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