Commit | Line | Data |
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189171c5 | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006, 2007, 2008 Free Software Foundation, Inc. |
ba74ef4e MV |
2 | * |
3 | * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories | |
4 | * and Bellcore. See scm_divide. | |
5 | * | |
f81e080b | 6 | * |
73be1d9e MV |
7 | * This library is free software; you can redistribute it and/or |
8 | * modify it under the terms of the GNU Lesser General Public | |
9 | * License as published by the Free Software Foundation; either | |
10 | * version 2.1 of the License, or (at your option) any later version. | |
0f2d19dd | 11 | * |
73be1d9e MV |
12 | * This library is distributed in the hope that it will be useful, |
13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
15 | * Lesser General Public License for more details. | |
0f2d19dd | 16 | * |
73be1d9e MV |
17 | * You should have received a copy of the GNU Lesser General Public |
18 | * License along with this library; if not, write to the Free Software | |
92205699 | 19 | * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA |
73be1d9e | 20 | */ |
1bbd0b84 | 21 | |
0f2d19dd | 22 | \f |
ca46fb90 RB |
23 | /* General assumptions: |
24 | * All objects satisfying SCM_COMPLEXP() have a non-zero complex component. | |
25 | * All objects satisfying SCM_BIGP() are too large to fit in a fixnum. | |
26 | * If an object satisfies integer?, it's either an inum, a bignum, or a real. | |
27 | * If floor (r) == r, r is an int, and mpz_set_d will DTRT. | |
f92e85f7 | 28 | * All objects satisfying SCM_FRACTIONP are never an integer. |
ca46fb90 RB |
29 | */ |
30 | ||
31 | /* TODO: | |
32 | ||
33 | - see if special casing bignums and reals in integer-exponent when | |
34 | possible (to use mpz_pow and mpf_pow_ui) is faster. | |
35 | ||
36 | - look in to better short-circuiting of common cases in | |
37 | integer-expt and elsewhere. | |
38 | ||
39 | - see if direct mpz operations can help in ash and elsewhere. | |
40 | ||
41 | */ | |
0f2d19dd | 42 | |
8ab3d8a0 | 43 | /* tell glibc (2.3) to give prototype for C99 trunc(), csqrt(), etc */ |
fa605590 KR |
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> |
f92e85f7 | 53 | |
8ab3d8a0 KR |
54 | #if HAVE_COMPLEX_H |
55 | #include <complex.h> | |
56 | #endif | |
57 | ||
a0599745 | 58 | #include "libguile/_scm.h" |
a0599745 MD |
59 | #include "libguile/feature.h" |
60 | #include "libguile/ports.h" | |
61 | #include "libguile/root.h" | |
62 | #include "libguile/smob.h" | |
63 | #include "libguile/strings.h" | |
a0599745 MD |
64 | |
65 | #include "libguile/validate.h" | |
66 | #include "libguile/numbers.h" | |
1be6b49c | 67 | #include "libguile/deprecation.h" |
f4c627b3 | 68 | |
f92e85f7 MV |
69 | #include "libguile/eq.h" |
70 | ||
55f26379 MV |
71 | #include "libguile/discouraged.h" |
72 | ||
8ab3d8a0 KR |
73 | /* values per glibc, if not already defined */ |
74 | #ifndef M_LOG10E | |
75 | #define M_LOG10E 0.43429448190325182765 | |
76 | #endif | |
77 | #ifndef M_PI | |
78 | #define M_PI 3.14159265358979323846 | |
79 | #endif | |
80 | ||
0f2d19dd | 81 | \f |
f4c627b3 | 82 | |
ca46fb90 RB |
83 | /* |
84 | Wonder if this might be faster for some of our code? A switch on | |
85 | the numtag would jump directly to the right case, and the | |
86 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
87 | ||
88 | #define SCM_I_NUMTAG_NOTNUM 0 | |
89 | #define SCM_I_NUMTAG_INUM 1 | |
90 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
91 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
92 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
93 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 94 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 95 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 96 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
97 | : SCM_I_NUMTAG_NOTNUM))) |
98 | */ | |
f92e85f7 | 99 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
100 | |
101 | ||
34d19ef6 | 102 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 103 | |
56e55ac7 | 104 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
105 | * printed or scm_string representation of an inexact number. |
106 | */ | |
0b799eea | 107 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 108 | |
7351e207 MV |
109 | #if defined (SCO) |
110 | #if ! defined (HAVE_ISNAN) | |
111 | #define HAVE_ISNAN | |
112 | static int | |
113 | isnan (double x) | |
114 | { | |
115 | return (IsNANorINF (x) && NaN (x) && ! IsINF (x)) ? 1 : 0; | |
116 | } | |
0f2d19dd | 117 | #endif |
7351e207 MV |
118 | #if ! defined (HAVE_ISINF) |
119 | #define HAVE_ISINF | |
120 | static int | |
121 | isinf (double x) | |
122 | { | |
123 | return (IsNANorINF (x) && IsINF (x)) ? 1 : 0; | |
124 | } | |
0f2d19dd | 125 | |
7351e207 | 126 | #endif |
e6f3ef58 MD |
127 | #endif |
128 | ||
b127c712 | 129 | |
f8a8200b KR |
130 | /* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses |
131 | an explicit check. In some future gmp (don't know what version number), | |
132 | mpz_cmp_d is supposed to do this itself. */ | |
133 | #if 1 | |
b127c712 KR |
134 | #define xmpz_cmp_d(z, d) \ |
135 | (xisinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) | |
136 | #else | |
137 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
138 | #endif | |
139 | ||
a98ce907 KR |
140 | /* For reference, sparc solaris 7 has infinities (IEEE) but doesn't have |
141 | isinf. It does have finite and isnan though, hence the use of those. | |
142 | fpclass would be a possibility on that system too. */ | |
f92e85f7 MV |
143 | static int |
144 | xisinf (double x) | |
145 | { | |
146 | #if defined (HAVE_ISINF) | |
147 | return isinf (x); | |
148 | #elif defined (HAVE_FINITE) && defined (HAVE_ISNAN) | |
149 | return (! (finite (x) || isnan (x))); | |
150 | #else | |
151 | return 0; | |
152 | #endif | |
153 | } | |
154 | ||
155 | static int | |
156 | xisnan (double x) | |
157 | { | |
158 | #if defined (HAVE_ISNAN) | |
159 | return isnan (x); | |
160 | #else | |
161 | return 0; | |
162 | #endif | |
163 | } | |
164 | ||
4b26c03e | 165 | #if defined (GUILE_I) |
bca69a9f NJ |
166 | #if HAVE_COMPLEX_DOUBLE |
167 | ||
8ab3d8a0 KR |
168 | /* For an SCM object Z which is a complex number (ie. satisfies |
169 | SCM_COMPLEXP), return its value as a C level "complex double". */ | |
170 | #define SCM_COMPLEX_VALUE(z) \ | |
4b26c03e | 171 | (SCM_COMPLEX_REAL (z) + GUILE_I * SCM_COMPLEX_IMAG (z)) |
8ab3d8a0 KR |
172 | |
173 | /* Convert a C "complex double" to an SCM value. */ | |
8ab3d8a0 KR |
174 | static SCM |
175 | scm_from_complex_double (complex double z) | |
176 | { | |
177 | return scm_c_make_rectangular (creal (z), cimag (z)); | |
178 | } | |
bca69a9f | 179 | |
8ab3d8a0 | 180 | #endif /* HAVE_COMPLEX_DOUBLE */ |
bca69a9f | 181 | #endif /* GUILE_I */ |
8ab3d8a0 | 182 | |
0f2d19dd JB |
183 | \f |
184 | ||
713a4259 | 185 | static mpz_t z_negative_one; |
ac0c002c DH |
186 | |
187 | \f | |
188 | ||
189171c5 | 189 | SCM |
ca46fb90 RB |
190 | scm_i_mkbig () |
191 | { | |
192 | /* Return a newly created bignum. */ | |
193 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
194 | mpz_init (SCM_I_BIG_MPZ (z)); | |
195 | return z; | |
196 | } | |
197 | ||
189171c5 | 198 | SCM |
c71b0706 MV |
199 | scm_i_long2big (long x) |
200 | { | |
201 | /* Return a newly created bignum initialized to X. */ | |
202 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
203 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
204 | return z; | |
205 | } | |
206 | ||
189171c5 | 207 | SCM |
c71b0706 MV |
208 | scm_i_ulong2big (unsigned long x) |
209 | { | |
210 | /* Return a newly created bignum initialized to X. */ | |
211 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
212 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); | |
213 | return z; | |
214 | } | |
215 | ||
189171c5 | 216 | SCM |
ca46fb90 RB |
217 | scm_i_clonebig (SCM src_big, int same_sign_p) |
218 | { | |
219 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
220 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
221 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); | |
0aacf84e MD |
222 | if (!same_sign_p) |
223 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
224 | return z; |
225 | } | |
226 | ||
189171c5 | 227 | int |
ca46fb90 RB |
228 | scm_i_bigcmp (SCM x, SCM y) |
229 | { | |
230 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
231 | /* presume we already know x and y are bignums */ | |
232 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
233 | scm_remember_upto_here_2 (x, y); | |
234 | return result; | |
235 | } | |
236 | ||
189171c5 | 237 | SCM |
ca46fb90 RB |
238 | scm_i_dbl2big (double d) |
239 | { | |
240 | /* results are only defined if d is an integer */ | |
241 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
242 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); | |
243 | return z; | |
244 | } | |
245 | ||
f92e85f7 MV |
246 | /* Convert a integer in double representation to a SCM number. */ |
247 | ||
189171c5 | 248 | SCM |
f92e85f7 MV |
249 | scm_i_dbl2num (double u) |
250 | { | |
251 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
252 | powers of 2, so there's no rounding when making "double" values | |
253 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
254 | get rounded on a 64-bit machine, hence the "+1". | |
255 | ||
256 | The use of floor() to force to an integer value ensures we get a | |
257 | "numerically closest" value without depending on how a | |
258 | double->long cast or how mpz_set_d will round. For reference, | |
259 | double->long probably follows the hardware rounding mode, | |
260 | mpz_set_d truncates towards zero. */ | |
261 | ||
262 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
263 | representable as a double? */ | |
264 | ||
265 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
266 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
d956fa6f | 267 | return SCM_I_MAKINUM ((long) u); |
f92e85f7 MV |
268 | else |
269 | return scm_i_dbl2big (u); | |
270 | } | |
271 | ||
089c9a59 KR |
272 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
273 | with R5RS exact->inexact. | |
274 | ||
275 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
276 | (ie. truncate towards zero), then adjust to get the closest double by |
277 | examining the next lower bit and adding 1 (to the absolute value) if | |
278 | necessary. | |
279 | ||
280 | Bignums exactly half way between representable doubles are rounded to the | |
281 | next higher absolute value (ie. away from zero). This seems like an | |
282 | adequate interpretation of R5RS "numerically closest", and it's easier | |
283 | and faster than a full "nearest-even" style. | |
284 | ||
285 | The bit test must be done on the absolute value of the mpz_t, which means | |
286 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
287 | negatives as twos complement. | |
288 | ||
289 | In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up | |
290 | following the hardware rounding mode, but applied to the absolute value | |
291 | of the mpz_t operand. This is not what we want so we put the high | |
292 | DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when, | |
293 | mpz_get_d is supposed to always truncate towards zero. | |
294 | ||
295 | ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3 | |
296 | is a slowdown. It'd be faster to pick out the relevant high bits with | |
297 | mpz_getlimbn if we could be bothered coding that, and if the new | |
298 | truncating gmp doesn't come out. */ | |
089c9a59 KR |
299 | |
300 | double | |
ca46fb90 RB |
301 | scm_i_big2dbl (SCM b) |
302 | { | |
089c9a59 KR |
303 | double result; |
304 | size_t bits; | |
305 | ||
306 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
307 | ||
f8a8200b | 308 | #if 1 |
089c9a59 | 309 | { |
f8a8200b | 310 | /* Current GMP, eg. 4.1.3, force truncation towards zero */ |
089c9a59 KR |
311 | mpz_t tmp; |
312 | if (bits > DBL_MANT_DIG) | |
313 | { | |
314 | size_t shift = bits - DBL_MANT_DIG; | |
315 | mpz_init2 (tmp, DBL_MANT_DIG); | |
316 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
317 | result = ldexp (mpz_get_d (tmp), shift); | |
318 | mpz_clear (tmp); | |
319 | } | |
320 | else | |
321 | { | |
322 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
323 | } | |
324 | } | |
325 | #else | |
f8a8200b | 326 | /* Future GMP */ |
089c9a59 KR |
327 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
328 | #endif | |
329 | ||
330 | if (bits > DBL_MANT_DIG) | |
331 | { | |
332 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
333 | /* test bit number "pos" in absolute value */ | |
334 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
335 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
336 | { | |
337 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
338 | } | |
339 | } | |
340 | ||
ca46fb90 RB |
341 | scm_remember_upto_here_1 (b); |
342 | return result; | |
343 | } | |
344 | ||
189171c5 | 345 | SCM |
ca46fb90 RB |
346 | scm_i_normbig (SCM b) |
347 | { | |
348 | /* convert a big back to a fixnum if it'll fit */ | |
349 | /* presume b is a bignum */ | |
350 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
351 | { | |
352 | long val = mpz_get_si (SCM_I_BIG_MPZ (b)); | |
353 | if (SCM_FIXABLE (val)) | |
d956fa6f | 354 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
355 | } |
356 | return b; | |
357 | } | |
f872b822 | 358 | |
f92e85f7 MV |
359 | static SCM_C_INLINE_KEYWORD SCM |
360 | scm_i_mpz2num (mpz_t b) | |
361 | { | |
362 | /* convert a mpz number to a SCM number. */ | |
363 | if (mpz_fits_slong_p (b)) | |
364 | { | |
365 | long val = mpz_get_si (b); | |
366 | if (SCM_FIXABLE (val)) | |
d956fa6f | 367 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
368 | } |
369 | ||
370 | { | |
371 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
372 | mpz_init_set (SCM_I_BIG_MPZ (z), b); | |
373 | return z; | |
374 | } | |
375 | } | |
376 | ||
377 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
378 | static SCM scm_divide2real (SCM x, SCM y); | |
379 | ||
cba42c93 MV |
380 | static SCM |
381 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 382 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 383 | { |
c60e130c MV |
384 | /* First make sure the arguments are proper. |
385 | */ | |
e11e83f3 | 386 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 387 | { |
bc36d050 | 388 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 389 | scm_num_overflow ("make-ratio"); |
bc36d050 | 390 | if (scm_is_eq (denominator, SCM_I_MAKINUM(1))) |
f92e85f7 MV |
391 | return numerator; |
392 | } | |
393 | else | |
394 | { | |
395 | if (!(SCM_BIGP(denominator))) | |
396 | SCM_WRONG_TYPE_ARG (2, denominator); | |
397 | } | |
e11e83f3 | 398 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
399 | SCM_WRONG_TYPE_ARG (1, numerator); |
400 | ||
401 | /* Then flip signs so that the denominator is positive. | |
402 | */ | |
73e4de09 | 403 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
404 | { |
405 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
406 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
407 | } | |
408 | ||
409 | /* Now consider for each of the four fixnum/bignum combinations | |
410 | whether the rational number is really an integer. | |
411 | */ | |
e11e83f3 | 412 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 413 | { |
e11e83f3 | 414 | long x = SCM_I_INUM (numerator); |
bc36d050 | 415 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 416 | return SCM_INUM0; |
e11e83f3 | 417 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 418 | { |
dd5130ca | 419 | long y; |
e11e83f3 | 420 | y = SCM_I_INUM (denominator); |
f92e85f7 | 421 | if (x == y) |
d956fa6f | 422 | return SCM_I_MAKINUM(1); |
f92e85f7 | 423 | if ((x % y) == 0) |
d956fa6f | 424 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 425 | } |
dd5130ca KR |
426 | else |
427 | { | |
428 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
429 | of that value for the denominator, as a bignum. Apart from |
430 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
431 | integer. */ | |
432 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
433 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
434 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 435 | return SCM_I_MAKINUM(-1); |
dd5130ca | 436 | } |
f92e85f7 | 437 | } |
c60e130c | 438 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 439 | { |
e11e83f3 | 440 | if (SCM_I_INUMP (denominator)) |
c60e130c | 441 | { |
e11e83f3 | 442 | long yy = SCM_I_INUM (denominator); |
c60e130c MV |
443 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
444 | return scm_divide (numerator, denominator); | |
445 | } | |
446 | else | |
f92e85f7 | 447 | { |
bc36d050 | 448 | if (scm_is_eq (numerator, denominator)) |
d956fa6f | 449 | return SCM_I_MAKINUM(1); |
c60e130c MV |
450 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
451 | SCM_I_BIG_MPZ (denominator))) | |
452 | return scm_divide(numerator, denominator); | |
f92e85f7 | 453 | } |
f92e85f7 | 454 | } |
c60e130c MV |
455 | |
456 | /* No, it's a proper fraction. | |
457 | */ | |
e2bf3b19 HWN |
458 | { |
459 | SCM divisor = scm_gcd (numerator, denominator); | |
460 | if (!(scm_is_eq (divisor, SCM_I_MAKINUM(1)))) | |
461 | { | |
462 | numerator = scm_divide (numerator, divisor); | |
463 | denominator = scm_divide (denominator, divisor); | |
464 | } | |
465 | ||
466 | return scm_double_cell (scm_tc16_fraction, | |
467 | SCM_UNPACK (numerator), | |
468 | SCM_UNPACK (denominator), 0); | |
469 | } | |
f92e85f7 | 470 | } |
c60e130c | 471 | #undef FUNC_NAME |
f92e85f7 | 472 | |
f92e85f7 MV |
473 | double |
474 | scm_i_fraction2double (SCM z) | |
475 | { | |
55f26379 MV |
476 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
477 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
478 | } |
479 | ||
a1ec6916 | 480 | SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0, |
1bbd0b84 | 481 | (SCM x), |
942e5b91 MG |
482 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
483 | "otherwise.") | |
1bbd0b84 | 484 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 485 | { |
e11e83f3 | 486 | if (SCM_I_INUMP (x)) |
0aacf84e MD |
487 | return SCM_BOOL_T; |
488 | if (SCM_BIGP (x)) | |
489 | return SCM_BOOL_T; | |
f92e85f7 MV |
490 | if (SCM_FRACTIONP (x)) |
491 | return SCM_BOOL_T; | |
eb927cb9 MV |
492 | if (SCM_NUMBERP (x)) |
493 | return SCM_BOOL_F; | |
494 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 495 | } |
1bbd0b84 | 496 | #undef FUNC_NAME |
0f2d19dd | 497 | |
4219f20d | 498 | |
a1ec6916 | 499 | SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 500 | (SCM n), |
942e5b91 MG |
501 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
502 | "otherwise.") | |
1bbd0b84 | 503 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 504 | { |
e11e83f3 | 505 | if (SCM_I_INUMP (n)) |
0aacf84e | 506 | { |
e11e83f3 | 507 | long val = SCM_I_INUM (n); |
73e4de09 | 508 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
509 | } |
510 | else if (SCM_BIGP (n)) | |
511 | { | |
512 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
513 | scm_remember_upto_here_1 (n); | |
73e4de09 | 514 | return scm_from_bool (odd_p); |
0aacf84e | 515 | } |
73e4de09 | 516 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 517 | return SCM_BOOL_T; |
f92e85f7 MV |
518 | else if (SCM_REALP (n)) |
519 | { | |
520 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
521 | if (rem == 1.0) | |
522 | return SCM_BOOL_T; | |
523 | else if (rem == 0.0) | |
524 | return SCM_BOOL_F; | |
525 | else | |
526 | SCM_WRONG_TYPE_ARG (1, n); | |
527 | } | |
0aacf84e | 528 | else |
a1a33b0f | 529 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 530 | } |
1bbd0b84 | 531 | #undef FUNC_NAME |
0f2d19dd | 532 | |
4219f20d | 533 | |
a1ec6916 | 534 | SCM_DEFINE (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 535 | (SCM n), |
942e5b91 MG |
536 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
537 | "otherwise.") | |
1bbd0b84 | 538 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 539 | { |
e11e83f3 | 540 | if (SCM_I_INUMP (n)) |
0aacf84e | 541 | { |
e11e83f3 | 542 | long val = SCM_I_INUM (n); |
73e4de09 | 543 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
544 | } |
545 | else if (SCM_BIGP (n)) | |
546 | { | |
547 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
548 | scm_remember_upto_here_1 (n); | |
73e4de09 | 549 | return scm_from_bool (even_p); |
0aacf84e | 550 | } |
73e4de09 | 551 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 552 | return SCM_BOOL_T; |
f92e85f7 MV |
553 | else if (SCM_REALP (n)) |
554 | { | |
555 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
556 | if (rem == 1.0) | |
557 | return SCM_BOOL_F; | |
558 | else if (rem == 0.0) | |
559 | return SCM_BOOL_T; | |
560 | else | |
561 | SCM_WRONG_TYPE_ARG (1, n); | |
562 | } | |
0aacf84e | 563 | else |
a1a33b0f | 564 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 565 | } |
1bbd0b84 | 566 | #undef FUNC_NAME |
0f2d19dd | 567 | |
7351e207 | 568 | SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0, |
b1092b3a MV |
569 | (SCM x), |
570 | "Return @code{#t} if @var{x} is either @samp{+inf.0}\n" | |
571 | "or @samp{-inf.0}, @code{#f} otherwise.") | |
7351e207 MV |
572 | #define FUNC_NAME s_scm_inf_p |
573 | { | |
b1092b3a MV |
574 | if (SCM_REALP (x)) |
575 | return scm_from_bool (xisinf (SCM_REAL_VALUE (x))); | |
576 | else if (SCM_COMPLEXP (x)) | |
577 | return scm_from_bool (xisinf (SCM_COMPLEX_REAL (x)) | |
578 | || xisinf (SCM_COMPLEX_IMAG (x))); | |
0aacf84e | 579 | else |
7351e207 | 580 | return SCM_BOOL_F; |
7351e207 MV |
581 | } |
582 | #undef FUNC_NAME | |
583 | ||
584 | SCM_DEFINE (scm_nan_p, "nan?", 1, 0, 0, | |
585 | (SCM n), | |
586 | "Return @code{#t} if @var{n} is a NaN, @code{#f}\n" | |
587 | "otherwise.") | |
588 | #define FUNC_NAME s_scm_nan_p | |
589 | { | |
0aacf84e | 590 | if (SCM_REALP (n)) |
73e4de09 | 591 | return scm_from_bool (xisnan (SCM_REAL_VALUE (n))); |
0aacf84e | 592 | else if (SCM_COMPLEXP (n)) |
73e4de09 | 593 | return scm_from_bool (xisnan (SCM_COMPLEX_REAL (n)) |
7351e207 | 594 | || xisnan (SCM_COMPLEX_IMAG (n))); |
0aacf84e | 595 | else |
7351e207 | 596 | return SCM_BOOL_F; |
7351e207 MV |
597 | } |
598 | #undef FUNC_NAME | |
599 | ||
600 | /* Guile's idea of infinity. */ | |
601 | static double guile_Inf; | |
602 | ||
603 | /* Guile's idea of not a number. */ | |
604 | static double guile_NaN; | |
605 | ||
606 | static void | |
607 | guile_ieee_init (void) | |
608 | { | |
609 | #if defined (HAVE_ISINF) || defined (HAVE_FINITE) | |
610 | ||
611 | /* Some version of gcc on some old version of Linux used to crash when | |
612 | trying to make Inf and NaN. */ | |
613 | ||
240a27d2 KR |
614 | #ifdef INFINITY |
615 | /* C99 INFINITY, when available. | |
616 | FIXME: The standard allows for INFINITY to be something that overflows | |
617 | at compile time. We ought to have a configure test to check for that | |
618 | before trying to use it. (But in practice we believe this is not a | |
619 | problem on any system guile is likely to target.) */ | |
620 | guile_Inf = INFINITY; | |
621 | #elif HAVE_DINFINITY | |
622 | /* OSF */ | |
7351e207 | 623 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 624 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
625 | #else |
626 | double tmp = 1e+10; | |
627 | guile_Inf = tmp; | |
628 | for (;;) | |
629 | { | |
630 | guile_Inf *= 1e+10; | |
631 | if (guile_Inf == tmp) | |
632 | break; | |
633 | tmp = guile_Inf; | |
634 | } | |
635 | #endif | |
636 | ||
637 | #endif | |
638 | ||
639 | #if defined (HAVE_ISNAN) | |
640 | ||
240a27d2 KR |
641 | #ifdef NAN |
642 | /* C99 NAN, when available */ | |
643 | guile_NaN = NAN; | |
644 | #elif HAVE_DQNAN | |
eaa94eaa LC |
645 | { |
646 | /* OSF */ | |
647 | extern unsigned int DQNAN[2]; | |
648 | guile_NaN = (*((double *)(DQNAN))); | |
649 | } | |
7351e207 MV |
650 | #else |
651 | guile_NaN = guile_Inf / guile_Inf; | |
652 | #endif | |
653 | ||
654 | #endif | |
655 | } | |
656 | ||
657 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
658 | (void), | |
659 | "Return Inf.") | |
660 | #define FUNC_NAME s_scm_inf | |
661 | { | |
662 | static int initialized = 0; | |
663 | if (! initialized) | |
664 | { | |
665 | guile_ieee_init (); | |
666 | initialized = 1; | |
667 | } | |
55f26379 | 668 | return scm_from_double (guile_Inf); |
7351e207 MV |
669 | } |
670 | #undef FUNC_NAME | |
671 | ||
672 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
673 | (void), | |
674 | "Return NaN.") | |
675 | #define FUNC_NAME s_scm_nan | |
676 | { | |
677 | static int initialized = 0; | |
0aacf84e | 678 | if (!initialized) |
7351e207 MV |
679 | { |
680 | guile_ieee_init (); | |
681 | initialized = 1; | |
682 | } | |
55f26379 | 683 | return scm_from_double (guile_NaN); |
7351e207 MV |
684 | } |
685 | #undef FUNC_NAME | |
686 | ||
4219f20d | 687 | |
a48d60b1 MD |
688 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
689 | (SCM x), | |
690 | "Return the absolute value of @var{x}.") | |
691 | #define FUNC_NAME | |
0f2d19dd | 692 | { |
e11e83f3 | 693 | if (SCM_I_INUMP (x)) |
0aacf84e | 694 | { |
e11e83f3 | 695 | long int xx = SCM_I_INUM (x); |
0aacf84e MD |
696 | if (xx >= 0) |
697 | return x; | |
698 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 699 | return SCM_I_MAKINUM (-xx); |
0aacf84e MD |
700 | else |
701 | return scm_i_long2big (-xx); | |
4219f20d | 702 | } |
0aacf84e MD |
703 | else if (SCM_BIGP (x)) |
704 | { | |
705 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
706 | if (sgn < 0) | |
707 | return scm_i_clonebig (x, 0); | |
708 | else | |
709 | return x; | |
4219f20d | 710 | } |
0aacf84e | 711 | else if (SCM_REALP (x)) |
ae38324d KR |
712 | { |
713 | /* note that if x is a NaN then xx<0 is false so we return x unchanged */ | |
714 | double xx = SCM_REAL_VALUE (x); | |
715 | if (xx < 0.0) | |
55f26379 | 716 | return scm_from_double (-xx); |
ae38324d KR |
717 | else |
718 | return x; | |
719 | } | |
f92e85f7 MV |
720 | else if (SCM_FRACTIONP (x)) |
721 | { | |
73e4de09 | 722 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 723 | return x; |
cba42c93 | 724 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
725 | SCM_FRACTION_DENOMINATOR (x)); |
726 | } | |
0aacf84e | 727 | else |
a48d60b1 | 728 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 729 | } |
a48d60b1 | 730 | #undef FUNC_NAME |
0f2d19dd | 731 | |
4219f20d | 732 | |
9de33deb | 733 | SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); |
942e5b91 MG |
734 | /* "Return the quotient of the numbers @var{x} and @var{y}." |
735 | */ | |
0f2d19dd | 736 | SCM |
6e8d25a6 | 737 | scm_quotient (SCM x, SCM y) |
0f2d19dd | 738 | { |
e11e83f3 | 739 | if (SCM_I_INUMP (x)) |
0aacf84e | 740 | { |
e11e83f3 MV |
741 | long xx = SCM_I_INUM (x); |
742 | if (SCM_I_INUMP (y)) | |
0aacf84e | 743 | { |
e11e83f3 | 744 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
745 | if (yy == 0) |
746 | scm_num_overflow (s_quotient); | |
747 | else | |
748 | { | |
749 | long z = xx / yy; | |
750 | if (SCM_FIXABLE (z)) | |
d956fa6f | 751 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
752 | else |
753 | return scm_i_long2big (z); | |
754 | } | |
828865c3 | 755 | } |
0aacf84e | 756 | else if (SCM_BIGP (y)) |
ac0c002c | 757 | { |
e11e83f3 | 758 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
759 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
760 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
761 | { | |
762 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
763 | scm_remember_upto_here_1 (y); | |
d956fa6f | 764 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 765 | } |
0aacf84e | 766 | else |
d956fa6f | 767 | return SCM_I_MAKINUM (0); |
ac0c002c DH |
768 | } |
769 | else | |
0aacf84e | 770 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); |
828865c3 | 771 | } |
0aacf84e MD |
772 | else if (SCM_BIGP (x)) |
773 | { | |
e11e83f3 | 774 | if (SCM_I_INUMP (y)) |
0aacf84e | 775 | { |
e11e83f3 | 776 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
777 | if (yy == 0) |
778 | scm_num_overflow (s_quotient); | |
779 | else if (yy == 1) | |
780 | return x; | |
781 | else | |
782 | { | |
783 | SCM result = scm_i_mkbig (); | |
784 | if (yy < 0) | |
785 | { | |
786 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
787 | SCM_I_BIG_MPZ (x), | |
788 | - yy); | |
789 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
790 | } | |
791 | else | |
792 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
793 | scm_remember_upto_here_1 (x); | |
794 | return scm_i_normbig (result); | |
795 | } | |
796 | } | |
797 | else if (SCM_BIGP (y)) | |
798 | { | |
799 | SCM result = scm_i_mkbig (); | |
800 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
801 | SCM_I_BIG_MPZ (x), | |
802 | SCM_I_BIG_MPZ (y)); | |
803 | scm_remember_upto_here_2 (x, y); | |
804 | return scm_i_normbig (result); | |
805 | } | |
806 | else | |
807 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); | |
f872b822 | 808 | } |
0aacf84e | 809 | else |
89a7e495 | 810 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient); |
0f2d19dd JB |
811 | } |
812 | ||
9de33deb | 813 | SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); |
942e5b91 MG |
814 | /* "Return the remainder of the numbers @var{x} and @var{y}.\n" |
815 | * "@lisp\n" | |
816 | * "(remainder 13 4) @result{} 1\n" | |
817 | * "(remainder -13 4) @result{} -1\n" | |
818 | * "@end lisp" | |
819 | */ | |
0f2d19dd | 820 | SCM |
6e8d25a6 | 821 | scm_remainder (SCM x, SCM y) |
0f2d19dd | 822 | { |
e11e83f3 | 823 | if (SCM_I_INUMP (x)) |
0aacf84e | 824 | { |
e11e83f3 | 825 | if (SCM_I_INUMP (y)) |
0aacf84e | 826 | { |
e11e83f3 | 827 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
828 | if (yy == 0) |
829 | scm_num_overflow (s_remainder); | |
830 | else | |
831 | { | |
e11e83f3 | 832 | long z = SCM_I_INUM (x) % yy; |
d956fa6f | 833 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
834 | } |
835 | } | |
836 | else if (SCM_BIGP (y)) | |
ac0c002c | 837 | { |
e11e83f3 | 838 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
839 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
840 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
841 | { | |
842 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
843 | scm_remember_upto_here_1 (y); | |
d956fa6f | 844 | return SCM_I_MAKINUM (0); |
4dc09ee4 | 845 | } |
0aacf84e MD |
846 | else |
847 | return x; | |
ac0c002c DH |
848 | } |
849 | else | |
0aacf84e | 850 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); |
89a7e495 | 851 | } |
0aacf84e MD |
852 | else if (SCM_BIGP (x)) |
853 | { | |
e11e83f3 | 854 | if (SCM_I_INUMP (y)) |
0aacf84e | 855 | { |
e11e83f3 | 856 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
857 | if (yy == 0) |
858 | scm_num_overflow (s_remainder); | |
859 | else | |
860 | { | |
861 | SCM result = scm_i_mkbig (); | |
862 | if (yy < 0) | |
863 | yy = - yy; | |
864 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
865 | scm_remember_upto_here_1 (x); | |
866 | return scm_i_normbig (result); | |
867 | } | |
868 | } | |
869 | else if (SCM_BIGP (y)) | |
870 | { | |
871 | SCM result = scm_i_mkbig (); | |
872 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
873 | SCM_I_BIG_MPZ (x), | |
874 | SCM_I_BIG_MPZ (y)); | |
875 | scm_remember_upto_here_2 (x, y); | |
876 | return scm_i_normbig (result); | |
877 | } | |
878 | else | |
879 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); | |
f872b822 | 880 | } |
0aacf84e | 881 | else |
89a7e495 | 882 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder); |
0f2d19dd JB |
883 | } |
884 | ||
89a7e495 | 885 | |
9de33deb | 886 | SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); |
942e5b91 MG |
887 | /* "Return the modulo of the numbers @var{x} and @var{y}.\n" |
888 | * "@lisp\n" | |
889 | * "(modulo 13 4) @result{} 1\n" | |
890 | * "(modulo -13 4) @result{} 3\n" | |
891 | * "@end lisp" | |
892 | */ | |
0f2d19dd | 893 | SCM |
6e8d25a6 | 894 | scm_modulo (SCM x, SCM y) |
0f2d19dd | 895 | { |
e11e83f3 | 896 | if (SCM_I_INUMP (x)) |
0aacf84e | 897 | { |
e11e83f3 MV |
898 | long xx = SCM_I_INUM (x); |
899 | if (SCM_I_INUMP (y)) | |
0aacf84e | 900 | { |
e11e83f3 | 901 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
902 | if (yy == 0) |
903 | scm_num_overflow (s_modulo); | |
904 | else | |
905 | { | |
66b1c775 KR |
906 | /* C99 specifies that "%" is the remainder corresponding to a |
907 | quotient rounded towards zero, and that's also traditional | |
908 | for machine division, so z here should be well defined. */ | |
0aacf84e MD |
909 | long z = xx % yy; |
910 | long result; | |
911 | ||
912 | if (yy < 0) | |
913 | { | |
914 | if (z > 0) | |
915 | result = z + yy; | |
916 | else | |
917 | result = z; | |
918 | } | |
919 | else | |
920 | { | |
921 | if (z < 0) | |
922 | result = z + yy; | |
923 | else | |
924 | result = z; | |
925 | } | |
d956fa6f | 926 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
927 | } |
928 | } | |
929 | else if (SCM_BIGP (y)) | |
930 | { | |
931 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
932 | { |
933 | mpz_t z_x; | |
934 | SCM result; | |
935 | ||
936 | if (sgn_y < 0) | |
937 | { | |
938 | SCM pos_y = scm_i_clonebig (y, 0); | |
939 | /* do this after the last scm_op */ | |
940 | mpz_init_set_si (z_x, xx); | |
941 | result = pos_y; /* re-use this bignum */ | |
942 | mpz_mod (SCM_I_BIG_MPZ (result), | |
943 | z_x, | |
944 | SCM_I_BIG_MPZ (pos_y)); | |
945 | scm_remember_upto_here_1 (pos_y); | |
946 | } | |
947 | else | |
948 | { | |
949 | result = scm_i_mkbig (); | |
950 | /* do this after the last scm_op */ | |
951 | mpz_init_set_si (z_x, xx); | |
952 | mpz_mod (SCM_I_BIG_MPZ (result), | |
953 | z_x, | |
954 | SCM_I_BIG_MPZ (y)); | |
955 | scm_remember_upto_here_1 (y); | |
956 | } | |
ca46fb90 | 957 | |
0aacf84e MD |
958 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
959 | mpz_add (SCM_I_BIG_MPZ (result), | |
960 | SCM_I_BIG_MPZ (y), | |
961 | SCM_I_BIG_MPZ (result)); | |
962 | scm_remember_upto_here_1 (y); | |
963 | /* and do this before the next one */ | |
964 | mpz_clear (z_x); | |
965 | return scm_i_normbig (result); | |
966 | } | |
967 | } | |
968 | else | |
969 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
f872b822 | 970 | } |
0aacf84e MD |
971 | else if (SCM_BIGP (x)) |
972 | { | |
e11e83f3 | 973 | if (SCM_I_INUMP (y)) |
0aacf84e | 974 | { |
e11e83f3 | 975 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
976 | if (yy == 0) |
977 | scm_num_overflow (s_modulo); | |
978 | else | |
979 | { | |
980 | SCM result = scm_i_mkbig (); | |
981 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
982 | SCM_I_BIG_MPZ (x), | |
983 | (yy < 0) ? - yy : yy); | |
984 | scm_remember_upto_here_1 (x); | |
985 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
986 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
987 | SCM_I_BIG_MPZ (result), | |
988 | - yy); | |
989 | return scm_i_normbig (result); | |
990 | } | |
991 | } | |
992 | else if (SCM_BIGP (y)) | |
993 | { | |
0aacf84e MD |
994 | { |
995 | SCM result = scm_i_mkbig (); | |
996 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
997 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
998 | mpz_mod (SCM_I_BIG_MPZ (result), | |
999 | SCM_I_BIG_MPZ (x), | |
1000 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 1001 | |
0aacf84e MD |
1002 | scm_remember_upto_here_1 (x); |
1003 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
1004 | mpz_add (SCM_I_BIG_MPZ (result), | |
1005 | SCM_I_BIG_MPZ (y), | |
1006 | SCM_I_BIG_MPZ (result)); | |
1007 | scm_remember_upto_here_2 (y, pos_y); | |
1008 | return scm_i_normbig (result); | |
1009 | } | |
1010 | } | |
1011 | else | |
1012 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
828865c3 | 1013 | } |
0aacf84e | 1014 | else |
09fb7599 | 1015 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); |
0f2d19dd JB |
1016 | } |
1017 | ||
9de33deb | 1018 | SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd); |
942e5b91 MG |
1019 | /* "Return the greatest common divisor of all arguments.\n" |
1020 | * "If called without arguments, 0 is returned." | |
1021 | */ | |
0f2d19dd | 1022 | SCM |
6e8d25a6 | 1023 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 1024 | { |
ca46fb90 | 1025 | if (SCM_UNBNDP (y)) |
0aacf84e | 1026 | return SCM_UNBNDP (x) ? SCM_INUM0 : x; |
ca46fb90 | 1027 | |
e11e83f3 | 1028 | if (SCM_I_INUMP (x)) |
ca46fb90 | 1029 | { |
e11e83f3 | 1030 | if (SCM_I_INUMP (y)) |
ca46fb90 | 1031 | { |
e11e83f3 MV |
1032 | long xx = SCM_I_INUM (x); |
1033 | long yy = SCM_I_INUM (y); | |
ca46fb90 RB |
1034 | long u = xx < 0 ? -xx : xx; |
1035 | long v = yy < 0 ? -yy : yy; | |
1036 | long result; | |
0aacf84e MD |
1037 | if (xx == 0) |
1038 | result = v; | |
1039 | else if (yy == 0) | |
1040 | result = u; | |
1041 | else | |
1042 | { | |
1043 | long k = 1; | |
1044 | long t; | |
1045 | /* Determine a common factor 2^k */ | |
1046 | while (!(1 & (u | v))) | |
1047 | { | |
1048 | k <<= 1; | |
1049 | u >>= 1; | |
1050 | v >>= 1; | |
1051 | } | |
1052 | /* Now, any factor 2^n can be eliminated */ | |
1053 | if (u & 1) | |
1054 | t = -v; | |
1055 | else | |
1056 | { | |
1057 | t = u; | |
1058 | b3: | |
1059 | t = SCM_SRS (t, 1); | |
1060 | } | |
1061 | if (!(1 & t)) | |
1062 | goto b3; | |
1063 | if (t > 0) | |
1064 | u = t; | |
1065 | else | |
1066 | v = -t; | |
1067 | t = u - v; | |
1068 | if (t != 0) | |
1069 | goto b3; | |
1070 | result = u * k; | |
1071 | } | |
1072 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 1073 | ? SCM_I_MAKINUM (result) |
0aacf84e | 1074 | : scm_i_long2big (result)); |
ca46fb90 RB |
1075 | } |
1076 | else if (SCM_BIGP (y)) | |
1077 | { | |
0bff4dce KR |
1078 | SCM_SWAP (x, y); |
1079 | goto big_inum; | |
ca46fb90 RB |
1080 | } |
1081 | else | |
1082 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 1083 | } |
ca46fb90 RB |
1084 | else if (SCM_BIGP (x)) |
1085 | { | |
e11e83f3 | 1086 | if (SCM_I_INUMP (y)) |
ca46fb90 RB |
1087 | { |
1088 | unsigned long result; | |
0bff4dce KR |
1089 | long yy; |
1090 | big_inum: | |
e11e83f3 | 1091 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
1092 | if (yy == 0) |
1093 | return scm_abs (x); | |
0aacf84e MD |
1094 | if (yy < 0) |
1095 | yy = -yy; | |
ca46fb90 RB |
1096 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
1097 | scm_remember_upto_here_1 (x); | |
0aacf84e | 1098 | return (SCM_POSFIXABLE (result) |
d956fa6f | 1099 | ? SCM_I_MAKINUM (result) |
c71b0706 | 1100 | : scm_from_ulong (result)); |
ca46fb90 RB |
1101 | } |
1102 | else if (SCM_BIGP (y)) | |
1103 | { | |
1104 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
1105 | mpz_gcd (SCM_I_BIG_MPZ (result), |
1106 | SCM_I_BIG_MPZ (x), | |
1107 | SCM_I_BIG_MPZ (y)); | |
1108 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
1109 | return scm_i_normbig (result); |
1110 | } | |
1111 | else | |
1112 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 1113 | } |
ca46fb90 | 1114 | else |
09fb7599 | 1115 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
1116 | } |
1117 | ||
9de33deb | 1118 | SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm); |
942e5b91 MG |
1119 | /* "Return the least common multiple of the arguments.\n" |
1120 | * "If called without arguments, 1 is returned." | |
1121 | */ | |
0f2d19dd | 1122 | SCM |
6e8d25a6 | 1123 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 1124 | { |
ca46fb90 RB |
1125 | if (SCM_UNBNDP (n2)) |
1126 | { | |
1127 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
1128 | return SCM_I_MAKINUM (1L); |
1129 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 1130 | } |
09fb7599 | 1131 | |
e11e83f3 | 1132 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 1133 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 1134 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 1135 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 1136 | |
e11e83f3 | 1137 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 1138 | { |
e11e83f3 | 1139 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1140 | { |
1141 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 1142 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
1143 | return d; |
1144 | else | |
1145 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
1146 | } | |
1147 | else | |
1148 | { | |
1149 | /* inum n1, big n2 */ | |
1150 | inumbig: | |
1151 | { | |
1152 | SCM result = scm_i_mkbig (); | |
e11e83f3 | 1153 | long nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
1154 | if (nn1 == 0) return SCM_INUM0; |
1155 | if (nn1 < 0) nn1 = - nn1; | |
1156 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
1157 | scm_remember_upto_here_1 (n2); | |
1158 | return result; | |
1159 | } | |
1160 | } | |
1161 | } | |
1162 | else | |
1163 | { | |
1164 | /* big n1 */ | |
e11e83f3 | 1165 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1166 | { |
1167 | SCM_SWAP (n1, n2); | |
1168 | goto inumbig; | |
1169 | } | |
1170 | else | |
1171 | { | |
1172 | SCM result = scm_i_mkbig (); | |
1173 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
1174 | SCM_I_BIG_MPZ (n1), | |
1175 | SCM_I_BIG_MPZ (n2)); | |
1176 | scm_remember_upto_here_2(n1, n2); | |
1177 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
1178 | return result; | |
1179 | } | |
f872b822 | 1180 | } |
0f2d19dd JB |
1181 | } |
1182 | ||
8a525303 GB |
1183 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
1184 | ||
1185 | Logand: | |
1186 | X Y Result Method: | |
1187 | (len) | |
1188 | + + + x (map digit:logand X Y) | |
1189 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
1190 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
1191 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
1192 | ||
1193 | Logior: | |
1194 | X Y Result Method: | |
1195 | ||
1196 | + + + (map digit:logior X Y) | |
1197 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
1198 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
1199 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
1200 | ||
1201 | Logxor: | |
1202 | X Y Result Method: | |
1203 | ||
1204 | + + + (map digit:logxor X Y) | |
1205 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
1206 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
1207 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
1208 | ||
1209 | Logtest: | |
1210 | X Y Result | |
1211 | ||
1212 | + + (any digit:logand X Y) | |
1213 | + - (any digit:logand X (lognot (+ -1 Y))) | |
1214 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
1215 | - - #t | |
1216 | ||
1217 | */ | |
1218 | ||
c3ee7520 | 1219 | SCM_DEFINE1 (scm_logand, "logand", scm_tc7_asubr, |
1bbd0b84 | 1220 | (SCM n1, SCM n2), |
3c3db128 GH |
1221 | "Return the bitwise AND of the integer arguments.\n\n" |
1222 | "@lisp\n" | |
1223 | "(logand) @result{} -1\n" | |
1224 | "(logand 7) @result{} 7\n" | |
535f2a51 | 1225 | "(logand #b111 #b011 #b001) @result{} 1\n" |
3c3db128 | 1226 | "@end lisp") |
1bbd0b84 | 1227 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 1228 | { |
9a00c9fc DH |
1229 | long int nn1; |
1230 | ||
0aacf84e MD |
1231 | if (SCM_UNBNDP (n2)) |
1232 | { | |
1233 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 1234 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
1235 | else if (!SCM_NUMBERP (n1)) |
1236 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1237 | else if (SCM_NUMBERP (n1)) | |
1238 | return n1; | |
1239 | else | |
1240 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1241 | } |
09fb7599 | 1242 | |
e11e83f3 | 1243 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1244 | { |
e11e83f3 MV |
1245 | nn1 = SCM_I_INUM (n1); |
1246 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1247 | { |
e11e83f3 | 1248 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1249 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
1250 | } |
1251 | else if SCM_BIGP (n2) | |
1252 | { | |
1253 | intbig: | |
1254 | if (n1 == 0) | |
1255 | return SCM_INUM0; | |
1256 | { | |
1257 | SCM result_z = scm_i_mkbig (); | |
1258 | mpz_t nn1_z; | |
1259 | mpz_init_set_si (nn1_z, nn1); | |
1260 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1261 | scm_remember_upto_here_1 (n2); | |
1262 | mpz_clear (nn1_z); | |
1263 | return scm_i_normbig (result_z); | |
1264 | } | |
1265 | } | |
1266 | else | |
1267 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1268 | } | |
1269 | else if (SCM_BIGP (n1)) | |
1270 | { | |
e11e83f3 | 1271 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1272 | { |
1273 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1274 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1275 | goto intbig; |
1276 | } | |
1277 | else if (SCM_BIGP (n2)) | |
1278 | { | |
1279 | SCM result_z = scm_i_mkbig (); | |
1280 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
1281 | SCM_I_BIG_MPZ (n1), | |
1282 | SCM_I_BIG_MPZ (n2)); | |
1283 | scm_remember_upto_here_2 (n1, n2); | |
1284 | return scm_i_normbig (result_z); | |
1285 | } | |
1286 | else | |
1287 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1288 | } |
0aacf84e | 1289 | else |
09fb7599 | 1290 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1291 | } |
1bbd0b84 | 1292 | #undef FUNC_NAME |
0f2d19dd | 1293 | |
09fb7599 | 1294 | |
c3ee7520 | 1295 | SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr, |
1bbd0b84 | 1296 | (SCM n1, SCM n2), |
3c3db128 GH |
1297 | "Return the bitwise OR of the integer arguments.\n\n" |
1298 | "@lisp\n" | |
1299 | "(logior) @result{} 0\n" | |
1300 | "(logior 7) @result{} 7\n" | |
1301 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1e6808ea | 1302 | "@end lisp") |
1bbd0b84 | 1303 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 1304 | { |
9a00c9fc DH |
1305 | long int nn1; |
1306 | ||
0aacf84e MD |
1307 | if (SCM_UNBNDP (n2)) |
1308 | { | |
1309 | if (SCM_UNBNDP (n1)) | |
1310 | return SCM_INUM0; | |
1311 | else if (SCM_NUMBERP (n1)) | |
1312 | return n1; | |
1313 | else | |
1314 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1315 | } |
09fb7599 | 1316 | |
e11e83f3 | 1317 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1318 | { |
e11e83f3 MV |
1319 | nn1 = SCM_I_INUM (n1); |
1320 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1321 | { |
e11e83f3 | 1322 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1323 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
1324 | } |
1325 | else if (SCM_BIGP (n2)) | |
1326 | { | |
1327 | intbig: | |
1328 | if (nn1 == 0) | |
1329 | return n2; | |
1330 | { | |
1331 | SCM result_z = scm_i_mkbig (); | |
1332 | mpz_t nn1_z; | |
1333 | mpz_init_set_si (nn1_z, nn1); | |
1334 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1335 | scm_remember_upto_here_1 (n2); | |
1336 | mpz_clear (nn1_z); | |
9806de0d | 1337 | return scm_i_normbig (result_z); |
0aacf84e MD |
1338 | } |
1339 | } | |
1340 | else | |
1341 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1342 | } | |
1343 | else if (SCM_BIGP (n1)) | |
1344 | { | |
e11e83f3 | 1345 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1346 | { |
1347 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1348 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1349 | goto intbig; |
1350 | } | |
1351 | else if (SCM_BIGP (n2)) | |
1352 | { | |
1353 | SCM result_z = scm_i_mkbig (); | |
1354 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
1355 | SCM_I_BIG_MPZ (n1), | |
1356 | SCM_I_BIG_MPZ (n2)); | |
1357 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 1358 | return scm_i_normbig (result_z); |
0aacf84e MD |
1359 | } |
1360 | else | |
1361 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1362 | } |
0aacf84e | 1363 | else |
09fb7599 | 1364 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1365 | } |
1bbd0b84 | 1366 | #undef FUNC_NAME |
0f2d19dd | 1367 | |
09fb7599 | 1368 | |
c3ee7520 | 1369 | SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr, |
1bbd0b84 | 1370 | (SCM n1, SCM n2), |
3c3db128 GH |
1371 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1372 | "set in the result if it is set in an odd number of arguments.\n" | |
1373 | "@lisp\n" | |
1374 | "(logxor) @result{} 0\n" | |
1375 | "(logxor 7) @result{} 7\n" | |
1376 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1377 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1378 | "@end lisp") |
1bbd0b84 | 1379 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1380 | { |
9a00c9fc DH |
1381 | long int nn1; |
1382 | ||
0aacf84e MD |
1383 | if (SCM_UNBNDP (n2)) |
1384 | { | |
1385 | if (SCM_UNBNDP (n1)) | |
1386 | return SCM_INUM0; | |
1387 | else if (SCM_NUMBERP (n1)) | |
1388 | return n1; | |
1389 | else | |
1390 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1391 | } |
09fb7599 | 1392 | |
e11e83f3 | 1393 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1394 | { |
e11e83f3 MV |
1395 | nn1 = SCM_I_INUM (n1); |
1396 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1397 | { |
e11e83f3 | 1398 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1399 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
1400 | } |
1401 | else if (SCM_BIGP (n2)) | |
1402 | { | |
1403 | intbig: | |
1404 | { | |
1405 | SCM result_z = scm_i_mkbig (); | |
1406 | mpz_t nn1_z; | |
1407 | mpz_init_set_si (nn1_z, nn1); | |
1408 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1409 | scm_remember_upto_here_1 (n2); | |
1410 | mpz_clear (nn1_z); | |
1411 | return scm_i_normbig (result_z); | |
1412 | } | |
1413 | } | |
1414 | else | |
1415 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1416 | } | |
1417 | else if (SCM_BIGP (n1)) | |
1418 | { | |
e11e83f3 | 1419 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1420 | { |
1421 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1422 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1423 | goto intbig; |
1424 | } | |
1425 | else if (SCM_BIGP (n2)) | |
1426 | { | |
1427 | SCM result_z = scm_i_mkbig (); | |
1428 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
1429 | SCM_I_BIG_MPZ (n1), | |
1430 | SCM_I_BIG_MPZ (n2)); | |
1431 | scm_remember_upto_here_2 (n1, n2); | |
1432 | return scm_i_normbig (result_z); | |
1433 | } | |
1434 | else | |
1435 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1436 | } |
0aacf84e | 1437 | else |
09fb7599 | 1438 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1439 | } |
1bbd0b84 | 1440 | #undef FUNC_NAME |
0f2d19dd | 1441 | |
09fb7599 | 1442 | |
a1ec6916 | 1443 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 1444 | (SCM j, SCM k), |
ba6e7231 KR |
1445 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
1446 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
1447 | "without actually calculating the @code{logand}, just testing\n" | |
1448 | "for non-zero.\n" | |
1449 | "\n" | |
1e6808ea | 1450 | "@lisp\n" |
b380b885 MD |
1451 | "(logtest #b0100 #b1011) @result{} #f\n" |
1452 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1453 | "@end lisp") |
1bbd0b84 | 1454 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1455 | { |
1e6808ea | 1456 | long int nj; |
9a00c9fc | 1457 | |
e11e83f3 | 1458 | if (SCM_I_INUMP (j)) |
0aacf84e | 1459 | { |
e11e83f3 MV |
1460 | nj = SCM_I_INUM (j); |
1461 | if (SCM_I_INUMP (k)) | |
0aacf84e | 1462 | { |
e11e83f3 | 1463 | long nk = SCM_I_INUM (k); |
73e4de09 | 1464 | return scm_from_bool (nj & nk); |
0aacf84e MD |
1465 | } |
1466 | else if (SCM_BIGP (k)) | |
1467 | { | |
1468 | intbig: | |
1469 | if (nj == 0) | |
1470 | return SCM_BOOL_F; | |
1471 | { | |
1472 | SCM result; | |
1473 | mpz_t nj_z; | |
1474 | mpz_init_set_si (nj_z, nj); | |
1475 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
1476 | scm_remember_upto_here_1 (k); | |
73e4de09 | 1477 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
1478 | mpz_clear (nj_z); |
1479 | return result; | |
1480 | } | |
1481 | } | |
1482 | else | |
1483 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1484 | } | |
1485 | else if (SCM_BIGP (j)) | |
1486 | { | |
e11e83f3 | 1487 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
1488 | { |
1489 | SCM_SWAP (j, k); | |
e11e83f3 | 1490 | nj = SCM_I_INUM (j); |
0aacf84e MD |
1491 | goto intbig; |
1492 | } | |
1493 | else if (SCM_BIGP (k)) | |
1494 | { | |
1495 | SCM result; | |
1496 | mpz_t result_z; | |
1497 | mpz_init (result_z); | |
1498 | mpz_and (result_z, | |
1499 | SCM_I_BIG_MPZ (j), | |
1500 | SCM_I_BIG_MPZ (k)); | |
1501 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 1502 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
1503 | mpz_clear (result_z); |
1504 | return result; | |
1505 | } | |
1506 | else | |
1507 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1508 | } | |
1509 | else | |
1510 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 1511 | } |
1bbd0b84 | 1512 | #undef FUNC_NAME |
0f2d19dd | 1513 | |
c1bfcf60 | 1514 | |
a1ec6916 | 1515 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1516 | (SCM index, SCM j), |
ba6e7231 KR |
1517 | "Test whether bit number @var{index} in @var{j} is set.\n" |
1518 | "@var{index} starts from 0 for the least significant bit.\n" | |
1519 | "\n" | |
1e6808ea | 1520 | "@lisp\n" |
b380b885 MD |
1521 | "(logbit? 0 #b1101) @result{} #t\n" |
1522 | "(logbit? 1 #b1101) @result{} #f\n" | |
1523 | "(logbit? 2 #b1101) @result{} #t\n" | |
1524 | "(logbit? 3 #b1101) @result{} #t\n" | |
1525 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1526 | "@end lisp") |
1bbd0b84 | 1527 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1528 | { |
78166ad5 | 1529 | unsigned long int iindex; |
5efd3c7d | 1530 | iindex = scm_to_ulong (index); |
78166ad5 | 1531 | |
e11e83f3 | 1532 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
1533 | { |
1534 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 1535 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 1536 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 1537 | } |
0aacf84e MD |
1538 | else if (SCM_BIGP (j)) |
1539 | { | |
1540 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
1541 | scm_remember_upto_here_1 (j); | |
73e4de09 | 1542 | return scm_from_bool (val); |
0aacf84e MD |
1543 | } |
1544 | else | |
78166ad5 | 1545 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 1546 | } |
1bbd0b84 | 1547 | #undef FUNC_NAME |
0f2d19dd | 1548 | |
78166ad5 | 1549 | |
a1ec6916 | 1550 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1551 | (SCM n), |
4d814788 | 1552 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
1553 | "argument.\n" |
1554 | "\n" | |
b380b885 MD |
1555 | "@lisp\n" |
1556 | "(number->string (lognot #b10000000) 2)\n" | |
1557 | " @result{} \"-10000001\"\n" | |
1558 | "(number->string (lognot #b0) 2)\n" | |
1559 | " @result{} \"-1\"\n" | |
1e6808ea | 1560 | "@end lisp") |
1bbd0b84 | 1561 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1562 | { |
e11e83f3 | 1563 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
1564 | /* No overflow here, just need to toggle all the bits making up the inum. |
1565 | Enhancement: No need to strip the tag and add it back, could just xor | |
1566 | a block of 1 bits, if that worked with the various debug versions of | |
1567 | the SCM typedef. */ | |
e11e83f3 | 1568 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
1569 | |
1570 | } else if (SCM_BIGP (n)) { | |
1571 | SCM result = scm_i_mkbig (); | |
1572 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
1573 | scm_remember_upto_here_1 (n); | |
1574 | return result; | |
1575 | ||
1576 | } else { | |
1577 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1578 | } | |
0f2d19dd | 1579 | } |
1bbd0b84 | 1580 | #undef FUNC_NAME |
0f2d19dd | 1581 | |
518b7508 KR |
1582 | /* returns 0 if IN is not an integer. OUT must already be |
1583 | initialized. */ | |
1584 | static int | |
1585 | coerce_to_big (SCM in, mpz_t out) | |
1586 | { | |
1587 | if (SCM_BIGP (in)) | |
1588 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
1589 | else if (SCM_I_INUMP (in)) |
1590 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
1591 | else |
1592 | return 0; | |
1593 | ||
1594 | return 1; | |
1595 | } | |
1596 | ||
d885e204 | 1597 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
1598 | (SCM n, SCM k, SCM m), |
1599 | "Return @var{n} raised to the integer exponent\n" | |
1600 | "@var{k}, modulo @var{m}.\n" | |
1601 | "\n" | |
1602 | "@lisp\n" | |
1603 | "(modulo-expt 2 3 5)\n" | |
1604 | " @result{} 3\n" | |
1605 | "@end lisp") | |
d885e204 | 1606 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
1607 | { |
1608 | mpz_t n_tmp; | |
1609 | mpz_t k_tmp; | |
1610 | mpz_t m_tmp; | |
1611 | ||
1612 | /* There are two classes of error we might encounter -- | |
1613 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
1614 | and | |
1615 | 2) wrong-type errors, which of course we'll report by calling | |
1616 | SCM_WRONG_TYPE_ARG. | |
1617 | We don't report those errors immediately, however; instead we do | |
1618 | some cleanup first. These variables tell us which error (if | |
1619 | any) we should report after cleaning up. | |
1620 | */ | |
1621 | int report_overflow = 0; | |
1622 | ||
1623 | int position_of_wrong_type = 0; | |
1624 | SCM value_of_wrong_type = SCM_INUM0; | |
1625 | ||
1626 | SCM result = SCM_UNDEFINED; | |
1627 | ||
1628 | mpz_init (n_tmp); | |
1629 | mpz_init (k_tmp); | |
1630 | mpz_init (m_tmp); | |
1631 | ||
bc36d050 | 1632 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
1633 | { |
1634 | report_overflow = 1; | |
1635 | goto cleanup; | |
1636 | } | |
1637 | ||
1638 | if (!coerce_to_big (n, n_tmp)) | |
1639 | { | |
1640 | value_of_wrong_type = n; | |
1641 | position_of_wrong_type = 1; | |
1642 | goto cleanup; | |
1643 | } | |
1644 | ||
1645 | if (!coerce_to_big (k, k_tmp)) | |
1646 | { | |
1647 | value_of_wrong_type = k; | |
1648 | position_of_wrong_type = 2; | |
1649 | goto cleanup; | |
1650 | } | |
1651 | ||
1652 | if (!coerce_to_big (m, m_tmp)) | |
1653 | { | |
1654 | value_of_wrong_type = m; | |
1655 | position_of_wrong_type = 3; | |
1656 | goto cleanup; | |
1657 | } | |
1658 | ||
1659 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
1660 | will get a divide-by-zero exception when an inverse 1/n mod m | |
1661 | doesn't exist (or is not unique). Since exceptions are hard to | |
1662 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
1663 | a simple failure code, which is easy to handle. */ | |
1664 | ||
1665 | if (-1 == mpz_sgn (k_tmp)) | |
1666 | { | |
1667 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
1668 | { | |
1669 | report_overflow = 1; | |
1670 | goto cleanup; | |
1671 | } | |
1672 | mpz_neg (k_tmp, k_tmp); | |
1673 | } | |
1674 | ||
1675 | result = scm_i_mkbig (); | |
1676 | mpz_powm (SCM_I_BIG_MPZ (result), | |
1677 | n_tmp, | |
1678 | k_tmp, | |
1679 | m_tmp); | |
b7b8c575 KR |
1680 | |
1681 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
1682 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
1683 | ||
518b7508 KR |
1684 | cleanup: |
1685 | mpz_clear (m_tmp); | |
1686 | mpz_clear (k_tmp); | |
1687 | mpz_clear (n_tmp); | |
1688 | ||
1689 | if (report_overflow) | |
1690 | scm_num_overflow (FUNC_NAME); | |
1691 | ||
1692 | if (position_of_wrong_type) | |
1693 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
1694 | value_of_wrong_type); | |
1695 | ||
1696 | return scm_i_normbig (result); | |
1697 | } | |
1698 | #undef FUNC_NAME | |
1699 | ||
a1ec6916 | 1700 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1701 | (SCM n, SCM k), |
ba6e7231 KR |
1702 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
1703 | "exact integer, @var{n} can be any number.\n" | |
1704 | "\n" | |
1705 | "Negative @var{k} is supported, and results in @math{1/n^abs(k)}\n" | |
1706 | "in the usual way. @math{@var{n}^0} is 1, as usual, and that\n" | |
1707 | "includes @math{0^0} is 1.\n" | |
1e6808ea | 1708 | "\n" |
b380b885 | 1709 | "@lisp\n" |
ba6e7231 KR |
1710 | "(integer-expt 2 5) @result{} 32\n" |
1711 | "(integer-expt -3 3) @result{} -27\n" | |
1712 | "(integer-expt 5 -3) @result{} 1/125\n" | |
1713 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 1714 | "@end lisp") |
1bbd0b84 | 1715 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1716 | { |
1c35cb19 RB |
1717 | long i2 = 0; |
1718 | SCM z_i2 = SCM_BOOL_F; | |
1719 | int i2_is_big = 0; | |
d956fa6f | 1720 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 1721 | |
d57ed702 | 1722 | /* 0^0 == 1 according to R5RS */ |
bc36d050 | 1723 | if (scm_is_eq (n, SCM_INUM0) || scm_is_eq (n, acc)) |
73e4de09 | 1724 | return scm_is_false (scm_zero_p(k)) ? n : acc; |
bc36d050 | 1725 | else if (scm_is_eq (n, SCM_I_MAKINUM (-1L))) |
73e4de09 | 1726 | return scm_is_false (scm_even_p (k)) ? n : acc; |
ca46fb90 | 1727 | |
e11e83f3 MV |
1728 | if (SCM_I_INUMP (k)) |
1729 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
1730 | else if (SCM_BIGP (k)) |
1731 | { | |
1732 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
1733 | scm_remember_upto_here_1 (k); |
1734 | i2_is_big = 1; | |
1735 | } | |
2830fd91 | 1736 | else |
ca46fb90 RB |
1737 | SCM_WRONG_TYPE_ARG (2, k); |
1738 | ||
1739 | if (i2_is_big) | |
f872b822 | 1740 | { |
ca46fb90 RB |
1741 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
1742 | { | |
1743 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
1744 | n = scm_divide (n, SCM_UNDEFINED); | |
1745 | } | |
1746 | while (1) | |
1747 | { | |
1748 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
1749 | { | |
ca46fb90 RB |
1750 | return acc; |
1751 | } | |
1752 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
1753 | { | |
ca46fb90 RB |
1754 | return scm_product (acc, n); |
1755 | } | |
1756 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
1757 | acc = scm_product (acc, n); | |
1758 | n = scm_product (n, n); | |
1759 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
1760 | } | |
f872b822 | 1761 | } |
ca46fb90 | 1762 | else |
f872b822 | 1763 | { |
ca46fb90 RB |
1764 | if (i2 < 0) |
1765 | { | |
1766 | i2 = -i2; | |
1767 | n = scm_divide (n, SCM_UNDEFINED); | |
1768 | } | |
1769 | while (1) | |
1770 | { | |
1771 | if (0 == i2) | |
1772 | return acc; | |
1773 | if (1 == i2) | |
1774 | return scm_product (acc, n); | |
1775 | if (i2 & 1) | |
1776 | acc = scm_product (acc, n); | |
1777 | n = scm_product (n, n); | |
1778 | i2 >>= 1; | |
1779 | } | |
f872b822 | 1780 | } |
0f2d19dd | 1781 | } |
1bbd0b84 | 1782 | #undef FUNC_NAME |
0f2d19dd | 1783 | |
a1ec6916 | 1784 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1785 | (SCM n, SCM cnt), |
32f19569 KR |
1786 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
1787 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 1788 | "\n" |
e7644cb2 | 1789 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
1790 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
1791 | "infinity. (Note that this is not the same rounding as\n" | |
1792 | "@code{quotient} does.)\n" | |
1793 | "\n" | |
1794 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
1795 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
1796 | "shift dropping bits.\n" | |
1e6808ea | 1797 | "\n" |
b380b885 | 1798 | "@lisp\n" |
1e6808ea MG |
1799 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1800 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
1801 | "\n" |
1802 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
1803 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 1804 | "@end lisp") |
1bbd0b84 | 1805 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1806 | { |
3ab9f56e | 1807 | long bits_to_shift; |
5efd3c7d | 1808 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 1809 | |
788aca27 KR |
1810 | if (SCM_I_INUMP (n)) |
1811 | { | |
1812 | long nn = SCM_I_INUM (n); | |
1813 | ||
1814 | if (bits_to_shift > 0) | |
1815 | { | |
1816 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
1817 | overflow a non-zero fixnum. For smaller shifts we check the | |
1818 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
1819 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
1820 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
1821 | bits_to_shift)". */ | |
1822 | ||
1823 | if (nn == 0) | |
1824 | return n; | |
1825 | ||
1826 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
1827 | && ((unsigned long) | |
1828 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) | |
1829 | <= 1)) | |
1830 | { | |
1831 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
1832 | } | |
1833 | else | |
1834 | { | |
1835 | SCM result = scm_i_long2big (nn); | |
1836 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1837 | bits_to_shift); | |
1838 | return result; | |
1839 | } | |
1840 | } | |
1841 | else | |
1842 | { | |
1843 | bits_to_shift = -bits_to_shift; | |
1844 | if (bits_to_shift >= SCM_LONG_BIT) | |
1845 | return (nn >= 0 ? SCM_I_MAKINUM (0) : SCM_I_MAKINUM(-1)); | |
1846 | else | |
1847 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
1848 | } | |
1849 | ||
1850 | } | |
1851 | else if (SCM_BIGP (n)) | |
ca46fb90 | 1852 | { |
788aca27 KR |
1853 | SCM result; |
1854 | ||
1855 | if (bits_to_shift == 0) | |
1856 | return n; | |
1857 | ||
1858 | result = scm_i_mkbig (); | |
1859 | if (bits_to_shift >= 0) | |
1860 | { | |
1861 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1862 | bits_to_shift); | |
1863 | return result; | |
1864 | } | |
ca46fb90 | 1865 | else |
788aca27 KR |
1866 | { |
1867 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
1868 | we have to allocate a bignum even if the result is going to be a | |
1869 | fixnum. */ | |
1870 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1871 | -bits_to_shift); | |
1872 | return scm_i_normbig (result); | |
1873 | } | |
1874 | ||
ca46fb90 RB |
1875 | } |
1876 | else | |
788aca27 KR |
1877 | { |
1878 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1879 | } | |
0f2d19dd | 1880 | } |
1bbd0b84 | 1881 | #undef FUNC_NAME |
0f2d19dd | 1882 | |
3c9f20f8 | 1883 | |
a1ec6916 | 1884 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 1885 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
1886 | "Return the integer composed of the @var{start} (inclusive)\n" |
1887 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
1888 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
1889 | "\n" | |
b380b885 MD |
1890 | "@lisp\n" |
1891 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
1892 | " @result{} \"1010\"\n" | |
1893 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
1894 | " @result{} \"10110\"\n" | |
1895 | "@end lisp") | |
1bbd0b84 | 1896 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 1897 | { |
7f848242 | 1898 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
1899 | istart = scm_to_ulong (start); |
1900 | iend = scm_to_ulong (end); | |
c1bfcf60 | 1901 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 1902 | |
7f848242 KR |
1903 | /* how many bits to keep */ |
1904 | bits = iend - istart; | |
1905 | ||
e11e83f3 | 1906 | if (SCM_I_INUMP (n)) |
0aacf84e | 1907 | { |
e11e83f3 | 1908 | long int in = SCM_I_INUM (n); |
7f848242 KR |
1909 | |
1910 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 1911 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 1912 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 1913 | |
0aacf84e MD |
1914 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
1915 | { | |
1916 | /* Since we emulate two's complement encoded numbers, this | |
1917 | * special case requires us to produce a result that has | |
7f848242 | 1918 | * more bits than can be stored in a fixnum. |
0aacf84e | 1919 | */ |
7f848242 KR |
1920 | SCM result = scm_i_long2big (in); |
1921 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1922 | bits); | |
1923 | return result; | |
0aacf84e | 1924 | } |
ac0c002c | 1925 | |
7f848242 | 1926 | /* mask down to requisite bits */ |
857ae6af | 1927 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 1928 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
1929 | } |
1930 | else if (SCM_BIGP (n)) | |
ac0c002c | 1931 | { |
7f848242 KR |
1932 | SCM result; |
1933 | if (bits == 1) | |
1934 | { | |
d956fa6f | 1935 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
1936 | } |
1937 | else | |
1938 | { | |
1939 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
1940 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
1941 | such bits into a ulong. */ | |
1942 | result = scm_i_mkbig (); | |
1943 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
1944 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
1945 | result = scm_i_normbig (result); | |
1946 | } | |
1947 | scm_remember_upto_here_1 (n); | |
1948 | return result; | |
ac0c002c | 1949 | } |
0aacf84e | 1950 | else |
78166ad5 | 1951 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 1952 | } |
1bbd0b84 | 1953 | #undef FUNC_NAME |
0f2d19dd | 1954 | |
7f848242 | 1955 | |
e4755e5c JB |
1956 | static const char scm_logtab[] = { |
1957 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
1958 | }; | |
1cc91f1b | 1959 | |
a1ec6916 | 1960 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 1961 | (SCM n), |
1e6808ea MG |
1962 | "Return the number of bits in integer @var{n}. If integer is\n" |
1963 | "positive, the 1-bits in its binary representation are counted.\n" | |
1964 | "If negative, the 0-bits in its two's-complement binary\n" | |
1965 | "representation are counted. If 0, 0 is returned.\n" | |
1966 | "\n" | |
b380b885 MD |
1967 | "@lisp\n" |
1968 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
1969 | " @result{} 4\n" |
1970 | "(logcount 0)\n" | |
1971 | " @result{} 0\n" | |
1972 | "(logcount -2)\n" | |
1973 | " @result{} 1\n" | |
1974 | "@end lisp") | |
1975 | #define FUNC_NAME s_scm_logcount | |
1976 | { | |
e11e83f3 | 1977 | if (SCM_I_INUMP (n)) |
f872b822 | 1978 | { |
ca46fb90 | 1979 | unsigned long int c = 0; |
e11e83f3 | 1980 | long int nn = SCM_I_INUM (n); |
ca46fb90 RB |
1981 | if (nn < 0) |
1982 | nn = -1 - nn; | |
1983 | while (nn) | |
1984 | { | |
1985 | c += scm_logtab[15 & nn]; | |
1986 | nn >>= 4; | |
1987 | } | |
d956fa6f | 1988 | return SCM_I_MAKINUM (c); |
f872b822 | 1989 | } |
ca46fb90 | 1990 | else if (SCM_BIGP (n)) |
f872b822 | 1991 | { |
ca46fb90 | 1992 | unsigned long count; |
713a4259 KR |
1993 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
1994 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 1995 | else |
713a4259 KR |
1996 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
1997 | scm_remember_upto_here_1 (n); | |
d956fa6f | 1998 | return SCM_I_MAKINUM (count); |
f872b822 | 1999 | } |
ca46fb90 RB |
2000 | else |
2001 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 2002 | } |
ca46fb90 | 2003 | #undef FUNC_NAME |
0f2d19dd JB |
2004 | |
2005 | ||
ca46fb90 RB |
2006 | static const char scm_ilentab[] = { |
2007 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
2008 | }; | |
2009 | ||
0f2d19dd | 2010 | |
ca46fb90 RB |
2011 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
2012 | (SCM n), | |
2013 | "Return the number of bits necessary to represent @var{n}.\n" | |
2014 | "\n" | |
2015 | "@lisp\n" | |
2016 | "(integer-length #b10101010)\n" | |
2017 | " @result{} 8\n" | |
2018 | "(integer-length 0)\n" | |
2019 | " @result{} 0\n" | |
2020 | "(integer-length #b1111)\n" | |
2021 | " @result{} 4\n" | |
2022 | "@end lisp") | |
2023 | #define FUNC_NAME s_scm_integer_length | |
2024 | { | |
e11e83f3 | 2025 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2026 | { |
2027 | unsigned long int c = 0; | |
2028 | unsigned int l = 4; | |
e11e83f3 | 2029 | long int nn = SCM_I_INUM (n); |
0aacf84e MD |
2030 | if (nn < 0) |
2031 | nn = -1 - nn; | |
2032 | while (nn) | |
2033 | { | |
2034 | c += 4; | |
2035 | l = scm_ilentab [15 & nn]; | |
2036 | nn >>= 4; | |
2037 | } | |
d956fa6f | 2038 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
2039 | } |
2040 | else if (SCM_BIGP (n)) | |
2041 | { | |
2042 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
2043 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
2044 | 1 too big, so check for that and adjust. */ | |
2045 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
2046 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
2047 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
2048 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
2049 | size--; | |
2050 | scm_remember_upto_here_1 (n); | |
d956fa6f | 2051 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
2052 | } |
2053 | else | |
ca46fb90 | 2054 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
2055 | } |
2056 | #undef FUNC_NAME | |
0f2d19dd JB |
2057 | |
2058 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
2059 | #define SCM_MAX_DBL_PREC 60 |
2060 | #define SCM_MAX_DBL_RADIX 36 | |
2061 | ||
2062 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
2063 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
2064 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
2065 | ||
2066 | static | |
2067 | void init_dblprec(int *prec, int radix) { | |
2068 | /* determine floating point precision by adding successively | |
2069 | smaller increments to 1.0 until it is considered == 1.0 */ | |
2070 | double f = ((double)1.0)/radix; | |
2071 | double fsum = 1.0 + f; | |
2072 | ||
2073 | *prec = 0; | |
2074 | while (fsum != 1.0) | |
2075 | { | |
2076 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
2077 | fsum = 1.0; | |
2078 | else | |
2079 | { | |
2080 | f /= radix; | |
2081 | fsum = f + 1.0; | |
2082 | } | |
2083 | } | |
2084 | (*prec) -= 1; | |
2085 | } | |
2086 | ||
2087 | static | |
2088 | void init_fx_radix(double *fx_list, int radix) | |
2089 | { | |
2090 | /* initialize a per-radix list of tolerances. When added | |
2091 | to a number < 1.0, we can determine if we should raund | |
2092 | up and quit converting a number to a string. */ | |
2093 | int i; | |
2094 | fx_list[0] = 0.0; | |
2095 | fx_list[1] = 0.5; | |
2096 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
2097 | fx_list[i] = (fx_list[i-1] / radix); | |
2098 | } | |
2099 | ||
2100 | /* use this array as a way to generate a single digit */ | |
2101 | static const char*number_chars="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; | |
0f2d19dd | 2102 | |
1be6b49c | 2103 | static size_t |
0b799eea | 2104 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 2105 | { |
0b799eea MV |
2106 | int efmt, dpt, d, i, wp; |
2107 | double *fx; | |
2108 | #ifdef DBL_MIN_10_EXP | |
2109 | double f_cpy; | |
2110 | int exp_cpy; | |
2111 | #endif /* DBL_MIN_10_EXP */ | |
2112 | size_t ch = 0; | |
2113 | int exp = 0; | |
2114 | ||
2115 | if(radix < 2 || | |
2116 | radix > SCM_MAX_DBL_RADIX) | |
2117 | { | |
2118 | /* revert to existing behavior */ | |
2119 | radix = 10; | |
2120 | } | |
2121 | ||
2122 | wp = scm_dblprec[radix-2]; | |
2123 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 2124 | |
f872b822 | 2125 | if (f == 0.0) |
abb7e44d MV |
2126 | { |
2127 | #ifdef HAVE_COPYSIGN | |
2128 | double sgn = copysign (1.0, f); | |
2129 | ||
2130 | if (sgn < 0.0) | |
2131 | a[ch++] = '-'; | |
2132 | #endif | |
abb7e44d MV |
2133 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
2134 | } | |
7351e207 MV |
2135 | |
2136 | if (xisinf (f)) | |
2137 | { | |
2138 | if (f < 0) | |
2139 | strcpy (a, "-inf.0"); | |
2140 | else | |
2141 | strcpy (a, "+inf.0"); | |
2142 | return ch+6; | |
2143 | } | |
2144 | else if (xisnan (f)) | |
2145 | { | |
2146 | strcpy (a, "+nan.0"); | |
2147 | return ch+6; | |
2148 | } | |
2149 | ||
f872b822 MD |
2150 | if (f < 0.0) |
2151 | { | |
2152 | f = -f; | |
2153 | a[ch++] = '-'; | |
2154 | } | |
7351e207 | 2155 | |
f872b822 MD |
2156 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
2157 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
2158 | /* just do the checking...if it passes, we do the conversion for our |
2159 | radix again below */ | |
2160 | f_cpy = f; | |
2161 | exp_cpy = exp; | |
2162 | ||
2163 | while (f_cpy < 1.0) | |
f872b822 | 2164 | { |
0b799eea MV |
2165 | f_cpy *= 10.0; |
2166 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
2167 | { |
2168 | a[ch++] = '#'; | |
2169 | a[ch++] = '.'; | |
2170 | a[ch++] = '#'; | |
2171 | return ch; | |
2172 | } | |
f872b822 | 2173 | } |
0b799eea | 2174 | while (f_cpy > 10.0) |
f872b822 | 2175 | { |
0b799eea MV |
2176 | f_cpy *= 0.10; |
2177 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
2178 | { |
2179 | a[ch++] = '#'; | |
2180 | a[ch++] = '.'; | |
2181 | a[ch++] = '#'; | |
2182 | return ch; | |
2183 | } | |
f872b822 | 2184 | } |
0b799eea MV |
2185 | #endif |
2186 | ||
f872b822 MD |
2187 | while (f < 1.0) |
2188 | { | |
0b799eea | 2189 | f *= radix; |
f872b822 MD |
2190 | exp--; |
2191 | } | |
0b799eea | 2192 | while (f > radix) |
f872b822 | 2193 | { |
0b799eea | 2194 | f /= radix; |
f872b822 MD |
2195 | exp++; |
2196 | } | |
0b799eea MV |
2197 | |
2198 | if (f + fx[wp] >= radix) | |
f872b822 MD |
2199 | { |
2200 | f = 1.0; | |
2201 | exp++; | |
2202 | } | |
0f2d19dd | 2203 | zero: |
0b799eea MV |
2204 | #ifdef ENGNOT |
2205 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 2206 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
2207 | exp -= dpt++; |
2208 | efmt = 1; | |
f872b822 MD |
2209 | #else |
2210 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 2211 | if (!efmt) |
cda139a7 MD |
2212 | { |
2213 | if (exp < 0) | |
2214 | { | |
2215 | a[ch++] = '0'; | |
2216 | a[ch++] = '.'; | |
2217 | dpt = exp; | |
f872b822 MD |
2218 | while (++dpt) |
2219 | a[ch++] = '0'; | |
cda139a7 MD |
2220 | } |
2221 | else | |
f872b822 | 2222 | dpt = exp + 1; |
cda139a7 | 2223 | } |
0f2d19dd JB |
2224 | else |
2225 | dpt = 1; | |
f872b822 MD |
2226 | #endif |
2227 | ||
2228 | do | |
2229 | { | |
2230 | d = f; | |
2231 | f -= d; | |
0b799eea | 2232 | a[ch++] = number_chars[d]; |
f872b822 MD |
2233 | if (f < fx[wp]) |
2234 | break; | |
2235 | if (f + fx[wp] >= 1.0) | |
2236 | { | |
0b799eea | 2237 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
2238 | break; |
2239 | } | |
0b799eea | 2240 | f *= radix; |
f872b822 MD |
2241 | if (!(--dpt)) |
2242 | a[ch++] = '.'; | |
0f2d19dd | 2243 | } |
f872b822 | 2244 | while (wp--); |
0f2d19dd JB |
2245 | |
2246 | if (dpt > 0) | |
cda139a7 | 2247 | { |
f872b822 | 2248 | #ifndef ENGNOT |
cda139a7 MD |
2249 | if ((dpt > 4) && (exp > 6)) |
2250 | { | |
f872b822 | 2251 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 2252 | for (i = ch++; i > d; i--) |
f872b822 | 2253 | a[i] = a[i - 1]; |
cda139a7 MD |
2254 | a[d] = '.'; |
2255 | efmt = 1; | |
2256 | } | |
2257 | else | |
f872b822 | 2258 | #endif |
cda139a7 | 2259 | { |
f872b822 MD |
2260 | while (--dpt) |
2261 | a[ch++] = '0'; | |
cda139a7 MD |
2262 | a[ch++] = '.'; |
2263 | } | |
2264 | } | |
f872b822 MD |
2265 | if (a[ch - 1] == '.') |
2266 | a[ch++] = '0'; /* trailing zero */ | |
2267 | if (efmt && exp) | |
2268 | { | |
2269 | a[ch++] = 'e'; | |
2270 | if (exp < 0) | |
2271 | { | |
2272 | exp = -exp; | |
2273 | a[ch++] = '-'; | |
2274 | } | |
0b799eea MV |
2275 | for (i = radix; i <= exp; i *= radix); |
2276 | for (i /= radix; i; i /= radix) | |
f872b822 | 2277 | { |
0b799eea | 2278 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
2279 | exp %= i; |
2280 | } | |
0f2d19dd | 2281 | } |
0f2d19dd JB |
2282 | return ch; |
2283 | } | |
2284 | ||
7a1aba42 MV |
2285 | |
2286 | static size_t | |
2287 | icmplx2str (double real, double imag, char *str, int radix) | |
2288 | { | |
2289 | size_t i; | |
2290 | ||
2291 | i = idbl2str (real, str, radix); | |
2292 | if (imag != 0.0) | |
2293 | { | |
2294 | /* Don't output a '+' for negative numbers or for Inf and | |
2295 | NaN. They will provide their own sign. */ | |
2296 | if (0 <= imag && !xisinf (imag) && !xisnan (imag)) | |
2297 | str[i++] = '+'; | |
2298 | i += idbl2str (imag, &str[i], radix); | |
2299 | str[i++] = 'i'; | |
2300 | } | |
2301 | return i; | |
2302 | } | |
2303 | ||
1be6b49c | 2304 | static size_t |
0b799eea | 2305 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 2306 | { |
1be6b49c | 2307 | size_t i; |
3c9a524f | 2308 | if (SCM_REALP (flt)) |
0b799eea | 2309 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 2310 | else |
7a1aba42 MV |
2311 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
2312 | str, radix); | |
0f2d19dd JB |
2313 | return i; |
2314 | } | |
0f2d19dd | 2315 | |
2881e77b | 2316 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
2317 | characters in the result. |
2318 | rad is output base | |
2319 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2320 | size_t |
2881e77b MV |
2321 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
2322 | { | |
2323 | if (num < 0) | |
2324 | { | |
2325 | *p++ = '-'; | |
2326 | return scm_iuint2str (-num, rad, p) + 1; | |
2327 | } | |
2328 | else | |
2329 | return scm_iuint2str (num, rad, p); | |
2330 | } | |
2331 | ||
2332 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
2333 | characters in the result. | |
2334 | rad is output base | |
2335 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
2336 | size_t | |
2337 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 2338 | { |
1be6b49c ML |
2339 | size_t j = 1; |
2340 | size_t i; | |
2881e77b | 2341 | scm_t_uintmax n = num; |
5c11cc9d | 2342 | |
f872b822 | 2343 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2344 | j++; |
2345 | ||
2346 | i = j; | |
2881e77b | 2347 | n = num; |
f872b822 MD |
2348 | while (i--) |
2349 | { | |
5c11cc9d GH |
2350 | int d = n % rad; |
2351 | ||
f872b822 MD |
2352 | n /= rad; |
2353 | p[i] = d + ((d < 10) ? '0' : 'a' - 10); | |
2354 | } | |
0f2d19dd JB |
2355 | return j; |
2356 | } | |
2357 | ||
a1ec6916 | 2358 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2359 | (SCM n, SCM radix), |
2360 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2361 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2362 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2363 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2364 | { |
1bbd0b84 | 2365 | int base; |
98cb6e75 | 2366 | |
0aacf84e | 2367 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 2368 | base = 10; |
0aacf84e | 2369 | else |
5efd3c7d | 2370 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 2371 | |
e11e83f3 | 2372 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2373 | { |
2374 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 2375 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 2376 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
2377 | } |
2378 | else if (SCM_BIGP (n)) | |
2379 | { | |
2380 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
2381 | scm_remember_upto_here_1 (n); | |
cc95e00a | 2382 | return scm_take_locale_string (str); |
0aacf84e | 2383 | } |
f92e85f7 MV |
2384 | else if (SCM_FRACTIONP (n)) |
2385 | { | |
f92e85f7 | 2386 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), |
cc95e00a | 2387 | scm_from_locale_string ("/"), |
f92e85f7 MV |
2388 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
2389 | } | |
0aacf84e MD |
2390 | else if (SCM_INEXACTP (n)) |
2391 | { | |
2392 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 2393 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
2394 | } |
2395 | else | |
bb628794 | 2396 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 2397 | } |
1bbd0b84 | 2398 | #undef FUNC_NAME |
0f2d19dd JB |
2399 | |
2400 | ||
ca46fb90 RB |
2401 | /* These print routines used to be stubbed here so that scm_repl.c |
2402 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 2403 | |
0f2d19dd | 2404 | int |
e81d98ec | 2405 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2406 | { |
56e55ac7 | 2407 | char num_buf[FLOBUFLEN]; |
0b799eea | 2408 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
2409 | return !0; |
2410 | } | |
2411 | ||
b479fe9a MV |
2412 | void |
2413 | scm_i_print_double (double val, SCM port) | |
2414 | { | |
2415 | char num_buf[FLOBUFLEN]; | |
2416 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
2417 | } | |
2418 | ||
f3ae5d60 | 2419 | int |
e81d98ec | 2420 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 2421 | |
f3ae5d60 | 2422 | { |
56e55ac7 | 2423 | char num_buf[FLOBUFLEN]; |
0b799eea | 2424 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
2425 | return !0; |
2426 | } | |
1cc91f1b | 2427 | |
7a1aba42 MV |
2428 | void |
2429 | scm_i_print_complex (double real, double imag, SCM port) | |
2430 | { | |
2431 | char num_buf[FLOBUFLEN]; | |
2432 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
2433 | } | |
2434 | ||
f92e85f7 MV |
2435 | int |
2436 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
2437 | { | |
2438 | SCM str; | |
f92e85f7 | 2439 | str = scm_number_to_string (sexp, SCM_UNDEFINED); |
cc95e00a | 2440 | scm_lfwrite (scm_i_string_chars (str), scm_i_string_length (str), port); |
f92e85f7 MV |
2441 | scm_remember_upto_here_1 (str); |
2442 | return !0; | |
2443 | } | |
2444 | ||
0f2d19dd | 2445 | int |
e81d98ec | 2446 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2447 | { |
ca46fb90 RB |
2448 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
2449 | scm_remember_upto_here_1 (exp); | |
2450 | scm_lfwrite (str, (size_t) strlen (str), port); | |
2451 | free (str); | |
0f2d19dd JB |
2452 | return !0; |
2453 | } | |
2454 | /*** END nums->strs ***/ | |
2455 | ||
3c9a524f | 2456 | |
0f2d19dd | 2457 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2458 | |
3c9a524f DH |
2459 | /* The following functions implement the conversion from strings to numbers. |
2460 | * The implementation somehow follows the grammar for numbers as it is given | |
2461 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2462 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2463 | * points should be noted about the implementation: | |
2464 | * * Each function keeps a local index variable 'idx' that points at the | |
2465 | * current position within the parsed string. The global index is only | |
2466 | * updated if the function could parse the corresponding syntactic unit | |
2467 | * successfully. | |
2468 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2469 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2470 | * global exactness information is only updated after each part has been | |
2471 | * successfully parsed. | |
2472 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2473 | * Only if these fixnums would overflow, the result variables are updated | |
2474 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2475 | * the temporary variables holding the fixnums are cleared, and the process | |
2476 | * starts over again. If for example fixnums were able to store five decimal | |
2477 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2478 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2479 | * only every five digits two bignum operations were performed. | |
2480 | */ | |
2481 | ||
2482 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2483 | ||
2484 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2485 | ||
2486 | /* In non ASCII-style encodings the following macro might not work. */ | |
71df73ac KR |
2487 | #define XDIGIT2UINT(d) \ |
2488 | (isdigit ((int) (unsigned char) d) \ | |
2489 | ? (d) - '0' \ | |
2490 | : tolower ((int) (unsigned char) d) - 'a' + 10) | |
3c9a524f | 2491 | |
2a8fecee | 2492 | static SCM |
3c9a524f DH |
2493 | mem2uinteger (const char* mem, size_t len, unsigned int *p_idx, |
2494 | unsigned int radix, enum t_exactness *p_exactness) | |
2a8fecee | 2495 | { |
3c9a524f DH |
2496 | unsigned int idx = *p_idx; |
2497 | unsigned int hash_seen = 0; | |
2498 | scm_t_bits shift = 1; | |
2499 | scm_t_bits add = 0; | |
2500 | unsigned int digit_value; | |
2501 | SCM result; | |
2502 | char c; | |
2503 | ||
2504 | if (idx == len) | |
2505 | return SCM_BOOL_F; | |
2a8fecee | 2506 | |
3c9a524f | 2507 | c = mem[idx]; |
71df73ac | 2508 | if (!isxdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2509 | return SCM_BOOL_F; |
2510 | digit_value = XDIGIT2UINT (c); | |
2511 | if (digit_value >= radix) | |
2512 | return SCM_BOOL_F; | |
2513 | ||
2514 | idx++; | |
d956fa6f | 2515 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 2516 | while (idx != len) |
f872b822 | 2517 | { |
3c9a524f | 2518 | char c = mem[idx]; |
71df73ac | 2519 | if (isxdigit ((int) (unsigned char) c)) |
f872b822 | 2520 | { |
3c9a524f | 2521 | if (hash_seen) |
1fe5e088 | 2522 | break; |
3c9a524f DH |
2523 | digit_value = XDIGIT2UINT (c); |
2524 | if (digit_value >= radix) | |
1fe5e088 | 2525 | break; |
f872b822 | 2526 | } |
3c9a524f DH |
2527 | else if (c == '#') |
2528 | { | |
2529 | hash_seen = 1; | |
2530 | digit_value = 0; | |
2531 | } | |
2532 | else | |
2533 | break; | |
2534 | ||
2535 | idx++; | |
2536 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2537 | { | |
d956fa6f | 2538 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2539 | if (add > 0) |
d956fa6f | 2540 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2541 | |
2542 | shift = radix; | |
2543 | add = digit_value; | |
2544 | } | |
2545 | else | |
2546 | { | |
2547 | shift = shift * radix; | |
2548 | add = add * radix + digit_value; | |
2549 | } | |
2550 | }; | |
2551 | ||
2552 | if (shift > 1) | |
d956fa6f | 2553 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2554 | if (add > 0) |
d956fa6f | 2555 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2556 | |
2557 | *p_idx = idx; | |
2558 | if (hash_seen) | |
2559 | *p_exactness = INEXACT; | |
2560 | ||
2561 | return result; | |
2a8fecee JB |
2562 | } |
2563 | ||
2564 | ||
3c9a524f DH |
2565 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2566 | * covers the parts of the rules that start at a potential point. The value | |
2567 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2568 | * in variable result. The content of *p_exactness indicates, whether a hash |
2569 | * has already been seen in the digits before the point. | |
3c9a524f | 2570 | */ |
1cc91f1b | 2571 | |
3c9a524f DH |
2572 | /* In non ASCII-style encodings the following macro might not work. */ |
2573 | #define DIGIT2UINT(d) ((d) - '0') | |
2574 | ||
2575 | static SCM | |
79d34f68 | 2576 | mem2decimal_from_point (SCM result, const char* mem, size_t len, |
3c9a524f | 2577 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2578 | { |
3c9a524f DH |
2579 | unsigned int idx = *p_idx; |
2580 | enum t_exactness x = *p_exactness; | |
3c9a524f DH |
2581 | |
2582 | if (idx == len) | |
79d34f68 | 2583 | return result; |
3c9a524f DH |
2584 | |
2585 | if (mem[idx] == '.') | |
2586 | { | |
2587 | scm_t_bits shift = 1; | |
2588 | scm_t_bits add = 0; | |
2589 | unsigned int digit_value; | |
d956fa6f | 2590 | SCM big_shift = SCM_I_MAKINUM (1); |
3c9a524f DH |
2591 | |
2592 | idx++; | |
2593 | while (idx != len) | |
2594 | { | |
2595 | char c = mem[idx]; | |
71df73ac | 2596 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2597 | { |
2598 | if (x == INEXACT) | |
2599 | return SCM_BOOL_F; | |
2600 | else | |
2601 | digit_value = DIGIT2UINT (c); | |
2602 | } | |
2603 | else if (c == '#') | |
2604 | { | |
2605 | x = INEXACT; | |
2606 | digit_value = 0; | |
2607 | } | |
2608 | else | |
2609 | break; | |
2610 | ||
2611 | idx++; | |
2612 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2613 | { | |
d956fa6f MV |
2614 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2615 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 2616 | if (add > 0) |
d956fa6f | 2617 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2618 | |
2619 | shift = 10; | |
2620 | add = digit_value; | |
2621 | } | |
2622 | else | |
2623 | { | |
2624 | shift = shift * 10; | |
2625 | add = add * 10 + digit_value; | |
2626 | } | |
2627 | }; | |
2628 | ||
2629 | if (add > 0) | |
2630 | { | |
d956fa6f MV |
2631 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2632 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
2633 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
2634 | } |
2635 | ||
d8592269 | 2636 | result = scm_divide (result, big_shift); |
79d34f68 | 2637 | |
3c9a524f DH |
2638 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2639 | x = INEXACT; | |
f872b822 | 2640 | } |
3c9a524f | 2641 | |
3c9a524f | 2642 | if (idx != len) |
f872b822 | 2643 | { |
3c9a524f DH |
2644 | int sign = 1; |
2645 | unsigned int start; | |
2646 | char c; | |
2647 | int exponent; | |
2648 | SCM e; | |
2649 | ||
2650 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2651 | ||
2652 | switch (mem[idx]) | |
f872b822 | 2653 | { |
3c9a524f DH |
2654 | case 'd': case 'D': |
2655 | case 'e': case 'E': | |
2656 | case 'f': case 'F': | |
2657 | case 'l': case 'L': | |
2658 | case 's': case 'S': | |
2659 | idx++; | |
2660 | start = idx; | |
2661 | c = mem[idx]; | |
2662 | if (c == '-') | |
2663 | { | |
2664 | idx++; | |
2665 | sign = -1; | |
2666 | c = mem[idx]; | |
2667 | } | |
2668 | else if (c == '+') | |
2669 | { | |
2670 | idx++; | |
2671 | sign = 1; | |
2672 | c = mem[idx]; | |
2673 | } | |
2674 | else | |
2675 | sign = 1; | |
2676 | ||
71df73ac | 2677 | if (!isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2678 | return SCM_BOOL_F; |
2679 | ||
2680 | idx++; | |
2681 | exponent = DIGIT2UINT (c); | |
2682 | while (idx != len) | |
f872b822 | 2683 | { |
3c9a524f | 2684 | char c = mem[idx]; |
71df73ac | 2685 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2686 | { |
2687 | idx++; | |
2688 | if (exponent <= SCM_MAXEXP) | |
2689 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2690 | } | |
2691 | else | |
2692 | break; | |
f872b822 | 2693 | } |
3c9a524f DH |
2694 | |
2695 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2696 | { |
3c9a524f | 2697 | size_t exp_len = idx - start; |
cc95e00a | 2698 | SCM exp_string = scm_from_locale_stringn (&mem[start], exp_len); |
3c9a524f DH |
2699 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
2700 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2701 | } |
3c9a524f | 2702 | |
d956fa6f | 2703 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
2704 | if (sign == 1) |
2705 | result = scm_product (result, e); | |
2706 | else | |
f92e85f7 | 2707 | result = scm_divide2real (result, e); |
3c9a524f DH |
2708 | |
2709 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2710 | x = INEXACT; | |
2711 | ||
f872b822 | 2712 | break; |
3c9a524f | 2713 | |
f872b822 | 2714 | default: |
3c9a524f | 2715 | break; |
f872b822 | 2716 | } |
0f2d19dd | 2717 | } |
3c9a524f DH |
2718 | |
2719 | *p_idx = idx; | |
2720 | if (x == INEXACT) | |
2721 | *p_exactness = x; | |
2722 | ||
2723 | return result; | |
0f2d19dd | 2724 | } |
0f2d19dd | 2725 | |
3c9a524f DH |
2726 | |
2727 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2728 | ||
2729 | static SCM | |
2730 | mem2ureal (const char* mem, size_t len, unsigned int *p_idx, | |
2731 | unsigned int radix, enum t_exactness *p_exactness) | |
0f2d19dd | 2732 | { |
3c9a524f | 2733 | unsigned int idx = *p_idx; |
164d2481 | 2734 | SCM result; |
3c9a524f DH |
2735 | |
2736 | if (idx == len) | |
2737 | return SCM_BOOL_F; | |
2738 | ||
7351e207 MV |
2739 | if (idx+5 <= len && !strncmp (mem+idx, "inf.0", 5)) |
2740 | { | |
2741 | *p_idx = idx+5; | |
2742 | return scm_inf (); | |
2743 | } | |
2744 | ||
2745 | if (idx+4 < len && !strncmp (mem+idx, "nan.", 4)) | |
2746 | { | |
2747 | enum t_exactness x = EXACT; | |
2748 | ||
d8592269 MV |
2749 | /* Cobble up the fractional part. We might want to set the |
2750 | NaN's mantissa from it. */ | |
7351e207 MV |
2751 | idx += 4; |
2752 | mem2uinteger (mem, len, &idx, 10, &x); | |
2753 | *p_idx = idx; | |
2754 | return scm_nan (); | |
2755 | } | |
2756 | ||
3c9a524f DH |
2757 | if (mem[idx] == '.') |
2758 | { | |
2759 | if (radix != 10) | |
2760 | return SCM_BOOL_F; | |
2761 | else if (idx + 1 == len) | |
2762 | return SCM_BOOL_F; | |
71df73ac | 2763 | else if (!isdigit ((int) (unsigned char) mem[idx + 1])) |
3c9a524f DH |
2764 | return SCM_BOOL_F; |
2765 | else | |
d956fa6f | 2766 | result = mem2decimal_from_point (SCM_I_MAKINUM (0), mem, len, |
164d2481 | 2767 | p_idx, p_exactness); |
f872b822 | 2768 | } |
3c9a524f DH |
2769 | else |
2770 | { | |
2771 | enum t_exactness x = EXACT; | |
2772 | SCM uinteger; | |
3c9a524f DH |
2773 | |
2774 | uinteger = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2775 | if (scm_is_false (uinteger)) |
3c9a524f DH |
2776 | return SCM_BOOL_F; |
2777 | ||
2778 | if (idx == len) | |
2779 | result = uinteger; | |
2780 | else if (mem[idx] == '/') | |
f872b822 | 2781 | { |
3c9a524f DH |
2782 | SCM divisor; |
2783 | ||
2784 | idx++; | |
2785 | ||
2786 | divisor = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2787 | if (scm_is_false (divisor)) |
3c9a524f DH |
2788 | return SCM_BOOL_F; |
2789 | ||
f92e85f7 | 2790 | /* both are int/big here, I assume */ |
cba42c93 | 2791 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 2792 | } |
3c9a524f DH |
2793 | else if (radix == 10) |
2794 | { | |
2795 | result = mem2decimal_from_point (uinteger, mem, len, &idx, &x); | |
73e4de09 | 2796 | if (scm_is_false (result)) |
3c9a524f DH |
2797 | return SCM_BOOL_F; |
2798 | } | |
2799 | else | |
2800 | result = uinteger; | |
2801 | ||
2802 | *p_idx = idx; | |
2803 | if (x == INEXACT) | |
2804 | *p_exactness = x; | |
f872b822 | 2805 | } |
164d2481 MV |
2806 | |
2807 | /* When returning an inexact zero, make sure it is represented as a | |
2808 | floating point value so that we can change its sign. | |
2809 | */ | |
bc36d050 | 2810 | if (scm_is_eq (result, SCM_I_MAKINUM(0)) && *p_exactness == INEXACT) |
55f26379 | 2811 | result = scm_from_double (0.0); |
164d2481 MV |
2812 | |
2813 | return result; | |
3c9a524f | 2814 | } |
0f2d19dd | 2815 | |
0f2d19dd | 2816 | |
3c9a524f | 2817 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2818 | |
3c9a524f DH |
2819 | static SCM |
2820 | mem2complex (const char* mem, size_t len, unsigned int idx, | |
2821 | unsigned int radix, enum t_exactness *p_exactness) | |
2822 | { | |
2823 | char c; | |
2824 | int sign = 0; | |
2825 | SCM ureal; | |
2826 | ||
2827 | if (idx == len) | |
2828 | return SCM_BOOL_F; | |
2829 | ||
2830 | c = mem[idx]; | |
2831 | if (c == '+') | |
2832 | { | |
2833 | idx++; | |
2834 | sign = 1; | |
2835 | } | |
2836 | else if (c == '-') | |
2837 | { | |
2838 | idx++; | |
2839 | sign = -1; | |
0f2d19dd | 2840 | } |
0f2d19dd | 2841 | |
3c9a524f DH |
2842 | if (idx == len) |
2843 | return SCM_BOOL_F; | |
2844 | ||
2845 | ureal = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2846 | if (scm_is_false (ureal)) |
f872b822 | 2847 | { |
3c9a524f DH |
2848 | /* input must be either +i or -i */ |
2849 | ||
2850 | if (sign == 0) | |
2851 | return SCM_BOOL_F; | |
2852 | ||
2853 | if (mem[idx] == 'i' || mem[idx] == 'I') | |
f872b822 | 2854 | { |
3c9a524f DH |
2855 | idx++; |
2856 | if (idx != len) | |
2857 | return SCM_BOOL_F; | |
2858 | ||
d956fa6f | 2859 | return scm_make_rectangular (SCM_I_MAKINUM (0), SCM_I_MAKINUM (sign)); |
f872b822 | 2860 | } |
3c9a524f DH |
2861 | else |
2862 | return SCM_BOOL_F; | |
0f2d19dd | 2863 | } |
3c9a524f DH |
2864 | else |
2865 | { | |
73e4de09 | 2866 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 2867 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 2868 | |
3c9a524f DH |
2869 | if (idx == len) |
2870 | return ureal; | |
2871 | ||
2872 | c = mem[idx]; | |
2873 | switch (c) | |
f872b822 | 2874 | { |
3c9a524f DH |
2875 | case 'i': case 'I': |
2876 | /* either +<ureal>i or -<ureal>i */ | |
2877 | ||
2878 | idx++; | |
2879 | if (sign == 0) | |
2880 | return SCM_BOOL_F; | |
2881 | if (idx != len) | |
2882 | return SCM_BOOL_F; | |
d956fa6f | 2883 | return scm_make_rectangular (SCM_I_MAKINUM (0), ureal); |
3c9a524f DH |
2884 | |
2885 | case '@': | |
2886 | /* polar input: <real>@<real>. */ | |
2887 | ||
2888 | idx++; | |
2889 | if (idx == len) | |
2890 | return SCM_BOOL_F; | |
2891 | else | |
f872b822 | 2892 | { |
3c9a524f DH |
2893 | int sign; |
2894 | SCM angle; | |
2895 | SCM result; | |
2896 | ||
2897 | c = mem[idx]; | |
2898 | if (c == '+') | |
2899 | { | |
2900 | idx++; | |
2901 | sign = 1; | |
2902 | } | |
2903 | else if (c == '-') | |
2904 | { | |
2905 | idx++; | |
2906 | sign = -1; | |
2907 | } | |
2908 | else | |
2909 | sign = 1; | |
2910 | ||
2911 | angle = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2912 | if (scm_is_false (angle)) |
3c9a524f DH |
2913 | return SCM_BOOL_F; |
2914 | if (idx != len) | |
2915 | return SCM_BOOL_F; | |
2916 | ||
73e4de09 | 2917 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
2918 | angle = scm_difference (angle, SCM_UNDEFINED); |
2919 | ||
2920 | result = scm_make_polar (ureal, angle); | |
2921 | return result; | |
f872b822 | 2922 | } |
3c9a524f DH |
2923 | case '+': |
2924 | case '-': | |
2925 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 2926 | |
3c9a524f DH |
2927 | idx++; |
2928 | if (idx == len) | |
2929 | return SCM_BOOL_F; | |
2930 | else | |
2931 | { | |
2932 | int sign = (c == '+') ? 1 : -1; | |
2933 | SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness); | |
0f2d19dd | 2934 | |
73e4de09 | 2935 | if (scm_is_false (imag)) |
d956fa6f | 2936 | imag = SCM_I_MAKINUM (sign); |
73e4de09 | 2937 | else if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
1fe5e088 | 2938 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 2939 | |
3c9a524f DH |
2940 | if (idx == len) |
2941 | return SCM_BOOL_F; | |
2942 | if (mem[idx] != 'i' && mem[idx] != 'I') | |
2943 | return SCM_BOOL_F; | |
0f2d19dd | 2944 | |
3c9a524f DH |
2945 | idx++; |
2946 | if (idx != len) | |
2947 | return SCM_BOOL_F; | |
0f2d19dd | 2948 | |
1fe5e088 | 2949 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
2950 | } |
2951 | default: | |
2952 | return SCM_BOOL_F; | |
2953 | } | |
2954 | } | |
0f2d19dd | 2955 | } |
0f2d19dd JB |
2956 | |
2957 | ||
3c9a524f DH |
2958 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
2959 | ||
2960 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 2961 | |
0f2d19dd | 2962 | SCM |
2b829bbb KR |
2963 | scm_c_locale_stringn_to_number (const char* mem, size_t len, |
2964 | unsigned int default_radix) | |
0f2d19dd | 2965 | { |
3c9a524f DH |
2966 | unsigned int idx = 0; |
2967 | unsigned int radix = NO_RADIX; | |
2968 | enum t_exactness forced_x = NO_EXACTNESS; | |
2969 | enum t_exactness implicit_x = EXACT; | |
2970 | SCM result; | |
2971 | ||
2972 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
2973 | while (idx + 2 < len && mem[idx] == '#') | |
2974 | { | |
2975 | switch (mem[idx + 1]) | |
2976 | { | |
2977 | case 'b': case 'B': | |
2978 | if (radix != NO_RADIX) | |
2979 | return SCM_BOOL_F; | |
2980 | radix = DUAL; | |
2981 | break; | |
2982 | case 'd': case 'D': | |
2983 | if (radix != NO_RADIX) | |
2984 | return SCM_BOOL_F; | |
2985 | radix = DEC; | |
2986 | break; | |
2987 | case 'i': case 'I': | |
2988 | if (forced_x != NO_EXACTNESS) | |
2989 | return SCM_BOOL_F; | |
2990 | forced_x = INEXACT; | |
2991 | break; | |
2992 | case 'e': case 'E': | |
2993 | if (forced_x != NO_EXACTNESS) | |
2994 | return SCM_BOOL_F; | |
2995 | forced_x = EXACT; | |
2996 | break; | |
2997 | case 'o': case 'O': | |
2998 | if (radix != NO_RADIX) | |
2999 | return SCM_BOOL_F; | |
3000 | radix = OCT; | |
3001 | break; | |
3002 | case 'x': case 'X': | |
3003 | if (radix != NO_RADIX) | |
3004 | return SCM_BOOL_F; | |
3005 | radix = HEX; | |
3006 | break; | |
3007 | default: | |
f872b822 | 3008 | return SCM_BOOL_F; |
3c9a524f DH |
3009 | } |
3010 | idx += 2; | |
3011 | } | |
3012 | ||
3013 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
3014 | if (radix == NO_RADIX) | |
3015 | result = mem2complex (mem, len, idx, default_radix, &implicit_x); | |
3016 | else | |
3017 | result = mem2complex (mem, len, idx, (unsigned int) radix, &implicit_x); | |
3018 | ||
73e4de09 | 3019 | if (scm_is_false (result)) |
3c9a524f | 3020 | return SCM_BOOL_F; |
f872b822 | 3021 | |
3c9a524f | 3022 | switch (forced_x) |
f872b822 | 3023 | { |
3c9a524f DH |
3024 | case EXACT: |
3025 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
3026 | return scm_inexact_to_exact (result); |
3027 | else | |
3028 | return result; | |
3029 | case INEXACT: | |
3030 | if (SCM_INEXACTP (result)) | |
3031 | return result; | |
3032 | else | |
3033 | return scm_exact_to_inexact (result); | |
3034 | case NO_EXACTNESS: | |
3035 | default: | |
3036 | if (implicit_x == INEXACT) | |
3037 | { | |
3038 | if (SCM_INEXACTP (result)) | |
3039 | return result; | |
3040 | else | |
3041 | return scm_exact_to_inexact (result); | |
3042 | } | |
3043 | else | |
3044 | return result; | |
f872b822 | 3045 | } |
0f2d19dd JB |
3046 | } |
3047 | ||
3048 | ||
a1ec6916 | 3049 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 3050 | (SCM string, SCM radix), |
1e6808ea | 3051 | "Return a number of the maximally precise representation\n" |
942e5b91 | 3052 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
3053 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
3054 | "is a default radix that may be overridden by an explicit radix\n" | |
3055 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
3056 | "supplied, then the default radix is 10. If string is not a\n" | |
3057 | "syntactically valid notation for a number, then\n" | |
3058 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 3059 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
3060 | { |
3061 | SCM answer; | |
5efd3c7d | 3062 | unsigned int base; |
a6d9e5ab | 3063 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
3064 | |
3065 | if (SCM_UNBNDP (radix)) | |
3066 | base = 10; | |
3067 | else | |
3068 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
3069 | ||
2b829bbb KR |
3070 | answer = scm_c_locale_stringn_to_number (scm_i_string_chars (string), |
3071 | scm_i_string_length (string), | |
3072 | base); | |
8824ac88 MV |
3073 | scm_remember_upto_here_1 (string); |
3074 | return answer; | |
0f2d19dd | 3075 | } |
1bbd0b84 | 3076 | #undef FUNC_NAME |
3c9a524f DH |
3077 | |
3078 | ||
0f2d19dd JB |
3079 | /*** END strs->nums ***/ |
3080 | ||
5986c47d | 3081 | |
0f2d19dd | 3082 | SCM |
1bbd0b84 | 3083 | scm_bigequal (SCM x, SCM y) |
0f2d19dd | 3084 | { |
47ae1f0e | 3085 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
ca46fb90 | 3086 | scm_remember_upto_here_2 (x, y); |
73e4de09 | 3087 | return scm_from_bool (0 == result); |
0f2d19dd JB |
3088 | } |
3089 | ||
0f2d19dd | 3090 | SCM |
f3ae5d60 | 3091 | scm_real_equalp (SCM x, SCM y) |
0f2d19dd | 3092 | { |
73e4de09 | 3093 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0f2d19dd JB |
3094 | } |
3095 | ||
f3ae5d60 MD |
3096 | SCM |
3097 | scm_complex_equalp (SCM x, SCM y) | |
3098 | { | |
73e4de09 | 3099 | return scm_from_bool (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) |
f3ae5d60 MD |
3100 | && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); |
3101 | } | |
0f2d19dd | 3102 | |
f92e85f7 MV |
3103 | SCM |
3104 | scm_i_fraction_equalp (SCM x, SCM y) | |
3105 | { | |
73e4de09 | 3106 | if (scm_is_false (scm_equal_p (SCM_FRACTION_NUMERATOR (x), |
02164269 | 3107 | SCM_FRACTION_NUMERATOR (y))) |
73e4de09 | 3108 | || scm_is_false (scm_equal_p (SCM_FRACTION_DENOMINATOR (x), |
02164269 MV |
3109 | SCM_FRACTION_DENOMINATOR (y)))) |
3110 | return SCM_BOOL_F; | |
3111 | else | |
3112 | return SCM_BOOL_T; | |
f92e85f7 | 3113 | } |
0f2d19dd JB |
3114 | |
3115 | ||
8507ec80 MV |
3116 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
3117 | (SCM x), | |
3118 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
3119 | "otherwise.") | |
3120 | #define FUNC_NAME s_scm_number_p | |
3121 | { | |
3122 | return scm_from_bool (SCM_NUMBERP (x)); | |
3123 | } | |
3124 | #undef FUNC_NAME | |
3125 | ||
3126 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 3127 | (SCM x), |
942e5b91 | 3128 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 3129 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
3130 | "values form subsets of the set of complex numbers, i. e. the\n" |
3131 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
3132 | "rational or integer number.") | |
8507ec80 | 3133 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 3134 | { |
8507ec80 MV |
3135 | /* all numbers are complex. */ |
3136 | return scm_number_p (x); | |
0f2d19dd | 3137 | } |
1bbd0b84 | 3138 | #undef FUNC_NAME |
0f2d19dd | 3139 | |
f92e85f7 MV |
3140 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
3141 | (SCM x), | |
3142 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
3143 | "otherwise. Note that the set of integer values forms a subset of\n" | |
3144 | "the set of real numbers, i. e. the predicate will also be\n" | |
3145 | "fulfilled if @var{x} is an integer number.") | |
3146 | #define FUNC_NAME s_scm_real_p | |
3147 | { | |
3148 | /* we can't represent irrational numbers. */ | |
3149 | return scm_rational_p (x); | |
3150 | } | |
3151 | #undef FUNC_NAME | |
3152 | ||
3153 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 3154 | (SCM x), |
942e5b91 | 3155 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 3156 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 3157 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
3158 | "fulfilled if @var{x} is an integer number.") |
3159 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 3160 | { |
e11e83f3 | 3161 | if (SCM_I_INUMP (x)) |
0f2d19dd | 3162 | return SCM_BOOL_T; |
0aacf84e | 3163 | else if (SCM_IMP (x)) |
0f2d19dd | 3164 | return SCM_BOOL_F; |
0aacf84e | 3165 | else if (SCM_BIGP (x)) |
0f2d19dd | 3166 | return SCM_BOOL_T; |
f92e85f7 MV |
3167 | else if (SCM_FRACTIONP (x)) |
3168 | return SCM_BOOL_T; | |
3169 | else if (SCM_REALP (x)) | |
3170 | /* due to their limited precision, all floating point numbers are | |
3171 | rational as well. */ | |
3172 | return SCM_BOOL_T; | |
0aacf84e | 3173 | else |
bb628794 | 3174 | return SCM_BOOL_F; |
0f2d19dd | 3175 | } |
1bbd0b84 | 3176 | #undef FUNC_NAME |
0f2d19dd | 3177 | |
a1ec6916 | 3178 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 3179 | (SCM x), |
942e5b91 MG |
3180 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
3181 | "else.") | |
1bbd0b84 | 3182 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd JB |
3183 | { |
3184 | double r; | |
e11e83f3 | 3185 | if (SCM_I_INUMP (x)) |
f872b822 MD |
3186 | return SCM_BOOL_T; |
3187 | if (SCM_IMP (x)) | |
3188 | return SCM_BOOL_F; | |
f872b822 MD |
3189 | if (SCM_BIGP (x)) |
3190 | return SCM_BOOL_T; | |
3c9a524f | 3191 | if (!SCM_INEXACTP (x)) |
f872b822 | 3192 | return SCM_BOOL_F; |
3c9a524f | 3193 | if (SCM_COMPLEXP (x)) |
f872b822 | 3194 | return SCM_BOOL_F; |
5986c47d | 3195 | r = SCM_REAL_VALUE (x); |
1e35a229 | 3196 | /* +/-inf passes r==floor(r), making those #t */ |
f872b822 MD |
3197 | if (r == floor (r)) |
3198 | return SCM_BOOL_T; | |
0f2d19dd JB |
3199 | return SCM_BOOL_F; |
3200 | } | |
1bbd0b84 | 3201 | #undef FUNC_NAME |
0f2d19dd JB |
3202 | |
3203 | ||
a1ec6916 | 3204 | SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, |
1bbd0b84 | 3205 | (SCM x), |
942e5b91 MG |
3206 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" |
3207 | "else.") | |
1bbd0b84 | 3208 | #define FUNC_NAME s_scm_inexact_p |
0f2d19dd | 3209 | { |
eb927cb9 MV |
3210 | if (SCM_INEXACTP (x)) |
3211 | return SCM_BOOL_T; | |
3212 | if (SCM_NUMBERP (x)) | |
3213 | return SCM_BOOL_F; | |
3214 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 3215 | } |
1bbd0b84 | 3216 | #undef FUNC_NAME |
0f2d19dd JB |
3217 | |
3218 | ||
152f82bf | 3219 | SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p); |
942e5b91 | 3220 | /* "Return @code{#t} if all parameters are numerically equal." */ |
0f2d19dd | 3221 | SCM |
6e8d25a6 | 3222 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 3223 | { |
d8b95e27 | 3224 | again: |
e11e83f3 | 3225 | if (SCM_I_INUMP (x)) |
0aacf84e | 3226 | { |
e11e83f3 MV |
3227 | long xx = SCM_I_INUM (x); |
3228 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3229 | { |
e11e83f3 | 3230 | long yy = SCM_I_INUM (y); |
73e4de09 | 3231 | return scm_from_bool (xx == yy); |
0aacf84e MD |
3232 | } |
3233 | else if (SCM_BIGP (y)) | |
3234 | return SCM_BOOL_F; | |
3235 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
3236 | { |
3237 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
3238 | to a double and compare. | |
3239 | ||
3240 | But on a 64-bit system an inum is bigger than a double and | |
3241 | casting it to a double (call that dxx) will round. dxx is at | |
3242 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
3243 | an integer and fits a long. So we cast yy to a long and | |
3244 | compare with plain xx. | |
3245 | ||
3246 | An alternative (for any size system actually) would be to check | |
3247 | yy is an integer (with floor) and is in range of an inum | |
3248 | (compare against appropriate powers of 2) then test | |
3249 | xx==(long)yy. It's just a matter of which casts/comparisons | |
3250 | might be fastest or easiest for the cpu. */ | |
3251 | ||
3252 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
3253 | return scm_from_bool ((double) xx == yy |
3254 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
3255 | || xx == (long) yy)); | |
e8c5b1f2 | 3256 | } |
0aacf84e | 3257 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3258 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3259 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
3260 | else if (SCM_FRACTIONP (y)) |
3261 | return SCM_BOOL_F; | |
0aacf84e MD |
3262 | else |
3263 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3264 | } |
0aacf84e MD |
3265 | else if (SCM_BIGP (x)) |
3266 | { | |
e11e83f3 | 3267 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3268 | return SCM_BOOL_F; |
3269 | else if (SCM_BIGP (y)) | |
3270 | { | |
3271 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3272 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3273 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3274 | } |
3275 | else if (SCM_REALP (y)) | |
3276 | { | |
3277 | int cmp; | |
3278 | if (xisnan (SCM_REAL_VALUE (y))) | |
3279 | return SCM_BOOL_F; | |
3280 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3281 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3282 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3283 | } |
3284 | else if (SCM_COMPLEXP (y)) | |
3285 | { | |
3286 | int cmp; | |
3287 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
3288 | return SCM_BOOL_F; | |
3289 | if (xisnan (SCM_COMPLEX_REAL (y))) | |
3290 | return SCM_BOOL_F; | |
3291 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
3292 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3293 | return scm_from_bool (0 == cmp); |
0aacf84e | 3294 | } |
f92e85f7 MV |
3295 | else if (SCM_FRACTIONP (y)) |
3296 | return SCM_BOOL_F; | |
0aacf84e MD |
3297 | else |
3298 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3299 | } |
0aacf84e MD |
3300 | else if (SCM_REALP (x)) |
3301 | { | |
e8c5b1f2 | 3302 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 3303 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
3304 | { |
3305 | /* see comments with inum/real above */ | |
3306 | long yy = SCM_I_INUM (y); | |
3a1b45fd MV |
3307 | return scm_from_bool (xx == (double) yy |
3308 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
3309 | || (long) xx == yy)); | |
e8c5b1f2 | 3310 | } |
0aacf84e MD |
3311 | else if (SCM_BIGP (y)) |
3312 | { | |
3313 | int cmp; | |
3314 | if (xisnan (SCM_REAL_VALUE (x))) | |
3315 | return SCM_BOOL_F; | |
3316 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3317 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3318 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3319 | } |
3320 | else if (SCM_REALP (y)) | |
73e4de09 | 3321 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 3322 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3323 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3324 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3325 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3326 | { |
3327 | double xx = SCM_REAL_VALUE (x); | |
3328 | if (xisnan (xx)) | |
3329 | return SCM_BOOL_F; | |
3330 | if (xisinf (xx)) | |
73e4de09 | 3331 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3332 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3333 | goto again; | |
3334 | } | |
0aacf84e MD |
3335 | else |
3336 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3337 | } |
0aacf84e MD |
3338 | else if (SCM_COMPLEXP (x)) |
3339 | { | |
e11e83f3 MV |
3340 | if (SCM_I_INUMP (y)) |
3341 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
3342 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3343 | else if (SCM_BIGP (y)) | |
3344 | { | |
3345 | int cmp; | |
3346 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
3347 | return SCM_BOOL_F; | |
3348 | if (xisnan (SCM_COMPLEX_REAL (x))) | |
3349 | return SCM_BOOL_F; | |
3350 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
3351 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3352 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3353 | } |
3354 | else if (SCM_REALP (y)) | |
73e4de09 | 3355 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
3356 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3357 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 3358 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3359 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3360 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3361 | { |
3362 | double xx; | |
3363 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
3364 | return SCM_BOOL_F; | |
3365 | xx = SCM_COMPLEX_REAL (x); | |
3366 | if (xisnan (xx)) | |
3367 | return SCM_BOOL_F; | |
3368 | if (xisinf (xx)) | |
73e4de09 | 3369 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3370 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3371 | goto again; | |
3372 | } | |
f92e85f7 MV |
3373 | else |
3374 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
3375 | } | |
3376 | else if (SCM_FRACTIONP (x)) | |
3377 | { | |
e11e83f3 | 3378 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
3379 | return SCM_BOOL_F; |
3380 | else if (SCM_BIGP (y)) | |
3381 | return SCM_BOOL_F; | |
3382 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
3383 | { |
3384 | double yy = SCM_REAL_VALUE (y); | |
3385 | if (xisnan (yy)) | |
3386 | return SCM_BOOL_F; | |
3387 | if (xisinf (yy)) | |
73e4de09 | 3388 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3389 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3390 | goto again; | |
3391 | } | |
f92e85f7 | 3392 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
3393 | { |
3394 | double yy; | |
3395 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
3396 | return SCM_BOOL_F; | |
3397 | yy = SCM_COMPLEX_REAL (y); | |
3398 | if (xisnan (yy)) | |
3399 | return SCM_BOOL_F; | |
3400 | if (xisinf (yy)) | |
73e4de09 | 3401 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3402 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3403 | goto again; | |
3404 | } | |
f92e85f7 MV |
3405 | else if (SCM_FRACTIONP (y)) |
3406 | return scm_i_fraction_equalp (x, y); | |
0aacf84e MD |
3407 | else |
3408 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3409 | } |
0aacf84e | 3410 | else |
f4c627b3 | 3411 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p); |
0f2d19dd JB |
3412 | } |
3413 | ||
3414 | ||
a5f0b599 KR |
3415 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
3416 | done are good for inums, but for bignums an answer can almost always be | |
3417 | had by just examining a few high bits of the operands, as done by GMP in | |
3418 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
3419 | of the float exponent to take into account. */ | |
3420 | ||
152f82bf | 3421 | SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p); |
942e5b91 MG |
3422 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3423 | * "increasing." | |
3424 | */ | |
0f2d19dd | 3425 | SCM |
6e8d25a6 | 3426 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3427 | { |
a5f0b599 | 3428 | again: |
e11e83f3 | 3429 | if (SCM_I_INUMP (x)) |
0aacf84e | 3430 | { |
e11e83f3 MV |
3431 | long xx = SCM_I_INUM (x); |
3432 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3433 | { |
e11e83f3 | 3434 | long yy = SCM_I_INUM (y); |
73e4de09 | 3435 | return scm_from_bool (xx < yy); |
0aacf84e MD |
3436 | } |
3437 | else if (SCM_BIGP (y)) | |
3438 | { | |
3439 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3440 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3441 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3442 | } |
3443 | else if (SCM_REALP (y)) | |
73e4de09 | 3444 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 3445 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3446 | { |
3447 | /* "x < a/b" becomes "x*b < a" */ | |
3448 | int_frac: | |
3449 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
3450 | y = SCM_FRACTION_NUMERATOR (y); | |
3451 | goto again; | |
3452 | } | |
0aacf84e MD |
3453 | else |
3454 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3455 | } |
0aacf84e MD |
3456 | else if (SCM_BIGP (x)) |
3457 | { | |
e11e83f3 | 3458 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3459 | { |
3460 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3461 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3462 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3463 | } |
3464 | else if (SCM_BIGP (y)) | |
3465 | { | |
3466 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3467 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3468 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
3469 | } |
3470 | else if (SCM_REALP (y)) | |
3471 | { | |
3472 | int cmp; | |
3473 | if (xisnan (SCM_REAL_VALUE (y))) | |
3474 | return SCM_BOOL_F; | |
3475 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3476 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3477 | return scm_from_bool (cmp < 0); |
0aacf84e | 3478 | } |
f92e85f7 | 3479 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 3480 | goto int_frac; |
0aacf84e MD |
3481 | else |
3482 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f4c627b3 | 3483 | } |
0aacf84e MD |
3484 | else if (SCM_REALP (x)) |
3485 | { | |
e11e83f3 MV |
3486 | if (SCM_I_INUMP (y)) |
3487 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3488 | else if (SCM_BIGP (y)) |
3489 | { | |
3490 | int cmp; | |
3491 | if (xisnan (SCM_REAL_VALUE (x))) | |
3492 | return SCM_BOOL_F; | |
3493 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3494 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3495 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
3496 | } |
3497 | else if (SCM_REALP (y)) | |
73e4de09 | 3498 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 3499 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3500 | { |
3501 | double xx = SCM_REAL_VALUE (x); | |
3502 | if (xisnan (xx)) | |
3503 | return SCM_BOOL_F; | |
3504 | if (xisinf (xx)) | |
73e4de09 | 3505 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
3506 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3507 | goto again; | |
3508 | } | |
f92e85f7 MV |
3509 | else |
3510 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
3511 | } | |
3512 | else if (SCM_FRACTIONP (x)) | |
3513 | { | |
e11e83f3 | 3514 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
3515 | { |
3516 | /* "a/b < y" becomes "a < y*b" */ | |
3517 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
3518 | x = SCM_FRACTION_NUMERATOR (x); | |
3519 | goto again; | |
3520 | } | |
f92e85f7 | 3521 | else if (SCM_REALP (y)) |
a5f0b599 KR |
3522 | { |
3523 | double yy = SCM_REAL_VALUE (y); | |
3524 | if (xisnan (yy)) | |
3525 | return SCM_BOOL_F; | |
3526 | if (xisinf (yy)) | |
73e4de09 | 3527 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
3528 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3529 | goto again; | |
3530 | } | |
f92e85f7 | 3531 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3532 | { |
3533 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
3534 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
3535 | SCM_FRACTION_DENOMINATOR (y)); | |
3536 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
3537 | SCM_FRACTION_DENOMINATOR (x)); | |
3538 | x = new_x; | |
3539 | y = new_y; | |
3540 | goto again; | |
3541 | } | |
0aacf84e MD |
3542 | else |
3543 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3544 | } |
0aacf84e | 3545 | else |
f4c627b3 | 3546 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p); |
0f2d19dd JB |
3547 | } |
3548 | ||
3549 | ||
c76b1eaf | 3550 | SCM_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p); |
942e5b91 MG |
3551 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3552 | * "decreasing." | |
c76b1eaf | 3553 | */ |
1bbd0b84 | 3554 | #define FUNC_NAME s_scm_gr_p |
c76b1eaf MD |
3555 | SCM |
3556 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3557 | { |
c76b1eaf MD |
3558 | if (!SCM_NUMBERP (x)) |
3559 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME); | |
3560 | else if (!SCM_NUMBERP (y)) | |
3561 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME); | |
3562 | else | |
3563 | return scm_less_p (y, x); | |
0f2d19dd | 3564 | } |
1bbd0b84 | 3565 | #undef FUNC_NAME |
0f2d19dd JB |
3566 | |
3567 | ||
c76b1eaf | 3568 | SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p); |
942e5b91 | 3569 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3570 | * "non-decreasing." |
3571 | */ | |
1bbd0b84 | 3572 | #define FUNC_NAME s_scm_leq_p |
c76b1eaf MD |
3573 | SCM |
3574 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3575 | { |
c76b1eaf MD |
3576 | if (!SCM_NUMBERP (x)) |
3577 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3578 | else if (!SCM_NUMBERP (y)) | |
3579 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3580 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3581 | return SCM_BOOL_F; |
c76b1eaf | 3582 | else |
73e4de09 | 3583 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 3584 | } |
1bbd0b84 | 3585 | #undef FUNC_NAME |
0f2d19dd JB |
3586 | |
3587 | ||
c76b1eaf | 3588 | SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p); |
942e5b91 | 3589 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3590 | * "non-increasing." |
3591 | */ | |
1bbd0b84 | 3592 | #define FUNC_NAME s_scm_geq_p |
c76b1eaf MD |
3593 | SCM |
3594 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3595 | { |
c76b1eaf MD |
3596 | if (!SCM_NUMBERP (x)) |
3597 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3598 | else if (!SCM_NUMBERP (y)) | |
3599 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3600 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3601 | return SCM_BOOL_F; |
c76b1eaf | 3602 | else |
73e4de09 | 3603 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 3604 | } |
1bbd0b84 | 3605 | #undef FUNC_NAME |
0f2d19dd JB |
3606 | |
3607 | ||
152f82bf | 3608 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3609 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3610 | * "zero." | |
3611 | */ | |
0f2d19dd | 3612 | SCM |
6e8d25a6 | 3613 | scm_zero_p (SCM z) |
0f2d19dd | 3614 | { |
e11e83f3 | 3615 | if (SCM_I_INUMP (z)) |
bc36d050 | 3616 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 3617 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 3618 | return SCM_BOOL_F; |
0aacf84e | 3619 | else if (SCM_REALP (z)) |
73e4de09 | 3620 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 3621 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 3622 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 3623 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
3624 | else if (SCM_FRACTIONP (z)) |
3625 | return SCM_BOOL_F; | |
0aacf84e | 3626 | else |
c2ff8ab0 | 3627 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); |
0f2d19dd JB |
3628 | } |
3629 | ||
3630 | ||
152f82bf | 3631 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3632 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3633 | * "zero." | |
3634 | */ | |
0f2d19dd | 3635 | SCM |
6e8d25a6 | 3636 | scm_positive_p (SCM x) |
0f2d19dd | 3637 | { |
e11e83f3 MV |
3638 | if (SCM_I_INUMP (x)) |
3639 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
3640 | else if (SCM_BIGP (x)) |
3641 | { | |
3642 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3643 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3644 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3645 | } |
3646 | else if (SCM_REALP (x)) | |
73e4de09 | 3647 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
3648 | else if (SCM_FRACTIONP (x)) |
3649 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3650 | else |
c2ff8ab0 | 3651 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); |
0f2d19dd JB |
3652 | } |
3653 | ||
3654 | ||
152f82bf | 3655 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3656 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3657 | * "zero." | |
3658 | */ | |
0f2d19dd | 3659 | SCM |
6e8d25a6 | 3660 | scm_negative_p (SCM x) |
0f2d19dd | 3661 | { |
e11e83f3 MV |
3662 | if (SCM_I_INUMP (x)) |
3663 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
3664 | else if (SCM_BIGP (x)) |
3665 | { | |
3666 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3667 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3668 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3669 | } |
3670 | else if (SCM_REALP (x)) | |
73e4de09 | 3671 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
3672 | else if (SCM_FRACTIONP (x)) |
3673 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3674 | else |
c2ff8ab0 | 3675 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); |
0f2d19dd JB |
3676 | } |
3677 | ||
3678 | ||
2a06f791 KR |
3679 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
3680 | required by r5rs. On that basis, for exact/inexact combinations the | |
3681 | exact is converted to inexact to compare and possibly return. This is | |
3682 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
3683 | its test, such trouble is not required for min and max. */ | |
3684 | ||
9de33deb | 3685 | SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max); |
942e5b91 MG |
3686 | /* "Return the maximum of all parameter values." |
3687 | */ | |
0f2d19dd | 3688 | SCM |
6e8d25a6 | 3689 | scm_max (SCM x, SCM y) |
0f2d19dd | 3690 | { |
0aacf84e MD |
3691 | if (SCM_UNBNDP (y)) |
3692 | { | |
3693 | if (SCM_UNBNDP (x)) | |
3694 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 3695 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3696 | return x; |
3697 | else | |
3698 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3699 | } |
f4c627b3 | 3700 | |
e11e83f3 | 3701 | if (SCM_I_INUMP (x)) |
0aacf84e | 3702 | { |
e11e83f3 MV |
3703 | long xx = SCM_I_INUM (x); |
3704 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3705 | { |
e11e83f3 | 3706 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3707 | return (xx < yy) ? y : x; |
3708 | } | |
3709 | else if (SCM_BIGP (y)) | |
3710 | { | |
3711 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3712 | scm_remember_upto_here_1 (y); | |
3713 | return (sgn < 0) ? x : y; | |
3714 | } | |
3715 | else if (SCM_REALP (y)) | |
3716 | { | |
3717 | double z = xx; | |
3718 | /* if y==NaN then ">" is false and we return NaN */ | |
55f26379 | 3719 | return (z > SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3720 | } |
f92e85f7 MV |
3721 | else if (SCM_FRACTIONP (y)) |
3722 | { | |
e4bc5d6c | 3723 | use_less: |
73e4de09 | 3724 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 3725 | } |
0aacf84e MD |
3726 | else |
3727 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3728 | } |
0aacf84e MD |
3729 | else if (SCM_BIGP (x)) |
3730 | { | |
e11e83f3 | 3731 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3732 | { |
3733 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3734 | scm_remember_upto_here_1 (x); | |
3735 | return (sgn < 0) ? y : x; | |
3736 | } | |
3737 | else if (SCM_BIGP (y)) | |
3738 | { | |
3739 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3740 | scm_remember_upto_here_2 (x, y); | |
3741 | return (cmp > 0) ? x : y; | |
3742 | } | |
3743 | else if (SCM_REALP (y)) | |
3744 | { | |
2a06f791 KR |
3745 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
3746 | double xx, yy; | |
3747 | big_real: | |
3748 | xx = scm_i_big2dbl (x); | |
3749 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3750 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 3751 | } |
f92e85f7 MV |
3752 | else if (SCM_FRACTIONP (y)) |
3753 | { | |
e4bc5d6c | 3754 | goto use_less; |
f92e85f7 | 3755 | } |
0aacf84e MD |
3756 | else |
3757 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 3758 | } |
0aacf84e MD |
3759 | else if (SCM_REALP (x)) |
3760 | { | |
e11e83f3 | 3761 | if (SCM_I_INUMP (y)) |
0aacf84e | 3762 | { |
e11e83f3 | 3763 | double z = SCM_I_INUM (y); |
0aacf84e | 3764 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3765 | return (SCM_REAL_VALUE (x) < z) ? scm_from_double (z) : x; |
0aacf84e MD |
3766 | } |
3767 | else if (SCM_BIGP (y)) | |
3768 | { | |
b6f8f763 | 3769 | SCM_SWAP (x, y); |
2a06f791 | 3770 | goto big_real; |
0aacf84e MD |
3771 | } |
3772 | else if (SCM_REALP (y)) | |
3773 | { | |
3774 | /* if x==NaN then our explicit check means we return NaN | |
3775 | if y==NaN then ">" is false and we return NaN | |
3776 | calling isnan is unavoidable, since it's the only way to know | |
3777 | which of x or y causes any compares to be false */ | |
3778 | double xx = SCM_REAL_VALUE (x); | |
3779 | return (xisnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y; | |
3780 | } | |
f92e85f7 MV |
3781 | else if (SCM_FRACTIONP (y)) |
3782 | { | |
3783 | double yy = scm_i_fraction2double (y); | |
3784 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3785 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
3786 | } |
3787 | else | |
3788 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3789 | } | |
3790 | else if (SCM_FRACTIONP (x)) | |
3791 | { | |
e11e83f3 | 3792 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3793 | { |
e4bc5d6c | 3794 | goto use_less; |
f92e85f7 MV |
3795 | } |
3796 | else if (SCM_BIGP (y)) | |
3797 | { | |
e4bc5d6c | 3798 | goto use_less; |
f92e85f7 MV |
3799 | } |
3800 | else if (SCM_REALP (y)) | |
3801 | { | |
3802 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3803 | return (xx < SCM_REAL_VALUE (y)) ? y : scm_from_double (xx); |
f92e85f7 MV |
3804 | } |
3805 | else if (SCM_FRACTIONP (y)) | |
3806 | { | |
e4bc5d6c | 3807 | goto use_less; |
f92e85f7 | 3808 | } |
0aacf84e MD |
3809 | else |
3810 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3811 | } |
0aacf84e | 3812 | else |
f4c627b3 | 3813 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
3814 | } |
3815 | ||
3816 | ||
9de33deb | 3817 | SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min); |
942e5b91 MG |
3818 | /* "Return the minium of all parameter values." |
3819 | */ | |
0f2d19dd | 3820 | SCM |
6e8d25a6 | 3821 | scm_min (SCM x, SCM y) |
0f2d19dd | 3822 | { |
0aacf84e MD |
3823 | if (SCM_UNBNDP (y)) |
3824 | { | |
3825 | if (SCM_UNBNDP (x)) | |
3826 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 3827 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3828 | return x; |
3829 | else | |
3830 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 3831 | } |
f4c627b3 | 3832 | |
e11e83f3 | 3833 | if (SCM_I_INUMP (x)) |
0aacf84e | 3834 | { |
e11e83f3 MV |
3835 | long xx = SCM_I_INUM (x); |
3836 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3837 | { |
e11e83f3 | 3838 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3839 | return (xx < yy) ? x : y; |
3840 | } | |
3841 | else if (SCM_BIGP (y)) | |
3842 | { | |
3843 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3844 | scm_remember_upto_here_1 (y); | |
3845 | return (sgn < 0) ? y : x; | |
3846 | } | |
3847 | else if (SCM_REALP (y)) | |
3848 | { | |
3849 | double z = xx; | |
3850 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 3851 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3852 | } |
f92e85f7 MV |
3853 | else if (SCM_FRACTIONP (y)) |
3854 | { | |
e4bc5d6c | 3855 | use_less: |
73e4de09 | 3856 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 3857 | } |
0aacf84e MD |
3858 | else |
3859 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3860 | } |
0aacf84e MD |
3861 | else if (SCM_BIGP (x)) |
3862 | { | |
e11e83f3 | 3863 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3864 | { |
3865 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3866 | scm_remember_upto_here_1 (x); | |
3867 | return (sgn < 0) ? x : y; | |
3868 | } | |
3869 | else if (SCM_BIGP (y)) | |
3870 | { | |
3871 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3872 | scm_remember_upto_here_2 (x, y); | |
3873 | return (cmp > 0) ? y : x; | |
3874 | } | |
3875 | else if (SCM_REALP (y)) | |
3876 | { | |
2a06f791 KR |
3877 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
3878 | double xx, yy; | |
3879 | big_real: | |
3880 | xx = scm_i_big2dbl (x); | |
3881 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3882 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 3883 | } |
f92e85f7 MV |
3884 | else if (SCM_FRACTIONP (y)) |
3885 | { | |
e4bc5d6c | 3886 | goto use_less; |
f92e85f7 | 3887 | } |
0aacf84e MD |
3888 | else |
3889 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 3890 | } |
0aacf84e MD |
3891 | else if (SCM_REALP (x)) |
3892 | { | |
e11e83f3 | 3893 | if (SCM_I_INUMP (y)) |
0aacf84e | 3894 | { |
e11e83f3 | 3895 | double z = SCM_I_INUM (y); |
0aacf84e | 3896 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3897 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
3898 | } |
3899 | else if (SCM_BIGP (y)) | |
3900 | { | |
b6f8f763 | 3901 | SCM_SWAP (x, y); |
2a06f791 | 3902 | goto big_real; |
0aacf84e MD |
3903 | } |
3904 | else if (SCM_REALP (y)) | |
3905 | { | |
3906 | /* if x==NaN then our explicit check means we return NaN | |
3907 | if y==NaN then "<" is false and we return NaN | |
3908 | calling isnan is unavoidable, since it's the only way to know | |
3909 | which of x or y causes any compares to be false */ | |
3910 | double xx = SCM_REAL_VALUE (x); | |
3911 | return (xisnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y; | |
3912 | } | |
f92e85f7 MV |
3913 | else if (SCM_FRACTIONP (y)) |
3914 | { | |
3915 | double yy = scm_i_fraction2double (y); | |
3916 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3917 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 3918 | } |
0aacf84e MD |
3919 | else |
3920 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3921 | } |
f92e85f7 MV |
3922 | else if (SCM_FRACTIONP (x)) |
3923 | { | |
e11e83f3 | 3924 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3925 | { |
e4bc5d6c | 3926 | goto use_less; |
f92e85f7 MV |
3927 | } |
3928 | else if (SCM_BIGP (y)) | |
3929 | { | |
e4bc5d6c | 3930 | goto use_less; |
f92e85f7 MV |
3931 | } |
3932 | else if (SCM_REALP (y)) | |
3933 | { | |
3934 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3935 | return (SCM_REAL_VALUE (y) < xx) ? y : scm_from_double (xx); |
f92e85f7 MV |
3936 | } |
3937 | else if (SCM_FRACTIONP (y)) | |
3938 | { | |
e4bc5d6c | 3939 | goto use_less; |
f92e85f7 MV |
3940 | } |
3941 | else | |
3942 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3943 | } | |
0aacf84e | 3944 | else |
f4c627b3 | 3945 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
3946 | } |
3947 | ||
3948 | ||
9de33deb | 3949 | SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum); |
942e5b91 MG |
3950 | /* "Return the sum of all parameter values. Return 0 if called without\n" |
3951 | * "any parameters." | |
3952 | */ | |
0f2d19dd | 3953 | SCM |
6e8d25a6 | 3954 | scm_sum (SCM x, SCM y) |
0f2d19dd | 3955 | { |
9cc37597 | 3956 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
3957 | { |
3958 | if (SCM_NUMBERP (x)) return x; | |
3959 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 3960 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 3961 | } |
c209c88e | 3962 | |
9cc37597 | 3963 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
ca46fb90 | 3964 | { |
9cc37597 | 3965 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
ca46fb90 | 3966 | { |
e11e83f3 MV |
3967 | long xx = SCM_I_INUM (x); |
3968 | long yy = SCM_I_INUM (y); | |
ca46fb90 | 3969 | long int z = xx + yy; |
d956fa6f | 3970 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_long2big (z); |
ca46fb90 RB |
3971 | } |
3972 | else if (SCM_BIGP (y)) | |
3973 | { | |
3974 | SCM_SWAP (x, y); | |
3975 | goto add_big_inum; | |
3976 | } | |
3977 | else if (SCM_REALP (y)) | |
3978 | { | |
e11e83f3 | 3979 | long int xx = SCM_I_INUM (x); |
55f26379 | 3980 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
3981 | } |
3982 | else if (SCM_COMPLEXP (y)) | |
3983 | { | |
e11e83f3 | 3984 | long int xx = SCM_I_INUM (x); |
8507ec80 | 3985 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
3986 | SCM_COMPLEX_IMAG (y)); |
3987 | } | |
f92e85f7 | 3988 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 3989 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
3990 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
3991 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
3992 | else |
3993 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
3994 | } else if (SCM_BIGP (x)) |
3995 | { | |
e11e83f3 | 3996 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3997 | { |
3998 | long int inum; | |
3999 | int bigsgn; | |
4000 | add_big_inum: | |
e11e83f3 | 4001 | inum = SCM_I_INUM (y); |
0aacf84e MD |
4002 | if (inum == 0) |
4003 | return x; | |
4004 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4005 | if (inum < 0) | |
4006 | { | |
4007 | SCM result = scm_i_mkbig (); | |
4008 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
4009 | scm_remember_upto_here_1 (x); | |
4010 | /* we know the result will have to be a bignum */ | |
4011 | if (bigsgn == -1) | |
4012 | return result; | |
4013 | return scm_i_normbig (result); | |
4014 | } | |
4015 | else | |
4016 | { | |
4017 | SCM result = scm_i_mkbig (); | |
4018 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
4019 | scm_remember_upto_here_1 (x); | |
4020 | /* we know the result will have to be a bignum */ | |
4021 | if (bigsgn == 1) | |
4022 | return result; | |
4023 | return scm_i_normbig (result); | |
4024 | } | |
4025 | } | |
4026 | else if (SCM_BIGP (y)) | |
4027 | { | |
4028 | SCM result = scm_i_mkbig (); | |
4029 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4030 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4031 | mpz_add (SCM_I_BIG_MPZ (result), | |
4032 | SCM_I_BIG_MPZ (x), | |
4033 | SCM_I_BIG_MPZ (y)); | |
4034 | scm_remember_upto_here_2 (x, y); | |
4035 | /* we know the result will have to be a bignum */ | |
4036 | if (sgn_x == sgn_y) | |
4037 | return result; | |
4038 | return scm_i_normbig (result); | |
4039 | } | |
4040 | else if (SCM_REALP (y)) | |
4041 | { | |
4042 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
4043 | scm_remember_upto_here_1 (x); | |
55f26379 | 4044 | return scm_from_double (result); |
0aacf84e MD |
4045 | } |
4046 | else if (SCM_COMPLEXP (y)) | |
4047 | { | |
4048 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4049 | + SCM_COMPLEX_REAL (y)); | |
4050 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4051 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4052 | } |
f92e85f7 | 4053 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4054 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
4055 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
4056 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4057 | else |
4058 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 4059 | } |
0aacf84e MD |
4060 | else if (SCM_REALP (x)) |
4061 | { | |
e11e83f3 | 4062 | if (SCM_I_INUMP (y)) |
55f26379 | 4063 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
4064 | else if (SCM_BIGP (y)) |
4065 | { | |
4066 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
4067 | scm_remember_upto_here_1 (y); | |
55f26379 | 4068 | return scm_from_double (result); |
0aacf84e MD |
4069 | } |
4070 | else if (SCM_REALP (y)) | |
55f26379 | 4071 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 4072 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4073 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4074 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4075 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4076 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
4077 | else |
4078 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 4079 | } |
0aacf84e MD |
4080 | else if (SCM_COMPLEXP (x)) |
4081 | { | |
e11e83f3 | 4082 | if (SCM_I_INUMP (y)) |
8507ec80 | 4083 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
4084 | SCM_COMPLEX_IMAG (x)); |
4085 | else if (SCM_BIGP (y)) | |
4086 | { | |
4087 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
4088 | + SCM_COMPLEX_REAL (x)); | |
4089 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4090 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4091 | } |
4092 | else if (SCM_REALP (y)) | |
8507ec80 | 4093 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
4094 | SCM_COMPLEX_IMAG (x)); |
4095 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4096 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4097 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4098 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4099 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
4100 | SCM_COMPLEX_IMAG (x)); |
4101 | else | |
4102 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
4103 | } | |
4104 | else if (SCM_FRACTIONP (x)) | |
4105 | { | |
e11e83f3 | 4106 | if (SCM_I_INUMP (y)) |
cba42c93 | 4107 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4108 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4109 | SCM_FRACTION_DENOMINATOR (x)); | |
4110 | else if (SCM_BIGP (y)) | |
cba42c93 | 4111 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4112 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4113 | SCM_FRACTION_DENOMINATOR (x)); | |
4114 | else if (SCM_REALP (y)) | |
55f26379 | 4115 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 4116 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4117 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
4118 | SCM_COMPLEX_IMAG (y)); |
4119 | else if (SCM_FRACTIONP (y)) | |
4120 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 4121 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4122 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4123 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4124 | else |
4125 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 4126 | } |
0aacf84e | 4127 | else |
98cb6e75 | 4128 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
4129 | } |
4130 | ||
4131 | ||
40882e3d KR |
4132 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
4133 | (SCM x), | |
4134 | "Return @math{@var{x}+1}.") | |
4135 | #define FUNC_NAME s_scm_oneplus | |
4136 | { | |
4137 | return scm_sum (x, SCM_I_MAKINUM (1)); | |
4138 | } | |
4139 | #undef FUNC_NAME | |
4140 | ||
4141 | ||
9de33deb | 4142 | SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference); |
609c3d30 MG |
4143 | /* If called with one argument @var{z1}, -@var{z1} returned. Otherwise |
4144 | * the sum of all but the first argument are subtracted from the first | |
4145 | * argument. */ | |
c05e97b7 | 4146 | #define FUNC_NAME s_difference |
0f2d19dd | 4147 | SCM |
6e8d25a6 | 4148 | scm_difference (SCM x, SCM y) |
0f2d19dd | 4149 | { |
9cc37597 | 4150 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
ca46fb90 RB |
4151 | { |
4152 | if (SCM_UNBNDP (x)) | |
4153 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
4154 | else | |
e11e83f3 | 4155 | if (SCM_I_INUMP (x)) |
ca46fb90 | 4156 | { |
e11e83f3 | 4157 | long xx = -SCM_I_INUM (x); |
ca46fb90 | 4158 | if (SCM_FIXABLE (xx)) |
d956fa6f | 4159 | return SCM_I_MAKINUM (xx); |
ca46fb90 RB |
4160 | else |
4161 | return scm_i_long2big (xx); | |
4162 | } | |
4163 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
4164 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
4165 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
4166 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
4167 | else if (SCM_REALP (x)) | |
55f26379 | 4168 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 4169 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 4170 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 4171 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 4172 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4173 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 4174 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
4175 | else |
4176 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 4177 | } |
ca46fb90 | 4178 | |
9cc37597 | 4179 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 4180 | { |
9cc37597 | 4181 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4182 | { |
e11e83f3 MV |
4183 | long int xx = SCM_I_INUM (x); |
4184 | long int yy = SCM_I_INUM (y); | |
0aacf84e MD |
4185 | long int z = xx - yy; |
4186 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4187 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4188 | else |
4189 | return scm_i_long2big (z); | |
4190 | } | |
4191 | else if (SCM_BIGP (y)) | |
4192 | { | |
4193 | /* inum-x - big-y */ | |
e11e83f3 | 4194 | long xx = SCM_I_INUM (x); |
ca46fb90 | 4195 | |
0aacf84e MD |
4196 | if (xx == 0) |
4197 | return scm_i_clonebig (y, 0); | |
4198 | else | |
4199 | { | |
4200 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4201 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4202 | |
0aacf84e MD |
4203 | if (xx >= 0) |
4204 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
4205 | else | |
4206 | { | |
4207 | /* x - y == -(y + -x) */ | |
4208 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
4209 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4210 | } | |
4211 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 4212 | |
0aacf84e MD |
4213 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
4214 | /* we know the result will have to be a bignum */ | |
4215 | return result; | |
4216 | else | |
4217 | return scm_i_normbig (result); | |
4218 | } | |
4219 | } | |
4220 | else if (SCM_REALP (y)) | |
4221 | { | |
e11e83f3 | 4222 | long int xx = SCM_I_INUM (x); |
55f26379 | 4223 | return scm_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
4224 | } |
4225 | else if (SCM_COMPLEXP (y)) | |
4226 | { | |
e11e83f3 | 4227 | long int xx = SCM_I_INUM (x); |
8507ec80 | 4228 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4229 | - SCM_COMPLEX_IMAG (y)); |
4230 | } | |
f92e85f7 MV |
4231 | else if (SCM_FRACTIONP (y)) |
4232 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 4233 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4234 | SCM_FRACTION_NUMERATOR (y)), |
4235 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4236 | else |
4237 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 4238 | } |
0aacf84e MD |
4239 | else if (SCM_BIGP (x)) |
4240 | { | |
e11e83f3 | 4241 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4242 | { |
4243 | /* big-x - inum-y */ | |
e11e83f3 | 4244 | long yy = SCM_I_INUM (y); |
0aacf84e | 4245 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 4246 | |
0aacf84e MD |
4247 | scm_remember_upto_here_1 (x); |
4248 | if (sgn_x == 0) | |
c71b0706 MV |
4249 | return (SCM_FIXABLE (-yy) ? |
4250 | SCM_I_MAKINUM (-yy) : scm_from_long (-yy)); | |
0aacf84e MD |
4251 | else |
4252 | { | |
4253 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4254 | |
708f22c6 KR |
4255 | if (yy >= 0) |
4256 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
4257 | else | |
4258 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 4259 | scm_remember_upto_here_1 (x); |
ca46fb90 | 4260 | |
0aacf84e MD |
4261 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
4262 | /* we know the result will have to be a bignum */ | |
4263 | return result; | |
4264 | else | |
4265 | return scm_i_normbig (result); | |
4266 | } | |
4267 | } | |
4268 | else if (SCM_BIGP (y)) | |
4269 | { | |
4270 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4271 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4272 | SCM result = scm_i_mkbig (); | |
4273 | mpz_sub (SCM_I_BIG_MPZ (result), | |
4274 | SCM_I_BIG_MPZ (x), | |
4275 | SCM_I_BIG_MPZ (y)); | |
4276 | scm_remember_upto_here_2 (x, y); | |
4277 | /* we know the result will have to be a bignum */ | |
4278 | if ((sgn_x == 1) && (sgn_y == -1)) | |
4279 | return result; | |
4280 | if ((sgn_x == -1) && (sgn_y == 1)) | |
4281 | return result; | |
4282 | return scm_i_normbig (result); | |
4283 | } | |
4284 | else if (SCM_REALP (y)) | |
4285 | { | |
4286 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
4287 | scm_remember_upto_here_1 (x); | |
55f26379 | 4288 | return scm_from_double (result); |
0aacf84e MD |
4289 | } |
4290 | else if (SCM_COMPLEXP (y)) | |
4291 | { | |
4292 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4293 | - SCM_COMPLEX_REAL (y)); | |
4294 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4295 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4296 | } |
f92e85f7 | 4297 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4298 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4299 | SCM_FRACTION_NUMERATOR (y)), |
4300 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 4301 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 4302 | } |
0aacf84e MD |
4303 | else if (SCM_REALP (x)) |
4304 | { | |
e11e83f3 | 4305 | if (SCM_I_INUMP (y)) |
55f26379 | 4306 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
4307 | else if (SCM_BIGP (y)) |
4308 | { | |
4309 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4310 | scm_remember_upto_here_1 (x); | |
55f26379 | 4311 | return scm_from_double (result); |
0aacf84e MD |
4312 | } |
4313 | else if (SCM_REALP (y)) | |
55f26379 | 4314 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 4315 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4316 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4317 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4318 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4319 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
4320 | else |
4321 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4322 | } |
0aacf84e MD |
4323 | else if (SCM_COMPLEXP (x)) |
4324 | { | |
e11e83f3 | 4325 | if (SCM_I_INUMP (y)) |
8507ec80 | 4326 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
4327 | SCM_COMPLEX_IMAG (x)); |
4328 | else if (SCM_BIGP (y)) | |
4329 | { | |
4330 | double real_part = (SCM_COMPLEX_REAL (x) | |
4331 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
4332 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4333 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
4334 | } |
4335 | else if (SCM_REALP (y)) | |
8507ec80 | 4336 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
4337 | SCM_COMPLEX_IMAG (x)); |
4338 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4339 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4340 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4341 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4342 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
4343 | SCM_COMPLEX_IMAG (x)); |
4344 | else | |
4345 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
4346 | } | |
4347 | else if (SCM_FRACTIONP (x)) | |
4348 | { | |
e11e83f3 | 4349 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4350 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 4351 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4352 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4353 | SCM_FRACTION_DENOMINATOR (x)); | |
4354 | else if (SCM_BIGP (y)) | |
cba42c93 | 4355 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4356 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4357 | SCM_FRACTION_DENOMINATOR (x)); | |
4358 | else if (SCM_REALP (y)) | |
55f26379 | 4359 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 4360 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4361 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4362 | -SCM_COMPLEX_IMAG (y)); |
4363 | else if (SCM_FRACTIONP (y)) | |
4364 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 4365 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4366 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4367 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4368 | else |
4369 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4370 | } |
0aacf84e | 4371 | else |
98cb6e75 | 4372 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 4373 | } |
c05e97b7 | 4374 | #undef FUNC_NAME |
0f2d19dd | 4375 | |
ca46fb90 | 4376 | |
40882e3d KR |
4377 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
4378 | (SCM x), | |
4379 | "Return @math{@var{x}-1}.") | |
4380 | #define FUNC_NAME s_scm_oneminus | |
4381 | { | |
4382 | return scm_difference (x, SCM_I_MAKINUM (1)); | |
4383 | } | |
4384 | #undef FUNC_NAME | |
4385 | ||
4386 | ||
9de33deb | 4387 | SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product); |
942e5b91 MG |
4388 | /* "Return the product of all arguments. If called without arguments,\n" |
4389 | * "1 is returned." | |
4390 | */ | |
0f2d19dd | 4391 | SCM |
6e8d25a6 | 4392 | scm_product (SCM x, SCM y) |
0f2d19dd | 4393 | { |
9cc37597 | 4394 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
4395 | { |
4396 | if (SCM_UNBNDP (x)) | |
d956fa6f | 4397 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
4398 | else if (SCM_NUMBERP (x)) |
4399 | return x; | |
4400 | else | |
4401 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 4402 | } |
ca46fb90 | 4403 | |
9cc37597 | 4404 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e MD |
4405 | { |
4406 | long xx; | |
f4c627b3 | 4407 | |
0aacf84e | 4408 | intbig: |
e11e83f3 | 4409 | xx = SCM_I_INUM (x); |
f4c627b3 | 4410 | |
0aacf84e MD |
4411 | switch (xx) |
4412 | { | |
ca46fb90 RB |
4413 | case 0: return x; break; |
4414 | case 1: return y; break; | |
0aacf84e | 4415 | } |
f4c627b3 | 4416 | |
9cc37597 | 4417 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4418 | { |
e11e83f3 | 4419 | long yy = SCM_I_INUM (y); |
0aacf84e | 4420 | long kk = xx * yy; |
d956fa6f | 4421 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 4422 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
4423 | return k; |
4424 | else | |
4425 | { | |
4426 | SCM result = scm_i_long2big (xx); | |
4427 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); | |
4428 | return scm_i_normbig (result); | |
4429 | } | |
4430 | } | |
4431 | else if (SCM_BIGP (y)) | |
4432 | { | |
4433 | SCM result = scm_i_mkbig (); | |
4434 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
4435 | scm_remember_upto_here_1 (y); | |
4436 | return result; | |
4437 | } | |
4438 | else if (SCM_REALP (y)) | |
55f26379 | 4439 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 4440 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4441 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 4442 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4443 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4444 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4445 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4446 | else |
4447 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4448 | } |
0aacf84e MD |
4449 | else if (SCM_BIGP (x)) |
4450 | { | |
e11e83f3 | 4451 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4452 | { |
4453 | SCM_SWAP (x, y); | |
4454 | goto intbig; | |
4455 | } | |
4456 | else if (SCM_BIGP (y)) | |
4457 | { | |
4458 | SCM result = scm_i_mkbig (); | |
4459 | mpz_mul (SCM_I_BIG_MPZ (result), | |
4460 | SCM_I_BIG_MPZ (x), | |
4461 | SCM_I_BIG_MPZ (y)); | |
4462 | scm_remember_upto_here_2 (x, y); | |
4463 | return result; | |
4464 | } | |
4465 | else if (SCM_REALP (y)) | |
4466 | { | |
4467 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
4468 | scm_remember_upto_here_1 (x); | |
55f26379 | 4469 | return scm_from_double (result); |
0aacf84e MD |
4470 | } |
4471 | else if (SCM_COMPLEXP (y)) | |
4472 | { | |
4473 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4474 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4475 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4476 | z * SCM_COMPLEX_IMAG (y)); |
4477 | } | |
f92e85f7 | 4478 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4479 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4480 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4481 | else |
4482 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4483 | } |
0aacf84e MD |
4484 | else if (SCM_REALP (x)) |
4485 | { | |
e11e83f3 | 4486 | if (SCM_I_INUMP (y)) |
23d72566 KR |
4487 | { |
4488 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
4489 | if (scm_is_eq (y, SCM_INUM0)) | |
4490 | return y; | |
4491 | return scm_from_double (SCM_I_INUM (y) * SCM_REAL_VALUE (x)); | |
4492 | } | |
0aacf84e MD |
4493 | else if (SCM_BIGP (y)) |
4494 | { | |
4495 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
4496 | scm_remember_upto_here_1 (y); | |
55f26379 | 4497 | return scm_from_double (result); |
0aacf84e MD |
4498 | } |
4499 | else if (SCM_REALP (y)) | |
55f26379 | 4500 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 4501 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4502 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 4503 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4504 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4505 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
4506 | else |
4507 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4508 | } |
0aacf84e MD |
4509 | else if (SCM_COMPLEXP (x)) |
4510 | { | |
e11e83f3 | 4511 | if (SCM_I_INUMP (y)) |
23d72566 KR |
4512 | { |
4513 | /* inexact*exact0 => exact 0, per R5RS "Exactness" section */ | |
4514 | if (scm_is_eq (y, SCM_INUM0)) | |
4515 | return y; | |
4516 | return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x), | |
4517 | SCM_I_INUM (y) * SCM_COMPLEX_IMAG (x)); | |
4518 | } | |
0aacf84e MD |
4519 | else if (SCM_BIGP (y)) |
4520 | { | |
4521 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4522 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4523 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 4524 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4525 | } |
4526 | else if (SCM_REALP (y)) | |
8507ec80 | 4527 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
4528 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
4529 | else if (SCM_COMPLEXP (y)) | |
4530 | { | |
8507ec80 | 4531 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
4532 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
4533 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
4534 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
4535 | } | |
f92e85f7 MV |
4536 | else if (SCM_FRACTIONP (y)) |
4537 | { | |
4538 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4539 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
4540 | yy * SCM_COMPLEX_IMAG (x)); |
4541 | } | |
4542 | else | |
4543 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
4544 | } | |
4545 | else if (SCM_FRACTIONP (x)) | |
4546 | { | |
e11e83f3 | 4547 | if (SCM_I_INUMP (y)) |
cba42c93 | 4548 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4549 | SCM_FRACTION_DENOMINATOR (x)); |
4550 | else if (SCM_BIGP (y)) | |
cba42c93 | 4551 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4552 | SCM_FRACTION_DENOMINATOR (x)); |
4553 | else if (SCM_REALP (y)) | |
55f26379 | 4554 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
4555 | else if (SCM_COMPLEXP (y)) |
4556 | { | |
4557 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 4558 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4559 | xx * SCM_COMPLEX_IMAG (y)); |
4560 | } | |
4561 | else if (SCM_FRACTIONP (y)) | |
4562 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 4563 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4564 | SCM_FRACTION_NUMERATOR (y)), |
4565 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
4566 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4567 | else |
4568 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4569 | } |
0aacf84e | 4570 | else |
f4c627b3 | 4571 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
4572 | } |
4573 | ||
7351e207 MV |
4574 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
4575 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
4576 | #define ALLOW_DIVIDE_BY_ZERO | |
4577 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
4578 | #endif | |
0f2d19dd | 4579 | |
ba74ef4e MV |
4580 | /* The code below for complex division is adapted from the GNU |
4581 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
4582 | this copyright: */ | |
4583 | ||
4584 | /**************************************************************** | |
4585 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
4586 | ||
4587 | Permission to use, copy, modify, and distribute this software | |
4588 | and its documentation for any purpose and without fee is hereby | |
4589 | granted, provided that the above copyright notice appear in all | |
4590 | copies and that both that the copyright notice and this | |
4591 | permission notice and warranty disclaimer appear in supporting | |
4592 | documentation, and that the names of AT&T Bell Laboratories or | |
4593 | Bellcore or any of their entities not be used in advertising or | |
4594 | publicity pertaining to distribution of the software without | |
4595 | specific, written prior permission. | |
4596 | ||
4597 | AT&T and Bellcore disclaim all warranties with regard to this | |
4598 | software, including all implied warranties of merchantability | |
4599 | and fitness. In no event shall AT&T or Bellcore be liable for | |
4600 | any special, indirect or consequential damages or any damages | |
4601 | whatsoever resulting from loss of use, data or profits, whether | |
4602 | in an action of contract, negligence or other tortious action, | |
4603 | arising out of or in connection with the use or performance of | |
4604 | this software. | |
4605 | ****************************************************************/ | |
4606 | ||
9de33deb | 4607 | SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide); |
609c3d30 MG |
4608 | /* Divide the first argument by the product of the remaining |
4609 | arguments. If called with one argument @var{z1}, 1/@var{z1} is | |
4610 | returned. */ | |
c05e97b7 | 4611 | #define FUNC_NAME s_divide |
f92e85f7 MV |
4612 | static SCM |
4613 | scm_i_divide (SCM x, SCM y, int inexact) | |
0f2d19dd | 4614 | { |
f8de44c1 DH |
4615 | double a; |
4616 | ||
9cc37597 | 4617 | if (SCM_UNLIKELY (SCM_UNBNDP (y))) |
0aacf84e MD |
4618 | { |
4619 | if (SCM_UNBNDP (x)) | |
4620 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 4621 | else if (SCM_I_INUMP (x)) |
0aacf84e | 4622 | { |
e11e83f3 | 4623 | long xx = SCM_I_INUM (x); |
0aacf84e MD |
4624 | if (xx == 1 || xx == -1) |
4625 | return x; | |
7351e207 | 4626 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4627 | else if (xx == 0) |
4628 | scm_num_overflow (s_divide); | |
7351e207 | 4629 | #endif |
0aacf84e | 4630 | else |
f92e85f7 MV |
4631 | { |
4632 | if (inexact) | |
55f26379 | 4633 | return scm_from_double (1.0 / (double) xx); |
cba42c93 | 4634 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4635 | } |
0aacf84e MD |
4636 | } |
4637 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
4638 | { |
4639 | if (inexact) | |
55f26379 | 4640 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cba42c93 | 4641 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4642 | } |
0aacf84e MD |
4643 | else if (SCM_REALP (x)) |
4644 | { | |
4645 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 4646 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4647 | if (xx == 0.0) |
4648 | scm_num_overflow (s_divide); | |
4649 | else | |
7351e207 | 4650 | #endif |
55f26379 | 4651 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
4652 | } |
4653 | else if (SCM_COMPLEXP (x)) | |
4654 | { | |
4655 | double r = SCM_COMPLEX_REAL (x); | |
4656 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 4657 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
4658 | { |
4659 | double t = r / i; | |
4660 | double d = i * (1.0 + t * t); | |
8507ec80 | 4661 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
4662 | } |
4663 | else | |
4664 | { | |
4665 | double t = i / r; | |
4666 | double d = r * (1.0 + t * t); | |
8507ec80 | 4667 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
4668 | } |
4669 | } | |
f92e85f7 | 4670 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4671 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 4672 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
4673 | else |
4674 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 4675 | } |
f8de44c1 | 4676 | |
9cc37597 | 4677 | if (SCM_LIKELY (SCM_I_INUMP (x))) |
0aacf84e | 4678 | { |
e11e83f3 | 4679 | long xx = SCM_I_INUM (x); |
9cc37597 | 4680 | if (SCM_LIKELY (SCM_I_INUMP (y))) |
0aacf84e | 4681 | { |
e11e83f3 | 4682 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
4683 | if (yy == 0) |
4684 | { | |
7351e207 | 4685 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4686 | scm_num_overflow (s_divide); |
7351e207 | 4687 | #else |
55f26379 | 4688 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 4689 | #endif |
0aacf84e MD |
4690 | } |
4691 | else if (xx % yy != 0) | |
f92e85f7 MV |
4692 | { |
4693 | if (inexact) | |
55f26379 | 4694 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 4695 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4696 | } |
0aacf84e MD |
4697 | else |
4698 | { | |
4699 | long z = xx / yy; | |
4700 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4701 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4702 | else |
4703 | return scm_i_long2big (z); | |
4704 | } | |
f872b822 | 4705 | } |
0aacf84e | 4706 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
4707 | { |
4708 | if (inexact) | |
55f26379 | 4709 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 4710 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4711 | } |
0aacf84e MD |
4712 | else if (SCM_REALP (y)) |
4713 | { | |
4714 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4715 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4716 | if (yy == 0.0) |
4717 | scm_num_overflow (s_divide); | |
4718 | else | |
7351e207 | 4719 | #endif |
55f26379 | 4720 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 4721 | } |
0aacf84e MD |
4722 | else if (SCM_COMPLEXP (y)) |
4723 | { | |
4724 | a = xx; | |
4725 | complex_div: /* y _must_ be a complex number */ | |
4726 | { | |
4727 | double r = SCM_COMPLEX_REAL (y); | |
4728 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 4729 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
4730 | { |
4731 | double t = r / i; | |
4732 | double d = i * (1.0 + t * t); | |
8507ec80 | 4733 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
4734 | } |
4735 | else | |
4736 | { | |
4737 | double t = i / r; | |
4738 | double d = r * (1.0 + t * t); | |
8507ec80 | 4739 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
4740 | } |
4741 | } | |
4742 | } | |
f92e85f7 MV |
4743 | else if (SCM_FRACTIONP (y)) |
4744 | /* a / b/c = ac / b */ | |
cba42c93 | 4745 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4746 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4747 | else |
4748 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4749 | } |
0aacf84e MD |
4750 | else if (SCM_BIGP (x)) |
4751 | { | |
e11e83f3 | 4752 | if (SCM_I_INUMP (y)) |
0aacf84e | 4753 | { |
e11e83f3 | 4754 | long int yy = SCM_I_INUM (y); |
0aacf84e MD |
4755 | if (yy == 0) |
4756 | { | |
7351e207 | 4757 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4758 | scm_num_overflow (s_divide); |
7351e207 | 4759 | #else |
0aacf84e MD |
4760 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4761 | scm_remember_upto_here_1 (x); | |
4762 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 4763 | #endif |
0aacf84e MD |
4764 | } |
4765 | else if (yy == 1) | |
4766 | return x; | |
4767 | else | |
4768 | { | |
4769 | /* FIXME: HMM, what are the relative performance issues here? | |
4770 | We need to test. Is it faster on average to test | |
4771 | divisible_p, then perform whichever operation, or is it | |
4772 | faster to perform the integer div opportunistically and | |
4773 | switch to real if there's a remainder? For now we take the | |
4774 | middle ground: test, then if divisible, use the faster div | |
4775 | func. */ | |
4776 | ||
4777 | long abs_yy = yy < 0 ? -yy : yy; | |
4778 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); | |
4779 | ||
4780 | if (divisible_p) | |
4781 | { | |
4782 | SCM result = scm_i_mkbig (); | |
4783 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
4784 | scm_remember_upto_here_1 (x); | |
4785 | if (yy < 0) | |
4786 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4787 | return scm_i_normbig (result); | |
4788 | } | |
4789 | else | |
f92e85f7 MV |
4790 | { |
4791 | if (inexact) | |
55f26379 | 4792 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 4793 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4794 | } |
0aacf84e MD |
4795 | } |
4796 | } | |
4797 | else if (SCM_BIGP (y)) | |
4798 | { | |
4799 | int y_is_zero = (mpz_sgn (SCM_I_BIG_MPZ (y)) == 0); | |
4800 | if (y_is_zero) | |
4801 | { | |
ca46fb90 | 4802 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4803 | scm_num_overflow (s_divide); |
f872b822 | 4804 | #else |
0aacf84e MD |
4805 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4806 | scm_remember_upto_here_1 (x); | |
4807 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
f872b822 | 4808 | #endif |
0aacf84e MD |
4809 | } |
4810 | else | |
4811 | { | |
4812 | /* big_x / big_y */ | |
23f2b9a3 KR |
4813 | if (inexact) |
4814 | { | |
4815 | /* It's easily possible for the ratio x/y to fit a double | |
4816 | but one or both x and y be too big to fit a double, | |
4817 | hence the use of mpq_get_d rather than converting and | |
4818 | dividing. */ | |
4819 | mpq_t q; | |
4820 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
4821 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
4822 | return scm_from_double (mpq_get_d (q)); | |
4823 | } | |
4824 | else | |
4825 | { | |
4826 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), | |
4827 | SCM_I_BIG_MPZ (y)); | |
4828 | if (divisible_p) | |
4829 | { | |
4830 | SCM result = scm_i_mkbig (); | |
4831 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
4832 | SCM_I_BIG_MPZ (x), | |
4833 | SCM_I_BIG_MPZ (y)); | |
4834 | scm_remember_upto_here_2 (x, y); | |
4835 | return scm_i_normbig (result); | |
4836 | } | |
4837 | else | |
4838 | return scm_i_make_ratio (x, y); | |
4839 | } | |
0aacf84e MD |
4840 | } |
4841 | } | |
4842 | else if (SCM_REALP (y)) | |
4843 | { | |
4844 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4845 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4846 | if (yy == 0.0) |
4847 | scm_num_overflow (s_divide); | |
4848 | else | |
7351e207 | 4849 | #endif |
55f26379 | 4850 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
4851 | } |
4852 | else if (SCM_COMPLEXP (y)) | |
4853 | { | |
4854 | a = scm_i_big2dbl (x); | |
4855 | goto complex_div; | |
4856 | } | |
f92e85f7 | 4857 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4858 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4859 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4860 | else |
4861 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4862 | } |
0aacf84e MD |
4863 | else if (SCM_REALP (x)) |
4864 | { | |
4865 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 4866 | if (SCM_I_INUMP (y)) |
0aacf84e | 4867 | { |
e11e83f3 | 4868 | long int yy = SCM_I_INUM (y); |
7351e207 | 4869 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4870 | if (yy == 0) |
4871 | scm_num_overflow (s_divide); | |
4872 | else | |
7351e207 | 4873 | #endif |
55f26379 | 4874 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
4875 | } |
4876 | else if (SCM_BIGP (y)) | |
4877 | { | |
4878 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4879 | scm_remember_upto_here_1 (y); | |
55f26379 | 4880 | return scm_from_double (rx / dby); |
0aacf84e MD |
4881 | } |
4882 | else if (SCM_REALP (y)) | |
4883 | { | |
4884 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4885 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4886 | if (yy == 0.0) |
4887 | scm_num_overflow (s_divide); | |
4888 | else | |
7351e207 | 4889 | #endif |
55f26379 | 4890 | return scm_from_double (rx / yy); |
0aacf84e MD |
4891 | } |
4892 | else if (SCM_COMPLEXP (y)) | |
4893 | { | |
4894 | a = rx; | |
4895 | goto complex_div; | |
4896 | } | |
f92e85f7 | 4897 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4898 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
4899 | else |
4900 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4901 | } |
0aacf84e MD |
4902 | else if (SCM_COMPLEXP (x)) |
4903 | { | |
4904 | double rx = SCM_COMPLEX_REAL (x); | |
4905 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 4906 | if (SCM_I_INUMP (y)) |
0aacf84e | 4907 | { |
e11e83f3 | 4908 | long int yy = SCM_I_INUM (y); |
7351e207 | 4909 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4910 | if (yy == 0) |
4911 | scm_num_overflow (s_divide); | |
4912 | else | |
7351e207 | 4913 | #endif |
0aacf84e MD |
4914 | { |
4915 | double d = yy; | |
8507ec80 | 4916 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
4917 | } |
4918 | } | |
4919 | else if (SCM_BIGP (y)) | |
4920 | { | |
4921 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4922 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4923 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
4924 | } |
4925 | else if (SCM_REALP (y)) | |
4926 | { | |
4927 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4928 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4929 | if (yy == 0.0) |
4930 | scm_num_overflow (s_divide); | |
4931 | else | |
7351e207 | 4932 | #endif |
8507ec80 | 4933 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
4934 | } |
4935 | else if (SCM_COMPLEXP (y)) | |
4936 | { | |
4937 | double ry = SCM_COMPLEX_REAL (y); | |
4938 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 4939 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
4940 | { |
4941 | double t = ry / iy; | |
4942 | double d = iy * (1.0 + t * t); | |
8507ec80 | 4943 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
4944 | } |
4945 | else | |
4946 | { | |
4947 | double t = iy / ry; | |
4948 | double d = ry * (1.0 + t * t); | |
8507ec80 | 4949 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
4950 | } |
4951 | } | |
f92e85f7 MV |
4952 | else if (SCM_FRACTIONP (y)) |
4953 | { | |
4954 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4955 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 4956 | } |
0aacf84e MD |
4957 | else |
4958 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4959 | } |
f92e85f7 MV |
4960 | else if (SCM_FRACTIONP (x)) |
4961 | { | |
e11e83f3 | 4962 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4963 | { |
e11e83f3 | 4964 | long int yy = SCM_I_INUM (y); |
f92e85f7 MV |
4965 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
4966 | if (yy == 0) | |
4967 | scm_num_overflow (s_divide); | |
4968 | else | |
4969 | #endif | |
cba42c93 | 4970 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4971 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4972 | } | |
4973 | else if (SCM_BIGP (y)) | |
4974 | { | |
cba42c93 | 4975 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4976 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4977 | } | |
4978 | else if (SCM_REALP (y)) | |
4979 | { | |
4980 | double yy = SCM_REAL_VALUE (y); | |
4981 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
4982 | if (yy == 0.0) | |
4983 | scm_num_overflow (s_divide); | |
4984 | else | |
4985 | #endif | |
55f26379 | 4986 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
4987 | } |
4988 | else if (SCM_COMPLEXP (y)) | |
4989 | { | |
4990 | a = scm_i_fraction2double (x); | |
4991 | goto complex_div; | |
4992 | } | |
4993 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 4994 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4995 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
4996 | else | |
4997 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
4998 | } | |
0aacf84e | 4999 | else |
f8de44c1 | 5000 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 5001 | } |
f92e85f7 MV |
5002 | |
5003 | SCM | |
5004 | scm_divide (SCM x, SCM y) | |
5005 | { | |
5006 | return scm_i_divide (x, y, 0); | |
5007 | } | |
5008 | ||
5009 | static SCM scm_divide2real (SCM x, SCM y) | |
5010 | { | |
5011 | return scm_i_divide (x, y, 1); | |
5012 | } | |
c05e97b7 | 5013 | #undef FUNC_NAME |
0f2d19dd | 5014 | |
fa605590 | 5015 | |
0f2d19dd | 5016 | double |
6e8d25a6 | 5017 | scm_asinh (double x) |
0f2d19dd | 5018 | { |
fa605590 KR |
5019 | #if HAVE_ASINH |
5020 | return asinh (x); | |
5021 | #else | |
5022 | #define asinh scm_asinh | |
f872b822 | 5023 | return log (x + sqrt (x * x + 1)); |
fa605590 | 5024 | #endif |
0f2d19dd | 5025 | } |
fa605590 KR |
5026 | SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_dsubr, (SCM (*)()) asinh, g_asinh); |
5027 | /* "Return the inverse hyperbolic sine of @var{x}." | |
5028 | */ | |
0f2d19dd JB |
5029 | |
5030 | ||
0f2d19dd | 5031 | double |
6e8d25a6 | 5032 | scm_acosh (double x) |
0f2d19dd | 5033 | { |
fa605590 KR |
5034 | #if HAVE_ACOSH |
5035 | return acosh (x); | |
5036 | #else | |
5037 | #define acosh scm_acosh | |
f872b822 | 5038 | return log (x + sqrt (x * x - 1)); |
fa605590 | 5039 | #endif |
0f2d19dd | 5040 | } |
fa605590 KR |
5041 | SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_dsubr, (SCM (*)()) acosh, g_acosh); |
5042 | /* "Return the inverse hyperbolic cosine of @var{x}." | |
5043 | */ | |
0f2d19dd JB |
5044 | |
5045 | ||
0f2d19dd | 5046 | double |
6e8d25a6 | 5047 | scm_atanh (double x) |
0f2d19dd | 5048 | { |
fa605590 KR |
5049 | #if HAVE_ATANH |
5050 | return atanh (x); | |
5051 | #else | |
5052 | #define atanh scm_atanh | |
f872b822 | 5053 | return 0.5 * log ((1 + x) / (1 - x)); |
fa605590 | 5054 | #endif |
0f2d19dd | 5055 | } |
fa605590 KR |
5056 | SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_dsubr, (SCM (*)()) atanh, g_atanh); |
5057 | /* "Return the inverse hyperbolic tangent of @var{x}." | |
5058 | */ | |
0f2d19dd JB |
5059 | |
5060 | ||
0f2d19dd | 5061 | double |
3101f40f | 5062 | scm_c_truncate (double x) |
0f2d19dd | 5063 | { |
fa605590 KR |
5064 | #if HAVE_TRUNC |
5065 | return trunc (x); | |
5066 | #else | |
f872b822 MD |
5067 | if (x < 0.0) |
5068 | return -floor (-x); | |
5069 | return floor (x); | |
fa605590 | 5070 | #endif |
0f2d19dd | 5071 | } |
0f2d19dd | 5072 | |
3101f40f MV |
5073 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
5074 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
5075 | Then half-way cases are identified and adjusted down if the | |
5076 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
5077 | |
5078 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
5079 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
5080 | ||
5081 | An odd "result" value is identified with result/2 != floor(result/2). | |
5082 | This is done with plus_half, since that value is ready for use sooner in | |
5083 | a pipelined cpu, and we're already requiring plus_half == result. | |
5084 | ||
5085 | Note however that we need to be careful when x is big and already an | |
5086 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
5087 | us to return such a value, incorrectly. For instance if the hardware is | |
5088 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
5089 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
5090 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
5091 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
5092 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
5093 | ||
5094 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
5095 | x is already an integer. If it is then clearly that's the desired result | |
5096 | already. And if it's not then the exponent must be small enough to allow | |
5097 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
5098 | ||
0f2d19dd | 5099 | double |
3101f40f | 5100 | scm_c_round (double x) |
0f2d19dd | 5101 | { |
6187f48b KR |
5102 | double plus_half, result; |
5103 | ||
5104 | if (x == floor (x)) | |
5105 | return x; | |
5106 | ||
5107 | plus_half = x + 0.5; | |
5108 | result = floor (plus_half); | |
3101f40f | 5109 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
5110 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
5111 | ? result - 1 | |
5112 | : result); | |
0f2d19dd JB |
5113 | } |
5114 | ||
f92e85f7 MV |
5115 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
5116 | (SCM x), | |
5117 | "Round the number @var{x} towards zero.") | |
5118 | #define FUNC_NAME s_scm_truncate_number | |
5119 | { | |
73e4de09 | 5120 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5121 | return scm_floor (x); |
5122 | else | |
5123 | return scm_ceiling (x); | |
5124 | } | |
5125 | #undef FUNC_NAME | |
5126 | ||
5127 | static SCM exactly_one_half; | |
5128 | ||
5129 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, | |
5130 | (SCM x), | |
5131 | "Round the number @var{x} towards the nearest integer. " | |
5132 | "When it is exactly halfway between two integers, " | |
5133 | "round towards the even one.") | |
5134 | #define FUNC_NAME s_scm_round_number | |
5135 | { | |
e11e83f3 | 5136 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
5137 | return x; |
5138 | else if (SCM_REALP (x)) | |
3101f40f | 5139 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 5140 | else |
bae30667 KR |
5141 | { |
5142 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
5143 | single quotient+remainder division then examining to see which way | |
5144 | the rounding should go. */ | |
5145 | SCM plus_half = scm_sum (x, exactly_one_half); | |
5146 | SCM result = scm_floor (plus_half); | |
3101f40f | 5147 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
5148 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
5149 | && scm_is_true (scm_odd_p (result))) | |
d956fa6f | 5150 | return scm_difference (result, SCM_I_MAKINUM (1)); |
bae30667 KR |
5151 | else |
5152 | return result; | |
5153 | } | |
f92e85f7 MV |
5154 | } |
5155 | #undef FUNC_NAME | |
5156 | ||
5157 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
5158 | (SCM x), | |
5159 | "Round the number @var{x} towards minus infinity.") | |
5160 | #define FUNC_NAME s_scm_floor | |
5161 | { | |
e11e83f3 | 5162 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5163 | return x; |
5164 | else if (SCM_REALP (x)) | |
55f26379 | 5165 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5166 | else if (SCM_FRACTIONP (x)) |
5167 | { | |
5168 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5169 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5170 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5171 | { |
5172 | /* For positive x, rounding towards zero is correct. */ | |
5173 | return q; | |
5174 | } | |
5175 | else | |
5176 | { | |
5177 | /* For negative x, we need to return q-1 unless x is an | |
5178 | integer. But fractions are never integer, per our | |
5179 | assumptions. */ | |
d956fa6f | 5180 | return scm_difference (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5181 | } |
5182 | } | |
5183 | else | |
5184 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
5185 | } | |
5186 | #undef FUNC_NAME | |
5187 | ||
5188 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
5189 | (SCM x), | |
5190 | "Round the number @var{x} towards infinity.") | |
5191 | #define FUNC_NAME s_scm_ceiling | |
5192 | { | |
e11e83f3 | 5193 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5194 | return x; |
5195 | else if (SCM_REALP (x)) | |
55f26379 | 5196 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5197 | else if (SCM_FRACTIONP (x)) |
5198 | { | |
5199 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5200 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5201 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
5202 | { |
5203 | /* For negative x, rounding towards zero is correct. */ | |
5204 | return q; | |
5205 | } | |
5206 | else | |
5207 | { | |
5208 | /* For positive x, we need to return q+1 unless x is an | |
5209 | integer. But fractions are never integer, per our | |
5210 | assumptions. */ | |
d956fa6f | 5211 | return scm_sum (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5212 | } |
5213 | } | |
5214 | else | |
5215 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
5216 | } | |
5217 | #undef FUNC_NAME | |
0f2d19dd | 5218 | |
14b18ed6 | 5219 | SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_dsubr, (SCM (*)()) sqrt, g_i_sqrt); |
942e5b91 MG |
5220 | /* "Return the square root of the real number @var{x}." |
5221 | */ | |
14b18ed6 | 5222 | SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_dsubr, (SCM (*)()) fabs, g_i_abs); |
942e5b91 MG |
5223 | /* "Return the absolute value of the real number @var{x}." |
5224 | */ | |
14b18ed6 | 5225 | SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_dsubr, (SCM (*)()) exp, g_i_exp); |
942e5b91 MG |
5226 | /* "Return the @var{x}th power of e." |
5227 | */ | |
14b18ed6 | 5228 | SCM_GPROC1 (s_i_log, "$log", scm_tc7_dsubr, (SCM (*)()) log, g_i_log); |
b3fcac34 | 5229 | /* "Return the natural logarithm of the real number @var{x}." |
942e5b91 | 5230 | */ |
14b18ed6 | 5231 | SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_dsubr, (SCM (*)()) sin, g_i_sin); |
942e5b91 MG |
5232 | /* "Return the sine of the real number @var{x}." |
5233 | */ | |
14b18ed6 | 5234 | SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_dsubr, (SCM (*)()) cos, g_i_cos); |
942e5b91 MG |
5235 | /* "Return the cosine of the real number @var{x}." |
5236 | */ | |
14b18ed6 | 5237 | SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_dsubr, (SCM (*)()) tan, g_i_tan); |
942e5b91 MG |
5238 | /* "Return the tangent of the real number @var{x}." |
5239 | */ | |
14b18ed6 | 5240 | SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_dsubr, (SCM (*)()) asin, g_i_asin); |
942e5b91 MG |
5241 | /* "Return the arc sine of the real number @var{x}." |
5242 | */ | |
14b18ed6 | 5243 | SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_dsubr, (SCM (*)()) acos, g_i_acos); |
942e5b91 MG |
5244 | /* "Return the arc cosine of the real number @var{x}." |
5245 | */ | |
14b18ed6 | 5246 | SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_dsubr, (SCM (*)()) atan, g_i_atan); |
942e5b91 MG |
5247 | /* "Return the arc tangent of the real number @var{x}." |
5248 | */ | |
14b18ed6 | 5249 | SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_dsubr, (SCM (*)()) sinh, g_i_sinh); |
942e5b91 MG |
5250 | /* "Return the hyperbolic sine of the real number @var{x}." |
5251 | */ | |
14b18ed6 | 5252 | SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_dsubr, (SCM (*)()) cosh, g_i_cosh); |
942e5b91 MG |
5253 | /* "Return the hyperbolic cosine of the real number @var{x}." |
5254 | */ | |
14b18ed6 | 5255 | SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_dsubr, (SCM (*)()) tanh, g_i_tanh); |
942e5b91 MG |
5256 | /* "Return the hyperbolic tangent of the real number @var{x}." |
5257 | */ | |
f872b822 MD |
5258 | |
5259 | struct dpair | |
5260 | { | |
5261 | double x, y; | |
5262 | }; | |
5263 | ||
27c37006 NJ |
5264 | static void scm_two_doubles (SCM x, |
5265 | SCM y, | |
3eeba8d4 JB |
5266 | const char *sstring, |
5267 | struct dpair * xy); | |
f872b822 MD |
5268 | |
5269 | static void | |
27c37006 NJ |
5270 | scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy) |
5271 | { | |
e11e83f3 MV |
5272 | if (SCM_I_INUMP (x)) |
5273 | xy->x = SCM_I_INUM (x); | |
0aacf84e | 5274 | else if (SCM_BIGP (x)) |
1be6b49c | 5275 | xy->x = scm_i_big2dbl (x); |
0aacf84e | 5276 | else if (SCM_REALP (x)) |
27c37006 | 5277 | xy->x = SCM_REAL_VALUE (x); |
f92e85f7 MV |
5278 | else if (SCM_FRACTIONP (x)) |
5279 | xy->x = scm_i_fraction2double (x); | |
0aacf84e | 5280 | else |
27c37006 | 5281 | scm_wrong_type_arg (sstring, SCM_ARG1, x); |
98cb6e75 | 5282 | |
e11e83f3 MV |
5283 | if (SCM_I_INUMP (y)) |
5284 | xy->y = SCM_I_INUM (y); | |
0aacf84e | 5285 | else if (SCM_BIGP (y)) |
1be6b49c | 5286 | xy->y = scm_i_big2dbl (y); |
0aacf84e | 5287 | else if (SCM_REALP (y)) |
27c37006 | 5288 | xy->y = SCM_REAL_VALUE (y); |
f92e85f7 MV |
5289 | else if (SCM_FRACTIONP (y)) |
5290 | xy->y = scm_i_fraction2double (y); | |
0aacf84e | 5291 | else |
27c37006 | 5292 | scm_wrong_type_arg (sstring, SCM_ARG2, y); |
0f2d19dd JB |
5293 | } |
5294 | ||
5295 | ||
a1ec6916 | 5296 | SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0, |
27c37006 NJ |
5297 | (SCM x, SCM y), |
5298 | "Return @var{x} raised to the power of @var{y}. This\n" | |
0137a31b | 5299 | "procedure does not accept complex arguments.") |
1bbd0b84 | 5300 | #define FUNC_NAME s_scm_sys_expt |
0f2d19dd JB |
5301 | { |
5302 | struct dpair xy; | |
27c37006 | 5303 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5304 | return scm_from_double (pow (xy.x, xy.y)); |
0f2d19dd | 5305 | } |
1bbd0b84 | 5306 | #undef FUNC_NAME |
0f2d19dd JB |
5307 | |
5308 | ||
a1ec6916 | 5309 | SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0, |
27c37006 NJ |
5310 | (SCM x, SCM y), |
5311 | "Return the arc tangent of the two arguments @var{x} and\n" | |
5312 | "@var{y}. This is similar to calculating the arc tangent of\n" | |
5313 | "@var{x} / @var{y}, except that the signs of both arguments\n" | |
0137a31b MG |
5314 | "are used to determine the quadrant of the result. This\n" |
5315 | "procedure does not accept complex arguments.") | |
1bbd0b84 | 5316 | #define FUNC_NAME s_scm_sys_atan2 |
0f2d19dd JB |
5317 | { |
5318 | struct dpair xy; | |
27c37006 | 5319 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5320 | return scm_from_double (atan2 (xy.x, xy.y)); |
0f2d19dd | 5321 | } |
1bbd0b84 | 5322 | #undef FUNC_NAME |
0f2d19dd | 5323 | |
8507ec80 MV |
5324 | SCM |
5325 | scm_c_make_rectangular (double re, double im) | |
5326 | { | |
5327 | if (im == 0.0) | |
5328 | return scm_from_double (re); | |
5329 | else | |
5330 | { | |
5331 | SCM z; | |
5332 | SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (sizeof (scm_t_complex), | |
5333 | "complex")); | |
5334 | SCM_COMPLEX_REAL (z) = re; | |
5335 | SCM_COMPLEX_IMAG (z) = im; | |
5336 | return z; | |
5337 | } | |
5338 | } | |
0f2d19dd | 5339 | |
a1ec6916 | 5340 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
a2c25234 LC |
5341 | (SCM real_part, SCM imaginary_part), |
5342 | "Return a complex number constructed of the given @var{real-part} " | |
5343 | "and @var{imaginary-part} parts.") | |
1bbd0b84 | 5344 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd JB |
5345 | { |
5346 | struct dpair xy; | |
a2c25234 | 5347 | scm_two_doubles (real_part, imaginary_part, FUNC_NAME, &xy); |
8507ec80 | 5348 | return scm_c_make_rectangular (xy.x, xy.y); |
0f2d19dd | 5349 | } |
1bbd0b84 | 5350 | #undef FUNC_NAME |
0f2d19dd | 5351 | |
8507ec80 MV |
5352 | SCM |
5353 | scm_c_make_polar (double mag, double ang) | |
5354 | { | |
5355 | double s, c; | |
5356 | #if HAVE_SINCOS | |
5357 | sincos (ang, &s, &c); | |
5358 | #else | |
5359 | s = sin (ang); | |
5360 | c = cos (ang); | |
5361 | #endif | |
5362 | return scm_c_make_rectangular (mag * c, mag * s); | |
5363 | } | |
0f2d19dd | 5364 | |
a1ec6916 | 5365 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 5366 | (SCM x, SCM y), |
942e5b91 | 5367 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 5368 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd JB |
5369 | { |
5370 | struct dpair xy; | |
27c37006 | 5371 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
8507ec80 | 5372 | return scm_c_make_polar (xy.x, xy.y); |
0f2d19dd | 5373 | } |
1bbd0b84 | 5374 | #undef FUNC_NAME |
0f2d19dd JB |
5375 | |
5376 | ||
152f82bf | 5377 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
5378 | /* "Return the real part of the number @var{z}." |
5379 | */ | |
0f2d19dd | 5380 | SCM |
6e8d25a6 | 5381 | scm_real_part (SCM z) |
0f2d19dd | 5382 | { |
e11e83f3 | 5383 | if (SCM_I_INUMP (z)) |
c2ff8ab0 | 5384 | return z; |
0aacf84e | 5385 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5386 | return z; |
0aacf84e | 5387 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5388 | return z; |
0aacf84e | 5389 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5390 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
f92e85f7 | 5391 | else if (SCM_FRACTIONP (z)) |
2fa2d879 | 5392 | return z; |
0aacf84e | 5393 | else |
c2ff8ab0 | 5394 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); |
0f2d19dd JB |
5395 | } |
5396 | ||
5397 | ||
152f82bf | 5398 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
5399 | /* "Return the imaginary part of the number @var{z}." |
5400 | */ | |
0f2d19dd | 5401 | SCM |
6e8d25a6 | 5402 | scm_imag_part (SCM z) |
0f2d19dd | 5403 | { |
e11e83f3 | 5404 | if (SCM_I_INUMP (z)) |
f872b822 | 5405 | return SCM_INUM0; |
0aacf84e | 5406 | else if (SCM_BIGP (z)) |
f872b822 | 5407 | return SCM_INUM0; |
0aacf84e | 5408 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5409 | return scm_flo0; |
0aacf84e | 5410 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5411 | return scm_from_double (SCM_COMPLEX_IMAG (z)); |
f92e85f7 MV |
5412 | else if (SCM_FRACTIONP (z)) |
5413 | return SCM_INUM0; | |
0aacf84e | 5414 | else |
c2ff8ab0 | 5415 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); |
0f2d19dd JB |
5416 | } |
5417 | ||
f92e85f7 MV |
5418 | SCM_GPROC (s_numerator, "numerator", 1, 0, 0, scm_numerator, g_numerator); |
5419 | /* "Return the numerator of the number @var{z}." | |
5420 | */ | |
5421 | SCM | |
5422 | scm_numerator (SCM z) | |
5423 | { | |
e11e83f3 | 5424 | if (SCM_I_INUMP (z)) |
f92e85f7 MV |
5425 | return z; |
5426 | else if (SCM_BIGP (z)) | |
5427 | return z; | |
5428 | else if (SCM_FRACTIONP (z)) | |
e2bf3b19 | 5429 | return SCM_FRACTION_NUMERATOR (z); |
f92e85f7 MV |
5430 | else if (SCM_REALP (z)) |
5431 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
5432 | else | |
5433 | SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator); | |
5434 | } | |
5435 | ||
5436 | ||
5437 | SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator); | |
5438 | /* "Return the denominator of the number @var{z}." | |
5439 | */ | |
5440 | SCM | |
5441 | scm_denominator (SCM z) | |
5442 | { | |
e11e83f3 | 5443 | if (SCM_I_INUMP (z)) |
d956fa6f | 5444 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5445 | else if (SCM_BIGP (z)) |
d956fa6f | 5446 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5447 | else if (SCM_FRACTIONP (z)) |
e2bf3b19 | 5448 | return SCM_FRACTION_DENOMINATOR (z); |
f92e85f7 MV |
5449 | else if (SCM_REALP (z)) |
5450 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
5451 | else | |
5452 | SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator); | |
5453 | } | |
0f2d19dd | 5454 | |
9de33deb | 5455 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
5456 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
5457 | * "@code{abs} for real arguments, but also allows complex numbers." | |
5458 | */ | |
0f2d19dd | 5459 | SCM |
6e8d25a6 | 5460 | scm_magnitude (SCM z) |
0f2d19dd | 5461 | { |
e11e83f3 | 5462 | if (SCM_I_INUMP (z)) |
0aacf84e | 5463 | { |
e11e83f3 | 5464 | long int zz = SCM_I_INUM (z); |
0aacf84e MD |
5465 | if (zz >= 0) |
5466 | return z; | |
5467 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 5468 | return SCM_I_MAKINUM (-zz); |
0aacf84e MD |
5469 | else |
5470 | return scm_i_long2big (-zz); | |
5986c47d | 5471 | } |
0aacf84e MD |
5472 | else if (SCM_BIGP (z)) |
5473 | { | |
5474 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5475 | scm_remember_upto_here_1 (z); | |
5476 | if (sgn < 0) | |
5477 | return scm_i_clonebig (z, 0); | |
5478 | else | |
5479 | return z; | |
5986c47d | 5480 | } |
0aacf84e | 5481 | else if (SCM_REALP (z)) |
55f26379 | 5482 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 5483 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5484 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
5485 | else if (SCM_FRACTIONP (z)) |
5486 | { | |
73e4de09 | 5487 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5488 | return z; |
cba42c93 | 5489 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
5490 | SCM_FRACTION_DENOMINATOR (z)); |
5491 | } | |
0aacf84e | 5492 | else |
c2ff8ab0 | 5493 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); |
0f2d19dd JB |
5494 | } |
5495 | ||
5496 | ||
9de33deb | 5497 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
5498 | /* "Return the angle of the complex number @var{z}." |
5499 | */ | |
0f2d19dd | 5500 | SCM |
6e8d25a6 | 5501 | scm_angle (SCM z) |
0f2d19dd | 5502 | { |
c8ae173e | 5503 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
55f26379 | 5504 | scm_flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
5505 | But if atan2 follows the floating point rounding mode, then the value |
5506 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 5507 | if (SCM_I_INUMP (z)) |
0aacf84e | 5508 | { |
e11e83f3 | 5509 | if (SCM_I_INUM (z) >= 0) |
c8ae173e | 5510 | return scm_flo0; |
0aacf84e | 5511 | else |
55f26379 | 5512 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 5513 | } |
0aacf84e MD |
5514 | else if (SCM_BIGP (z)) |
5515 | { | |
5516 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5517 | scm_remember_upto_here_1 (z); | |
5518 | if (sgn < 0) | |
55f26379 | 5519 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 5520 | else |
c8ae173e | 5521 | return scm_flo0; |
0f2d19dd | 5522 | } |
0aacf84e | 5523 | else if (SCM_REALP (z)) |
c8ae173e KR |
5524 | { |
5525 | if (SCM_REAL_VALUE (z) >= 0) | |
5526 | return scm_flo0; | |
5527 | else | |
55f26379 | 5528 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 5529 | } |
0aacf84e | 5530 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5531 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
5532 | else if (SCM_FRACTIONP (z)) |
5533 | { | |
73e4de09 | 5534 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5535 | return scm_flo0; |
55f26379 | 5536 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 5537 | } |
0aacf84e | 5538 | else |
f4c627b3 | 5539 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); |
0f2d19dd JB |
5540 | } |
5541 | ||
5542 | ||
3c9a524f DH |
5543 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
5544 | /* Convert the number @var{x} to its inexact representation.\n" | |
5545 | */ | |
5546 | SCM | |
5547 | scm_exact_to_inexact (SCM z) | |
5548 | { | |
e11e83f3 | 5549 | if (SCM_I_INUMP (z)) |
55f26379 | 5550 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 5551 | else if (SCM_BIGP (z)) |
55f26379 | 5552 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 5553 | else if (SCM_FRACTIONP (z)) |
55f26379 | 5554 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
5555 | else if (SCM_INEXACTP (z)) |
5556 | return z; | |
5557 | else | |
5558 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
5559 | } | |
5560 | ||
5561 | ||
a1ec6916 | 5562 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 5563 | (SCM z), |
1e6808ea | 5564 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 5565 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 5566 | { |
e11e83f3 | 5567 | if (SCM_I_INUMP (z)) |
f872b822 | 5568 | return z; |
0aacf84e | 5569 | else if (SCM_BIGP (z)) |
f872b822 | 5570 | return z; |
0aacf84e MD |
5571 | else if (SCM_REALP (z)) |
5572 | { | |
f92e85f7 MV |
5573 | if (xisinf (SCM_REAL_VALUE (z)) || xisnan (SCM_REAL_VALUE (z))) |
5574 | SCM_OUT_OF_RANGE (1, z); | |
2be24db4 | 5575 | else |
f92e85f7 MV |
5576 | { |
5577 | mpq_t frac; | |
5578 | SCM q; | |
5579 | ||
5580 | mpq_init (frac); | |
5581 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 5582 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
5583 | scm_i_mpz2num (mpq_denref (frac))); |
5584 | ||
cba42c93 | 5585 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
5586 | for frac... |
5587 | */ | |
5588 | mpq_clear (frac); | |
5589 | return q; | |
5590 | } | |
c2ff8ab0 | 5591 | } |
f92e85f7 MV |
5592 | else if (SCM_FRACTIONP (z)) |
5593 | return z; | |
0aacf84e | 5594 | else |
c2ff8ab0 | 5595 | SCM_WRONG_TYPE_ARG (1, z); |
0f2d19dd | 5596 | } |
1bbd0b84 | 5597 | #undef FUNC_NAME |
0f2d19dd | 5598 | |
f92e85f7 MV |
5599 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
5600 | (SCM x, SCM err), | |
5601 | "Return an exact number that is within @var{err} of @var{x}.") | |
5602 | #define FUNC_NAME s_scm_rationalize | |
5603 | { | |
e11e83f3 | 5604 | if (SCM_I_INUMP (x)) |
f92e85f7 MV |
5605 | return x; |
5606 | else if (SCM_BIGP (x)) | |
5607 | return x; | |
5608 | else if ((SCM_REALP (x)) || SCM_FRACTIONP (x)) | |
5609 | { | |
5610 | /* Use continued fractions to find closest ratio. All | |
5611 | arithmetic is done with exact numbers. | |
5612 | */ | |
5613 | ||
5614 | SCM ex = scm_inexact_to_exact (x); | |
5615 | SCM int_part = scm_floor (ex); | |
d956fa6f MV |
5616 | SCM tt = SCM_I_MAKINUM (1); |
5617 | SCM a1 = SCM_I_MAKINUM (0), a2 = SCM_I_MAKINUM (1), a = SCM_I_MAKINUM (0); | |
5618 | SCM b1 = SCM_I_MAKINUM (1), b2 = SCM_I_MAKINUM (0), b = SCM_I_MAKINUM (0); | |
f92e85f7 MV |
5619 | SCM rx; |
5620 | int i = 0; | |
5621 | ||
73e4de09 | 5622 | if (scm_is_true (scm_num_eq_p (ex, int_part))) |
f92e85f7 MV |
5623 | return ex; |
5624 | ||
5625 | ex = scm_difference (ex, int_part); /* x = x-int_part */ | |
5626 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
5627 | ||
5628 | /* We stop after a million iterations just to be absolutely sure | |
5629 | that we don't go into an infinite loop. The process normally | |
5630 | converges after less than a dozen iterations. | |
5631 | */ | |
5632 | ||
5633 | err = scm_abs (err); | |
5634 | while (++i < 1000000) | |
5635 | { | |
5636 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
5637 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
5638 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
5639 | scm_is_false | |
f92e85f7 MV |
5640 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
5641 | err))) /* abs(x-a/b) <= err */ | |
02164269 MV |
5642 | { |
5643 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
73e4de09 MV |
5644 | if (scm_is_false (scm_exact_p (x)) |
5645 | || scm_is_false (scm_exact_p (err))) | |
02164269 MV |
5646 | return scm_exact_to_inexact (res); |
5647 | else | |
5648 | return res; | |
5649 | } | |
f92e85f7 MV |
5650 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
5651 | SCM_UNDEFINED); | |
5652 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
5653 | a2 = a1; | |
5654 | b2 = b1; | |
5655 | a1 = a; | |
5656 | b1 = b; | |
5657 | } | |
5658 | scm_num_overflow (s_scm_rationalize); | |
5659 | } | |
5660 | else | |
5661 | SCM_WRONG_TYPE_ARG (1, x); | |
5662 | } | |
5663 | #undef FUNC_NAME | |
5664 | ||
73e4de09 MV |
5665 | /* conversion functions */ |
5666 | ||
5667 | int | |
5668 | scm_is_integer (SCM val) | |
5669 | { | |
5670 | return scm_is_true (scm_integer_p (val)); | |
5671 | } | |
5672 | ||
5673 | int | |
5674 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
5675 | { | |
e11e83f3 | 5676 | if (SCM_I_INUMP (val)) |
73e4de09 | 5677 | { |
e11e83f3 | 5678 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5679 | return n >= min && n <= max; |
5680 | } | |
5681 | else if (SCM_BIGP (val)) | |
5682 | { | |
5683 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
5684 | return 0; | |
5685 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
5686 | { |
5687 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
5688 | { | |
5689 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
5690 | return n >= min && n <= max; | |
5691 | } | |
5692 | else | |
5693 | return 0; | |
5694 | } | |
73e4de09 MV |
5695 | else |
5696 | { | |
d956fa6f MV |
5697 | scm_t_intmax n; |
5698 | size_t count; | |
73e4de09 | 5699 | |
d956fa6f MV |
5700 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5701 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
5702 | return 0; | |
5703 | ||
5704 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5705 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5706 | |
d956fa6f | 5707 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 5708 | { |
d956fa6f MV |
5709 | if (n < 0) |
5710 | return 0; | |
73e4de09 | 5711 | } |
73e4de09 MV |
5712 | else |
5713 | { | |
d956fa6f MV |
5714 | n = -n; |
5715 | if (n >= 0) | |
5716 | return 0; | |
73e4de09 | 5717 | } |
d956fa6f MV |
5718 | |
5719 | return n >= min && n <= max; | |
73e4de09 MV |
5720 | } |
5721 | } | |
73e4de09 MV |
5722 | else |
5723 | return 0; | |
5724 | } | |
5725 | ||
5726 | int | |
5727 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
5728 | { | |
e11e83f3 | 5729 | if (SCM_I_INUMP (val)) |
73e4de09 | 5730 | { |
e11e83f3 | 5731 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5732 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
5733 | } | |
5734 | else if (SCM_BIGP (val)) | |
5735 | { | |
5736 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
5737 | return 0; | |
5738 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
5739 | { |
5740 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
5741 | { | |
5742 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
5743 | return n >= min && n <= max; | |
5744 | } | |
5745 | else | |
5746 | return 0; | |
5747 | } | |
73e4de09 MV |
5748 | else |
5749 | { | |
d956fa6f MV |
5750 | scm_t_uintmax n; |
5751 | size_t count; | |
73e4de09 | 5752 | |
d956fa6f MV |
5753 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
5754 | return 0; | |
73e4de09 | 5755 | |
d956fa6f MV |
5756 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5757 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 5758 | return 0; |
d956fa6f MV |
5759 | |
5760 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5761 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5762 | |
d956fa6f | 5763 | return n >= min && n <= max; |
73e4de09 MV |
5764 | } |
5765 | } | |
73e4de09 MV |
5766 | else |
5767 | return 0; | |
5768 | } | |
5769 | ||
1713d319 MV |
5770 | static void |
5771 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
5772 | { | |
5773 | scm_error (scm_out_of_range_key, | |
5774 | NULL, | |
5775 | "Value out of range ~S to ~S: ~S", | |
5776 | scm_list_3 (min, max, bad_val), | |
5777 | scm_list_1 (bad_val)); | |
5778 | } | |
5779 | ||
bfd7932e MV |
5780 | #define TYPE scm_t_intmax |
5781 | #define TYPE_MIN min | |
5782 | #define TYPE_MAX max | |
5783 | #define SIZEOF_TYPE 0 | |
5784 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
5785 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
5786 | #include "libguile/conv-integer.i.c" | |
5787 | ||
5788 | #define TYPE scm_t_uintmax | |
5789 | #define TYPE_MIN min | |
5790 | #define TYPE_MAX max | |
5791 | #define SIZEOF_TYPE 0 | |
5792 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
5793 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
5794 | #include "libguile/conv-uinteger.i.c" | |
5795 | ||
5796 | #define TYPE scm_t_int8 | |
5797 | #define TYPE_MIN SCM_T_INT8_MIN | |
5798 | #define TYPE_MAX SCM_T_INT8_MAX | |
5799 | #define SIZEOF_TYPE 1 | |
5800 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
5801 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
5802 | #include "libguile/conv-integer.i.c" | |
5803 | ||
5804 | #define TYPE scm_t_uint8 | |
5805 | #define TYPE_MIN 0 | |
5806 | #define TYPE_MAX SCM_T_UINT8_MAX | |
5807 | #define SIZEOF_TYPE 1 | |
5808 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
5809 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
5810 | #include "libguile/conv-uinteger.i.c" | |
5811 | ||
5812 | #define TYPE scm_t_int16 | |
5813 | #define TYPE_MIN SCM_T_INT16_MIN | |
5814 | #define TYPE_MAX SCM_T_INT16_MAX | |
5815 | #define SIZEOF_TYPE 2 | |
5816 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
5817 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
5818 | #include "libguile/conv-integer.i.c" | |
5819 | ||
5820 | #define TYPE scm_t_uint16 | |
5821 | #define TYPE_MIN 0 | |
5822 | #define TYPE_MAX SCM_T_UINT16_MAX | |
5823 | #define SIZEOF_TYPE 2 | |
5824 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
5825 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
5826 | #include "libguile/conv-uinteger.i.c" | |
5827 | ||
5828 | #define TYPE scm_t_int32 | |
5829 | #define TYPE_MIN SCM_T_INT32_MIN | |
5830 | #define TYPE_MAX SCM_T_INT32_MAX | |
5831 | #define SIZEOF_TYPE 4 | |
5832 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
5833 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
5834 | #include "libguile/conv-integer.i.c" | |
5835 | ||
5836 | #define TYPE scm_t_uint32 | |
5837 | #define TYPE_MIN 0 | |
5838 | #define TYPE_MAX SCM_T_UINT32_MAX | |
5839 | #define SIZEOF_TYPE 4 | |
5840 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
5841 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
5842 | #include "libguile/conv-uinteger.i.c" | |
5843 | ||
5844 | #if SCM_HAVE_T_INT64 | |
5845 | ||
5846 | #define TYPE scm_t_int64 | |
5847 | #define TYPE_MIN SCM_T_INT64_MIN | |
5848 | #define TYPE_MAX SCM_T_INT64_MAX | |
5849 | #define SIZEOF_TYPE 8 | |
5850 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
5851 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
5852 | #include "libguile/conv-integer.i.c" | |
5853 | ||
5854 | #define TYPE scm_t_uint64 | |
5855 | #define TYPE_MIN 0 | |
5856 | #define TYPE_MAX SCM_T_UINT64_MAX | |
5857 | #define SIZEOF_TYPE 8 | |
5858 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
5859 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
5860 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 5861 | |
bfd7932e | 5862 | #endif |
73e4de09 | 5863 | |
cd036260 MV |
5864 | void |
5865 | scm_to_mpz (SCM val, mpz_t rop) | |
5866 | { | |
5867 | if (SCM_I_INUMP (val)) | |
5868 | mpz_set_si (rop, SCM_I_INUM (val)); | |
5869 | else if (SCM_BIGP (val)) | |
5870 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
5871 | else | |
5872 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
5873 | } | |
5874 | ||
5875 | SCM | |
5876 | scm_from_mpz (mpz_t val) | |
5877 | { | |
5878 | return scm_i_mpz2num (val); | |
5879 | } | |
5880 | ||
73e4de09 MV |
5881 | int |
5882 | scm_is_real (SCM val) | |
5883 | { | |
5884 | return scm_is_true (scm_real_p (val)); | |
5885 | } | |
5886 | ||
55f26379 MV |
5887 | int |
5888 | scm_is_rational (SCM val) | |
5889 | { | |
5890 | return scm_is_true (scm_rational_p (val)); | |
5891 | } | |
5892 | ||
73e4de09 MV |
5893 | double |
5894 | scm_to_double (SCM val) | |
5895 | { | |
55f26379 MV |
5896 | if (SCM_I_INUMP (val)) |
5897 | return SCM_I_INUM (val); | |
5898 | else if (SCM_BIGP (val)) | |
5899 | return scm_i_big2dbl (val); | |
5900 | else if (SCM_FRACTIONP (val)) | |
5901 | return scm_i_fraction2double (val); | |
5902 | else if (SCM_REALP (val)) | |
5903 | return SCM_REAL_VALUE (val); | |
5904 | else | |
7a1aba42 | 5905 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
5906 | } |
5907 | ||
5908 | SCM | |
5909 | scm_from_double (double val) | |
5910 | { | |
55f26379 MV |
5911 | SCM z = scm_double_cell (scm_tc16_real, 0, 0, 0); |
5912 | SCM_REAL_VALUE (z) = val; | |
5913 | return z; | |
73e4de09 MV |
5914 | } |
5915 | ||
55f26379 MV |
5916 | #if SCM_ENABLE_DISCOURAGED == 1 |
5917 | ||
5918 | float | |
5919 | scm_num2float (SCM num, unsigned long int pos, const char *s_caller) | |
5920 | { | |
5921 | if (SCM_BIGP (num)) | |
5922 | { | |
5923 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5924 | if (!xisinf (res)) | |
5925 | return res; | |
5926 | else | |
5927 | scm_out_of_range (NULL, num); | |
5928 | } | |
5929 | else | |
5930 | return scm_to_double (num); | |
5931 | } | |
5932 | ||
5933 | double | |
5934 | scm_num2double (SCM num, unsigned long int pos, const char *s_caller) | |
5935 | { | |
5936 | if (SCM_BIGP (num)) | |
5937 | { | |
5938 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5939 | if (!xisinf (res)) | |
5940 | return res; | |
5941 | else | |
5942 | scm_out_of_range (NULL, num); | |
5943 | } | |
5944 | else | |
5945 | return scm_to_double (num); | |
5946 | } | |
5947 | ||
5948 | #endif | |
5949 | ||
8507ec80 MV |
5950 | int |
5951 | scm_is_complex (SCM val) | |
5952 | { | |
5953 | return scm_is_true (scm_complex_p (val)); | |
5954 | } | |
5955 | ||
5956 | double | |
5957 | scm_c_real_part (SCM z) | |
5958 | { | |
5959 | if (SCM_COMPLEXP (z)) | |
5960 | return SCM_COMPLEX_REAL (z); | |
5961 | else | |
5962 | { | |
5963 | /* Use the scm_real_part to get proper error checking and | |
5964 | dispatching. | |
5965 | */ | |
5966 | return scm_to_double (scm_real_part (z)); | |
5967 | } | |
5968 | } | |
5969 | ||
5970 | double | |
5971 | scm_c_imag_part (SCM z) | |
5972 | { | |
5973 | if (SCM_COMPLEXP (z)) | |
5974 | return SCM_COMPLEX_IMAG (z); | |
5975 | else | |
5976 | { | |
5977 | /* Use the scm_imag_part to get proper error checking and | |
5978 | dispatching. The result will almost always be 0.0, but not | |
5979 | always. | |
5980 | */ | |
5981 | return scm_to_double (scm_imag_part (z)); | |
5982 | } | |
5983 | } | |
5984 | ||
5985 | double | |
5986 | scm_c_magnitude (SCM z) | |
5987 | { | |
5988 | return scm_to_double (scm_magnitude (z)); | |
5989 | } | |
5990 | ||
5991 | double | |
5992 | scm_c_angle (SCM z) | |
5993 | { | |
5994 | return scm_to_double (scm_angle (z)); | |
5995 | } | |
5996 | ||
5997 | int | |
5998 | scm_is_number (SCM z) | |
5999 | { | |
6000 | return scm_is_true (scm_number_p (z)); | |
6001 | } | |
6002 | ||
8ab3d8a0 KR |
6003 | |
6004 | /* In the following functions we dispatch to the real-arg funcs like log() | |
6005 | when we know the arg is real, instead of just handing everything to | |
6006 | clog() for instance. This is in case clog() doesn't optimize for a | |
6007 | real-only case, and because we have to test SCM_COMPLEXP anyway so may as | |
6008 | well use it to go straight to the applicable C func. */ | |
6009 | ||
6010 | SCM_DEFINE (scm_log, "log", 1, 0, 0, | |
6011 | (SCM z), | |
6012 | "Return the natural logarithm of @var{z}.") | |
6013 | #define FUNC_NAME s_scm_log | |
6014 | { | |
6015 | if (SCM_COMPLEXP (z)) | |
6016 | { | |
4b26c03e | 6017 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6018 | return scm_from_complex_double (clog (SCM_COMPLEX_VALUE (z))); |
6019 | #else | |
6020 | double re = SCM_COMPLEX_REAL (z); | |
6021 | double im = SCM_COMPLEX_IMAG (z); | |
6022 | return scm_c_make_rectangular (log (hypot (re, im)), | |
6023 | atan2 (im, re)); | |
6024 | #endif | |
6025 | } | |
6026 | else | |
6027 | { | |
6028 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6029 | although the value itself overflows. */ | |
6030 | double re = scm_to_double (z); | |
6031 | double l = log (fabs (re)); | |
6032 | if (re >= 0.0) | |
6033 | return scm_from_double (l); | |
6034 | else | |
6035 | return scm_c_make_rectangular (l, M_PI); | |
6036 | } | |
6037 | } | |
6038 | #undef FUNC_NAME | |
6039 | ||
6040 | ||
6041 | SCM_DEFINE (scm_log10, "log10", 1, 0, 0, | |
6042 | (SCM z), | |
6043 | "Return the base 10 logarithm of @var{z}.") | |
6044 | #define FUNC_NAME s_scm_log10 | |
6045 | { | |
6046 | if (SCM_COMPLEXP (z)) | |
6047 | { | |
6048 | /* Mingw has clog() but not clog10(). (Maybe it'd be worth using | |
6049 | clog() and a multiply by M_LOG10E, rather than the fallback | |
6050 | log10+hypot+atan2.) */ | |
4b26c03e | 6051 | #if HAVE_COMPLEX_DOUBLE && HAVE_CLOG10 && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6052 | return scm_from_complex_double (clog10 (SCM_COMPLEX_VALUE (z))); |
6053 | #else | |
6054 | double re = SCM_COMPLEX_REAL (z); | |
6055 | double im = SCM_COMPLEX_IMAG (z); | |
6056 | return scm_c_make_rectangular (log10 (hypot (re, im)), | |
6057 | M_LOG10E * atan2 (im, re)); | |
6058 | #endif | |
6059 | } | |
6060 | else | |
6061 | { | |
6062 | /* ENHANCE-ME: When z is a bignum the logarithm will fit a double | |
6063 | although the value itself overflows. */ | |
6064 | double re = scm_to_double (z); | |
6065 | double l = log10 (fabs (re)); | |
6066 | if (re >= 0.0) | |
6067 | return scm_from_double (l); | |
6068 | else | |
6069 | return scm_c_make_rectangular (l, M_LOG10E * M_PI); | |
6070 | } | |
6071 | } | |
6072 | #undef FUNC_NAME | |
6073 | ||
6074 | ||
6075 | SCM_DEFINE (scm_exp, "exp", 1, 0, 0, | |
6076 | (SCM z), | |
6077 | "Return @math{e} to the power of @var{z}, where @math{e} is the\n" | |
6078 | "base of natural logarithms (2.71828@dots{}).") | |
6079 | #define FUNC_NAME s_scm_exp | |
6080 | { | |
6081 | if (SCM_COMPLEXP (z)) | |
6082 | { | |
4b26c03e | 6083 | #if HAVE_COMPLEX_DOUBLE && HAVE_CEXP && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6084 | return scm_from_complex_double (cexp (SCM_COMPLEX_VALUE (z))); |
6085 | #else | |
6086 | return scm_c_make_polar (exp (SCM_COMPLEX_REAL (z)), | |
6087 | SCM_COMPLEX_IMAG (z)); | |
6088 | #endif | |
6089 | } | |
6090 | else | |
6091 | { | |
6092 | /* When z is a negative bignum the conversion to double overflows, | |
6093 | giving -infinity, but that's ok, the exp is still 0.0. */ | |
6094 | return scm_from_double (exp (scm_to_double (z))); | |
6095 | } | |
6096 | } | |
6097 | #undef FUNC_NAME | |
6098 | ||
6099 | ||
6100 | SCM_DEFINE (scm_sqrt, "sqrt", 1, 0, 0, | |
6101 | (SCM x), | |
6102 | "Return the square root of @var{z}. Of the two possible roots\n" | |
6103 | "(positive and negative), the one with the a positive real part\n" | |
6104 | "is returned, or if that's zero then a positive imaginary part.\n" | |
6105 | "Thus,\n" | |
6106 | "\n" | |
6107 | "@example\n" | |
6108 | "(sqrt 9.0) @result{} 3.0\n" | |
6109 | "(sqrt -9.0) @result{} 0.0+3.0i\n" | |
6110 | "(sqrt 1.0+1.0i) @result{} 1.09868411346781+0.455089860562227i\n" | |
6111 | "(sqrt -1.0-1.0i) @result{} 0.455089860562227-1.09868411346781i\n" | |
6112 | "@end example") | |
6113 | #define FUNC_NAME s_scm_sqrt | |
6114 | { | |
6115 | if (SCM_COMPLEXP (x)) | |
6116 | { | |
4b26c03e | 6117 | #if HAVE_COMPLEX_DOUBLE && HAVE_USABLE_CSQRT && defined (SCM_COMPLEX_VALUE) |
8ab3d8a0 KR |
6118 | return scm_from_complex_double (csqrt (SCM_COMPLEX_VALUE (x))); |
6119 | #else | |
6120 | double re = SCM_COMPLEX_REAL (x); | |
6121 | double im = SCM_COMPLEX_IMAG (x); | |
6122 | return scm_c_make_polar (sqrt (hypot (re, im)), | |
6123 | 0.5 * atan2 (im, re)); | |
6124 | #endif | |
6125 | } | |
6126 | else | |
6127 | { | |
6128 | double xx = scm_to_double (x); | |
6129 | if (xx < 0) | |
6130 | return scm_c_make_rectangular (0.0, sqrt (-xx)); | |
6131 | else | |
6132 | return scm_from_double (sqrt (xx)); | |
6133 | } | |
6134 | } | |
6135 | #undef FUNC_NAME | |
6136 | ||
6137 | ||
6138 | ||
0f2d19dd JB |
6139 | void |
6140 | scm_init_numbers () | |
0f2d19dd | 6141 | { |
0b799eea MV |
6142 | int i; |
6143 | ||
713a4259 KR |
6144 | mpz_init_set_si (z_negative_one, -1); |
6145 | ||
a261c0e9 DH |
6146 | /* It may be possible to tune the performance of some algorithms by using |
6147 | * the following constants to avoid the creation of bignums. Please, before | |
6148 | * using these values, remember the two rules of program optimization: | |
6149 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 6150 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 6151 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 6152 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 6153 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 6154 | |
f3ae5d60 MD |
6155 | scm_add_feature ("complex"); |
6156 | scm_add_feature ("inexact"); | |
55f26379 | 6157 | scm_flo0 = scm_from_double (0.0); |
0b799eea MV |
6158 | |
6159 | /* determine floating point precision */ | |
55f26379 | 6160 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
6161 | { |
6162 | init_dblprec(&scm_dblprec[i-2],i); | |
6163 | init_fx_radix(fx_per_radix[i-2],i); | |
6164 | } | |
f872b822 | 6165 | #ifdef DBL_DIG |
0b799eea MV |
6166 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
6167 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; | |
6168 | #endif | |
1be6b49c | 6169 | |
d956fa6f MV |
6170 | exactly_one_half = scm_permanent_object (scm_divide (SCM_I_MAKINUM (1), |
6171 | SCM_I_MAKINUM (2))); | |
a0599745 | 6172 | #include "libguile/numbers.x" |
0f2d19dd | 6173 | } |
89e00824 ML |
6174 | |
6175 | /* | |
6176 | Local Variables: | |
6177 | c-file-style: "gnu" | |
6178 | End: | |
6179 | */ |