I_INUMP (x)) |
0aacf84e | 3708 | { |
e11e83f3 MV |
3709 | long xx = SCM_I_INUM (x); |
3710 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3711 | { |
e11e83f3 | 3712 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3713 | return (xx < yy) ? x : y; |
3714 | } | |
3715 | else if (SCM_BIGP (y)) | |
3716 | { | |
3717 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3718 | scm_remember_upto_here_1 (y); | |
3719 | return (sgn < 0) ? y : x; | |
3720 | } | |
3721 | else if (SCM_REALP (y)) | |
3722 | { | |
3723 | double z = xx; | |
3724 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 3725 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3726 | } |
f92e85f7 MV |
3727 | else if (SCM_FRACTIONP (y)) |
3728 | { | |
e4bc5d6c | 3729 | use_less: |
73e4de09 | 3730 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 3731 | } |
0aacf84e MD |
3732 | else |
3733 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3734 | } |
0aacf84e MD |
3735 | else if (SCM_BIGP (x)) |
3736 | { | |
e11e83f3 | 3737 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3738 | { |
3739 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3740 | scm_remember_upto_here_1 (x); | |
3741 | return (sgn < 0) ? x : y; | |
3742 | } | |
3743 | else if (SCM_BIGP (y)) | |
3744 | { | |
3745 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3746 | scm_remember_upto_here_2 (x, y); | |
3747 | return (cmp > 0) ? y : x; | |
3748 | } | |
3749 | else if (SCM_REALP (y)) | |
3750 | { | |
2a06f791 KR |
3751 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
3752 | double xx, yy; | |
3753 | big_real: | |
3754 | xx = scm_i_big2dbl (x); | |
3755 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3756 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 3757 | } |
f92e85f7 MV |
3758 | else if (SCM_FRACTIONP (y)) |
3759 | { | |
e4bc5d6c | 3760 | goto use_less; |
f92e85f7 | 3761 | } |
0aacf84e MD |
3762 | else |
3763 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 3764 | } |
0aacf84e MD |
3765 | else if (SCM_REALP (x)) |
3766 | { | |
e11e83f3 | 3767 | if (SCM_I_INUMP (y)) |
0aacf84e | 3768 | { |
e11e83f3 | 3769 | double z = SCM_I_INUM (y); |
0aacf84e | 3770 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3771 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
3772 | } |
3773 | else if (SCM_BIGP (y)) | |
3774 | { | |
b6f8f763 | 3775 | SCM_SWAP (x, y); |
2a06f791 | 3776 | goto big_real; |
0aacf84e MD |
3777 | } |
3778 | else if (SCM_REALP (y)) | |
3779 | { | |
3780 | /* if x==NaN then our explicit check means we return NaN | |
3781 | if y==NaN then "<" is false and we return NaN | |
3782 | calling isnan is unavoidable, since it's the only way to know | |
3783 | which of x or y causes any compares to be false */ | |
3784 | double xx = SCM_REAL_VALUE (x); | |
3785 | return (xisnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y; | |
3786 | } | |
f92e85f7 MV |
3787 | else if (SCM_FRACTIONP (y)) |
3788 | { | |
3789 | double yy = scm_i_fraction2double (y); | |
3790 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3791 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 3792 | } |
0aacf84e MD |
3793 | else |
3794 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3795 | } |
f92e85f7 MV |
3796 | else if (SCM_FRACTIONP (x)) |
3797 | { | |
e11e83f3 | 3798 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3799 | { |
e4bc5d6c | 3800 | goto use_less; |
f92e85f7 MV |
3801 | } |
3802 | else if (SCM_BIGP (y)) | |
3803 | { | |
e4bc5d6c | 3804 | goto use_less; |
f92e85f7 MV |
3805 | } |
3806 | else if (SCM_REALP (y)) | |
3807 | { | |
3808 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3809 | return (SCM_REAL_VALUE (y) < xx) ? y : scm_from_double (xx); |
f92e85f7 MV |
3810 | } |
3811 | else if (SCM_FRACTIONP (y)) | |
3812 | { | |
e4bc5d6c | 3813 | goto use_less; |
f92e85f7 MV |
3814 | } |
3815 | else | |
3816 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3817 | } | |
0aacf84e | 3818 | else |
f4c627b3 | 3819 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
3820 | } |
3821 | ||
3822 | ||
9de33deb | 3823 | SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum); |
942e5b91 MG |
3824 | /* "Return the sum of all parameter values. Return 0 if called without\n" |
3825 | * "any parameters." | |
3826 | */ | |
0f2d19dd | 3827 | SCM |
6e8d25a6 | 3828 | scm_sum (SCM x, SCM y) |
0f2d19dd | 3829 | { |
ca46fb90 RB |
3830 | if (SCM_UNBNDP (y)) |
3831 | { | |
3832 | if (SCM_NUMBERP (x)) return x; | |
3833 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 3834 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 3835 | } |
c209c88e | 3836 | |
e11e83f3 | 3837 | if (SCM_I_INUMP (x)) |
ca46fb90 | 3838 | { |
e11e83f3 | 3839 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3840 | { |
e11e83f3 MV |
3841 | long xx = SCM_I_INUM (x); |
3842 | long yy = SCM_I_INUM (y); | |
ca46fb90 | 3843 | long int z = xx + yy; |
d956fa6f | 3844 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_long2big (z); |
ca46fb90 RB |
3845 | } |
3846 | else if (SCM_BIGP (y)) | |
3847 | { | |
3848 | SCM_SWAP (x, y); | |
3849 | goto add_big_inum; | |
3850 | } | |
3851 | else if (SCM_REALP (y)) | |
3852 | { | |
e11e83f3 | 3853 | long int xx = SCM_I_INUM (x); |
55f26379 | 3854 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
3855 | } |
3856 | else if (SCM_COMPLEXP (y)) | |
3857 | { | |
e11e83f3 | 3858 | long int xx = SCM_I_INUM (x); |
8507ec80 | 3859 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
3860 | SCM_COMPLEX_IMAG (y)); |
3861 | } | |
f92e85f7 | 3862 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 3863 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
3864 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
3865 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
3866 | else |
3867 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
3868 | } else if (SCM_BIGP (x)) |
3869 | { | |
e11e83f3 | 3870 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3871 | { |
3872 | long int inum; | |
3873 | int bigsgn; | |
3874 | add_big_inum: | |
e11e83f3 | 3875 | inum = SCM_I_INUM (y); |
0aacf84e MD |
3876 | if (inum == 0) |
3877 | return x; | |
3878 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3879 | if (inum < 0) | |
3880 | { | |
3881 | SCM result = scm_i_mkbig (); | |
3882 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
3883 | scm_remember_upto_here_1 (x); | |
3884 | /* we know the result will have to be a bignum */ | |
3885 | if (bigsgn == -1) | |
3886 | return result; | |
3887 | return scm_i_normbig (result); | |
3888 | } | |
3889 | else | |
3890 | { | |
3891 | SCM result = scm_i_mkbig (); | |
3892 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
3893 | scm_remember_upto_here_1 (x); | |
3894 | /* we know the result will have to be a bignum */ | |
3895 | if (bigsgn == 1) | |
3896 | return result; | |
3897 | return scm_i_normbig (result); | |
3898 | } | |
3899 | } | |
3900 | else if (SCM_BIGP (y)) | |
3901 | { | |
3902 | SCM result = scm_i_mkbig (); | |
3903 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3904 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3905 | mpz_add (SCM_I_BIG_MPZ (result), | |
3906 | SCM_I_BIG_MPZ (x), | |
3907 | SCM_I_BIG_MPZ (y)); | |
3908 | scm_remember_upto_here_2 (x, y); | |
3909 | /* we know the result will have to be a bignum */ | |
3910 | if (sgn_x == sgn_y) | |
3911 | return result; | |
3912 | return scm_i_normbig (result); | |
3913 | } | |
3914 | else if (SCM_REALP (y)) | |
3915 | { | |
3916 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
3917 | scm_remember_upto_here_1 (x); | |
55f26379 | 3918 | return scm_from_double (result); |
0aacf84e MD |
3919 | } |
3920 | else if (SCM_COMPLEXP (y)) | |
3921 | { | |
3922 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
3923 | + SCM_COMPLEX_REAL (y)); | |
3924 | scm_remember_upto_here_1 (x); | |
8507ec80 | 3925 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 3926 | } |
f92e85f7 | 3927 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 3928 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
3929 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
3930 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
3931 | else |
3932 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 3933 | } |
0aacf84e MD |
3934 | else if (SCM_REALP (x)) |
3935 | { | |
e11e83f3 | 3936 | if (SCM_I_INUMP (y)) |
55f26379 | 3937 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
3938 | else if (SCM_BIGP (y)) |
3939 | { | |
3940 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
3941 | scm_remember_upto_here_1 (y); | |
55f26379 | 3942 | return scm_from_double (result); |
0aacf84e MD |
3943 | } |
3944 | else if (SCM_REALP (y)) | |
55f26379 | 3945 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 3946 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 3947 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 3948 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 3949 | else if (SCM_FRACTIONP (y)) |
55f26379 | 3950 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
3951 | else |
3952 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 3953 | } |
0aacf84e MD |
3954 | else if (SCM_COMPLEXP (x)) |
3955 | { | |
e11e83f3 | 3956 | if (SCM_I_INUMP (y)) |
8507ec80 | 3957 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
3958 | SCM_COMPLEX_IMAG (x)); |
3959 | else if (SCM_BIGP (y)) | |
3960 | { | |
3961 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
3962 | + SCM_COMPLEX_REAL (x)); | |
3963 | scm_remember_upto_here_1 (y); | |
8507ec80 | 3964 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
3965 | } |
3966 | else if (SCM_REALP (y)) | |
8507ec80 | 3967 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
3968 | SCM_COMPLEX_IMAG (x)); |
3969 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 3970 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 3971 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 3972 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 3973 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
3974 | SCM_COMPLEX_IMAG (x)); |
3975 | else | |
3976 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
3977 | } | |
3978 | else if (SCM_FRACTIONP (x)) | |
3979 | { | |
e11e83f3 | 3980 | if (SCM_I_INUMP (y)) |
cba42c93 | 3981 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
3982 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
3983 | SCM_FRACTION_DENOMINATOR (x)); | |
3984 | else if (SCM_BIGP (y)) | |
cba42c93 | 3985 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
3986 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
3987 | SCM_FRACTION_DENOMINATOR (x)); | |
3988 | else if (SCM_REALP (y)) | |
55f26379 | 3989 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 3990 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 3991 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
3992 | SCM_COMPLEX_IMAG (y)); |
3993 | else if (SCM_FRACTIONP (y)) | |
3994 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 3995 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
3996 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
3997 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
3998 | else |
3999 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 4000 | } |
0aacf84e | 4001 | else |
98cb6e75 | 4002 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
4003 | } |
4004 | ||
4005 | ||
9de33deb | 4006 | SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference); |
609c3d30 MG |
4007 | /* If called with one argument @var{z1}, -@var{z1} returned. Otherwise |
4008 | * the sum of all but the first argument are subtracted from the first | |
4009 | * argument. */ | |
c05e97b7 | 4010 | #define FUNC_NAME s_difference |
0f2d19dd | 4011 | SCM |
6e8d25a6 | 4012 | scm_difference (SCM x, SCM y) |
0f2d19dd | 4013 | { |
ca46fb90 RB |
4014 | if (SCM_UNBNDP (y)) |
4015 | { | |
4016 | if (SCM_UNBNDP (x)) | |
4017 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
4018 | else | |
e11e83f3 | 4019 | if (SCM_I_INUMP (x)) |
ca46fb90 | 4020 | { |
e11e83f3 | 4021 | long xx = -SCM_I_INUM (x); |
ca46fb90 | 4022 | if (SCM_FIXABLE (xx)) |
d956fa6f | 4023 | return SCM_I_MAKINUM (xx); |
ca46fb90 RB |
4024 | else |
4025 | return scm_i_long2big (xx); | |
4026 | } | |
4027 | else if (SCM_BIGP (x)) | |
4028 | /* FIXME: do we really need to normalize here? */ | |
4029 | return scm_i_normbig (scm_i_clonebig (x, 0)); | |
4030 | else if (SCM_REALP (x)) | |
55f26379 | 4031 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 4032 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 4033 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 4034 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 4035 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4036 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 4037 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
4038 | else |
4039 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 4040 | } |
ca46fb90 | 4041 | |
e11e83f3 | 4042 | if (SCM_I_INUMP (x)) |
0aacf84e | 4043 | { |
e11e83f3 | 4044 | if (SCM_I_INUMP (y)) |
0aacf84e | 4045 | { |
e11e83f3 MV |
4046 | long int xx = SCM_I_INUM (x); |
4047 | long int yy = SCM_I_INUM (y); | |
0aacf84e MD |
4048 | long int z = xx - yy; |
4049 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4050 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4051 | else |
4052 | return scm_i_long2big (z); | |
4053 | } | |
4054 | else if (SCM_BIGP (y)) | |
4055 | { | |
4056 | /* inum-x - big-y */ | |
e11e83f3 | 4057 | long xx = SCM_I_INUM (x); |
ca46fb90 | 4058 | |
0aacf84e MD |
4059 | if (xx == 0) |
4060 | return scm_i_clonebig (y, 0); | |
4061 | else | |
4062 | { | |
4063 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4064 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4065 | |
0aacf84e MD |
4066 | if (xx >= 0) |
4067 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
4068 | else | |
4069 | { | |
4070 | /* x - y == -(y + -x) */ | |
4071 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
4072 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4073 | } | |
4074 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 4075 | |
0aacf84e MD |
4076 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
4077 | /* we know the result will have to be a bignum */ | |
4078 | return result; | |
4079 | else | |
4080 | return scm_i_normbig (result); | |
4081 | } | |
4082 | } | |
4083 | else if (SCM_REALP (y)) | |
4084 | { | |
e11e83f3 | 4085 | long int xx = SCM_I_INUM (x); |
55f26379 | 4086 | return scm_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
4087 | } |
4088 | else if (SCM_COMPLEXP (y)) | |
4089 | { | |
e11e83f3 | 4090 | long int xx = SCM_I_INUM (x); |
8507ec80 | 4091 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4092 | - SCM_COMPLEX_IMAG (y)); |
4093 | } | |
f92e85f7 MV |
4094 | else if (SCM_FRACTIONP (y)) |
4095 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 4096 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4097 | SCM_FRACTION_NUMERATOR (y)), |
4098 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4099 | else |
4100 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 4101 | } |
0aacf84e MD |
4102 | else if (SCM_BIGP (x)) |
4103 | { | |
e11e83f3 | 4104 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4105 | { |
4106 | /* big-x - inum-y */ | |
e11e83f3 | 4107 | long yy = SCM_I_INUM (y); |
0aacf84e | 4108 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 4109 | |
0aacf84e MD |
4110 | scm_remember_upto_here_1 (x); |
4111 | if (sgn_x == 0) | |
c71b0706 MV |
4112 | return (SCM_FIXABLE (-yy) ? |
4113 | SCM_I_MAKINUM (-yy) : scm_from_long (-yy)); | |
0aacf84e MD |
4114 | else |
4115 | { | |
4116 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4117 | |
708f22c6 KR |
4118 | if (yy >= 0) |
4119 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
4120 | else | |
4121 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 4122 | scm_remember_upto_here_1 (x); |
ca46fb90 | 4123 | |
0aacf84e MD |
4124 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
4125 | /* we know the result will have to be a bignum */ | |
4126 | return result; | |
4127 | else | |
4128 | return scm_i_normbig (result); | |
4129 | } | |
4130 | } | |
4131 | else if (SCM_BIGP (y)) | |
4132 | { | |
4133 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4134 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4135 | SCM result = scm_i_mkbig (); | |
4136 | mpz_sub (SCM_I_BIG_MPZ (result), | |
4137 | SCM_I_BIG_MPZ (x), | |
4138 | SCM_I_BIG_MPZ (y)); | |
4139 | scm_remember_upto_here_2 (x, y); | |
4140 | /* we know the result will have to be a bignum */ | |
4141 | if ((sgn_x == 1) && (sgn_y == -1)) | |
4142 | return result; | |
4143 | if ((sgn_x == -1) && (sgn_y == 1)) | |
4144 | return result; | |
4145 | return scm_i_normbig (result); | |
4146 | } | |
4147 | else if (SCM_REALP (y)) | |
4148 | { | |
4149 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
4150 | scm_remember_upto_here_1 (x); | |
55f26379 | 4151 | return scm_from_double (result); |
0aacf84e MD |
4152 | } |
4153 | else if (SCM_COMPLEXP (y)) | |
4154 | { | |
4155 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4156 | - SCM_COMPLEX_REAL (y)); | |
4157 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4158 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4159 | } |
f92e85f7 | 4160 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4161 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4162 | SCM_FRACTION_NUMERATOR (y)), |
4163 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 4164 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 4165 | } |
0aacf84e MD |
4166 | else if (SCM_REALP (x)) |
4167 | { | |
e11e83f3 | 4168 | if (SCM_I_INUMP (y)) |
55f26379 | 4169 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
4170 | else if (SCM_BIGP (y)) |
4171 | { | |
4172 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4173 | scm_remember_upto_here_1 (x); | |
55f26379 | 4174 | return scm_from_double (result); |
0aacf84e MD |
4175 | } |
4176 | else if (SCM_REALP (y)) | |
55f26379 | 4177 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 4178 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4179 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4180 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4181 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4182 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
4183 | else |
4184 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4185 | } |
0aacf84e MD |
4186 | else if (SCM_COMPLEXP (x)) |
4187 | { | |
e11e83f3 | 4188 | if (SCM_I_INUMP (y)) |
8507ec80 | 4189 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
4190 | SCM_COMPLEX_IMAG (x)); |
4191 | else if (SCM_BIGP (y)) | |
4192 | { | |
4193 | double real_part = (SCM_COMPLEX_REAL (x) | |
4194 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
4195 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4196 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
4197 | } |
4198 | else if (SCM_REALP (y)) | |
8507ec80 | 4199 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
4200 | SCM_COMPLEX_IMAG (x)); |
4201 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4202 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4203 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4204 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4205 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
4206 | SCM_COMPLEX_IMAG (x)); |
4207 | else | |
4208 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
4209 | } | |
4210 | else if (SCM_FRACTIONP (x)) | |
4211 | { | |
e11e83f3 | 4212 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4213 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 4214 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4215 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4216 | SCM_FRACTION_DENOMINATOR (x)); | |
4217 | else if (SCM_BIGP (y)) | |
cba42c93 | 4218 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4219 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4220 | SCM_FRACTION_DENOMINATOR (x)); | |
4221 | else if (SCM_REALP (y)) | |
55f26379 | 4222 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 4223 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4224 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4225 | -SCM_COMPLEX_IMAG (y)); |
4226 | else if (SCM_FRACTIONP (y)) | |
4227 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 4228 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4229 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4230 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4231 | else |
4232 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4233 | } |
0aacf84e | 4234 | else |
98cb6e75 | 4235 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 4236 | } |
c05e97b7 | 4237 | #undef FUNC_NAME |
0f2d19dd | 4238 | |
ca46fb90 | 4239 | |
9de33deb | 4240 | SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product); |
942e5b91 MG |
4241 | /* "Return the product of all arguments. If called without arguments,\n" |
4242 | * "1 is returned." | |
4243 | */ | |
0f2d19dd | 4244 | SCM |
6e8d25a6 | 4245 | scm_product (SCM x, SCM y) |
0f2d19dd | 4246 | { |
0aacf84e MD |
4247 | if (SCM_UNBNDP (y)) |
4248 | { | |
4249 | if (SCM_UNBNDP (x)) | |
d956fa6f | 4250 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
4251 | else if (SCM_NUMBERP (x)) |
4252 | return x; | |
4253 | else | |
4254 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 4255 | } |
ca46fb90 | 4256 | |
e11e83f3 | 4257 | if (SCM_I_INUMP (x)) |
0aacf84e MD |
4258 | { |
4259 | long xx; | |
f4c627b3 | 4260 | |
0aacf84e | 4261 | intbig: |
e11e83f3 | 4262 | xx = SCM_I_INUM (x); |
f4c627b3 | 4263 | |
0aacf84e MD |
4264 | switch (xx) |
4265 | { | |
ca46fb90 RB |
4266 | case 0: return x; break; |
4267 | case 1: return y; break; | |
0aacf84e | 4268 | } |
f4c627b3 | 4269 | |
e11e83f3 | 4270 | if (SCM_I_INUMP (y)) |
0aacf84e | 4271 | { |
e11e83f3 | 4272 | long yy = SCM_I_INUM (y); |
0aacf84e | 4273 | long kk = xx * yy; |
d956fa6f | 4274 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 4275 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
4276 | return k; |
4277 | else | |
4278 | { | |
4279 | SCM result = scm_i_long2big (xx); | |
4280 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); | |
4281 | return scm_i_normbig (result); | |
4282 | } | |
4283 | } | |
4284 | else if (SCM_BIGP (y)) | |
4285 | { | |
4286 | SCM result = scm_i_mkbig (); | |
4287 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
4288 | scm_remember_upto_here_1 (y); | |
4289 | return result; | |
4290 | } | |
4291 | else if (SCM_REALP (y)) | |
55f26379 | 4292 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 4293 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4294 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 4295 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4296 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4297 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4298 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4299 | else |
4300 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4301 | } |
0aacf84e MD |
4302 | else if (SCM_BIGP (x)) |
4303 | { | |
e11e83f3 | 4304 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4305 | { |
4306 | SCM_SWAP (x, y); | |
4307 | goto intbig; | |
4308 | } | |
4309 | else if (SCM_BIGP (y)) | |
4310 | { | |
4311 | SCM result = scm_i_mkbig (); | |
4312 | mpz_mul (SCM_I_BIG_MPZ (result), | |
4313 | SCM_I_BIG_MPZ (x), | |
4314 | SCM_I_BIG_MPZ (y)); | |
4315 | scm_remember_upto_here_2 (x, y); | |
4316 | return result; | |
4317 | } | |
4318 | else if (SCM_REALP (y)) | |
4319 | { | |
4320 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
4321 | scm_remember_upto_here_1 (x); | |
55f26379 | 4322 | return scm_from_double (result); |
0aacf84e MD |
4323 | } |
4324 | else if (SCM_COMPLEXP (y)) | |
4325 | { | |
4326 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4327 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4328 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4329 | z * SCM_COMPLEX_IMAG (y)); |
4330 | } | |
f92e85f7 | 4331 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4332 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4333 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4334 | else |
4335 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4336 | } |
0aacf84e MD |
4337 | else if (SCM_REALP (x)) |
4338 | { | |
e11e83f3 | 4339 | if (SCM_I_INUMP (y)) |
55f26379 | 4340 | return scm_from_double (SCM_I_INUM (y) * SCM_REAL_VALUE (x)); |
0aacf84e MD |
4341 | else if (SCM_BIGP (y)) |
4342 | { | |
4343 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
4344 | scm_remember_upto_here_1 (y); | |
55f26379 | 4345 | return scm_from_double (result); |
0aacf84e MD |
4346 | } |
4347 | else if (SCM_REALP (y)) | |
55f26379 | 4348 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 4349 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4350 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 4351 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4352 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4353 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
4354 | else |
4355 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4356 | } |
0aacf84e MD |
4357 | else if (SCM_COMPLEXP (x)) |
4358 | { | |
e11e83f3 | 4359 | if (SCM_I_INUMP (y)) |
8507ec80 | 4360 | return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x), |
e11e83f3 | 4361 | SCM_I_INUM (y) * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4362 | else if (SCM_BIGP (y)) |
4363 | { | |
4364 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4365 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4366 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 4367 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4368 | } |
4369 | else if (SCM_REALP (y)) | |
8507ec80 | 4370 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
4371 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
4372 | else if (SCM_COMPLEXP (y)) | |
4373 | { | |
8507ec80 | 4374 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
4375 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
4376 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
4377 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
4378 | } | |
f92e85f7 MV |
4379 | else if (SCM_FRACTIONP (y)) |
4380 | { | |
4381 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4382 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
4383 | yy * SCM_COMPLEX_IMAG (x)); |
4384 | } | |
4385 | else | |
4386 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
4387 | } | |
4388 | else if (SCM_FRACTIONP (x)) | |
4389 | { | |
e11e83f3 | 4390 | if (SCM_I_INUMP (y)) |
cba42c93 | 4391 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4392 | SCM_FRACTION_DENOMINATOR (x)); |
4393 | else if (SCM_BIGP (y)) | |
cba42c93 | 4394 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4395 | SCM_FRACTION_DENOMINATOR (x)); |
4396 | else if (SCM_REALP (y)) | |
55f26379 | 4397 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
4398 | else if (SCM_COMPLEXP (y)) |
4399 | { | |
4400 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 4401 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4402 | xx * SCM_COMPLEX_IMAG (y)); |
4403 | } | |
4404 | else if (SCM_FRACTIONP (y)) | |
4405 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 4406 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4407 | SCM_FRACTION_NUMERATOR (y)), |
4408 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
4409 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4410 | else |
4411 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4412 | } |
0aacf84e | 4413 | else |
f4c627b3 | 4414 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
4415 | } |
4416 | ||
7351e207 MV |
4417 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
4418 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
4419 | #define ALLOW_DIVIDE_BY_ZERO | |
4420 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
4421 | #endif | |
0f2d19dd | 4422 | |
ba74ef4e MV |
4423 | /* The code below for complex division is adapted from the GNU |
4424 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
4425 | this copyright: */ | |
4426 | ||
4427 | /**************************************************************** | |
4428 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
4429 | ||
4430 | Permission to use, copy, modify, and distribute this software | |
4431 | and its documentation for any purpose and without fee is hereby | |
4432 | granted, provided that the above copyright notice appear in all | |
4433 | copies and that both that the copyright notice and this | |
4434 | permission notice and warranty disclaimer appear in supporting | |
4435 | documentation, and that the names of AT&T Bell Laboratories or | |
4436 | Bellcore or any of their entities not be used in advertising or | |
4437 | publicity pertaining to distribution of the software without | |
4438 | specific, written prior permission. | |
4439 | ||
4440 | AT&T and Bellcore disclaim all warranties with regard to this | |
4441 | software, including all implied warranties of merchantability | |
4442 | and fitness. In no event shall AT&T or Bellcore be liable for | |
4443 | any special, indirect or consequential damages or any damages | |
4444 | whatsoever resulting from loss of use, data or profits, whether | |
4445 | in an action of contract, negligence or other tortious action, | |
4446 | arising out of or in connection with the use or performance of | |
4447 | this software. | |
4448 | ****************************************************************/ | |
4449 | ||
9de33deb | 4450 | SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide); |
609c3d30 MG |
4451 | /* Divide the first argument by the product of the remaining |
4452 | arguments. If called with one argument @var{z1}, 1/@var{z1} is | |
4453 | returned. */ | |
c05e97b7 | 4454 | #define FUNC_NAME s_divide |
f92e85f7 MV |
4455 | static SCM |
4456 | scm_i_divide (SCM x, SCM y, int inexact) | |
0f2d19dd | 4457 | { |
f8de44c1 DH |
4458 | double a; |
4459 | ||
0aacf84e MD |
4460 | if (SCM_UNBNDP (y)) |
4461 | { | |
4462 | if (SCM_UNBNDP (x)) | |
4463 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 4464 | else if (SCM_I_INUMP (x)) |
0aacf84e | 4465 | { |
e11e83f3 | 4466 | long xx = SCM_I_INUM (x); |
0aacf84e MD |
4467 | if (xx == 1 || xx == -1) |
4468 | return x; | |
7351e207 | 4469 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4470 | else if (xx == 0) |
4471 | scm_num_overflow (s_divide); | |
7351e207 | 4472 | #endif |
0aacf84e | 4473 | else |
f92e85f7 MV |
4474 | { |
4475 | if (inexact) | |
55f26379 | 4476 | return scm_from_double (1.0 / (double) xx); |
cba42c93 | 4477 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4478 | } |
0aacf84e MD |
4479 | } |
4480 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
4481 | { |
4482 | if (inexact) | |
55f26379 | 4483 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cba42c93 | 4484 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4485 | } |
0aacf84e MD |
4486 | else if (SCM_REALP (x)) |
4487 | { | |
4488 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 4489 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4490 | if (xx == 0.0) |
4491 | scm_num_overflow (s_divide); | |
4492 | else | |
7351e207 | 4493 | #endif |
55f26379 | 4494 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
4495 | } |
4496 | else if (SCM_COMPLEXP (x)) | |
4497 | { | |
4498 | double r = SCM_COMPLEX_REAL (x); | |
4499 | double i = SCM_COMPLEX_IMAG (x); | |
4500 | if (r <= i) | |
4501 | { | |
4502 | double t = r / i; | |
4503 | double d = i * (1.0 + t * t); | |
8507ec80 | 4504 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
4505 | } |
4506 | else | |
4507 | { | |
4508 | double t = i / r; | |
4509 | double d = r * (1.0 + t * t); | |
8507ec80 | 4510 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
4511 | } |
4512 | } | |
f92e85f7 | 4513 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4514 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 4515 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
4516 | else |
4517 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 4518 | } |
f8de44c1 | 4519 | |
e11e83f3 | 4520 | if (SCM_I_INUMP (x)) |
0aacf84e | 4521 | { |
e11e83f3 MV |
4522 | long xx = SCM_I_INUM (x); |
4523 | if (SCM_I_INUMP (y)) | |
0aacf84e | 4524 | { |
e11e83f3 | 4525 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
4526 | if (yy == 0) |
4527 | { | |
7351e207 | 4528 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4529 | scm_num_overflow (s_divide); |
7351e207 | 4530 | #else |
55f26379 | 4531 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 4532 | #endif |
0aacf84e MD |
4533 | } |
4534 | else if (xx % yy != 0) | |
f92e85f7 MV |
4535 | { |
4536 | if (inexact) | |
55f26379 | 4537 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 4538 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4539 | } |
0aacf84e MD |
4540 | else |
4541 | { | |
4542 | long z = xx / yy; | |
4543 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4544 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4545 | else |
4546 | return scm_i_long2big (z); | |
4547 | } | |
f872b822 | 4548 | } |
0aacf84e | 4549 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
4550 | { |
4551 | if (inexact) | |
55f26379 | 4552 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 4553 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4554 | } |
0aacf84e MD |
4555 | else if (SCM_REALP (y)) |
4556 | { | |
4557 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4558 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4559 | if (yy == 0.0) |
4560 | scm_num_overflow (s_divide); | |
4561 | else | |
7351e207 | 4562 | #endif |
55f26379 | 4563 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 4564 | } |
0aacf84e MD |
4565 | else if (SCM_COMPLEXP (y)) |
4566 | { | |
4567 | a = xx; | |
4568 | complex_div: /* y _must_ be a complex number */ | |
4569 | { | |
4570 | double r = SCM_COMPLEX_REAL (y); | |
4571 | double i = SCM_COMPLEX_IMAG (y); | |
4572 | if (r <= i) | |
4573 | { | |
4574 | double t = r / i; | |
4575 | double d = i * (1.0 + t * t); | |
8507ec80 | 4576 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
4577 | } |
4578 | else | |
4579 | { | |
4580 | double t = i / r; | |
4581 | double d = r * (1.0 + t * t); | |
8507ec80 | 4582 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
4583 | } |
4584 | } | |
4585 | } | |
f92e85f7 MV |
4586 | else if (SCM_FRACTIONP (y)) |
4587 | /* a / b/c = ac / b */ | |
cba42c93 | 4588 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4589 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4590 | else |
4591 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4592 | } |
0aacf84e MD |
4593 | else if (SCM_BIGP (x)) |
4594 | { | |
e11e83f3 | 4595 | if (SCM_I_INUMP (y)) |
0aacf84e | 4596 | { |
e11e83f3 | 4597 | long int yy = SCM_I_INUM (y); |
0aacf84e MD |
4598 | if (yy == 0) |
4599 | { | |
7351e207 | 4600 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4601 | scm_num_overflow (s_divide); |
7351e207 | 4602 | #else |
0aacf84e MD |
4603 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4604 | scm_remember_upto_here_1 (x); | |
4605 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 4606 | #endif |
0aacf84e MD |
4607 | } |
4608 | else if (yy == 1) | |
4609 | return x; | |
4610 | else | |
4611 | { | |
4612 | /* FIXME: HMM, what are the relative performance issues here? | |
4613 | We need to test. Is it faster on average to test | |
4614 | divisible_p, then perform whichever operation, or is it | |
4615 | faster to perform the integer div opportunistically and | |
4616 | switch to real if there's a remainder? For now we take the | |
4617 | middle ground: test, then if divisible, use the faster div | |
4618 | func. */ | |
4619 | ||
4620 | long abs_yy = yy < 0 ? -yy : yy; | |
4621 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); | |
4622 | ||
4623 | if (divisible_p) | |
4624 | { | |
4625 | SCM result = scm_i_mkbig (); | |
4626 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
4627 | scm_remember_upto_here_1 (x); | |
4628 | if (yy < 0) | |
4629 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4630 | return scm_i_normbig (result); | |
4631 | } | |
4632 | else | |
f92e85f7 MV |
4633 | { |
4634 | if (inexact) | |
55f26379 | 4635 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 4636 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4637 | } |
0aacf84e MD |
4638 | } |
4639 | } | |
4640 | else if (SCM_BIGP (y)) | |
4641 | { | |
4642 | int y_is_zero = (mpz_sgn (SCM_I_BIG_MPZ (y)) == 0); | |
4643 | if (y_is_zero) | |
4644 | { | |
ca46fb90 | 4645 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4646 | scm_num_overflow (s_divide); |
f872b822 | 4647 | #else |
0aacf84e MD |
4648 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4649 | scm_remember_upto_here_1 (x); | |
4650 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
f872b822 | 4651 | #endif |
0aacf84e MD |
4652 | } |
4653 | else | |
4654 | { | |
4655 | /* big_x / big_y */ | |
4656 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), | |
4657 | SCM_I_BIG_MPZ (y)); | |
4658 | if (divisible_p) | |
4659 | { | |
4660 | SCM result = scm_i_mkbig (); | |
4661 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
4662 | SCM_I_BIG_MPZ (x), | |
4663 | SCM_I_BIG_MPZ (y)); | |
4664 | scm_remember_upto_here_2 (x, y); | |
4665 | return scm_i_normbig (result); | |
4666 | } | |
4667 | else | |
4668 | { | |
f92e85f7 MV |
4669 | if (inexact) |
4670 | { | |
4671 | double dbx = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4672 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4673 | scm_remember_upto_here_2 (x, y); | |
55f26379 | 4674 | return scm_from_double (dbx / dby); |
f92e85f7 | 4675 | } |
cba42c93 | 4676 | else return scm_i_make_ratio (x, y); |
0aacf84e MD |
4677 | } |
4678 | } | |
4679 | } | |
4680 | else if (SCM_REALP (y)) | |
4681 | { | |
4682 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4683 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4684 | if (yy == 0.0) |
4685 | scm_num_overflow (s_divide); | |
4686 | else | |
7351e207 | 4687 | #endif |
55f26379 | 4688 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
4689 | } |
4690 | else if (SCM_COMPLEXP (y)) | |
4691 | { | |
4692 | a = scm_i_big2dbl (x); | |
4693 | goto complex_div; | |
4694 | } | |
f92e85f7 | 4695 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4696 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4697 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4698 | else |
4699 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4700 | } |
0aacf84e MD |
4701 | else if (SCM_REALP (x)) |
4702 | { | |
4703 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 4704 | if (SCM_I_INUMP (y)) |
0aacf84e | 4705 | { |
e11e83f3 | 4706 | long int yy = SCM_I_INUM (y); |
7351e207 | 4707 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4708 | if (yy == 0) |
4709 | scm_num_overflow (s_divide); | |
4710 | else | |
7351e207 | 4711 | #endif |
55f26379 | 4712 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
4713 | } |
4714 | else if (SCM_BIGP (y)) | |
4715 | { | |
4716 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4717 | scm_remember_upto_here_1 (y); | |
55f26379 | 4718 | return scm_from_double (rx / dby); |
0aacf84e MD |
4719 | } |
4720 | else if (SCM_REALP (y)) | |
4721 | { | |
4722 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4723 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4724 | if (yy == 0.0) |
4725 | scm_num_overflow (s_divide); | |
4726 | else | |
7351e207 | 4727 | #endif |
55f26379 | 4728 | return scm_from_double (rx / yy); |
0aacf84e MD |
4729 | } |
4730 | else if (SCM_COMPLEXP (y)) | |
4731 | { | |
4732 | a = rx; | |
4733 | goto complex_div; | |
4734 | } | |
f92e85f7 | 4735 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4736 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
4737 | else |
4738 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4739 | } |
0aacf84e MD |
4740 | else if (SCM_COMPLEXP (x)) |
4741 | { | |
4742 | double rx = SCM_COMPLEX_REAL (x); | |
4743 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 4744 | if (SCM_I_INUMP (y)) |
0aacf84e | 4745 | { |
e11e83f3 | 4746 | long int yy = SCM_I_INUM (y); |
7351e207 | 4747 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4748 | if (yy == 0) |
4749 | scm_num_overflow (s_divide); | |
4750 | else | |
7351e207 | 4751 | #endif |
0aacf84e MD |
4752 | { |
4753 | double d = yy; | |
8507ec80 | 4754 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
4755 | } |
4756 | } | |
4757 | else if (SCM_BIGP (y)) | |
4758 | { | |
4759 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4760 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4761 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
4762 | } |
4763 | else if (SCM_REALP (y)) | |
4764 | { | |
4765 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4766 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4767 | if (yy == 0.0) |
4768 | scm_num_overflow (s_divide); | |
4769 | else | |
7351e207 | 4770 | #endif |
8507ec80 | 4771 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
4772 | } |
4773 | else if (SCM_COMPLEXP (y)) | |
4774 | { | |
4775 | double ry = SCM_COMPLEX_REAL (y); | |
4776 | double iy = SCM_COMPLEX_IMAG (y); | |
4777 | if (ry <= iy) | |
4778 | { | |
4779 | double t = ry / iy; | |
4780 | double d = iy * (1.0 + t * t); | |
8507ec80 | 4781 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
4782 | } |
4783 | else | |
4784 | { | |
4785 | double t = iy / ry; | |
4786 | double d = ry * (1.0 + t * t); | |
8507ec80 | 4787 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
4788 | } |
4789 | } | |
f92e85f7 MV |
4790 | else if (SCM_FRACTIONP (y)) |
4791 | { | |
4792 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4793 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 4794 | } |
0aacf84e MD |
4795 | else |
4796 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4797 | } |
f92e85f7 MV |
4798 | else if (SCM_FRACTIONP (x)) |
4799 | { | |
e11e83f3 | 4800 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4801 | { |
e11e83f3 | 4802 | long int yy = SCM_I_INUM (y); |
f92e85f7 MV |
4803 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
4804 | if (yy == 0) | |
4805 | scm_num_overflow (s_divide); | |
4806 | else | |
4807 | #endif | |
cba42c93 | 4808 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4809 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4810 | } | |
4811 | else if (SCM_BIGP (y)) | |
4812 | { | |
cba42c93 | 4813 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4814 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4815 | } | |
4816 | else if (SCM_REALP (y)) | |
4817 | { | |
4818 | double yy = SCM_REAL_VALUE (y); | |
4819 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
4820 | if (yy == 0.0) | |
4821 | scm_num_overflow (s_divide); | |
4822 | else | |
4823 | #endif | |
55f26379 | 4824 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
4825 | } |
4826 | else if (SCM_COMPLEXP (y)) | |
4827 | { | |
4828 | a = scm_i_fraction2double (x); | |
4829 | goto complex_div; | |
4830 | } | |
4831 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 4832 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4833 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
4834 | else | |
4835 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
4836 | } | |
0aacf84e | 4837 | else |
f8de44c1 | 4838 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 4839 | } |
f92e85f7 MV |
4840 | |
4841 | SCM | |
4842 | scm_divide (SCM x, SCM y) | |
4843 | { | |
4844 | return scm_i_divide (x, y, 0); | |
4845 | } | |
4846 | ||
4847 | static SCM scm_divide2real (SCM x, SCM y) | |
4848 | { | |
4849 | return scm_i_divide (x, y, 1); | |
4850 | } | |
c05e97b7 | 4851 | #undef FUNC_NAME |
0f2d19dd | 4852 | |
fa605590 | 4853 | |
0f2d19dd | 4854 | double |
6e8d25a6 | 4855 | scm_asinh (double x) |
0f2d19dd | 4856 | { |
fa605590 KR |
4857 | #if HAVE_ASINH |
4858 | return asinh (x); | |
4859 | #else | |
4860 | #define asinh scm_asinh | |
f872b822 | 4861 | return log (x + sqrt (x * x + 1)); |
fa605590 | 4862 | #endif |
0f2d19dd | 4863 | } |
fa605590 KR |
4864 | SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_dsubr, (SCM (*)()) asinh, g_asinh); |
4865 | /* "Return the inverse hyperbolic sine of @var{x}." | |
4866 | */ | |
0f2d19dd JB |
4867 | |
4868 | ||
0f2d19dd | 4869 | double |
6e8d25a6 | 4870 | scm_acosh (double x) |
0f2d19dd | 4871 | { |
fa605590 KR |
4872 | #if HAVE_ACOSH |
4873 | return acosh (x); | |
4874 | #else | |
4875 | #define acosh scm_acosh | |
f872b822 | 4876 | return log (x + sqrt (x * x - 1)); |
fa605590 | 4877 | #endif |
0f2d19dd | 4878 | } |
fa605590 KR |
4879 | SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_dsubr, (SCM (*)()) acosh, g_acosh); |
4880 | /* "Return the inverse hyperbolic cosine of @var{x}." | |
4881 | */ | |
0f2d19dd JB |
4882 | |
4883 | ||
0f2d19dd | 4884 | double |
6e8d25a6 | 4885 | scm_atanh (double x) |
0f2d19dd | 4886 | { |
fa605590 KR |
4887 | #if HAVE_ATANH |
4888 | return atanh (x); | |
4889 | #else | |
4890 | #define atanh scm_atanh | |
f872b822 | 4891 | return 0.5 * log ((1 + x) / (1 - x)); |
fa605590 | 4892 | #endif |
0f2d19dd | 4893 | } |
fa605590 KR |
4894 | SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_dsubr, (SCM (*)()) atanh, g_atanh); |
4895 | /* "Return the inverse hyperbolic tangent of @var{x}." | |
4896 | */ | |
0f2d19dd JB |
4897 | |
4898 | ||
0f2d19dd | 4899 | double |
3101f40f | 4900 | scm_c_truncate (double x) |
0f2d19dd | 4901 | { |
fa605590 KR |
4902 | #if HAVE_TRUNC |
4903 | return trunc (x); | |
4904 | #else | |
f872b822 MD |
4905 | if (x < 0.0) |
4906 | return -floor (-x); | |
4907 | return floor (x); | |
fa605590 | 4908 | #endif |
0f2d19dd | 4909 | } |
0f2d19dd | 4910 | |
3101f40f MV |
4911 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
4912 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
4913 | Then half-way cases are identified and adjusted down if the | |
4914 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
4915 | |
4916 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
4917 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
4918 | ||
4919 | An odd "result" value is identified with result/2 != floor(result/2). | |
4920 | This is done with plus_half, since that value is ready for use sooner in | |
4921 | a pipelined cpu, and we're already requiring plus_half == result. | |
4922 | ||
4923 | Note however that we need to be careful when x is big and already an | |
4924 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
4925 | us to return such a value, incorrectly. For instance if the hardware is | |
4926 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
4927 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
4928 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
4929 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
4930 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
4931 | ||
4932 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
4933 | x is already an integer. If it is then clearly that's the desired result | |
4934 | already. And if it's not then the exponent must be small enough to allow | |
4935 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
4936 | ||
0f2d19dd | 4937 | double |
3101f40f | 4938 | scm_c_round (double x) |
0f2d19dd | 4939 | { |
6187f48b KR |
4940 | double plus_half, result; |
4941 | ||
4942 | if (x == floor (x)) | |
4943 | return x; | |
4944 | ||
4945 | plus_half = x + 0.5; | |
4946 | result = floor (plus_half); | |
3101f40f | 4947 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
4948 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
4949 | ? result - 1 | |
4950 | : result); | |
0f2d19dd JB |
4951 | } |
4952 | ||
f92e85f7 MV |
4953 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
4954 | (SCM x), | |
4955 | "Round the number @var{x} towards zero.") | |
4956 | #define FUNC_NAME s_scm_truncate_number | |
4957 | { | |
73e4de09 | 4958 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
4959 | return scm_floor (x); |
4960 | else | |
4961 | return scm_ceiling (x); | |
4962 | } | |
4963 | #undef FUNC_NAME | |
4964 | ||
4965 | static SCM exactly_one_half; | |
4966 | ||
4967 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, | |
4968 | (SCM x), | |
4969 | "Round the number @var{x} towards the nearest integer. " | |
4970 | "When it is exactly halfway between two integers, " | |
4971 | "round towards the even one.") | |
4972 | #define FUNC_NAME s_scm_round_number | |
4973 | { | |
e11e83f3 | 4974 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
4975 | return x; |
4976 | else if (SCM_REALP (x)) | |
3101f40f | 4977 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 4978 | else |
bae30667 KR |
4979 | { |
4980 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
4981 | single quotient+remainder division then examining to see which way | |
4982 | the rounding should go. */ | |
4983 | SCM plus_half = scm_sum (x, exactly_one_half); | |
4984 | SCM result = scm_floor (plus_half); | |
3101f40f | 4985 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
4986 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
4987 | && scm_is_true (scm_odd_p (result))) | |
d956fa6f | 4988 | return scm_difference (result, SCM_I_MAKINUM (1)); |
bae30667 KR |
4989 | else |
4990 | return result; | |
4991 | } | |
f92e85f7 MV |
4992 | } |
4993 | #undef FUNC_NAME | |
4994 | ||
4995 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
4996 | (SCM x), | |
4997 | "Round the number @var{x} towards minus infinity.") | |
4998 | #define FUNC_NAME s_scm_floor | |
4999 | { | |
e11e83f3 | 5000 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5001 | return x; |
5002 | else if (SCM_REALP (x)) | |
55f26379 | 5003 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5004 | else if (SCM_FRACTIONP (x)) |
5005 | { | |
5006 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5007 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5008 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5009 | { |
5010 | /* For positive x, rounding towards zero is correct. */ | |
5011 | return q; | |
5012 | } | |
5013 | else | |
5014 | { | |
5015 | /* For negative x, we need to return q-1 unless x is an | |
5016 | integer. But fractions are never integer, per our | |
5017 | assumptions. */ | |
d956fa6f | 5018 | return scm_difference (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5019 | } |
5020 | } | |
5021 | else | |
5022 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
5023 | } | |
5024 | #undef FUNC_NAME | |
5025 | ||
5026 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
5027 | (SCM x), | |
5028 | "Round the number @var{x} towards infinity.") | |
5029 | #define FUNC_NAME s_scm_ceiling | |
5030 | { | |
e11e83f3 | 5031 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5032 | return x; |
5033 | else if (SCM_REALP (x)) | |
55f26379 | 5034 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5035 | else if (SCM_FRACTIONP (x)) |
5036 | { | |
5037 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5038 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5039 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
5040 | { |
5041 | /* For negative x, rounding towards zero is correct. */ | |
5042 | return q; | |
5043 | } | |
5044 | else | |
5045 | { | |
5046 | /* For positive x, we need to return q+1 unless x is an | |
5047 | integer. But fractions are never integer, per our | |
5048 | assumptions. */ | |
d956fa6f | 5049 | return scm_sum (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5050 | } |
5051 | } | |
5052 | else | |
5053 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
5054 | } | |
5055 | #undef FUNC_NAME | |
0f2d19dd | 5056 | |
14b18ed6 | 5057 | SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_dsubr, (SCM (*)()) sqrt, g_i_sqrt); |
942e5b91 MG |
5058 | /* "Return the square root of the real number @var{x}." |
5059 | */ | |
14b18ed6 | 5060 | SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_dsubr, (SCM (*)()) fabs, g_i_abs); |
942e5b91 MG |
5061 | /* "Return the absolute value of the real number @var{x}." |
5062 | */ | |
14b18ed6 | 5063 | SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_dsubr, (SCM (*)()) exp, g_i_exp); |
942e5b91 MG |
5064 | /* "Return the @var{x}th power of e." |
5065 | */ | |
14b18ed6 | 5066 | SCM_GPROC1 (s_i_log, "$log", scm_tc7_dsubr, (SCM (*)()) log, g_i_log); |
b3fcac34 | 5067 | /* "Return the natural logarithm of the real number @var{x}." |
942e5b91 | 5068 | */ |
14b18ed6 | 5069 | SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_dsubr, (SCM (*)()) sin, g_i_sin); |
942e5b91 MG |
5070 | /* "Return the sine of the real number @var{x}." |
5071 | */ | |
14b18ed6 | 5072 | SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_dsubr, (SCM (*)()) cos, g_i_cos); |
942e5b91 MG |
5073 | /* "Return the cosine of the real number @var{x}." |
5074 | */ | |
14b18ed6 | 5075 | SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_dsubr, (SCM (*)()) tan, g_i_tan); |
942e5b91 MG |
5076 | /* "Return the tangent of the real number @var{x}." |
5077 | */ | |
14b18ed6 | 5078 | SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_dsubr, (SCM (*)()) asin, g_i_asin); |
942e5b91 MG |
5079 | /* "Return the arc sine of the real number @var{x}." |
5080 | */ | |
14b18ed6 | 5081 | SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_dsubr, (SCM (*)()) acos, g_i_acos); |
942e5b91 MG |
5082 | /* "Return the arc cosine of the real number @var{x}." |
5083 | */ | |
14b18ed6 | 5084 | SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_dsubr, (SCM (*)()) atan, g_i_atan); |
942e5b91 MG |
5085 | /* "Return the arc tangent of the real number @var{x}." |
5086 | */ | |
14b18ed6 | 5087 | SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_dsubr, (SCM (*)()) sinh, g_i_sinh); |
942e5b91 MG |
5088 | /* "Return the hyperbolic sine of the real number @var{x}." |
5089 | */ | |
14b18ed6 | 5090 | SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_dsubr, (SCM (*)()) cosh, g_i_cosh); |
942e5b91 MG |
5091 | /* "Return the hyperbolic cosine of the real number @var{x}." |
5092 | */ | |
14b18ed6 | 5093 | SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_dsubr, (SCM (*)()) tanh, g_i_tanh); |
942e5b91 MG |
5094 | /* "Return the hyperbolic tangent of the real number @var{x}." |
5095 | */ | |
f872b822 MD |
5096 | |
5097 | struct dpair | |
5098 | { | |
5099 | double x, y; | |
5100 | }; | |
5101 | ||
27c37006 NJ |
5102 | static void scm_two_doubles (SCM x, |
5103 | SCM y, | |
3eeba8d4 JB |
5104 | const char *sstring, |
5105 | struct dpair * xy); | |
f872b822 MD |
5106 | |
5107 | static void | |
27c37006 NJ |
5108 | scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy) |
5109 | { | |
e11e83f3 MV |
5110 | if (SCM_I_INUMP (x)) |
5111 | xy->x = SCM_I_INUM (x); | |
0aacf84e | 5112 | else if (SCM_BIGP (x)) |
1be6b49c | 5113 | xy->x = scm_i_big2dbl (x); |
0aacf84e | 5114 | else if (SCM_REALP (x)) |
27c37006 | 5115 | xy->x = SCM_REAL_VALUE (x); |
f92e85f7 MV |
5116 | else if (SCM_FRACTIONP (x)) |
5117 | xy->x = scm_i_fraction2double (x); | |
0aacf84e | 5118 | else |
27c37006 | 5119 | scm_wrong_type_arg (sstring, SCM_ARG1, x); |
98cb6e75 | 5120 | |
e11e83f3 MV |
5121 | if (SCM_I_INUMP (y)) |
5122 | xy->y = SCM_I_INUM (y); | |
0aacf84e | 5123 | else if (SCM_BIGP (y)) |
1be6b49c | 5124 | xy->y = scm_i_big2dbl (y); |
0aacf84e | 5125 | else if (SCM_REALP (y)) |
27c37006 | 5126 | xy->y = SCM_REAL_VALUE (y); |
f92e85f7 MV |
5127 | else if (SCM_FRACTIONP (y)) |
5128 | xy->y = scm_i_fraction2double (y); | |
0aacf84e | 5129 | else |
27c37006 | 5130 | scm_wrong_type_arg (sstring, SCM_ARG2, y); |
0f2d19dd JB |
5131 | } |
5132 | ||
5133 | ||
a1ec6916 | 5134 | SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0, |
27c37006 NJ |
5135 | (SCM x, SCM y), |
5136 | "Return @var{x} raised to the power of @var{y}. This\n" | |
0137a31b | 5137 | "procedure does not accept complex arguments.") |
1bbd0b84 | 5138 | #define FUNC_NAME s_scm_sys_expt |
0f2d19dd JB |
5139 | { |
5140 | struct dpair xy; | |
27c37006 | 5141 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5142 | return scm_from_double (pow (xy.x, xy.y)); |
0f2d19dd | 5143 | } |
1bbd0b84 | 5144 | #undef FUNC_NAME |
0f2d19dd JB |
5145 | |
5146 | ||
a1ec6916 | 5147 | SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0, |
27c37006 NJ |
5148 | (SCM x, SCM y), |
5149 | "Return the arc tangent of the two arguments @var{x} and\n" | |
5150 | "@var{y}. This is similar to calculating the arc tangent of\n" | |
5151 | "@var{x} / @var{y}, except that the signs of both arguments\n" | |
0137a31b MG |
5152 | "are used to determine the quadrant of the result. This\n" |
5153 | "procedure does not accept complex arguments.") | |
1bbd0b84 | 5154 | #define FUNC_NAME s_scm_sys_atan2 |
0f2d19dd JB |
5155 | { |
5156 | struct dpair xy; | |
27c37006 | 5157 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5158 | return scm_from_double (atan2 (xy.x, xy.y)); |
0f2d19dd | 5159 | } |
1bbd0b84 | 5160 | #undef FUNC_NAME |
0f2d19dd | 5161 | |
8507ec80 MV |
5162 | SCM |
5163 | scm_c_make_rectangular (double re, double im) | |
5164 | { | |
5165 | if (im == 0.0) | |
5166 | return scm_from_double (re); | |
5167 | else | |
5168 | { | |
5169 | SCM z; | |
5170 | SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (sizeof (scm_t_complex), | |
5171 | "complex")); | |
5172 | SCM_COMPLEX_REAL (z) = re; | |
5173 | SCM_COMPLEX_IMAG (z) = im; | |
5174 | return z; | |
5175 | } | |
5176 | } | |
0f2d19dd | 5177 | |
a1ec6916 | 5178 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
bb628794 | 5179 | (SCM real, SCM imaginary), |
942e5b91 MG |
5180 | "Return a complex number constructed of the given @var{real} and\n" |
5181 | "@var{imaginary} parts.") | |
1bbd0b84 | 5182 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd JB |
5183 | { |
5184 | struct dpair xy; | |
bb628794 | 5185 | scm_two_doubles (real, imaginary, FUNC_NAME, &xy); |
8507ec80 | 5186 | return scm_c_make_rectangular (xy.x, xy.y); |
0f2d19dd | 5187 | } |
1bbd0b84 | 5188 | #undef FUNC_NAME |
0f2d19dd | 5189 | |
8507ec80 MV |
5190 | SCM |
5191 | scm_c_make_polar (double mag, double ang) | |
5192 | { | |
5193 | double s, c; | |
5194 | #if HAVE_SINCOS | |
5195 | sincos (ang, &s, &c); | |
5196 | #else | |
5197 | s = sin (ang); | |
5198 | c = cos (ang); | |
5199 | #endif | |
5200 | return scm_c_make_rectangular (mag * c, mag * s); | |
5201 | } | |
0f2d19dd | 5202 | |
a1ec6916 | 5203 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 5204 | (SCM x, SCM y), |
942e5b91 | 5205 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 5206 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd JB |
5207 | { |
5208 | struct dpair xy; | |
27c37006 | 5209 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
8507ec80 | 5210 | return scm_c_make_polar (xy.x, xy.y); |
0f2d19dd | 5211 | } |
1bbd0b84 | 5212 | #undef FUNC_NAME |
0f2d19dd JB |
5213 | |
5214 | ||
152f82bf | 5215 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
5216 | /* "Return the real part of the number @var{z}." |
5217 | */ | |
0f2d19dd | 5218 | SCM |
6e8d25a6 | 5219 | scm_real_part (SCM z) |
0f2d19dd | 5220 | { |
e11e83f3 | 5221 | if (SCM_I_INUMP (z)) |
c2ff8ab0 | 5222 | return z; |
0aacf84e | 5223 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5224 | return z; |
0aacf84e | 5225 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5226 | return z; |
0aacf84e | 5227 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5228 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
f92e85f7 | 5229 | else if (SCM_FRACTIONP (z)) |
2fa2d879 | 5230 | return z; |
0aacf84e | 5231 | else |
c2ff8ab0 | 5232 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); |
0f2d19dd JB |
5233 | } |
5234 | ||
5235 | ||
152f82bf | 5236 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
5237 | /* "Return the imaginary part of the number @var{z}." |
5238 | */ | |
0f2d19dd | 5239 | SCM |
6e8d25a6 | 5240 | scm_imag_part (SCM z) |
0f2d19dd | 5241 | { |
e11e83f3 | 5242 | if (SCM_I_INUMP (z)) |
f872b822 | 5243 | return SCM_INUM0; |
0aacf84e | 5244 | else if (SCM_BIGP (z)) |
f872b822 | 5245 | return SCM_INUM0; |
0aacf84e | 5246 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5247 | return scm_flo0; |
0aacf84e | 5248 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5249 | return scm_from_double (SCM_COMPLEX_IMAG (z)); |
f92e85f7 MV |
5250 | else if (SCM_FRACTIONP (z)) |
5251 | return SCM_INUM0; | |
0aacf84e | 5252 | else |
c2ff8ab0 | 5253 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); |
0f2d19dd JB |
5254 | } |
5255 | ||
f92e85f7 MV |
5256 | SCM_GPROC (s_numerator, "numerator", 1, 0, 0, scm_numerator, g_numerator); |
5257 | /* "Return the numerator of the number @var{z}." | |
5258 | */ | |
5259 | SCM | |
5260 | scm_numerator (SCM z) | |
5261 | { | |
e11e83f3 | 5262 | if (SCM_I_INUMP (z)) |
f92e85f7 MV |
5263 | return z; |
5264 | else if (SCM_BIGP (z)) | |
5265 | return z; | |
5266 | else if (SCM_FRACTIONP (z)) | |
5267 | { | |
5268 | scm_i_fraction_reduce (z); | |
5269 | return SCM_FRACTION_NUMERATOR (z); | |
5270 | } | |
5271 | else if (SCM_REALP (z)) | |
5272 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
5273 | else | |
5274 | SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator); | |
5275 | } | |
5276 | ||
5277 | ||
5278 | SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator); | |
5279 | /* "Return the denominator of the number @var{z}." | |
5280 | */ | |
5281 | SCM | |
5282 | scm_denominator (SCM z) | |
5283 | { | |
e11e83f3 | 5284 | if (SCM_I_INUMP (z)) |
d956fa6f | 5285 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5286 | else if (SCM_BIGP (z)) |
d956fa6f | 5287 | return SCM_I_MAKINUM (1); |
f92e85f7 MV |
5288 | else if (SCM_FRACTIONP (z)) |
5289 | { | |
5290 | scm_i_fraction_reduce (z); | |
5291 | return SCM_FRACTION_DENOMINATOR (z); | |
5292 | } | |
5293 | else if (SCM_REALP (z)) | |
5294 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
5295 | else | |
5296 | SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator); | |
5297 | } | |
0f2d19dd | 5298 | |
9de33deb | 5299 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
5300 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
5301 | * "@code{abs} for real arguments, but also allows complex numbers." | |
5302 | */ | |
0f2d19dd | 5303 | SCM |
6e8d25a6 | 5304 | scm_magnitude (SCM z) |
0f2d19dd | 5305 | { |
e11e83f3 | 5306 | if (SCM_I_INUMP (z)) |
0aacf84e | 5307 | { |
e11e83f3 | 5308 | long int zz = SCM_I_INUM (z); |
0aacf84e MD |
5309 | if (zz >= 0) |
5310 | return z; | |
5311 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 5312 | return SCM_I_MAKINUM (-zz); |
0aacf84e MD |
5313 | else |
5314 | return scm_i_long2big (-zz); | |
5986c47d | 5315 | } |
0aacf84e MD |
5316 | else if (SCM_BIGP (z)) |
5317 | { | |
5318 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5319 | scm_remember_upto_here_1 (z); | |
5320 | if (sgn < 0) | |
5321 | return scm_i_clonebig (z, 0); | |
5322 | else | |
5323 | return z; | |
5986c47d | 5324 | } |
0aacf84e | 5325 | else if (SCM_REALP (z)) |
55f26379 | 5326 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 5327 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5328 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
5329 | else if (SCM_FRACTIONP (z)) |
5330 | { | |
73e4de09 | 5331 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5332 | return z; |
cba42c93 | 5333 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
5334 | SCM_FRACTION_DENOMINATOR (z)); |
5335 | } | |
0aacf84e | 5336 | else |
c2ff8ab0 | 5337 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); |
0f2d19dd JB |
5338 | } |
5339 | ||
5340 | ||
9de33deb | 5341 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
5342 | /* "Return the angle of the complex number @var{z}." |
5343 | */ | |
0f2d19dd | 5344 | SCM |
6e8d25a6 | 5345 | scm_angle (SCM z) |
0f2d19dd | 5346 | { |
c8ae173e | 5347 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
55f26379 | 5348 | scm_flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
5349 | But if atan2 follows the floating point rounding mode, then the value |
5350 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 5351 | if (SCM_I_INUMP (z)) |
0aacf84e | 5352 | { |
e11e83f3 | 5353 | if (SCM_I_INUM (z) >= 0) |
c8ae173e | 5354 | return scm_flo0; |
0aacf84e | 5355 | else |
55f26379 | 5356 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 5357 | } |
0aacf84e MD |
5358 | else if (SCM_BIGP (z)) |
5359 | { | |
5360 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5361 | scm_remember_upto_here_1 (z); | |
5362 | if (sgn < 0) | |
55f26379 | 5363 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 5364 | else |
c8ae173e | 5365 | return scm_flo0; |
0f2d19dd | 5366 | } |
0aacf84e | 5367 | else if (SCM_REALP (z)) |
c8ae173e KR |
5368 | { |
5369 | if (SCM_REAL_VALUE (z) >= 0) | |
5370 | return scm_flo0; | |
5371 | else | |
55f26379 | 5372 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 5373 | } |
0aacf84e | 5374 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5375 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
5376 | else if (SCM_FRACTIONP (z)) |
5377 | { | |
73e4de09 | 5378 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5379 | return scm_flo0; |
55f26379 | 5380 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 5381 | } |
0aacf84e | 5382 | else |
f4c627b3 | 5383 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); |
0f2d19dd JB |
5384 | } |
5385 | ||
5386 | ||
3c9a524f DH |
5387 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
5388 | /* Convert the number @var{x} to its inexact representation.\n" | |
5389 | */ | |
5390 | SCM | |
5391 | scm_exact_to_inexact (SCM z) | |
5392 | { | |
e11e83f3 | 5393 | if (SCM_I_INUMP (z)) |
55f26379 | 5394 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 5395 | else if (SCM_BIGP (z)) |
55f26379 | 5396 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 5397 | else if (SCM_FRACTIONP (z)) |
55f26379 | 5398 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
5399 | else if (SCM_INEXACTP (z)) |
5400 | return z; | |
5401 | else | |
5402 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
5403 | } | |
5404 | ||
5405 | ||
a1ec6916 | 5406 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 5407 | (SCM z), |
1e6808ea | 5408 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 5409 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 5410 | { |
e11e83f3 | 5411 | if (SCM_I_INUMP (z)) |
f872b822 | 5412 | return z; |
0aacf84e | 5413 | else if (SCM_BIGP (z)) |
f872b822 | 5414 | return z; |
0aacf84e MD |
5415 | else if (SCM_REALP (z)) |
5416 | { | |
f92e85f7 MV |
5417 | if (xisinf (SCM_REAL_VALUE (z)) || xisnan (SCM_REAL_VALUE (z))) |
5418 | SCM_OUT_OF_RANGE (1, z); | |
2be24db4 | 5419 | else |
f92e85f7 MV |
5420 | { |
5421 | mpq_t frac; | |
5422 | SCM q; | |
5423 | ||
5424 | mpq_init (frac); | |
5425 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 5426 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
5427 | scm_i_mpz2num (mpq_denref (frac))); |
5428 | ||
cba42c93 | 5429 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
5430 | for frac... |
5431 | */ | |
5432 | mpq_clear (frac); | |
5433 | return q; | |
5434 | } | |
c2ff8ab0 | 5435 | } |
f92e85f7 MV |
5436 | else if (SCM_FRACTIONP (z)) |
5437 | return z; | |
0aacf84e | 5438 | else |
c2ff8ab0 | 5439 | SCM_WRONG_TYPE_ARG (1, z); |
0f2d19dd | 5440 | } |
1bbd0b84 | 5441 | #undef FUNC_NAME |
0f2d19dd | 5442 | |
f92e85f7 MV |
5443 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
5444 | (SCM x, SCM err), | |
5445 | "Return an exact number that is within @var{err} of @var{x}.") | |
5446 | #define FUNC_NAME s_scm_rationalize | |
5447 | { | |
e11e83f3 | 5448 | if (SCM_I_INUMP (x)) |
f92e85f7 MV |
5449 | return x; |
5450 | else if (SCM_BIGP (x)) | |
5451 | return x; | |
5452 | else if ((SCM_REALP (x)) || SCM_FRACTIONP (x)) | |
5453 | { | |
5454 | /* Use continued fractions to find closest ratio. All | |
5455 | arithmetic is done with exact numbers. | |
5456 | */ | |
5457 | ||
5458 | SCM ex = scm_inexact_to_exact (x); | |
5459 | SCM int_part = scm_floor (ex); | |
d956fa6f MV |
5460 | SCM tt = SCM_I_MAKINUM (1); |
5461 | SCM a1 = SCM_I_MAKINUM (0), a2 = SCM_I_MAKINUM (1), a = SCM_I_MAKINUM (0); | |
5462 | SCM b1 = SCM_I_MAKINUM (1), b2 = SCM_I_MAKINUM (0), b = SCM_I_MAKINUM (0); | |
f92e85f7 MV |
5463 | SCM rx; |
5464 | int i = 0; | |
5465 | ||
73e4de09 | 5466 | if (scm_is_true (scm_num_eq_p (ex, int_part))) |
f92e85f7 MV |
5467 | return ex; |
5468 | ||
5469 | ex = scm_difference (ex, int_part); /* x = x-int_part */ | |
5470 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
5471 | ||
5472 | /* We stop after a million iterations just to be absolutely sure | |
5473 | that we don't go into an infinite loop. The process normally | |
5474 | converges after less than a dozen iterations. | |
5475 | */ | |
5476 | ||
5477 | err = scm_abs (err); | |
5478 | while (++i < 1000000) | |
5479 | { | |
5480 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
5481 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
5482 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
5483 | scm_is_false | |
f92e85f7 MV |
5484 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
5485 | err))) /* abs(x-a/b) <= err */ | |
02164269 MV |
5486 | { |
5487 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
73e4de09 MV |
5488 | if (scm_is_false (scm_exact_p (x)) |
5489 | || scm_is_false (scm_exact_p (err))) | |
02164269 MV |
5490 | return scm_exact_to_inexact (res); |
5491 | else | |
5492 | return res; | |
5493 | } | |
f92e85f7 MV |
5494 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
5495 | SCM_UNDEFINED); | |
5496 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
5497 | a2 = a1; | |
5498 | b2 = b1; | |
5499 | a1 = a; | |
5500 | b1 = b; | |
5501 | } | |
5502 | scm_num_overflow (s_scm_rationalize); | |
5503 | } | |
5504 | else | |
5505 | SCM_WRONG_TYPE_ARG (1, x); | |
5506 | } | |
5507 | #undef FUNC_NAME | |
5508 | ||
73e4de09 MV |
5509 | /* conversion functions */ |
5510 | ||
5511 | int | |
5512 | scm_is_integer (SCM val) | |
5513 | { | |
5514 | return scm_is_true (scm_integer_p (val)); | |
5515 | } | |
5516 | ||
5517 | int | |
5518 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
5519 | { | |
e11e83f3 | 5520 | if (SCM_I_INUMP (val)) |
73e4de09 | 5521 | { |
e11e83f3 | 5522 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5523 | return n >= min && n <= max; |
5524 | } | |
5525 | else if (SCM_BIGP (val)) | |
5526 | { | |
5527 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
5528 | return 0; | |
5529 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
5530 | { |
5531 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
5532 | { | |
5533 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
5534 | return n >= min && n <= max; | |
5535 | } | |
5536 | else | |
5537 | return 0; | |
5538 | } | |
73e4de09 MV |
5539 | else |
5540 | { | |
d956fa6f MV |
5541 | scm_t_intmax n; |
5542 | size_t count; | |
73e4de09 | 5543 | |
d956fa6f MV |
5544 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5545 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
5546 | return 0; | |
5547 | ||
5548 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5549 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5550 | |
d956fa6f | 5551 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 5552 | { |
d956fa6f MV |
5553 | if (n < 0) |
5554 | return 0; | |
73e4de09 | 5555 | } |
73e4de09 MV |
5556 | else |
5557 | { | |
d956fa6f MV |
5558 | n = -n; |
5559 | if (n >= 0) | |
5560 | return 0; | |
73e4de09 | 5561 | } |
d956fa6f MV |
5562 | |
5563 | return n >= min && n <= max; | |
73e4de09 MV |
5564 | } |
5565 | } | |
73e4de09 MV |
5566 | else |
5567 | return 0; | |
5568 | } | |
5569 | ||
5570 | int | |
5571 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
5572 | { | |
e11e83f3 | 5573 | if (SCM_I_INUMP (val)) |
73e4de09 | 5574 | { |
e11e83f3 | 5575 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5576 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
5577 | } | |
5578 | else if (SCM_BIGP (val)) | |
5579 | { | |
5580 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
5581 | return 0; | |
5582 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
5583 | { |
5584 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
5585 | { | |
5586 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
5587 | return n >= min && n <= max; | |
5588 | } | |
5589 | else | |
5590 | return 0; | |
5591 | } | |
73e4de09 MV |
5592 | else |
5593 | { | |
d956fa6f MV |
5594 | scm_t_uintmax n; |
5595 | size_t count; | |
73e4de09 | 5596 | |
d956fa6f MV |
5597 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
5598 | return 0; | |
73e4de09 | 5599 | |
d956fa6f MV |
5600 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5601 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 5602 | return 0; |
d956fa6f MV |
5603 | |
5604 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5605 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5606 | |
d956fa6f | 5607 | return n >= min && n <= max; |
73e4de09 MV |
5608 | } |
5609 | } | |
73e4de09 MV |
5610 | else |
5611 | return 0; | |
5612 | } | |
5613 | ||
bfd7932e MV |
5614 | #define TYPE scm_t_intmax |
5615 | #define TYPE_MIN min | |
5616 | #define TYPE_MAX max | |
5617 | #define SIZEOF_TYPE 0 | |
5618 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
5619 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
5620 | #include "libguile/conv-integer.i.c" | |
5621 | ||
5622 | #define TYPE scm_t_uintmax | |
5623 | #define TYPE_MIN min | |
5624 | #define TYPE_MAX max | |
5625 | #define SIZEOF_TYPE 0 | |
5626 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
5627 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
5628 | #include "libguile/conv-uinteger.i.c" | |
5629 | ||
5630 | #define TYPE scm_t_int8 | |
5631 | #define TYPE_MIN SCM_T_INT8_MIN | |
5632 | #define TYPE_MAX SCM_T_INT8_MAX | |
5633 | #define SIZEOF_TYPE 1 | |
5634 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
5635 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
5636 | #include "libguile/conv-integer.i.c" | |
5637 | ||
5638 | #define TYPE scm_t_uint8 | |
5639 | #define TYPE_MIN 0 | |
5640 | #define TYPE_MAX SCM_T_UINT8_MAX | |
5641 | #define SIZEOF_TYPE 1 | |
5642 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
5643 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
5644 | #include "libguile/conv-uinteger.i.c" | |
5645 | ||
5646 | #define TYPE scm_t_int16 | |
5647 | #define TYPE_MIN SCM_T_INT16_MIN | |
5648 | #define TYPE_MAX SCM_T_INT16_MAX | |
5649 | #define SIZEOF_TYPE 2 | |
5650 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
5651 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
5652 | #include "libguile/conv-integer.i.c" | |
5653 | ||
5654 | #define TYPE scm_t_uint16 | |
5655 | #define TYPE_MIN 0 | |
5656 | #define TYPE_MAX SCM_T_UINT16_MAX | |
5657 | #define SIZEOF_TYPE 2 | |
5658 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
5659 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
5660 | #include "libguile/conv-uinteger.i.c" | |
5661 | ||
5662 | #define TYPE scm_t_int32 | |
5663 | #define TYPE_MIN SCM_T_INT32_MIN | |
5664 | #define TYPE_MAX SCM_T_INT32_MAX | |
5665 | #define SIZEOF_TYPE 4 | |
5666 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
5667 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
5668 | #include "libguile/conv-integer.i.c" | |
5669 | ||
5670 | #define TYPE scm_t_uint32 | |
5671 | #define TYPE_MIN 0 | |
5672 | #define TYPE_MAX SCM_T_UINT32_MAX | |
5673 | #define SIZEOF_TYPE 4 | |
5674 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
5675 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
5676 | #include "libguile/conv-uinteger.i.c" | |
5677 | ||
5678 | #if SCM_HAVE_T_INT64 | |
5679 | ||
5680 | #define TYPE scm_t_int64 | |
5681 | #define TYPE_MIN SCM_T_INT64_MIN | |
5682 | #define TYPE_MAX SCM_T_INT64_MAX | |
5683 | #define SIZEOF_TYPE 8 | |
5684 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
5685 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
5686 | #include "libguile/conv-integer.i.c" | |
5687 | ||
5688 | #define TYPE scm_t_uint64 | |
5689 | #define TYPE_MIN 0 | |
5690 | #define TYPE_MAX SCM_T_UINT64_MAX | |
5691 | #define SIZEOF_TYPE 8 | |
5692 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
5693 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
5694 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 5695 | |
bfd7932e | 5696 | #endif |
73e4de09 MV |
5697 | |
5698 | int | |
5699 | scm_is_real (SCM val) | |
5700 | { | |
5701 | return scm_is_true (scm_real_p (val)); | |
5702 | } | |
5703 | ||
55f26379 MV |
5704 | int |
5705 | scm_is_rational (SCM val) | |
5706 | { | |
5707 | return scm_is_true (scm_rational_p (val)); | |
5708 | } | |
5709 | ||
73e4de09 MV |
5710 | double |
5711 | scm_to_double (SCM val) | |
5712 | { | |
55f26379 MV |
5713 | if (SCM_I_INUMP (val)) |
5714 | return SCM_I_INUM (val); | |
5715 | else if (SCM_BIGP (val)) | |
5716 | return scm_i_big2dbl (val); | |
5717 | else if (SCM_FRACTIONP (val)) | |
5718 | return scm_i_fraction2double (val); | |
5719 | else if (SCM_REALP (val)) | |
5720 | return SCM_REAL_VALUE (val); | |
5721 | else | |
5722 | scm_wrong_type_arg (NULL, 0, val); | |
73e4de09 MV |
5723 | } |
5724 | ||
5725 | SCM | |
5726 | scm_from_double (double val) | |
5727 | { | |
55f26379 MV |
5728 | SCM z = scm_double_cell (scm_tc16_real, 0, 0, 0); |
5729 | SCM_REAL_VALUE (z) = val; | |
5730 | return z; | |
73e4de09 MV |
5731 | } |
5732 | ||
55f26379 MV |
5733 | #if SCM_ENABLE_DISCOURAGED == 1 |
5734 | ||
5735 | float | |
5736 | scm_num2float (SCM num, unsigned long int pos, const char *s_caller) | |
5737 | { | |
5738 | if (SCM_BIGP (num)) | |
5739 | { | |
5740 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5741 | if (!xisinf (res)) | |
5742 | return res; | |
5743 | else | |
5744 | scm_out_of_range (NULL, num); | |
5745 | } | |
5746 | else | |
5747 | return scm_to_double (num); | |
5748 | } | |
5749 | ||
5750 | double | |
5751 | scm_num2double (SCM num, unsigned long int pos, const char *s_caller) | |
5752 | { | |
5753 | if (SCM_BIGP (num)) | |
5754 | { | |
5755 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5756 | if (!xisinf (res)) | |
5757 | return res; | |
5758 | else | |
5759 | scm_out_of_range (NULL, num); | |
5760 | } | |
5761 | else | |
5762 | return scm_to_double (num); | |
5763 | } | |
5764 | ||
5765 | #endif | |
5766 | ||
8507ec80 MV |
5767 | int |
5768 | scm_is_complex (SCM val) | |
5769 | { | |
5770 | return scm_is_true (scm_complex_p (val)); | |
5771 | } | |
5772 | ||
5773 | double | |
5774 | scm_c_real_part (SCM z) | |
5775 | { | |
5776 | if (SCM_COMPLEXP (z)) | |
5777 | return SCM_COMPLEX_REAL (z); | |
5778 | else | |
5779 | { | |
5780 | /* Use the scm_real_part to get proper error checking and | |
5781 | dispatching. | |
5782 | */ | |
5783 | return scm_to_double (scm_real_part (z)); | |
5784 | } | |
5785 | } | |
5786 | ||
5787 | double | |
5788 | scm_c_imag_part (SCM z) | |
5789 | { | |
5790 | if (SCM_COMPLEXP (z)) | |
5791 | return SCM_COMPLEX_IMAG (z); | |
5792 | else | |
5793 | { | |
5794 | /* Use the scm_imag_part to get proper error checking and | |
5795 | dispatching. The result will almost always be 0.0, but not | |
5796 | always. | |
5797 | */ | |
5798 | return scm_to_double (scm_imag_part (z)); | |
5799 | } | |
5800 | } | |
5801 | ||
5802 | double | |
5803 | scm_c_magnitude (SCM z) | |
5804 | { | |
5805 | return scm_to_double (scm_magnitude (z)); | |
5806 | } | |
5807 | ||
5808 | double | |
5809 | scm_c_angle (SCM z) | |
5810 | { | |
5811 | return scm_to_double (scm_angle (z)); | |
5812 | } | |
5813 | ||
5814 | int | |
5815 | scm_is_number (SCM z) | |
5816 | { | |
5817 | return scm_is_true (scm_number_p (z)); | |
5818 | } | |
5819 | ||
0f2d19dd JB |
5820 | void |
5821 | scm_init_numbers () | |
0f2d19dd | 5822 | { |
0b799eea MV |
5823 | int i; |
5824 | ||
713a4259 KR |
5825 | mpz_init_set_si (z_negative_one, -1); |
5826 | ||
a261c0e9 DH |
5827 | /* It may be possible to tune the performance of some algorithms by using |
5828 | * the following constants to avoid the creation of bignums. Please, before | |
5829 | * using these values, remember the two rules of program optimization: | |
5830 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 5831 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 5832 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 5833 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 5834 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 5835 | |
f3ae5d60 MD |
5836 | scm_add_feature ("complex"); |
5837 | scm_add_feature ("inexact"); | |
55f26379 | 5838 | scm_flo0 = scm_from_double (0.0); |
0b799eea MV |
5839 | |
5840 | /* determine floating point precision */ | |
55f26379 | 5841 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
5842 | { |
5843 | init_dblprec(&scm_dblprec[i-2],i); | |
5844 | init_fx_radix(fx_per_radix[i-2],i); | |
5845 | } | |
f872b822 | 5846 | #ifdef DBL_DIG |
0b799eea MV |
5847 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
5848 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; | |
5849 | #endif | |
1be6b49c ML |
5850 | |
5851 | #ifdef GUILE_DEBUG | |
5852 | check_sanity (); | |
5853 | #endif | |
f92e85f7 | 5854 | |
d956fa6f MV |
5855 | exactly_one_half = scm_permanent_object (scm_divide (SCM_I_MAKINUM (1), |
5856 | SCM_I_MAKINUM (2))); | |
a0599745 | 5857 | #include "libguile/numbers.x" |
0f2d19dd | 5858 | } |
89e00824 ML |
5859 | |
5860 | /* | |
5861 | Local Variables: | |
5862 | c-file-style: "gnu" | |
5863 | End: | |
5864 | */ |