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2b829bbb | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005, 2006 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 | |
fa605590 KR |
43 | /* tell glibc (2.3) to give prototype for C99 trunc() */ |
44 | #define _GNU_SOURCE | |
45 | ||
ee33d62a RB |
46 | #if HAVE_CONFIG_H |
47 | # include <config.h> | |
48 | #endif | |
49 | ||
0f2d19dd | 50 | #include <math.h> |
3c9a524f | 51 | #include <ctype.h> |
fc194577 | 52 | #include <string.h> |
f92e85f7 | 53 | |
a0599745 | 54 | #include "libguile/_scm.h" |
a0599745 MD |
55 | #include "libguile/feature.h" |
56 | #include "libguile/ports.h" | |
57 | #include "libguile/root.h" | |
58 | #include "libguile/smob.h" | |
59 | #include "libguile/strings.h" | |
a0599745 MD |
60 | |
61 | #include "libguile/validate.h" | |
62 | #include "libguile/numbers.h" | |
1be6b49c | 63 | #include "libguile/deprecation.h" |
f4c627b3 | 64 | |
f92e85f7 MV |
65 | #include "libguile/eq.h" |
66 | ||
55f26379 MV |
67 | #include "libguile/discouraged.h" |
68 | ||
0f2d19dd | 69 | \f |
f4c627b3 | 70 | |
ca46fb90 RB |
71 | /* |
72 | Wonder if this might be faster for some of our code? A switch on | |
73 | the numtag would jump directly to the right case, and the | |
74 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
75 | ||
76 | #define SCM_I_NUMTAG_NOTNUM 0 | |
77 | #define SCM_I_NUMTAG_INUM 1 | |
78 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
79 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
80 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
81 | #define SCM_I_NUMTAG(x) \ | |
e11e83f3 | 82 | (SCM_I_INUMP(x) ? SCM_I_NUMTAG_INUM \ |
ca46fb90 | 83 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ |
534c55a9 | 84 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
85 | : SCM_I_NUMTAG_NOTNUM))) |
86 | */ | |
f92e85f7 | 87 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
88 | |
89 | ||
34d19ef6 | 90 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 91 | |
56e55ac7 | 92 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
93 | * printed or scm_string representation of an inexact number. |
94 | */ | |
0b799eea | 95 | #define FLOBUFLEN (40+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 96 | |
7351e207 MV |
97 | #if defined (SCO) |
98 | #if ! defined (HAVE_ISNAN) | |
99 | #define HAVE_ISNAN | |
100 | static int | |
101 | isnan (double x) | |
102 | { | |
103 | return (IsNANorINF (x) && NaN (x) && ! IsINF (x)) ? 1 : 0; | |
104 | } | |
0f2d19dd | 105 | #endif |
7351e207 MV |
106 | #if ! defined (HAVE_ISINF) |
107 | #define HAVE_ISINF | |
108 | static int | |
109 | isinf (double x) | |
110 | { | |
111 | return (IsNANorINF (x) && IsINF (x)) ? 1 : 0; | |
112 | } | |
0f2d19dd | 113 | |
7351e207 | 114 | #endif |
e6f3ef58 MD |
115 | #endif |
116 | ||
b127c712 | 117 | |
f8a8200b KR |
118 | /* mpz_cmp_d in gmp 4.1.3 doesn't recognise infinities, so xmpz_cmp_d uses |
119 | an explicit check. In some future gmp (don't know what version number), | |
120 | mpz_cmp_d is supposed to do this itself. */ | |
121 | #if 1 | |
b127c712 KR |
122 | #define xmpz_cmp_d(z, d) \ |
123 | (xisinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) | |
124 | #else | |
125 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
126 | #endif | |
127 | ||
a98ce907 KR |
128 | /* For reference, sparc solaris 7 has infinities (IEEE) but doesn't have |
129 | isinf. It does have finite and isnan though, hence the use of those. | |
130 | fpclass would be a possibility on that system too. */ | |
f92e85f7 MV |
131 | static int |
132 | xisinf (double x) | |
133 | { | |
134 | #if defined (HAVE_ISINF) | |
135 | return isinf (x); | |
136 | #elif defined (HAVE_FINITE) && defined (HAVE_ISNAN) | |
137 | return (! (finite (x) || isnan (x))); | |
138 | #else | |
139 | return 0; | |
140 | #endif | |
141 | } | |
142 | ||
143 | static int | |
144 | xisnan (double x) | |
145 | { | |
146 | #if defined (HAVE_ISNAN) | |
147 | return isnan (x); | |
148 | #else | |
149 | return 0; | |
150 | #endif | |
151 | } | |
152 | ||
0f2d19dd JB |
153 | \f |
154 | ||
713a4259 | 155 | static mpz_t z_negative_one; |
ac0c002c DH |
156 | |
157 | \f | |
158 | ||
570b6821 | 159 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
160 | scm_i_mkbig () |
161 | { | |
162 | /* Return a newly created bignum. */ | |
163 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
164 | mpz_init (SCM_I_BIG_MPZ (z)); | |
165 | return z; | |
166 | } | |
167 | ||
c71b0706 MV |
168 | SCM_C_INLINE_KEYWORD SCM |
169 | scm_i_long2big (long x) | |
170 | { | |
171 | /* Return a newly created bignum initialized to X. */ | |
172 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
173 | mpz_init_set_si (SCM_I_BIG_MPZ (z), x); | |
174 | return z; | |
175 | } | |
176 | ||
177 | SCM_C_INLINE_KEYWORD SCM | |
178 | scm_i_ulong2big (unsigned long x) | |
179 | { | |
180 | /* Return a newly created bignum initialized to X. */ | |
181 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
182 | mpz_init_set_ui (SCM_I_BIG_MPZ (z), x); | |
183 | return z; | |
184 | } | |
185 | ||
23c3b605 | 186 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
187 | scm_i_clonebig (SCM src_big, int same_sign_p) |
188 | { | |
189 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
190 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
191 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); | |
0aacf84e MD |
192 | if (!same_sign_p) |
193 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
194 | return z; |
195 | } | |
196 | ||
570b6821 | 197 | SCM_C_INLINE_KEYWORD int |
ca46fb90 RB |
198 | scm_i_bigcmp (SCM x, SCM y) |
199 | { | |
200 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
201 | /* presume we already know x and y are bignums */ | |
202 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
203 | scm_remember_upto_here_2 (x, y); | |
204 | return result; | |
205 | } | |
206 | ||
570b6821 | 207 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
208 | scm_i_dbl2big (double d) |
209 | { | |
210 | /* results are only defined if d is an integer */ | |
211 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
212 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); | |
213 | return z; | |
214 | } | |
215 | ||
f92e85f7 MV |
216 | /* Convert a integer in double representation to a SCM number. */ |
217 | ||
218 | SCM_C_INLINE_KEYWORD SCM | |
219 | scm_i_dbl2num (double u) | |
220 | { | |
221 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
222 | powers of 2, so there's no rounding when making "double" values | |
223 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
224 | get rounded on a 64-bit machine, hence the "+1". | |
225 | ||
226 | The use of floor() to force to an integer value ensures we get a | |
227 | "numerically closest" value without depending on how a | |
228 | double->long cast or how mpz_set_d will round. For reference, | |
229 | double->long probably follows the hardware rounding mode, | |
230 | mpz_set_d truncates towards zero. */ | |
231 | ||
232 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
233 | representable as a double? */ | |
234 | ||
235 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
236 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
d956fa6f | 237 | return SCM_I_MAKINUM ((long) u); |
f92e85f7 MV |
238 | else |
239 | return scm_i_dbl2big (u); | |
240 | } | |
241 | ||
089c9a59 KR |
242 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
243 | with R5RS exact->inexact. | |
244 | ||
245 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
f8a8200b KR |
246 | (ie. truncate towards zero), then adjust to get the closest double by |
247 | examining the next lower bit and adding 1 (to the absolute value) if | |
248 | necessary. | |
249 | ||
250 | Bignums exactly half way between representable doubles are rounded to the | |
251 | next higher absolute value (ie. away from zero). This seems like an | |
252 | adequate interpretation of R5RS "numerically closest", and it's easier | |
253 | and faster than a full "nearest-even" style. | |
254 | ||
255 | The bit test must be done on the absolute value of the mpz_t, which means | |
256 | we need to use mpz_getlimbn. mpz_tstbit is not right, it treats | |
257 | negatives as twos complement. | |
258 | ||
259 | In current gmp 4.1.3, mpz_get_d rounding is unspecified. It ends up | |
260 | following the hardware rounding mode, but applied to the absolute value | |
261 | of the mpz_t operand. This is not what we want so we put the high | |
262 | DBL_MANT_DIG bits into a temporary. In some future gmp, don't know when, | |
263 | mpz_get_d is supposed to always truncate towards zero. | |
264 | ||
265 | ENHANCE-ME: The temporary init+clear to force the rounding in gmp 4.1.3 | |
266 | is a slowdown. It'd be faster to pick out the relevant high bits with | |
267 | mpz_getlimbn if we could be bothered coding that, and if the new | |
268 | truncating gmp doesn't come out. */ | |
089c9a59 KR |
269 | |
270 | double | |
ca46fb90 RB |
271 | scm_i_big2dbl (SCM b) |
272 | { | |
089c9a59 KR |
273 | double result; |
274 | size_t bits; | |
275 | ||
276 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
277 | ||
f8a8200b | 278 | #if 1 |
089c9a59 | 279 | { |
f8a8200b | 280 | /* Current GMP, eg. 4.1.3, force truncation towards zero */ |
089c9a59 KR |
281 | mpz_t tmp; |
282 | if (bits > DBL_MANT_DIG) | |
283 | { | |
284 | size_t shift = bits - DBL_MANT_DIG; | |
285 | mpz_init2 (tmp, DBL_MANT_DIG); | |
286 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
287 | result = ldexp (mpz_get_d (tmp), shift); | |
288 | mpz_clear (tmp); | |
289 | } | |
290 | else | |
291 | { | |
292 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
293 | } | |
294 | } | |
295 | #else | |
f8a8200b | 296 | /* Future GMP */ |
089c9a59 KR |
297 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); |
298 | #endif | |
299 | ||
300 | if (bits > DBL_MANT_DIG) | |
301 | { | |
302 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
303 | /* test bit number "pos" in absolute value */ | |
304 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
305 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
306 | { | |
307 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
308 | } | |
309 | } | |
310 | ||
ca46fb90 RB |
311 | scm_remember_upto_here_1 (b); |
312 | return result; | |
313 | } | |
314 | ||
570b6821 | 315 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
316 | scm_i_normbig (SCM b) |
317 | { | |
318 | /* convert a big back to a fixnum if it'll fit */ | |
319 | /* presume b is a bignum */ | |
320 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
321 | { | |
322 | long val = mpz_get_si (SCM_I_BIG_MPZ (b)); | |
323 | if (SCM_FIXABLE (val)) | |
d956fa6f | 324 | b = SCM_I_MAKINUM (val); |
ca46fb90 RB |
325 | } |
326 | return b; | |
327 | } | |
f872b822 | 328 | |
f92e85f7 MV |
329 | static SCM_C_INLINE_KEYWORD SCM |
330 | scm_i_mpz2num (mpz_t b) | |
331 | { | |
332 | /* convert a mpz number to a SCM number. */ | |
333 | if (mpz_fits_slong_p (b)) | |
334 | { | |
335 | long val = mpz_get_si (b); | |
336 | if (SCM_FIXABLE (val)) | |
d956fa6f | 337 | return SCM_I_MAKINUM (val); |
f92e85f7 MV |
338 | } |
339 | ||
340 | { | |
341 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
342 | mpz_init_set (SCM_I_BIG_MPZ (z), b); | |
343 | return z; | |
344 | } | |
345 | } | |
346 | ||
347 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
348 | static SCM scm_divide2real (SCM x, SCM y); | |
349 | ||
cba42c93 MV |
350 | static SCM |
351 | scm_i_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 352 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 353 | { |
c60e130c MV |
354 | /* First make sure the arguments are proper. |
355 | */ | |
e11e83f3 | 356 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 357 | { |
bc36d050 | 358 | if (scm_is_eq (denominator, SCM_INUM0)) |
f92e85f7 | 359 | scm_num_overflow ("make-ratio"); |
bc36d050 | 360 | if (scm_is_eq (denominator, SCM_I_MAKINUM(1))) |
f92e85f7 MV |
361 | return numerator; |
362 | } | |
363 | else | |
364 | { | |
365 | if (!(SCM_BIGP(denominator))) | |
366 | SCM_WRONG_TYPE_ARG (2, denominator); | |
367 | } | |
e11e83f3 | 368 | if (!SCM_I_INUMP (numerator) && !SCM_BIGP (numerator)) |
c60e130c MV |
369 | SCM_WRONG_TYPE_ARG (1, numerator); |
370 | ||
371 | /* Then flip signs so that the denominator is positive. | |
372 | */ | |
73e4de09 | 373 | if (scm_is_true (scm_negative_p (denominator))) |
c60e130c MV |
374 | { |
375 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
376 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
377 | } | |
378 | ||
379 | /* Now consider for each of the four fixnum/bignum combinations | |
380 | whether the rational number is really an integer. | |
381 | */ | |
e11e83f3 | 382 | if (SCM_I_INUMP (numerator)) |
f92e85f7 | 383 | { |
e11e83f3 | 384 | long x = SCM_I_INUM (numerator); |
bc36d050 | 385 | if (scm_is_eq (numerator, SCM_INUM0)) |
f92e85f7 | 386 | return SCM_INUM0; |
e11e83f3 | 387 | if (SCM_I_INUMP (denominator)) |
f92e85f7 | 388 | { |
dd5130ca | 389 | long y; |
e11e83f3 | 390 | y = SCM_I_INUM (denominator); |
f92e85f7 | 391 | if (x == y) |
d956fa6f | 392 | return SCM_I_MAKINUM(1); |
f92e85f7 | 393 | if ((x % y) == 0) |
d956fa6f | 394 | return SCM_I_MAKINUM (x / y); |
f92e85f7 | 395 | } |
dd5130ca KR |
396 | else |
397 | { | |
398 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
3271a325 KR |
399 | of that value for the denominator, as a bignum. Apart from |
400 | that case, abs(bignum) > abs(inum) so inum/bignum is not an | |
401 | integer. */ | |
402 | if (x == SCM_MOST_NEGATIVE_FIXNUM | |
403 | && mpz_cmp_ui (SCM_I_BIG_MPZ (denominator), | |
404 | - SCM_MOST_NEGATIVE_FIXNUM) == 0) | |
d956fa6f | 405 | return SCM_I_MAKINUM(-1); |
dd5130ca | 406 | } |
f92e85f7 | 407 | } |
c60e130c | 408 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 409 | { |
e11e83f3 | 410 | if (SCM_I_INUMP (denominator)) |
c60e130c | 411 | { |
e11e83f3 | 412 | long yy = SCM_I_INUM (denominator); |
c60e130c MV |
413 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) |
414 | return scm_divide (numerator, denominator); | |
415 | } | |
416 | else | |
f92e85f7 | 417 | { |
bc36d050 | 418 | if (scm_is_eq (numerator, denominator)) |
d956fa6f | 419 | return SCM_I_MAKINUM(1); |
c60e130c MV |
420 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), |
421 | SCM_I_BIG_MPZ (denominator))) | |
422 | return scm_divide(numerator, denominator); | |
f92e85f7 | 423 | } |
f92e85f7 | 424 | } |
c60e130c MV |
425 | |
426 | /* No, it's a proper fraction. | |
427 | */ | |
428 | return scm_double_cell (scm_tc16_fraction, | |
429 | SCM_UNPACK (numerator), | |
430 | SCM_UNPACK (denominator), 0); | |
f92e85f7 | 431 | } |
c60e130c | 432 | #undef FUNC_NAME |
f92e85f7 MV |
433 | |
434 | static void scm_i_fraction_reduce (SCM z) | |
435 | { | |
436 | if (!(SCM_FRACTION_REDUCED (z))) | |
437 | { | |
438 | SCM divisor; | |
439 | divisor = scm_gcd (SCM_FRACTION_NUMERATOR (z), SCM_FRACTION_DENOMINATOR (z)); | |
bc36d050 | 440 | if (!(scm_is_eq (divisor, SCM_I_MAKINUM(1)))) |
f92e85f7 MV |
441 | { |
442 | /* is this safe? */ | |
443 | SCM_FRACTION_SET_NUMERATOR (z, scm_divide (SCM_FRACTION_NUMERATOR (z), divisor)); | |
444 | SCM_FRACTION_SET_DENOMINATOR (z, scm_divide (SCM_FRACTION_DENOMINATOR (z), divisor)); | |
445 | } | |
446 | SCM_FRACTION_REDUCED_SET (z); | |
447 | } | |
448 | } | |
449 | ||
450 | double | |
451 | scm_i_fraction2double (SCM z) | |
452 | { | |
55f26379 MV |
453 | return scm_to_double (scm_divide2real (SCM_FRACTION_NUMERATOR (z), |
454 | SCM_FRACTION_DENOMINATOR (z))); | |
f92e85f7 MV |
455 | } |
456 | ||
a1ec6916 | 457 | SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0, |
1bbd0b84 | 458 | (SCM x), |
942e5b91 MG |
459 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
460 | "otherwise.") | |
1bbd0b84 | 461 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 462 | { |
e11e83f3 | 463 | if (SCM_I_INUMP (x)) |
0aacf84e MD |
464 | return SCM_BOOL_T; |
465 | if (SCM_BIGP (x)) | |
466 | return SCM_BOOL_T; | |
f92e85f7 MV |
467 | if (SCM_FRACTIONP (x)) |
468 | return SCM_BOOL_T; | |
eb927cb9 MV |
469 | if (SCM_NUMBERP (x)) |
470 | return SCM_BOOL_F; | |
471 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 472 | } |
1bbd0b84 | 473 | #undef FUNC_NAME |
0f2d19dd | 474 | |
4219f20d | 475 | |
a1ec6916 | 476 | SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 477 | (SCM n), |
942e5b91 MG |
478 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
479 | "otherwise.") | |
1bbd0b84 | 480 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 481 | { |
e11e83f3 | 482 | if (SCM_I_INUMP (n)) |
0aacf84e | 483 | { |
e11e83f3 | 484 | long val = SCM_I_INUM (n); |
73e4de09 | 485 | return scm_from_bool ((val & 1L) != 0); |
0aacf84e MD |
486 | } |
487 | else if (SCM_BIGP (n)) | |
488 | { | |
489 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
490 | scm_remember_upto_here_1 (n); | |
73e4de09 | 491 | return scm_from_bool (odd_p); |
0aacf84e | 492 | } |
73e4de09 | 493 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 494 | return SCM_BOOL_T; |
f92e85f7 MV |
495 | else if (SCM_REALP (n)) |
496 | { | |
497 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
498 | if (rem == 1.0) | |
499 | return SCM_BOOL_T; | |
500 | else if (rem == 0.0) | |
501 | return SCM_BOOL_F; | |
502 | else | |
503 | SCM_WRONG_TYPE_ARG (1, n); | |
504 | } | |
0aacf84e | 505 | else |
a1a33b0f | 506 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 507 | } |
1bbd0b84 | 508 | #undef FUNC_NAME |
0f2d19dd | 509 | |
4219f20d | 510 | |
a1ec6916 | 511 | SCM_DEFINE (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 512 | (SCM n), |
942e5b91 MG |
513 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
514 | "otherwise.") | |
1bbd0b84 | 515 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 516 | { |
e11e83f3 | 517 | if (SCM_I_INUMP (n)) |
0aacf84e | 518 | { |
e11e83f3 | 519 | long val = SCM_I_INUM (n); |
73e4de09 | 520 | return scm_from_bool ((val & 1L) == 0); |
0aacf84e MD |
521 | } |
522 | else if (SCM_BIGP (n)) | |
523 | { | |
524 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
525 | scm_remember_upto_here_1 (n); | |
73e4de09 | 526 | return scm_from_bool (even_p); |
0aacf84e | 527 | } |
73e4de09 | 528 | else if (scm_is_true (scm_inf_p (n))) |
7351e207 | 529 | return SCM_BOOL_T; |
f92e85f7 MV |
530 | else if (SCM_REALP (n)) |
531 | { | |
532 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
533 | if (rem == 1.0) | |
534 | return SCM_BOOL_F; | |
535 | else if (rem == 0.0) | |
536 | return SCM_BOOL_T; | |
537 | else | |
538 | SCM_WRONG_TYPE_ARG (1, n); | |
539 | } | |
0aacf84e | 540 | else |
a1a33b0f | 541 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 542 | } |
1bbd0b84 | 543 | #undef FUNC_NAME |
0f2d19dd | 544 | |
7351e207 | 545 | SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0, |
b1092b3a MV |
546 | (SCM x), |
547 | "Return @code{#t} if @var{x} is either @samp{+inf.0}\n" | |
548 | "or @samp{-inf.0}, @code{#f} otherwise.") | |
7351e207 MV |
549 | #define FUNC_NAME s_scm_inf_p |
550 | { | |
b1092b3a MV |
551 | if (SCM_REALP (x)) |
552 | return scm_from_bool (xisinf (SCM_REAL_VALUE (x))); | |
553 | else if (SCM_COMPLEXP (x)) | |
554 | return scm_from_bool (xisinf (SCM_COMPLEX_REAL (x)) | |
555 | || xisinf (SCM_COMPLEX_IMAG (x))); | |
0aacf84e | 556 | else |
7351e207 | 557 | return SCM_BOOL_F; |
7351e207 MV |
558 | } |
559 | #undef FUNC_NAME | |
560 | ||
561 | SCM_DEFINE (scm_nan_p, "nan?", 1, 0, 0, | |
562 | (SCM n), | |
563 | "Return @code{#t} if @var{n} is a NaN, @code{#f}\n" | |
564 | "otherwise.") | |
565 | #define FUNC_NAME s_scm_nan_p | |
566 | { | |
0aacf84e | 567 | if (SCM_REALP (n)) |
73e4de09 | 568 | return scm_from_bool (xisnan (SCM_REAL_VALUE (n))); |
0aacf84e | 569 | else if (SCM_COMPLEXP (n)) |
73e4de09 | 570 | return scm_from_bool (xisnan (SCM_COMPLEX_REAL (n)) |
7351e207 | 571 | || xisnan (SCM_COMPLEX_IMAG (n))); |
0aacf84e | 572 | else |
7351e207 | 573 | return SCM_BOOL_F; |
7351e207 MV |
574 | } |
575 | #undef FUNC_NAME | |
576 | ||
577 | /* Guile's idea of infinity. */ | |
578 | static double guile_Inf; | |
579 | ||
580 | /* Guile's idea of not a number. */ | |
581 | static double guile_NaN; | |
582 | ||
583 | static void | |
584 | guile_ieee_init (void) | |
585 | { | |
586 | #if defined (HAVE_ISINF) || defined (HAVE_FINITE) | |
587 | ||
588 | /* Some version of gcc on some old version of Linux used to crash when | |
589 | trying to make Inf and NaN. */ | |
590 | ||
240a27d2 KR |
591 | #ifdef INFINITY |
592 | /* C99 INFINITY, when available. | |
593 | FIXME: The standard allows for INFINITY to be something that overflows | |
594 | at compile time. We ought to have a configure test to check for that | |
595 | before trying to use it. (But in practice we believe this is not a | |
596 | problem on any system guile is likely to target.) */ | |
597 | guile_Inf = INFINITY; | |
598 | #elif HAVE_DINFINITY | |
599 | /* OSF */ | |
7351e207 | 600 | extern unsigned int DINFINITY[2]; |
eaa94eaa | 601 | guile_Inf = (*((double *) (DINFINITY))); |
7351e207 MV |
602 | #else |
603 | double tmp = 1e+10; | |
604 | guile_Inf = tmp; | |
605 | for (;;) | |
606 | { | |
607 | guile_Inf *= 1e+10; | |
608 | if (guile_Inf == tmp) | |
609 | break; | |
610 | tmp = guile_Inf; | |
611 | } | |
612 | #endif | |
613 | ||
614 | #endif | |
615 | ||
616 | #if defined (HAVE_ISNAN) | |
617 | ||
240a27d2 KR |
618 | #ifdef NAN |
619 | /* C99 NAN, when available */ | |
620 | guile_NaN = NAN; | |
621 | #elif HAVE_DQNAN | |
eaa94eaa LC |
622 | { |
623 | /* OSF */ | |
624 | extern unsigned int DQNAN[2]; | |
625 | guile_NaN = (*((double *)(DQNAN))); | |
626 | } | |
7351e207 MV |
627 | #else |
628 | guile_NaN = guile_Inf / guile_Inf; | |
629 | #endif | |
630 | ||
631 | #endif | |
632 | } | |
633 | ||
634 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
635 | (void), | |
636 | "Return Inf.") | |
637 | #define FUNC_NAME s_scm_inf | |
638 | { | |
639 | static int initialized = 0; | |
640 | if (! initialized) | |
641 | { | |
642 | guile_ieee_init (); | |
643 | initialized = 1; | |
644 | } | |
55f26379 | 645 | return scm_from_double (guile_Inf); |
7351e207 MV |
646 | } |
647 | #undef FUNC_NAME | |
648 | ||
649 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
650 | (void), | |
651 | "Return NaN.") | |
652 | #define FUNC_NAME s_scm_nan | |
653 | { | |
654 | static int initialized = 0; | |
0aacf84e | 655 | if (!initialized) |
7351e207 MV |
656 | { |
657 | guile_ieee_init (); | |
658 | initialized = 1; | |
659 | } | |
55f26379 | 660 | return scm_from_double (guile_NaN); |
7351e207 MV |
661 | } |
662 | #undef FUNC_NAME | |
663 | ||
4219f20d | 664 | |
a48d60b1 MD |
665 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
666 | (SCM x), | |
667 | "Return the absolute value of @var{x}.") | |
668 | #define FUNC_NAME | |
0f2d19dd | 669 | { |
e11e83f3 | 670 | if (SCM_I_INUMP (x)) |
0aacf84e | 671 | { |
e11e83f3 | 672 | long int xx = SCM_I_INUM (x); |
0aacf84e MD |
673 | if (xx >= 0) |
674 | return x; | |
675 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 676 | return SCM_I_MAKINUM (-xx); |
0aacf84e MD |
677 | else |
678 | return scm_i_long2big (-xx); | |
4219f20d | 679 | } |
0aacf84e MD |
680 | else if (SCM_BIGP (x)) |
681 | { | |
682 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
683 | if (sgn < 0) | |
684 | return scm_i_clonebig (x, 0); | |
685 | else | |
686 | return x; | |
4219f20d | 687 | } |
0aacf84e | 688 | else if (SCM_REALP (x)) |
ae38324d KR |
689 | { |
690 | /* note that if x is a NaN then xx<0 is false so we return x unchanged */ | |
691 | double xx = SCM_REAL_VALUE (x); | |
692 | if (xx < 0.0) | |
55f26379 | 693 | return scm_from_double (-xx); |
ae38324d KR |
694 | else |
695 | return x; | |
696 | } | |
f92e85f7 MV |
697 | else if (SCM_FRACTIONP (x)) |
698 | { | |
73e4de09 | 699 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 700 | return x; |
cba42c93 | 701 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
702 | SCM_FRACTION_DENOMINATOR (x)); |
703 | } | |
0aacf84e | 704 | else |
a48d60b1 | 705 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 706 | } |
a48d60b1 | 707 | #undef FUNC_NAME |
0f2d19dd | 708 | |
4219f20d | 709 | |
9de33deb | 710 | SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); |
942e5b91 MG |
711 | /* "Return the quotient of the numbers @var{x} and @var{y}." |
712 | */ | |
0f2d19dd | 713 | SCM |
6e8d25a6 | 714 | scm_quotient (SCM x, SCM y) |
0f2d19dd | 715 | { |
e11e83f3 | 716 | if (SCM_I_INUMP (x)) |
0aacf84e | 717 | { |
e11e83f3 MV |
718 | long xx = SCM_I_INUM (x); |
719 | if (SCM_I_INUMP (y)) | |
0aacf84e | 720 | { |
e11e83f3 | 721 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
722 | if (yy == 0) |
723 | scm_num_overflow (s_quotient); | |
724 | else | |
725 | { | |
726 | long z = xx / yy; | |
727 | if (SCM_FIXABLE (z)) | |
d956fa6f | 728 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
729 | else |
730 | return scm_i_long2big (z); | |
731 | } | |
828865c3 | 732 | } |
0aacf84e | 733 | else if (SCM_BIGP (y)) |
ac0c002c | 734 | { |
e11e83f3 | 735 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
736 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
737 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
738 | { | |
739 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
740 | scm_remember_upto_here_1 (y); | |
d956fa6f | 741 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 742 | } |
0aacf84e | 743 | else |
d956fa6f | 744 | return SCM_I_MAKINUM (0); |
ac0c002c DH |
745 | } |
746 | else | |
0aacf84e | 747 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); |
828865c3 | 748 | } |
0aacf84e MD |
749 | else if (SCM_BIGP (x)) |
750 | { | |
e11e83f3 | 751 | if (SCM_I_INUMP (y)) |
0aacf84e | 752 | { |
e11e83f3 | 753 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
754 | if (yy == 0) |
755 | scm_num_overflow (s_quotient); | |
756 | else if (yy == 1) | |
757 | return x; | |
758 | else | |
759 | { | |
760 | SCM result = scm_i_mkbig (); | |
761 | if (yy < 0) | |
762 | { | |
763 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
764 | SCM_I_BIG_MPZ (x), | |
765 | - yy); | |
766 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
767 | } | |
768 | else | |
769 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
770 | scm_remember_upto_here_1 (x); | |
771 | return scm_i_normbig (result); | |
772 | } | |
773 | } | |
774 | else if (SCM_BIGP (y)) | |
775 | { | |
776 | SCM result = scm_i_mkbig (); | |
777 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
778 | SCM_I_BIG_MPZ (x), | |
779 | SCM_I_BIG_MPZ (y)); | |
780 | scm_remember_upto_here_2 (x, y); | |
781 | return scm_i_normbig (result); | |
782 | } | |
783 | else | |
784 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); | |
f872b822 | 785 | } |
0aacf84e | 786 | else |
89a7e495 | 787 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient); |
0f2d19dd JB |
788 | } |
789 | ||
9de33deb | 790 | SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); |
942e5b91 MG |
791 | /* "Return the remainder of the numbers @var{x} and @var{y}.\n" |
792 | * "@lisp\n" | |
793 | * "(remainder 13 4) @result{} 1\n" | |
794 | * "(remainder -13 4) @result{} -1\n" | |
795 | * "@end lisp" | |
796 | */ | |
0f2d19dd | 797 | SCM |
6e8d25a6 | 798 | scm_remainder (SCM x, SCM y) |
0f2d19dd | 799 | { |
e11e83f3 | 800 | if (SCM_I_INUMP (x)) |
0aacf84e | 801 | { |
e11e83f3 | 802 | if (SCM_I_INUMP (y)) |
0aacf84e | 803 | { |
e11e83f3 | 804 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
805 | if (yy == 0) |
806 | scm_num_overflow (s_remainder); | |
807 | else | |
808 | { | |
e11e83f3 | 809 | long z = SCM_I_INUM (x) % yy; |
d956fa6f | 810 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
811 | } |
812 | } | |
813 | else if (SCM_BIGP (y)) | |
ac0c002c | 814 | { |
e11e83f3 | 815 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
816 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
817 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
818 | { | |
819 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
820 | scm_remember_upto_here_1 (y); | |
d956fa6f | 821 | return SCM_I_MAKINUM (0); |
4dc09ee4 | 822 | } |
0aacf84e MD |
823 | else |
824 | return x; | |
ac0c002c DH |
825 | } |
826 | else | |
0aacf84e | 827 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); |
89a7e495 | 828 | } |
0aacf84e MD |
829 | else if (SCM_BIGP (x)) |
830 | { | |
e11e83f3 | 831 | if (SCM_I_INUMP (y)) |
0aacf84e | 832 | { |
e11e83f3 | 833 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
834 | if (yy == 0) |
835 | scm_num_overflow (s_remainder); | |
836 | else | |
837 | { | |
838 | SCM result = scm_i_mkbig (); | |
839 | if (yy < 0) | |
840 | yy = - yy; | |
841 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
842 | scm_remember_upto_here_1 (x); | |
843 | return scm_i_normbig (result); | |
844 | } | |
845 | } | |
846 | else if (SCM_BIGP (y)) | |
847 | { | |
848 | SCM result = scm_i_mkbig (); | |
849 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
850 | SCM_I_BIG_MPZ (x), | |
851 | SCM_I_BIG_MPZ (y)); | |
852 | scm_remember_upto_here_2 (x, y); | |
853 | return scm_i_normbig (result); | |
854 | } | |
855 | else | |
856 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); | |
f872b822 | 857 | } |
0aacf84e | 858 | else |
89a7e495 | 859 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder); |
0f2d19dd JB |
860 | } |
861 | ||
89a7e495 | 862 | |
9de33deb | 863 | SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); |
942e5b91 MG |
864 | /* "Return the modulo of the numbers @var{x} and @var{y}.\n" |
865 | * "@lisp\n" | |
866 | * "(modulo 13 4) @result{} 1\n" | |
867 | * "(modulo -13 4) @result{} 3\n" | |
868 | * "@end lisp" | |
869 | */ | |
0f2d19dd | 870 | SCM |
6e8d25a6 | 871 | scm_modulo (SCM x, SCM y) |
0f2d19dd | 872 | { |
e11e83f3 | 873 | if (SCM_I_INUMP (x)) |
0aacf84e | 874 | { |
e11e83f3 MV |
875 | long xx = SCM_I_INUM (x); |
876 | if (SCM_I_INUMP (y)) | |
0aacf84e | 877 | { |
e11e83f3 | 878 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
879 | if (yy == 0) |
880 | scm_num_overflow (s_modulo); | |
881 | else | |
882 | { | |
66b1c775 KR |
883 | /* C99 specifies that "%" is the remainder corresponding to a |
884 | quotient rounded towards zero, and that's also traditional | |
885 | for machine division, so z here should be well defined. */ | |
0aacf84e MD |
886 | long z = xx % yy; |
887 | long result; | |
888 | ||
889 | if (yy < 0) | |
890 | { | |
891 | if (z > 0) | |
892 | result = z + yy; | |
893 | else | |
894 | result = z; | |
895 | } | |
896 | else | |
897 | { | |
898 | if (z < 0) | |
899 | result = z + yy; | |
900 | else | |
901 | result = z; | |
902 | } | |
d956fa6f | 903 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
904 | } |
905 | } | |
906 | else if (SCM_BIGP (y)) | |
907 | { | |
908 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
909 | { |
910 | mpz_t z_x; | |
911 | SCM result; | |
912 | ||
913 | if (sgn_y < 0) | |
914 | { | |
915 | SCM pos_y = scm_i_clonebig (y, 0); | |
916 | /* do this after the last scm_op */ | |
917 | mpz_init_set_si (z_x, xx); | |
918 | result = pos_y; /* re-use this bignum */ | |
919 | mpz_mod (SCM_I_BIG_MPZ (result), | |
920 | z_x, | |
921 | SCM_I_BIG_MPZ (pos_y)); | |
922 | scm_remember_upto_here_1 (pos_y); | |
923 | } | |
924 | else | |
925 | { | |
926 | result = scm_i_mkbig (); | |
927 | /* do this after the last scm_op */ | |
928 | mpz_init_set_si (z_x, xx); | |
929 | mpz_mod (SCM_I_BIG_MPZ (result), | |
930 | z_x, | |
931 | SCM_I_BIG_MPZ (y)); | |
932 | scm_remember_upto_here_1 (y); | |
933 | } | |
ca46fb90 | 934 | |
0aacf84e MD |
935 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
936 | mpz_add (SCM_I_BIG_MPZ (result), | |
937 | SCM_I_BIG_MPZ (y), | |
938 | SCM_I_BIG_MPZ (result)); | |
939 | scm_remember_upto_here_1 (y); | |
940 | /* and do this before the next one */ | |
941 | mpz_clear (z_x); | |
942 | return scm_i_normbig (result); | |
943 | } | |
944 | } | |
945 | else | |
946 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
f872b822 | 947 | } |
0aacf84e MD |
948 | else if (SCM_BIGP (x)) |
949 | { | |
e11e83f3 | 950 | if (SCM_I_INUMP (y)) |
0aacf84e | 951 | { |
e11e83f3 | 952 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
953 | if (yy == 0) |
954 | scm_num_overflow (s_modulo); | |
955 | else | |
956 | { | |
957 | SCM result = scm_i_mkbig (); | |
958 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
959 | SCM_I_BIG_MPZ (x), | |
960 | (yy < 0) ? - yy : yy); | |
961 | scm_remember_upto_here_1 (x); | |
962 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
963 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
964 | SCM_I_BIG_MPZ (result), | |
965 | - yy); | |
966 | return scm_i_normbig (result); | |
967 | } | |
968 | } | |
969 | else if (SCM_BIGP (y)) | |
970 | { | |
0aacf84e MD |
971 | { |
972 | SCM result = scm_i_mkbig (); | |
973 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
974 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
975 | mpz_mod (SCM_I_BIG_MPZ (result), | |
976 | SCM_I_BIG_MPZ (x), | |
977 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 978 | |
0aacf84e MD |
979 | scm_remember_upto_here_1 (x); |
980 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
981 | mpz_add (SCM_I_BIG_MPZ (result), | |
982 | SCM_I_BIG_MPZ (y), | |
983 | SCM_I_BIG_MPZ (result)); | |
984 | scm_remember_upto_here_2 (y, pos_y); | |
985 | return scm_i_normbig (result); | |
986 | } | |
987 | } | |
988 | else | |
989 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
828865c3 | 990 | } |
0aacf84e | 991 | else |
09fb7599 | 992 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); |
0f2d19dd JB |
993 | } |
994 | ||
9de33deb | 995 | SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd); |
942e5b91 MG |
996 | /* "Return the greatest common divisor of all arguments.\n" |
997 | * "If called without arguments, 0 is returned." | |
998 | */ | |
0f2d19dd | 999 | SCM |
6e8d25a6 | 1000 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 1001 | { |
ca46fb90 | 1002 | if (SCM_UNBNDP (y)) |
0aacf84e | 1003 | return SCM_UNBNDP (x) ? SCM_INUM0 : x; |
ca46fb90 | 1004 | |
e11e83f3 | 1005 | if (SCM_I_INUMP (x)) |
ca46fb90 | 1006 | { |
e11e83f3 | 1007 | if (SCM_I_INUMP (y)) |
ca46fb90 | 1008 | { |
e11e83f3 MV |
1009 | long xx = SCM_I_INUM (x); |
1010 | long yy = SCM_I_INUM (y); | |
ca46fb90 RB |
1011 | long u = xx < 0 ? -xx : xx; |
1012 | long v = yy < 0 ? -yy : yy; | |
1013 | long result; | |
0aacf84e MD |
1014 | if (xx == 0) |
1015 | result = v; | |
1016 | else if (yy == 0) | |
1017 | result = u; | |
1018 | else | |
1019 | { | |
1020 | long k = 1; | |
1021 | long t; | |
1022 | /* Determine a common factor 2^k */ | |
1023 | while (!(1 & (u | v))) | |
1024 | { | |
1025 | k <<= 1; | |
1026 | u >>= 1; | |
1027 | v >>= 1; | |
1028 | } | |
1029 | /* Now, any factor 2^n can be eliminated */ | |
1030 | if (u & 1) | |
1031 | t = -v; | |
1032 | else | |
1033 | { | |
1034 | t = u; | |
1035 | b3: | |
1036 | t = SCM_SRS (t, 1); | |
1037 | } | |
1038 | if (!(1 & t)) | |
1039 | goto b3; | |
1040 | if (t > 0) | |
1041 | u = t; | |
1042 | else | |
1043 | v = -t; | |
1044 | t = u - v; | |
1045 | if (t != 0) | |
1046 | goto b3; | |
1047 | result = u * k; | |
1048 | } | |
1049 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 1050 | ? SCM_I_MAKINUM (result) |
0aacf84e | 1051 | : scm_i_long2big (result)); |
ca46fb90 RB |
1052 | } |
1053 | else if (SCM_BIGP (y)) | |
1054 | { | |
0bff4dce KR |
1055 | SCM_SWAP (x, y); |
1056 | goto big_inum; | |
ca46fb90 RB |
1057 | } |
1058 | else | |
1059 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 1060 | } |
ca46fb90 RB |
1061 | else if (SCM_BIGP (x)) |
1062 | { | |
e11e83f3 | 1063 | if (SCM_I_INUMP (y)) |
ca46fb90 RB |
1064 | { |
1065 | unsigned long result; | |
0bff4dce KR |
1066 | long yy; |
1067 | big_inum: | |
e11e83f3 | 1068 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
1069 | if (yy == 0) |
1070 | return scm_abs (x); | |
0aacf84e MD |
1071 | if (yy < 0) |
1072 | yy = -yy; | |
ca46fb90 RB |
1073 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
1074 | scm_remember_upto_here_1 (x); | |
0aacf84e | 1075 | return (SCM_POSFIXABLE (result) |
d956fa6f | 1076 | ? SCM_I_MAKINUM (result) |
c71b0706 | 1077 | : scm_from_ulong (result)); |
ca46fb90 RB |
1078 | } |
1079 | else if (SCM_BIGP (y)) | |
1080 | { | |
1081 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
1082 | mpz_gcd (SCM_I_BIG_MPZ (result), |
1083 | SCM_I_BIG_MPZ (x), | |
1084 | SCM_I_BIG_MPZ (y)); | |
1085 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
1086 | return scm_i_normbig (result); |
1087 | } | |
1088 | else | |
1089 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 1090 | } |
ca46fb90 | 1091 | else |
09fb7599 | 1092 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
1093 | } |
1094 | ||
9de33deb | 1095 | SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm); |
942e5b91 MG |
1096 | /* "Return the least common multiple of the arguments.\n" |
1097 | * "If called without arguments, 1 is returned." | |
1098 | */ | |
0f2d19dd | 1099 | SCM |
6e8d25a6 | 1100 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 1101 | { |
ca46fb90 RB |
1102 | if (SCM_UNBNDP (n2)) |
1103 | { | |
1104 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
1105 | return SCM_I_MAKINUM (1L); |
1106 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 1107 | } |
09fb7599 | 1108 | |
e11e83f3 | 1109 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 1110 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 1111 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 1112 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 1113 | |
e11e83f3 | 1114 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 1115 | { |
e11e83f3 | 1116 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1117 | { |
1118 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 1119 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
1120 | return d; |
1121 | else | |
1122 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
1123 | } | |
1124 | else | |
1125 | { | |
1126 | /* inum n1, big n2 */ | |
1127 | inumbig: | |
1128 | { | |
1129 | SCM result = scm_i_mkbig (); | |
e11e83f3 | 1130 | long nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
1131 | if (nn1 == 0) return SCM_INUM0; |
1132 | if (nn1 < 0) nn1 = - nn1; | |
1133 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
1134 | scm_remember_upto_here_1 (n2); | |
1135 | return result; | |
1136 | } | |
1137 | } | |
1138 | } | |
1139 | else | |
1140 | { | |
1141 | /* big n1 */ | |
e11e83f3 | 1142 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1143 | { |
1144 | SCM_SWAP (n1, n2); | |
1145 | goto inumbig; | |
1146 | } | |
1147 | else | |
1148 | { | |
1149 | SCM result = scm_i_mkbig (); | |
1150 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
1151 | SCM_I_BIG_MPZ (n1), | |
1152 | SCM_I_BIG_MPZ (n2)); | |
1153 | scm_remember_upto_here_2(n1, n2); | |
1154 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
1155 | return result; | |
1156 | } | |
f872b822 | 1157 | } |
0f2d19dd JB |
1158 | } |
1159 | ||
8a525303 GB |
1160 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
1161 | ||
1162 | Logand: | |
1163 | X Y Result Method: | |
1164 | (len) | |
1165 | + + + x (map digit:logand X Y) | |
1166 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
1167 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
1168 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
1169 | ||
1170 | Logior: | |
1171 | X Y Result Method: | |
1172 | ||
1173 | + + + (map digit:logior X Y) | |
1174 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
1175 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
1176 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
1177 | ||
1178 | Logxor: | |
1179 | X Y Result Method: | |
1180 | ||
1181 | + + + (map digit:logxor X Y) | |
1182 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
1183 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
1184 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
1185 | ||
1186 | Logtest: | |
1187 | X Y Result | |
1188 | ||
1189 | + + (any digit:logand X Y) | |
1190 | + - (any digit:logand X (lognot (+ -1 Y))) | |
1191 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
1192 | - - #t | |
1193 | ||
1194 | */ | |
1195 | ||
c3ee7520 | 1196 | SCM_DEFINE1 (scm_logand, "logand", scm_tc7_asubr, |
1bbd0b84 | 1197 | (SCM n1, SCM n2), |
3c3db128 GH |
1198 | "Return the bitwise AND of the integer arguments.\n\n" |
1199 | "@lisp\n" | |
1200 | "(logand) @result{} -1\n" | |
1201 | "(logand 7) @result{} 7\n" | |
535f2a51 | 1202 | "(logand #b111 #b011 #b001) @result{} 1\n" |
3c3db128 | 1203 | "@end lisp") |
1bbd0b84 | 1204 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 1205 | { |
9a00c9fc DH |
1206 | long int nn1; |
1207 | ||
0aacf84e MD |
1208 | if (SCM_UNBNDP (n2)) |
1209 | { | |
1210 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 1211 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
1212 | else if (!SCM_NUMBERP (n1)) |
1213 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1214 | else if (SCM_NUMBERP (n1)) | |
1215 | return n1; | |
1216 | else | |
1217 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1218 | } |
09fb7599 | 1219 | |
e11e83f3 | 1220 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1221 | { |
e11e83f3 MV |
1222 | nn1 = SCM_I_INUM (n1); |
1223 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1224 | { |
e11e83f3 | 1225 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1226 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
1227 | } |
1228 | else if SCM_BIGP (n2) | |
1229 | { | |
1230 | intbig: | |
1231 | if (n1 == 0) | |
1232 | return SCM_INUM0; | |
1233 | { | |
1234 | SCM result_z = scm_i_mkbig (); | |
1235 | mpz_t nn1_z; | |
1236 | mpz_init_set_si (nn1_z, nn1); | |
1237 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1238 | scm_remember_upto_here_1 (n2); | |
1239 | mpz_clear (nn1_z); | |
1240 | return scm_i_normbig (result_z); | |
1241 | } | |
1242 | } | |
1243 | else | |
1244 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1245 | } | |
1246 | else if (SCM_BIGP (n1)) | |
1247 | { | |
e11e83f3 | 1248 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1249 | { |
1250 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1251 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1252 | goto intbig; |
1253 | } | |
1254 | else if (SCM_BIGP (n2)) | |
1255 | { | |
1256 | SCM result_z = scm_i_mkbig (); | |
1257 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
1258 | SCM_I_BIG_MPZ (n1), | |
1259 | SCM_I_BIG_MPZ (n2)); | |
1260 | scm_remember_upto_here_2 (n1, n2); | |
1261 | return scm_i_normbig (result_z); | |
1262 | } | |
1263 | else | |
1264 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1265 | } |
0aacf84e | 1266 | else |
09fb7599 | 1267 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1268 | } |
1bbd0b84 | 1269 | #undef FUNC_NAME |
0f2d19dd | 1270 | |
09fb7599 | 1271 | |
c3ee7520 | 1272 | SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr, |
1bbd0b84 | 1273 | (SCM n1, SCM n2), |
3c3db128 GH |
1274 | "Return the bitwise OR of the integer arguments.\n\n" |
1275 | "@lisp\n" | |
1276 | "(logior) @result{} 0\n" | |
1277 | "(logior 7) @result{} 7\n" | |
1278 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1e6808ea | 1279 | "@end lisp") |
1bbd0b84 | 1280 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 1281 | { |
9a00c9fc DH |
1282 | long int nn1; |
1283 | ||
0aacf84e MD |
1284 | if (SCM_UNBNDP (n2)) |
1285 | { | |
1286 | if (SCM_UNBNDP (n1)) | |
1287 | return SCM_INUM0; | |
1288 | else if (SCM_NUMBERP (n1)) | |
1289 | return n1; | |
1290 | else | |
1291 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1292 | } |
09fb7599 | 1293 | |
e11e83f3 | 1294 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1295 | { |
e11e83f3 MV |
1296 | nn1 = SCM_I_INUM (n1); |
1297 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1298 | { |
e11e83f3 | 1299 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1300 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
1301 | } |
1302 | else if (SCM_BIGP (n2)) | |
1303 | { | |
1304 | intbig: | |
1305 | if (nn1 == 0) | |
1306 | return n2; | |
1307 | { | |
1308 | SCM result_z = scm_i_mkbig (); | |
1309 | mpz_t nn1_z; | |
1310 | mpz_init_set_si (nn1_z, nn1); | |
1311 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1312 | scm_remember_upto_here_1 (n2); | |
1313 | mpz_clear (nn1_z); | |
9806de0d | 1314 | return scm_i_normbig (result_z); |
0aacf84e MD |
1315 | } |
1316 | } | |
1317 | else | |
1318 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1319 | } | |
1320 | else if (SCM_BIGP (n1)) | |
1321 | { | |
e11e83f3 | 1322 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1323 | { |
1324 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1325 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1326 | goto intbig; |
1327 | } | |
1328 | else if (SCM_BIGP (n2)) | |
1329 | { | |
1330 | SCM result_z = scm_i_mkbig (); | |
1331 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
1332 | SCM_I_BIG_MPZ (n1), | |
1333 | SCM_I_BIG_MPZ (n2)); | |
1334 | scm_remember_upto_here_2 (n1, n2); | |
9806de0d | 1335 | return scm_i_normbig (result_z); |
0aacf84e MD |
1336 | } |
1337 | else | |
1338 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1339 | } |
0aacf84e | 1340 | else |
09fb7599 | 1341 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1342 | } |
1bbd0b84 | 1343 | #undef FUNC_NAME |
0f2d19dd | 1344 | |
09fb7599 | 1345 | |
c3ee7520 | 1346 | SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr, |
1bbd0b84 | 1347 | (SCM n1, SCM n2), |
3c3db128 GH |
1348 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1349 | "set in the result if it is set in an odd number of arguments.\n" | |
1350 | "@lisp\n" | |
1351 | "(logxor) @result{} 0\n" | |
1352 | "(logxor 7) @result{} 7\n" | |
1353 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1354 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1355 | "@end lisp") |
1bbd0b84 | 1356 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1357 | { |
9a00c9fc DH |
1358 | long int nn1; |
1359 | ||
0aacf84e MD |
1360 | if (SCM_UNBNDP (n2)) |
1361 | { | |
1362 | if (SCM_UNBNDP (n1)) | |
1363 | return SCM_INUM0; | |
1364 | else if (SCM_NUMBERP (n1)) | |
1365 | return n1; | |
1366 | else | |
1367 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1368 | } |
09fb7599 | 1369 | |
e11e83f3 | 1370 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1371 | { |
e11e83f3 MV |
1372 | nn1 = SCM_I_INUM (n1); |
1373 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1374 | { |
e11e83f3 | 1375 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1376 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
1377 | } |
1378 | else if (SCM_BIGP (n2)) | |
1379 | { | |
1380 | intbig: | |
1381 | { | |
1382 | SCM result_z = scm_i_mkbig (); | |
1383 | mpz_t nn1_z; | |
1384 | mpz_init_set_si (nn1_z, nn1); | |
1385 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1386 | scm_remember_upto_here_1 (n2); | |
1387 | mpz_clear (nn1_z); | |
1388 | return scm_i_normbig (result_z); | |
1389 | } | |
1390 | } | |
1391 | else | |
1392 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1393 | } | |
1394 | else if (SCM_BIGP (n1)) | |
1395 | { | |
e11e83f3 | 1396 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1397 | { |
1398 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1399 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1400 | goto intbig; |
1401 | } | |
1402 | else if (SCM_BIGP (n2)) | |
1403 | { | |
1404 | SCM result_z = scm_i_mkbig (); | |
1405 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
1406 | SCM_I_BIG_MPZ (n1), | |
1407 | SCM_I_BIG_MPZ (n2)); | |
1408 | scm_remember_upto_here_2 (n1, n2); | |
1409 | return scm_i_normbig (result_z); | |
1410 | } | |
1411 | else | |
1412 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1413 | } |
0aacf84e | 1414 | else |
09fb7599 | 1415 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1416 | } |
1bbd0b84 | 1417 | #undef FUNC_NAME |
0f2d19dd | 1418 | |
09fb7599 | 1419 | |
a1ec6916 | 1420 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 1421 | (SCM j, SCM k), |
ba6e7231 KR |
1422 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
1423 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
1424 | "without actually calculating the @code{logand}, just testing\n" | |
1425 | "for non-zero.\n" | |
1426 | "\n" | |
1e6808ea | 1427 | "@lisp\n" |
b380b885 MD |
1428 | "(logtest #b0100 #b1011) @result{} #f\n" |
1429 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1430 | "@end lisp") |
1bbd0b84 | 1431 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1432 | { |
1e6808ea | 1433 | long int nj; |
9a00c9fc | 1434 | |
e11e83f3 | 1435 | if (SCM_I_INUMP (j)) |
0aacf84e | 1436 | { |
e11e83f3 MV |
1437 | nj = SCM_I_INUM (j); |
1438 | if (SCM_I_INUMP (k)) | |
0aacf84e | 1439 | { |
e11e83f3 | 1440 | long nk = SCM_I_INUM (k); |
73e4de09 | 1441 | return scm_from_bool (nj & nk); |
0aacf84e MD |
1442 | } |
1443 | else if (SCM_BIGP (k)) | |
1444 | { | |
1445 | intbig: | |
1446 | if (nj == 0) | |
1447 | return SCM_BOOL_F; | |
1448 | { | |
1449 | SCM result; | |
1450 | mpz_t nj_z; | |
1451 | mpz_init_set_si (nj_z, nj); | |
1452 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
1453 | scm_remember_upto_here_1 (k); | |
73e4de09 | 1454 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
1455 | mpz_clear (nj_z); |
1456 | return result; | |
1457 | } | |
1458 | } | |
1459 | else | |
1460 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1461 | } | |
1462 | else if (SCM_BIGP (j)) | |
1463 | { | |
e11e83f3 | 1464 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
1465 | { |
1466 | SCM_SWAP (j, k); | |
e11e83f3 | 1467 | nj = SCM_I_INUM (j); |
0aacf84e MD |
1468 | goto intbig; |
1469 | } | |
1470 | else if (SCM_BIGP (k)) | |
1471 | { | |
1472 | SCM result; | |
1473 | mpz_t result_z; | |
1474 | mpz_init (result_z); | |
1475 | mpz_and (result_z, | |
1476 | SCM_I_BIG_MPZ (j), | |
1477 | SCM_I_BIG_MPZ (k)); | |
1478 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 1479 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
1480 | mpz_clear (result_z); |
1481 | return result; | |
1482 | } | |
1483 | else | |
1484 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1485 | } | |
1486 | else | |
1487 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 1488 | } |
1bbd0b84 | 1489 | #undef FUNC_NAME |
0f2d19dd | 1490 | |
c1bfcf60 | 1491 | |
a1ec6916 | 1492 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1493 | (SCM index, SCM j), |
ba6e7231 KR |
1494 | "Test whether bit number @var{index} in @var{j} is set.\n" |
1495 | "@var{index} starts from 0 for the least significant bit.\n" | |
1496 | "\n" | |
1e6808ea | 1497 | "@lisp\n" |
b380b885 MD |
1498 | "(logbit? 0 #b1101) @result{} #t\n" |
1499 | "(logbit? 1 #b1101) @result{} #f\n" | |
1500 | "(logbit? 2 #b1101) @result{} #t\n" | |
1501 | "(logbit? 3 #b1101) @result{} #t\n" | |
1502 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1503 | "@end lisp") |
1bbd0b84 | 1504 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1505 | { |
78166ad5 | 1506 | unsigned long int iindex; |
5efd3c7d | 1507 | iindex = scm_to_ulong (index); |
78166ad5 | 1508 | |
e11e83f3 | 1509 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
1510 | { |
1511 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 1512 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 1513 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 1514 | } |
0aacf84e MD |
1515 | else if (SCM_BIGP (j)) |
1516 | { | |
1517 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
1518 | scm_remember_upto_here_1 (j); | |
73e4de09 | 1519 | return scm_from_bool (val); |
0aacf84e MD |
1520 | } |
1521 | else | |
78166ad5 | 1522 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 1523 | } |
1bbd0b84 | 1524 | #undef FUNC_NAME |
0f2d19dd | 1525 | |
78166ad5 | 1526 | |
a1ec6916 | 1527 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1528 | (SCM n), |
4d814788 | 1529 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
1530 | "argument.\n" |
1531 | "\n" | |
b380b885 MD |
1532 | "@lisp\n" |
1533 | "(number->string (lognot #b10000000) 2)\n" | |
1534 | " @result{} \"-10000001\"\n" | |
1535 | "(number->string (lognot #b0) 2)\n" | |
1536 | " @result{} \"-1\"\n" | |
1e6808ea | 1537 | "@end lisp") |
1bbd0b84 | 1538 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1539 | { |
e11e83f3 | 1540 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
1541 | /* No overflow here, just need to toggle all the bits making up the inum. |
1542 | Enhancement: No need to strip the tag and add it back, could just xor | |
1543 | a block of 1 bits, if that worked with the various debug versions of | |
1544 | the SCM typedef. */ | |
e11e83f3 | 1545 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
1546 | |
1547 | } else if (SCM_BIGP (n)) { | |
1548 | SCM result = scm_i_mkbig (); | |
1549 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
1550 | scm_remember_upto_here_1 (n); | |
1551 | return result; | |
1552 | ||
1553 | } else { | |
1554 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1555 | } | |
0f2d19dd | 1556 | } |
1bbd0b84 | 1557 | #undef FUNC_NAME |
0f2d19dd | 1558 | |
518b7508 KR |
1559 | /* returns 0 if IN is not an integer. OUT must already be |
1560 | initialized. */ | |
1561 | static int | |
1562 | coerce_to_big (SCM in, mpz_t out) | |
1563 | { | |
1564 | if (SCM_BIGP (in)) | |
1565 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
1566 | else if (SCM_I_INUMP (in)) |
1567 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
1568 | else |
1569 | return 0; | |
1570 | ||
1571 | return 1; | |
1572 | } | |
1573 | ||
d885e204 | 1574 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
1575 | (SCM n, SCM k, SCM m), |
1576 | "Return @var{n} raised to the integer exponent\n" | |
1577 | "@var{k}, modulo @var{m}.\n" | |
1578 | "\n" | |
1579 | "@lisp\n" | |
1580 | "(modulo-expt 2 3 5)\n" | |
1581 | " @result{} 3\n" | |
1582 | "@end lisp") | |
d885e204 | 1583 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
1584 | { |
1585 | mpz_t n_tmp; | |
1586 | mpz_t k_tmp; | |
1587 | mpz_t m_tmp; | |
1588 | ||
1589 | /* There are two classes of error we might encounter -- | |
1590 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
1591 | and | |
1592 | 2) wrong-type errors, which of course we'll report by calling | |
1593 | SCM_WRONG_TYPE_ARG. | |
1594 | We don't report those errors immediately, however; instead we do | |
1595 | some cleanup first. These variables tell us which error (if | |
1596 | any) we should report after cleaning up. | |
1597 | */ | |
1598 | int report_overflow = 0; | |
1599 | ||
1600 | int position_of_wrong_type = 0; | |
1601 | SCM value_of_wrong_type = SCM_INUM0; | |
1602 | ||
1603 | SCM result = SCM_UNDEFINED; | |
1604 | ||
1605 | mpz_init (n_tmp); | |
1606 | mpz_init (k_tmp); | |
1607 | mpz_init (m_tmp); | |
1608 | ||
bc36d050 | 1609 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
1610 | { |
1611 | report_overflow = 1; | |
1612 | goto cleanup; | |
1613 | } | |
1614 | ||
1615 | if (!coerce_to_big (n, n_tmp)) | |
1616 | { | |
1617 | value_of_wrong_type = n; | |
1618 | position_of_wrong_type = 1; | |
1619 | goto cleanup; | |
1620 | } | |
1621 | ||
1622 | if (!coerce_to_big (k, k_tmp)) | |
1623 | { | |
1624 | value_of_wrong_type = k; | |
1625 | position_of_wrong_type = 2; | |
1626 | goto cleanup; | |
1627 | } | |
1628 | ||
1629 | if (!coerce_to_big (m, m_tmp)) | |
1630 | { | |
1631 | value_of_wrong_type = m; | |
1632 | position_of_wrong_type = 3; | |
1633 | goto cleanup; | |
1634 | } | |
1635 | ||
1636 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
1637 | will get a divide-by-zero exception when an inverse 1/n mod m | |
1638 | doesn't exist (or is not unique). Since exceptions are hard to | |
1639 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
1640 | a simple failure code, which is easy to handle. */ | |
1641 | ||
1642 | if (-1 == mpz_sgn (k_tmp)) | |
1643 | { | |
1644 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
1645 | { | |
1646 | report_overflow = 1; | |
1647 | goto cleanup; | |
1648 | } | |
1649 | mpz_neg (k_tmp, k_tmp); | |
1650 | } | |
1651 | ||
1652 | result = scm_i_mkbig (); | |
1653 | mpz_powm (SCM_I_BIG_MPZ (result), | |
1654 | n_tmp, | |
1655 | k_tmp, | |
1656 | m_tmp); | |
b7b8c575 KR |
1657 | |
1658 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
1659 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
1660 | ||
518b7508 KR |
1661 | cleanup: |
1662 | mpz_clear (m_tmp); | |
1663 | mpz_clear (k_tmp); | |
1664 | mpz_clear (n_tmp); | |
1665 | ||
1666 | if (report_overflow) | |
1667 | scm_num_overflow (FUNC_NAME); | |
1668 | ||
1669 | if (position_of_wrong_type) | |
1670 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
1671 | value_of_wrong_type); | |
1672 | ||
1673 | return scm_i_normbig (result); | |
1674 | } | |
1675 | #undef FUNC_NAME | |
1676 | ||
a1ec6916 | 1677 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1678 | (SCM n, SCM k), |
ba6e7231 KR |
1679 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
1680 | "exact integer, @var{n} can be any number.\n" | |
1681 | "\n" | |
1682 | "Negative @var{k} is supported, and results in @math{1/n^abs(k)}\n" | |
1683 | "in the usual way. @math{@var{n}^0} is 1, as usual, and that\n" | |
1684 | "includes @math{0^0} is 1.\n" | |
1e6808ea | 1685 | "\n" |
b380b885 | 1686 | "@lisp\n" |
ba6e7231 KR |
1687 | "(integer-expt 2 5) @result{} 32\n" |
1688 | "(integer-expt -3 3) @result{} -27\n" | |
1689 | "(integer-expt 5 -3) @result{} 1/125\n" | |
1690 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 1691 | "@end lisp") |
1bbd0b84 | 1692 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1693 | { |
1c35cb19 RB |
1694 | long i2 = 0; |
1695 | SCM z_i2 = SCM_BOOL_F; | |
1696 | int i2_is_big = 0; | |
d956fa6f | 1697 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 1698 | |
d57ed702 | 1699 | /* 0^0 == 1 according to R5RS */ |
bc36d050 | 1700 | if (scm_is_eq (n, SCM_INUM0) || scm_is_eq (n, acc)) |
73e4de09 | 1701 | return scm_is_false (scm_zero_p(k)) ? n : acc; |
bc36d050 | 1702 | else if (scm_is_eq (n, SCM_I_MAKINUM (-1L))) |
73e4de09 | 1703 | return scm_is_false (scm_even_p (k)) ? n : acc; |
ca46fb90 | 1704 | |
e11e83f3 MV |
1705 | if (SCM_I_INUMP (k)) |
1706 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
1707 | else if (SCM_BIGP (k)) |
1708 | { | |
1709 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
1710 | scm_remember_upto_here_1 (k); |
1711 | i2_is_big = 1; | |
1712 | } | |
2830fd91 | 1713 | else |
ca46fb90 RB |
1714 | SCM_WRONG_TYPE_ARG (2, k); |
1715 | ||
1716 | if (i2_is_big) | |
f872b822 | 1717 | { |
ca46fb90 RB |
1718 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
1719 | { | |
1720 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
1721 | n = scm_divide (n, SCM_UNDEFINED); | |
1722 | } | |
1723 | while (1) | |
1724 | { | |
1725 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
1726 | { | |
ca46fb90 RB |
1727 | return acc; |
1728 | } | |
1729 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
1730 | { | |
ca46fb90 RB |
1731 | return scm_product (acc, n); |
1732 | } | |
1733 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
1734 | acc = scm_product (acc, n); | |
1735 | n = scm_product (n, n); | |
1736 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
1737 | } | |
f872b822 | 1738 | } |
ca46fb90 | 1739 | else |
f872b822 | 1740 | { |
ca46fb90 RB |
1741 | if (i2 < 0) |
1742 | { | |
1743 | i2 = -i2; | |
1744 | n = scm_divide (n, SCM_UNDEFINED); | |
1745 | } | |
1746 | while (1) | |
1747 | { | |
1748 | if (0 == i2) | |
1749 | return acc; | |
1750 | if (1 == i2) | |
1751 | return scm_product (acc, n); | |
1752 | if (i2 & 1) | |
1753 | acc = scm_product (acc, n); | |
1754 | n = scm_product (n, n); | |
1755 | i2 >>= 1; | |
1756 | } | |
f872b822 | 1757 | } |
0f2d19dd | 1758 | } |
1bbd0b84 | 1759 | #undef FUNC_NAME |
0f2d19dd | 1760 | |
a1ec6916 | 1761 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1762 | (SCM n, SCM cnt), |
32f19569 KR |
1763 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
1764 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 1765 | "\n" |
e7644cb2 | 1766 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
1767 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
1768 | "infinity. (Note that this is not the same rounding as\n" | |
1769 | "@code{quotient} does.)\n" | |
1770 | "\n" | |
1771 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
1772 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
1773 | "shift dropping bits.\n" | |
1e6808ea | 1774 | "\n" |
b380b885 | 1775 | "@lisp\n" |
1e6808ea MG |
1776 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1777 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
1778 | "\n" |
1779 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
1780 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 1781 | "@end lisp") |
1bbd0b84 | 1782 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1783 | { |
3ab9f56e | 1784 | long bits_to_shift; |
5efd3c7d | 1785 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 1786 | |
788aca27 KR |
1787 | if (SCM_I_INUMP (n)) |
1788 | { | |
1789 | long nn = SCM_I_INUM (n); | |
1790 | ||
1791 | if (bits_to_shift > 0) | |
1792 | { | |
1793 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
1794 | overflow a non-zero fixnum. For smaller shifts we check the | |
1795 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
1796 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
1797 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
1798 | bits_to_shift)". */ | |
1799 | ||
1800 | if (nn == 0) | |
1801 | return n; | |
1802 | ||
1803 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
1804 | && ((unsigned long) | |
1805 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) | |
1806 | <= 1)) | |
1807 | { | |
1808 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
1809 | } | |
1810 | else | |
1811 | { | |
1812 | SCM result = scm_i_long2big (nn); | |
1813 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1814 | bits_to_shift); | |
1815 | return result; | |
1816 | } | |
1817 | } | |
1818 | else | |
1819 | { | |
1820 | bits_to_shift = -bits_to_shift; | |
1821 | if (bits_to_shift >= SCM_LONG_BIT) | |
1822 | return (nn >= 0 ? SCM_I_MAKINUM (0) : SCM_I_MAKINUM(-1)); | |
1823 | else | |
1824 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
1825 | } | |
1826 | ||
1827 | } | |
1828 | else if (SCM_BIGP (n)) | |
ca46fb90 | 1829 | { |
788aca27 KR |
1830 | SCM result; |
1831 | ||
1832 | if (bits_to_shift == 0) | |
1833 | return n; | |
1834 | ||
1835 | result = scm_i_mkbig (); | |
1836 | if (bits_to_shift >= 0) | |
1837 | { | |
1838 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1839 | bits_to_shift); | |
1840 | return result; | |
1841 | } | |
ca46fb90 | 1842 | else |
788aca27 KR |
1843 | { |
1844 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
1845 | we have to allocate a bignum even if the result is going to be a | |
1846 | fixnum. */ | |
1847 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1848 | -bits_to_shift); | |
1849 | return scm_i_normbig (result); | |
1850 | } | |
1851 | ||
ca46fb90 RB |
1852 | } |
1853 | else | |
788aca27 KR |
1854 | { |
1855 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1856 | } | |
0f2d19dd | 1857 | } |
1bbd0b84 | 1858 | #undef FUNC_NAME |
0f2d19dd | 1859 | |
3c9f20f8 | 1860 | |
a1ec6916 | 1861 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 1862 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
1863 | "Return the integer composed of the @var{start} (inclusive)\n" |
1864 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
1865 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
1866 | "\n" | |
b380b885 MD |
1867 | "@lisp\n" |
1868 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
1869 | " @result{} \"1010\"\n" | |
1870 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
1871 | " @result{} \"10110\"\n" | |
1872 | "@end lisp") | |
1bbd0b84 | 1873 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 1874 | { |
7f848242 | 1875 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
1876 | istart = scm_to_ulong (start); |
1877 | iend = scm_to_ulong (end); | |
c1bfcf60 | 1878 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 1879 | |
7f848242 KR |
1880 | /* how many bits to keep */ |
1881 | bits = iend - istart; | |
1882 | ||
e11e83f3 | 1883 | if (SCM_I_INUMP (n)) |
0aacf84e | 1884 | { |
e11e83f3 | 1885 | long int in = SCM_I_INUM (n); |
7f848242 KR |
1886 | |
1887 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 1888 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 1889 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 1890 | |
0aacf84e MD |
1891 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
1892 | { | |
1893 | /* Since we emulate two's complement encoded numbers, this | |
1894 | * special case requires us to produce a result that has | |
7f848242 | 1895 | * more bits than can be stored in a fixnum. |
0aacf84e | 1896 | */ |
7f848242 KR |
1897 | SCM result = scm_i_long2big (in); |
1898 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1899 | bits); | |
1900 | return result; | |
0aacf84e | 1901 | } |
ac0c002c | 1902 | |
7f848242 | 1903 | /* mask down to requisite bits */ |
857ae6af | 1904 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 1905 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
1906 | } |
1907 | else if (SCM_BIGP (n)) | |
ac0c002c | 1908 | { |
7f848242 KR |
1909 | SCM result; |
1910 | if (bits == 1) | |
1911 | { | |
d956fa6f | 1912 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
1913 | } |
1914 | else | |
1915 | { | |
1916 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
1917 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
1918 | such bits into a ulong. */ | |
1919 | result = scm_i_mkbig (); | |
1920 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
1921 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
1922 | result = scm_i_normbig (result); | |
1923 | } | |
1924 | scm_remember_upto_here_1 (n); | |
1925 | return result; | |
ac0c002c | 1926 | } |
0aacf84e | 1927 | else |
78166ad5 | 1928 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 1929 | } |
1bbd0b84 | 1930 | #undef FUNC_NAME |
0f2d19dd | 1931 | |
7f848242 | 1932 | |
e4755e5c JB |
1933 | static const char scm_logtab[] = { |
1934 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
1935 | }; | |
1cc91f1b | 1936 | |
a1ec6916 | 1937 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 1938 | (SCM n), |
1e6808ea MG |
1939 | "Return the number of bits in integer @var{n}. If integer is\n" |
1940 | "positive, the 1-bits in its binary representation are counted.\n" | |
1941 | "If negative, the 0-bits in its two's-complement binary\n" | |
1942 | "representation are counted. If 0, 0 is returned.\n" | |
1943 | "\n" | |
b380b885 MD |
1944 | "@lisp\n" |
1945 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
1946 | " @result{} 4\n" |
1947 | "(logcount 0)\n" | |
1948 | " @result{} 0\n" | |
1949 | "(logcount -2)\n" | |
1950 | " @result{} 1\n" | |
1951 | "@end lisp") | |
1952 | #define FUNC_NAME s_scm_logcount | |
1953 | { | |
e11e83f3 | 1954 | if (SCM_I_INUMP (n)) |
f872b822 | 1955 | { |
ca46fb90 | 1956 | unsigned long int c = 0; |
e11e83f3 | 1957 | long int nn = SCM_I_INUM (n); |
ca46fb90 RB |
1958 | if (nn < 0) |
1959 | nn = -1 - nn; | |
1960 | while (nn) | |
1961 | { | |
1962 | c += scm_logtab[15 & nn]; | |
1963 | nn >>= 4; | |
1964 | } | |
d956fa6f | 1965 | return SCM_I_MAKINUM (c); |
f872b822 | 1966 | } |
ca46fb90 | 1967 | else if (SCM_BIGP (n)) |
f872b822 | 1968 | { |
ca46fb90 | 1969 | unsigned long count; |
713a4259 KR |
1970 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
1971 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 1972 | else |
713a4259 KR |
1973 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
1974 | scm_remember_upto_here_1 (n); | |
d956fa6f | 1975 | return SCM_I_MAKINUM (count); |
f872b822 | 1976 | } |
ca46fb90 RB |
1977 | else |
1978 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 1979 | } |
ca46fb90 | 1980 | #undef FUNC_NAME |
0f2d19dd JB |
1981 | |
1982 | ||
ca46fb90 RB |
1983 | static const char scm_ilentab[] = { |
1984 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
1985 | }; | |
1986 | ||
0f2d19dd | 1987 | |
ca46fb90 RB |
1988 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
1989 | (SCM n), | |
1990 | "Return the number of bits necessary to represent @var{n}.\n" | |
1991 | "\n" | |
1992 | "@lisp\n" | |
1993 | "(integer-length #b10101010)\n" | |
1994 | " @result{} 8\n" | |
1995 | "(integer-length 0)\n" | |
1996 | " @result{} 0\n" | |
1997 | "(integer-length #b1111)\n" | |
1998 | " @result{} 4\n" | |
1999 | "@end lisp") | |
2000 | #define FUNC_NAME s_scm_integer_length | |
2001 | { | |
e11e83f3 | 2002 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2003 | { |
2004 | unsigned long int c = 0; | |
2005 | unsigned int l = 4; | |
e11e83f3 | 2006 | long int nn = SCM_I_INUM (n); |
0aacf84e MD |
2007 | if (nn < 0) |
2008 | nn = -1 - nn; | |
2009 | while (nn) | |
2010 | { | |
2011 | c += 4; | |
2012 | l = scm_ilentab [15 & nn]; | |
2013 | nn >>= 4; | |
2014 | } | |
d956fa6f | 2015 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
2016 | } |
2017 | else if (SCM_BIGP (n)) | |
2018 | { | |
2019 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
2020 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
2021 | 1 too big, so check for that and adjust. */ | |
2022 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
2023 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
2024 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
2025 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
2026 | size--; | |
2027 | scm_remember_upto_here_1 (n); | |
d956fa6f | 2028 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
2029 | } |
2030 | else | |
ca46fb90 | 2031 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
2032 | } |
2033 | #undef FUNC_NAME | |
0f2d19dd JB |
2034 | |
2035 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
2036 | #define SCM_MAX_DBL_PREC 60 |
2037 | #define SCM_MAX_DBL_RADIX 36 | |
2038 | ||
2039 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
2040 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
2041 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
2042 | ||
2043 | static | |
2044 | void init_dblprec(int *prec, int radix) { | |
2045 | /* determine floating point precision by adding successively | |
2046 | smaller increments to 1.0 until it is considered == 1.0 */ | |
2047 | double f = ((double)1.0)/radix; | |
2048 | double fsum = 1.0 + f; | |
2049 | ||
2050 | *prec = 0; | |
2051 | while (fsum != 1.0) | |
2052 | { | |
2053 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
2054 | fsum = 1.0; | |
2055 | else | |
2056 | { | |
2057 | f /= radix; | |
2058 | fsum = f + 1.0; | |
2059 | } | |
2060 | } | |
2061 | (*prec) -= 1; | |
2062 | } | |
2063 | ||
2064 | static | |
2065 | void init_fx_radix(double *fx_list, int radix) | |
2066 | { | |
2067 | /* initialize a per-radix list of tolerances. When added | |
2068 | to a number < 1.0, we can determine if we should raund | |
2069 | up and quit converting a number to a string. */ | |
2070 | int i; | |
2071 | fx_list[0] = 0.0; | |
2072 | fx_list[1] = 0.5; | |
2073 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
2074 | fx_list[i] = (fx_list[i-1] / radix); | |
2075 | } | |
2076 | ||
2077 | /* use this array as a way to generate a single digit */ | |
2078 | static const char*number_chars="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; | |
0f2d19dd | 2079 | |
1be6b49c | 2080 | static size_t |
0b799eea | 2081 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 2082 | { |
0b799eea MV |
2083 | int efmt, dpt, d, i, wp; |
2084 | double *fx; | |
2085 | #ifdef DBL_MIN_10_EXP | |
2086 | double f_cpy; | |
2087 | int exp_cpy; | |
2088 | #endif /* DBL_MIN_10_EXP */ | |
2089 | size_t ch = 0; | |
2090 | int exp = 0; | |
2091 | ||
2092 | if(radix < 2 || | |
2093 | radix > SCM_MAX_DBL_RADIX) | |
2094 | { | |
2095 | /* revert to existing behavior */ | |
2096 | radix = 10; | |
2097 | } | |
2098 | ||
2099 | wp = scm_dblprec[radix-2]; | |
2100 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 2101 | |
f872b822 | 2102 | if (f == 0.0) |
abb7e44d MV |
2103 | { |
2104 | #ifdef HAVE_COPYSIGN | |
2105 | double sgn = copysign (1.0, f); | |
2106 | ||
2107 | if (sgn < 0.0) | |
2108 | a[ch++] = '-'; | |
2109 | #endif | |
abb7e44d MV |
2110 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
2111 | } | |
7351e207 MV |
2112 | |
2113 | if (xisinf (f)) | |
2114 | { | |
2115 | if (f < 0) | |
2116 | strcpy (a, "-inf.0"); | |
2117 | else | |
2118 | strcpy (a, "+inf.0"); | |
2119 | return ch+6; | |
2120 | } | |
2121 | else if (xisnan (f)) | |
2122 | { | |
2123 | strcpy (a, "+nan.0"); | |
2124 | return ch+6; | |
2125 | } | |
2126 | ||
f872b822 MD |
2127 | if (f < 0.0) |
2128 | { | |
2129 | f = -f; | |
2130 | a[ch++] = '-'; | |
2131 | } | |
7351e207 | 2132 | |
f872b822 MD |
2133 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
2134 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
2135 | /* just do the checking...if it passes, we do the conversion for our |
2136 | radix again below */ | |
2137 | f_cpy = f; | |
2138 | exp_cpy = exp; | |
2139 | ||
2140 | while (f_cpy < 1.0) | |
f872b822 | 2141 | { |
0b799eea MV |
2142 | f_cpy *= 10.0; |
2143 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
2144 | { |
2145 | a[ch++] = '#'; | |
2146 | a[ch++] = '.'; | |
2147 | a[ch++] = '#'; | |
2148 | return ch; | |
2149 | } | |
f872b822 | 2150 | } |
0b799eea | 2151 | while (f_cpy > 10.0) |
f872b822 | 2152 | { |
0b799eea MV |
2153 | f_cpy *= 0.10; |
2154 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
2155 | { |
2156 | a[ch++] = '#'; | |
2157 | a[ch++] = '.'; | |
2158 | a[ch++] = '#'; | |
2159 | return ch; | |
2160 | } | |
f872b822 | 2161 | } |
0b799eea MV |
2162 | #endif |
2163 | ||
f872b822 MD |
2164 | while (f < 1.0) |
2165 | { | |
0b799eea | 2166 | f *= radix; |
f872b822 MD |
2167 | exp--; |
2168 | } | |
0b799eea | 2169 | while (f > radix) |
f872b822 | 2170 | { |
0b799eea | 2171 | f /= radix; |
f872b822 MD |
2172 | exp++; |
2173 | } | |
0b799eea MV |
2174 | |
2175 | if (f + fx[wp] >= radix) | |
f872b822 MD |
2176 | { |
2177 | f = 1.0; | |
2178 | exp++; | |
2179 | } | |
0f2d19dd | 2180 | zero: |
0b799eea MV |
2181 | #ifdef ENGNOT |
2182 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 2183 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
2184 | exp -= dpt++; |
2185 | efmt = 1; | |
f872b822 MD |
2186 | #else |
2187 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 2188 | if (!efmt) |
cda139a7 MD |
2189 | { |
2190 | if (exp < 0) | |
2191 | { | |
2192 | a[ch++] = '0'; | |
2193 | a[ch++] = '.'; | |
2194 | dpt = exp; | |
f872b822 MD |
2195 | while (++dpt) |
2196 | a[ch++] = '0'; | |
cda139a7 MD |
2197 | } |
2198 | else | |
f872b822 | 2199 | dpt = exp + 1; |
cda139a7 | 2200 | } |
0f2d19dd JB |
2201 | else |
2202 | dpt = 1; | |
f872b822 MD |
2203 | #endif |
2204 | ||
2205 | do | |
2206 | { | |
2207 | d = f; | |
2208 | f -= d; | |
0b799eea | 2209 | a[ch++] = number_chars[d]; |
f872b822 MD |
2210 | if (f < fx[wp]) |
2211 | break; | |
2212 | if (f + fx[wp] >= 1.0) | |
2213 | { | |
0b799eea | 2214 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
2215 | break; |
2216 | } | |
0b799eea | 2217 | f *= radix; |
f872b822 MD |
2218 | if (!(--dpt)) |
2219 | a[ch++] = '.'; | |
0f2d19dd | 2220 | } |
f872b822 | 2221 | while (wp--); |
0f2d19dd JB |
2222 | |
2223 | if (dpt > 0) | |
cda139a7 | 2224 | { |
f872b822 | 2225 | #ifndef ENGNOT |
cda139a7 MD |
2226 | if ((dpt > 4) && (exp > 6)) |
2227 | { | |
f872b822 | 2228 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 2229 | for (i = ch++; i > d; i--) |
f872b822 | 2230 | a[i] = a[i - 1]; |
cda139a7 MD |
2231 | a[d] = '.'; |
2232 | efmt = 1; | |
2233 | } | |
2234 | else | |
f872b822 | 2235 | #endif |
cda139a7 | 2236 | { |
f872b822 MD |
2237 | while (--dpt) |
2238 | a[ch++] = '0'; | |
cda139a7 MD |
2239 | a[ch++] = '.'; |
2240 | } | |
2241 | } | |
f872b822 MD |
2242 | if (a[ch - 1] == '.') |
2243 | a[ch++] = '0'; /* trailing zero */ | |
2244 | if (efmt && exp) | |
2245 | { | |
2246 | a[ch++] = 'e'; | |
2247 | if (exp < 0) | |
2248 | { | |
2249 | exp = -exp; | |
2250 | a[ch++] = '-'; | |
2251 | } | |
0b799eea MV |
2252 | for (i = radix; i <= exp; i *= radix); |
2253 | for (i /= radix; i; i /= radix) | |
f872b822 | 2254 | { |
0b799eea | 2255 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
2256 | exp %= i; |
2257 | } | |
0f2d19dd | 2258 | } |
0f2d19dd JB |
2259 | return ch; |
2260 | } | |
2261 | ||
7a1aba42 MV |
2262 | |
2263 | static size_t | |
2264 | icmplx2str (double real, double imag, char *str, int radix) | |
2265 | { | |
2266 | size_t i; | |
2267 | ||
2268 | i = idbl2str (real, str, radix); | |
2269 | if (imag != 0.0) | |
2270 | { | |
2271 | /* Don't output a '+' for negative numbers or for Inf and | |
2272 | NaN. They will provide their own sign. */ | |
2273 | if (0 <= imag && !xisinf (imag) && !xisnan (imag)) | |
2274 | str[i++] = '+'; | |
2275 | i += idbl2str (imag, &str[i], radix); | |
2276 | str[i++] = 'i'; | |
2277 | } | |
2278 | return i; | |
2279 | } | |
2280 | ||
1be6b49c | 2281 | static size_t |
0b799eea | 2282 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 2283 | { |
1be6b49c | 2284 | size_t i; |
3c9a524f | 2285 | if (SCM_REALP (flt)) |
0b799eea | 2286 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 2287 | else |
7a1aba42 MV |
2288 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
2289 | str, radix); | |
0f2d19dd JB |
2290 | return i; |
2291 | } | |
0f2d19dd | 2292 | |
2881e77b | 2293 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
2294 | characters in the result. |
2295 | rad is output base | |
2296 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2297 | size_t |
2881e77b MV |
2298 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
2299 | { | |
2300 | if (num < 0) | |
2301 | { | |
2302 | *p++ = '-'; | |
2303 | return scm_iuint2str (-num, rad, p) + 1; | |
2304 | } | |
2305 | else | |
2306 | return scm_iuint2str (num, rad, p); | |
2307 | } | |
2308 | ||
2309 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
2310 | characters in the result. | |
2311 | rad is output base | |
2312 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
2313 | size_t | |
2314 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 2315 | { |
1be6b49c ML |
2316 | size_t j = 1; |
2317 | size_t i; | |
2881e77b | 2318 | scm_t_uintmax n = num; |
5c11cc9d | 2319 | |
f872b822 | 2320 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2321 | j++; |
2322 | ||
2323 | i = j; | |
2881e77b | 2324 | n = num; |
f872b822 MD |
2325 | while (i--) |
2326 | { | |
5c11cc9d GH |
2327 | int d = n % rad; |
2328 | ||
f872b822 MD |
2329 | n /= rad; |
2330 | p[i] = d + ((d < 10) ? '0' : 'a' - 10); | |
2331 | } | |
0f2d19dd JB |
2332 | return j; |
2333 | } | |
2334 | ||
a1ec6916 | 2335 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2336 | (SCM n, SCM radix), |
2337 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2338 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2339 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2340 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2341 | { |
1bbd0b84 | 2342 | int base; |
98cb6e75 | 2343 | |
0aacf84e | 2344 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 2345 | base = 10; |
0aacf84e | 2346 | else |
5efd3c7d | 2347 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 2348 | |
e11e83f3 | 2349 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2350 | { |
2351 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 2352 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 2353 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
2354 | } |
2355 | else if (SCM_BIGP (n)) | |
2356 | { | |
2357 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
2358 | scm_remember_upto_here_1 (n); | |
cc95e00a | 2359 | return scm_take_locale_string (str); |
0aacf84e | 2360 | } |
f92e85f7 MV |
2361 | else if (SCM_FRACTIONP (n)) |
2362 | { | |
2363 | scm_i_fraction_reduce (n); | |
2364 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), | |
cc95e00a | 2365 | scm_from_locale_string ("/"), |
f92e85f7 MV |
2366 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
2367 | } | |
0aacf84e MD |
2368 | else if (SCM_INEXACTP (n)) |
2369 | { | |
2370 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 2371 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
2372 | } |
2373 | else | |
bb628794 | 2374 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 2375 | } |
1bbd0b84 | 2376 | #undef FUNC_NAME |
0f2d19dd JB |
2377 | |
2378 | ||
ca46fb90 RB |
2379 | /* These print routines used to be stubbed here so that scm_repl.c |
2380 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 2381 | |
0f2d19dd | 2382 | int |
e81d98ec | 2383 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2384 | { |
56e55ac7 | 2385 | char num_buf[FLOBUFLEN]; |
0b799eea | 2386 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
2387 | return !0; |
2388 | } | |
2389 | ||
b479fe9a MV |
2390 | void |
2391 | scm_i_print_double (double val, SCM port) | |
2392 | { | |
2393 | char num_buf[FLOBUFLEN]; | |
2394 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
2395 | } | |
2396 | ||
f3ae5d60 | 2397 | int |
e81d98ec | 2398 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 2399 | |
f3ae5d60 | 2400 | { |
56e55ac7 | 2401 | char num_buf[FLOBUFLEN]; |
0b799eea | 2402 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
2403 | return !0; |
2404 | } | |
1cc91f1b | 2405 | |
7a1aba42 MV |
2406 | void |
2407 | scm_i_print_complex (double real, double imag, SCM port) | |
2408 | { | |
2409 | char num_buf[FLOBUFLEN]; | |
2410 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
2411 | } | |
2412 | ||
f92e85f7 MV |
2413 | int |
2414 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
2415 | { | |
2416 | SCM str; | |
2417 | scm_i_fraction_reduce (sexp); | |
2418 | str = scm_number_to_string (sexp, SCM_UNDEFINED); | |
cc95e00a | 2419 | scm_lfwrite (scm_i_string_chars (str), scm_i_string_length (str), port); |
f92e85f7 MV |
2420 | scm_remember_upto_here_1 (str); |
2421 | return !0; | |
2422 | } | |
2423 | ||
0f2d19dd | 2424 | int |
e81d98ec | 2425 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2426 | { |
ca46fb90 RB |
2427 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
2428 | scm_remember_upto_here_1 (exp); | |
2429 | scm_lfwrite (str, (size_t) strlen (str), port); | |
2430 | free (str); | |
0f2d19dd JB |
2431 | return !0; |
2432 | } | |
2433 | /*** END nums->strs ***/ | |
2434 | ||
3c9a524f | 2435 | |
0f2d19dd | 2436 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2437 | |
3c9a524f DH |
2438 | /* The following functions implement the conversion from strings to numbers. |
2439 | * The implementation somehow follows the grammar for numbers as it is given | |
2440 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2441 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2442 | * points should be noted about the implementation: | |
2443 | * * Each function keeps a local index variable 'idx' that points at the | |
2444 | * current position within the parsed string. The global index is only | |
2445 | * updated if the function could parse the corresponding syntactic unit | |
2446 | * successfully. | |
2447 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2448 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2449 | * global exactness information is only updated after each part has been | |
2450 | * successfully parsed. | |
2451 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2452 | * Only if these fixnums would overflow, the result variables are updated | |
2453 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2454 | * the temporary variables holding the fixnums are cleared, and the process | |
2455 | * starts over again. If for example fixnums were able to store five decimal | |
2456 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2457 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2458 | * only every five digits two bignum operations were performed. | |
2459 | */ | |
2460 | ||
2461 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2462 | ||
2463 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2464 | ||
2465 | /* In non ASCII-style encodings the following macro might not work. */ | |
71df73ac KR |
2466 | #define XDIGIT2UINT(d) \ |
2467 | (isdigit ((int) (unsigned char) d) \ | |
2468 | ? (d) - '0' \ | |
2469 | : tolower ((int) (unsigned char) d) - 'a' + 10) | |
3c9a524f | 2470 | |
2a8fecee | 2471 | static SCM |
3c9a524f DH |
2472 | mem2uinteger (const char* mem, size_t len, unsigned int *p_idx, |
2473 | unsigned int radix, enum t_exactness *p_exactness) | |
2a8fecee | 2474 | { |
3c9a524f DH |
2475 | unsigned int idx = *p_idx; |
2476 | unsigned int hash_seen = 0; | |
2477 | scm_t_bits shift = 1; | |
2478 | scm_t_bits add = 0; | |
2479 | unsigned int digit_value; | |
2480 | SCM result; | |
2481 | char c; | |
2482 | ||
2483 | if (idx == len) | |
2484 | return SCM_BOOL_F; | |
2a8fecee | 2485 | |
3c9a524f | 2486 | c = mem[idx]; |
71df73ac | 2487 | if (!isxdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2488 | return SCM_BOOL_F; |
2489 | digit_value = XDIGIT2UINT (c); | |
2490 | if (digit_value >= radix) | |
2491 | return SCM_BOOL_F; | |
2492 | ||
2493 | idx++; | |
d956fa6f | 2494 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 2495 | while (idx != len) |
f872b822 | 2496 | { |
3c9a524f | 2497 | char c = mem[idx]; |
71df73ac | 2498 | if (isxdigit ((int) (unsigned char) c)) |
f872b822 | 2499 | { |
3c9a524f | 2500 | if (hash_seen) |
1fe5e088 | 2501 | break; |
3c9a524f DH |
2502 | digit_value = XDIGIT2UINT (c); |
2503 | if (digit_value >= radix) | |
1fe5e088 | 2504 | break; |
f872b822 | 2505 | } |
3c9a524f DH |
2506 | else if (c == '#') |
2507 | { | |
2508 | hash_seen = 1; | |
2509 | digit_value = 0; | |
2510 | } | |
2511 | else | |
2512 | break; | |
2513 | ||
2514 | idx++; | |
2515 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2516 | { | |
d956fa6f | 2517 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2518 | if (add > 0) |
d956fa6f | 2519 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2520 | |
2521 | shift = radix; | |
2522 | add = digit_value; | |
2523 | } | |
2524 | else | |
2525 | { | |
2526 | shift = shift * radix; | |
2527 | add = add * radix + digit_value; | |
2528 | } | |
2529 | }; | |
2530 | ||
2531 | if (shift > 1) | |
d956fa6f | 2532 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2533 | if (add > 0) |
d956fa6f | 2534 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2535 | |
2536 | *p_idx = idx; | |
2537 | if (hash_seen) | |
2538 | *p_exactness = INEXACT; | |
2539 | ||
2540 | return result; | |
2a8fecee JB |
2541 | } |
2542 | ||
2543 | ||
3c9a524f DH |
2544 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2545 | * covers the parts of the rules that start at a potential point. The value | |
2546 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2547 | * in variable result. The content of *p_exactness indicates, whether a hash |
2548 | * has already been seen in the digits before the point. | |
3c9a524f | 2549 | */ |
1cc91f1b | 2550 | |
3c9a524f DH |
2551 | /* In non ASCII-style encodings the following macro might not work. */ |
2552 | #define DIGIT2UINT(d) ((d) - '0') | |
2553 | ||
2554 | static SCM | |
79d34f68 | 2555 | mem2decimal_from_point (SCM result, const char* mem, size_t len, |
3c9a524f | 2556 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2557 | { |
3c9a524f DH |
2558 | unsigned int idx = *p_idx; |
2559 | enum t_exactness x = *p_exactness; | |
3c9a524f DH |
2560 | |
2561 | if (idx == len) | |
79d34f68 | 2562 | return result; |
3c9a524f DH |
2563 | |
2564 | if (mem[idx] == '.') | |
2565 | { | |
2566 | scm_t_bits shift = 1; | |
2567 | scm_t_bits add = 0; | |
2568 | unsigned int digit_value; | |
d956fa6f | 2569 | SCM big_shift = SCM_I_MAKINUM (1); |
3c9a524f DH |
2570 | |
2571 | idx++; | |
2572 | while (idx != len) | |
2573 | { | |
2574 | char c = mem[idx]; | |
71df73ac | 2575 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2576 | { |
2577 | if (x == INEXACT) | |
2578 | return SCM_BOOL_F; | |
2579 | else | |
2580 | digit_value = DIGIT2UINT (c); | |
2581 | } | |
2582 | else if (c == '#') | |
2583 | { | |
2584 | x = INEXACT; | |
2585 | digit_value = 0; | |
2586 | } | |
2587 | else | |
2588 | break; | |
2589 | ||
2590 | idx++; | |
2591 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2592 | { | |
d956fa6f MV |
2593 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2594 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 2595 | if (add > 0) |
d956fa6f | 2596 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2597 | |
2598 | shift = 10; | |
2599 | add = digit_value; | |
2600 | } | |
2601 | else | |
2602 | { | |
2603 | shift = shift * 10; | |
2604 | add = add * 10 + digit_value; | |
2605 | } | |
2606 | }; | |
2607 | ||
2608 | if (add > 0) | |
2609 | { | |
d956fa6f MV |
2610 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2611 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
2612 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
2613 | } |
2614 | ||
d8592269 | 2615 | result = scm_divide (result, big_shift); |
79d34f68 | 2616 | |
3c9a524f DH |
2617 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2618 | x = INEXACT; | |
f872b822 | 2619 | } |
3c9a524f | 2620 | |
3c9a524f | 2621 | if (idx != len) |
f872b822 | 2622 | { |
3c9a524f DH |
2623 | int sign = 1; |
2624 | unsigned int start; | |
2625 | char c; | |
2626 | int exponent; | |
2627 | SCM e; | |
2628 | ||
2629 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2630 | ||
2631 | switch (mem[idx]) | |
f872b822 | 2632 | { |
3c9a524f DH |
2633 | case 'd': case 'D': |
2634 | case 'e': case 'E': | |
2635 | case 'f': case 'F': | |
2636 | case 'l': case 'L': | |
2637 | case 's': case 'S': | |
2638 | idx++; | |
2639 | start = idx; | |
2640 | c = mem[idx]; | |
2641 | if (c == '-') | |
2642 | { | |
2643 | idx++; | |
2644 | sign = -1; | |
2645 | c = mem[idx]; | |
2646 | } | |
2647 | else if (c == '+') | |
2648 | { | |
2649 | idx++; | |
2650 | sign = 1; | |
2651 | c = mem[idx]; | |
2652 | } | |
2653 | else | |
2654 | sign = 1; | |
2655 | ||
71df73ac | 2656 | if (!isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2657 | return SCM_BOOL_F; |
2658 | ||
2659 | idx++; | |
2660 | exponent = DIGIT2UINT (c); | |
2661 | while (idx != len) | |
f872b822 | 2662 | { |
3c9a524f | 2663 | char c = mem[idx]; |
71df73ac | 2664 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2665 | { |
2666 | idx++; | |
2667 | if (exponent <= SCM_MAXEXP) | |
2668 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2669 | } | |
2670 | else | |
2671 | break; | |
f872b822 | 2672 | } |
3c9a524f DH |
2673 | |
2674 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2675 | { |
3c9a524f | 2676 | size_t exp_len = idx - start; |
cc95e00a | 2677 | SCM exp_string = scm_from_locale_stringn (&mem[start], exp_len); |
3c9a524f DH |
2678 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
2679 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2680 | } |
3c9a524f | 2681 | |
d956fa6f | 2682 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
2683 | if (sign == 1) |
2684 | result = scm_product (result, e); | |
2685 | else | |
f92e85f7 | 2686 | result = scm_divide2real (result, e); |
3c9a524f DH |
2687 | |
2688 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2689 | x = INEXACT; | |
2690 | ||
f872b822 | 2691 | break; |
3c9a524f | 2692 | |
f872b822 | 2693 | default: |
3c9a524f | 2694 | break; |
f872b822 | 2695 | } |
0f2d19dd | 2696 | } |
3c9a524f DH |
2697 | |
2698 | *p_idx = idx; | |
2699 | if (x == INEXACT) | |
2700 | *p_exactness = x; | |
2701 | ||
2702 | return result; | |
0f2d19dd | 2703 | } |
0f2d19dd | 2704 | |
3c9a524f DH |
2705 | |
2706 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2707 | ||
2708 | static SCM | |
2709 | mem2ureal (const char* mem, size_t len, unsigned int *p_idx, | |
2710 | unsigned int radix, enum t_exactness *p_exactness) | |
0f2d19dd | 2711 | { |
3c9a524f | 2712 | unsigned int idx = *p_idx; |
164d2481 | 2713 | SCM result; |
3c9a524f DH |
2714 | |
2715 | if (idx == len) | |
2716 | return SCM_BOOL_F; | |
2717 | ||
7351e207 MV |
2718 | if (idx+5 <= len && !strncmp (mem+idx, "inf.0", 5)) |
2719 | { | |
2720 | *p_idx = idx+5; | |
2721 | return scm_inf (); | |
2722 | } | |
2723 | ||
2724 | if (idx+4 < len && !strncmp (mem+idx, "nan.", 4)) | |
2725 | { | |
2726 | enum t_exactness x = EXACT; | |
2727 | ||
d8592269 MV |
2728 | /* Cobble up the fractional part. We might want to set the |
2729 | NaN's mantissa from it. */ | |
7351e207 MV |
2730 | idx += 4; |
2731 | mem2uinteger (mem, len, &idx, 10, &x); | |
2732 | *p_idx = idx; | |
2733 | return scm_nan (); | |
2734 | } | |
2735 | ||
3c9a524f DH |
2736 | if (mem[idx] == '.') |
2737 | { | |
2738 | if (radix != 10) | |
2739 | return SCM_BOOL_F; | |
2740 | else if (idx + 1 == len) | |
2741 | return SCM_BOOL_F; | |
71df73ac | 2742 | else if (!isdigit ((int) (unsigned char) mem[idx + 1])) |
3c9a524f DH |
2743 | return SCM_BOOL_F; |
2744 | else | |
d956fa6f | 2745 | result = mem2decimal_from_point (SCM_I_MAKINUM (0), mem, len, |
164d2481 | 2746 | p_idx, p_exactness); |
f872b822 | 2747 | } |
3c9a524f DH |
2748 | else |
2749 | { | |
2750 | enum t_exactness x = EXACT; | |
2751 | SCM uinteger; | |
3c9a524f DH |
2752 | |
2753 | uinteger = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2754 | if (scm_is_false (uinteger)) |
3c9a524f DH |
2755 | return SCM_BOOL_F; |
2756 | ||
2757 | if (idx == len) | |
2758 | result = uinteger; | |
2759 | else if (mem[idx] == '/') | |
f872b822 | 2760 | { |
3c9a524f DH |
2761 | SCM divisor; |
2762 | ||
2763 | idx++; | |
2764 | ||
2765 | divisor = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2766 | if (scm_is_false (divisor)) |
3c9a524f DH |
2767 | return SCM_BOOL_F; |
2768 | ||
f92e85f7 | 2769 | /* both are int/big here, I assume */ |
cba42c93 | 2770 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 2771 | } |
3c9a524f DH |
2772 | else if (radix == 10) |
2773 | { | |
2774 | result = mem2decimal_from_point (uinteger, mem, len, &idx, &x); | |
73e4de09 | 2775 | if (scm_is_false (result)) |
3c9a524f DH |
2776 | return SCM_BOOL_F; |
2777 | } | |
2778 | else | |
2779 | result = uinteger; | |
2780 | ||
2781 | *p_idx = idx; | |
2782 | if (x == INEXACT) | |
2783 | *p_exactness = x; | |
f872b822 | 2784 | } |
164d2481 MV |
2785 | |
2786 | /* When returning an inexact zero, make sure it is represented as a | |
2787 | floating point value so that we can change its sign. | |
2788 | */ | |
bc36d050 | 2789 | if (scm_is_eq (result, SCM_I_MAKINUM(0)) && *p_exactness == INEXACT) |
55f26379 | 2790 | result = scm_from_double (0.0); |
164d2481 MV |
2791 | |
2792 | return result; | |
3c9a524f | 2793 | } |
0f2d19dd | 2794 | |
0f2d19dd | 2795 | |
3c9a524f | 2796 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2797 | |
3c9a524f DH |
2798 | static SCM |
2799 | mem2complex (const char* mem, size_t len, unsigned int idx, | |
2800 | unsigned int radix, enum t_exactness *p_exactness) | |
2801 | { | |
2802 | char c; | |
2803 | int sign = 0; | |
2804 | SCM ureal; | |
2805 | ||
2806 | if (idx == len) | |
2807 | return SCM_BOOL_F; | |
2808 | ||
2809 | c = mem[idx]; | |
2810 | if (c == '+') | |
2811 | { | |
2812 | idx++; | |
2813 | sign = 1; | |
2814 | } | |
2815 | else if (c == '-') | |
2816 | { | |
2817 | idx++; | |
2818 | sign = -1; | |
0f2d19dd | 2819 | } |
0f2d19dd | 2820 | |
3c9a524f DH |
2821 | if (idx == len) |
2822 | return SCM_BOOL_F; | |
2823 | ||
2824 | ureal = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2825 | if (scm_is_false (ureal)) |
f872b822 | 2826 | { |
3c9a524f DH |
2827 | /* input must be either +i or -i */ |
2828 | ||
2829 | if (sign == 0) | |
2830 | return SCM_BOOL_F; | |
2831 | ||
2832 | if (mem[idx] == 'i' || mem[idx] == 'I') | |
f872b822 | 2833 | { |
3c9a524f DH |
2834 | idx++; |
2835 | if (idx != len) | |
2836 | return SCM_BOOL_F; | |
2837 | ||
d956fa6f | 2838 | return scm_make_rectangular (SCM_I_MAKINUM (0), SCM_I_MAKINUM (sign)); |
f872b822 | 2839 | } |
3c9a524f DH |
2840 | else |
2841 | return SCM_BOOL_F; | |
0f2d19dd | 2842 | } |
3c9a524f DH |
2843 | else |
2844 | { | |
73e4de09 | 2845 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 2846 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 2847 | |
3c9a524f DH |
2848 | if (idx == len) |
2849 | return ureal; | |
2850 | ||
2851 | c = mem[idx]; | |
2852 | switch (c) | |
f872b822 | 2853 | { |
3c9a524f DH |
2854 | case 'i': case 'I': |
2855 | /* either +<ureal>i or -<ureal>i */ | |
2856 | ||
2857 | idx++; | |
2858 | if (sign == 0) | |
2859 | return SCM_BOOL_F; | |
2860 | if (idx != len) | |
2861 | return SCM_BOOL_F; | |
d956fa6f | 2862 | return scm_make_rectangular (SCM_I_MAKINUM (0), ureal); |
3c9a524f DH |
2863 | |
2864 | case '@': | |
2865 | /* polar input: <real>@<real>. */ | |
2866 | ||
2867 | idx++; | |
2868 | if (idx == len) | |
2869 | return SCM_BOOL_F; | |
2870 | else | |
f872b822 | 2871 | { |
3c9a524f DH |
2872 | int sign; |
2873 | SCM angle; | |
2874 | SCM result; | |
2875 | ||
2876 | c = mem[idx]; | |
2877 | if (c == '+') | |
2878 | { | |
2879 | idx++; | |
2880 | sign = 1; | |
2881 | } | |
2882 | else if (c == '-') | |
2883 | { | |
2884 | idx++; | |
2885 | sign = -1; | |
2886 | } | |
2887 | else | |
2888 | sign = 1; | |
2889 | ||
2890 | angle = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2891 | if (scm_is_false (angle)) |
3c9a524f DH |
2892 | return SCM_BOOL_F; |
2893 | if (idx != len) | |
2894 | return SCM_BOOL_F; | |
2895 | ||
73e4de09 | 2896 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
2897 | angle = scm_difference (angle, SCM_UNDEFINED); |
2898 | ||
2899 | result = scm_make_polar (ureal, angle); | |
2900 | return result; | |
f872b822 | 2901 | } |
3c9a524f DH |
2902 | case '+': |
2903 | case '-': | |
2904 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 2905 | |
3c9a524f DH |
2906 | idx++; |
2907 | if (idx == len) | |
2908 | return SCM_BOOL_F; | |
2909 | else | |
2910 | { | |
2911 | int sign = (c == '+') ? 1 : -1; | |
2912 | SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness); | |
0f2d19dd | 2913 | |
73e4de09 | 2914 | if (scm_is_false (imag)) |
d956fa6f | 2915 | imag = SCM_I_MAKINUM (sign); |
73e4de09 | 2916 | else if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
1fe5e088 | 2917 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 2918 | |
3c9a524f DH |
2919 | if (idx == len) |
2920 | return SCM_BOOL_F; | |
2921 | if (mem[idx] != 'i' && mem[idx] != 'I') | |
2922 | return SCM_BOOL_F; | |
0f2d19dd | 2923 | |
3c9a524f DH |
2924 | idx++; |
2925 | if (idx != len) | |
2926 | return SCM_BOOL_F; | |
0f2d19dd | 2927 | |
1fe5e088 | 2928 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
2929 | } |
2930 | default: | |
2931 | return SCM_BOOL_F; | |
2932 | } | |
2933 | } | |
0f2d19dd | 2934 | } |
0f2d19dd JB |
2935 | |
2936 | ||
3c9a524f DH |
2937 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
2938 | ||
2939 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 2940 | |
0f2d19dd | 2941 | SCM |
2b829bbb KR |
2942 | scm_c_locale_stringn_to_number (const char* mem, size_t len, |
2943 | unsigned int default_radix) | |
0f2d19dd | 2944 | { |
3c9a524f DH |
2945 | unsigned int idx = 0; |
2946 | unsigned int radix = NO_RADIX; | |
2947 | enum t_exactness forced_x = NO_EXACTNESS; | |
2948 | enum t_exactness implicit_x = EXACT; | |
2949 | SCM result; | |
2950 | ||
2951 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
2952 | while (idx + 2 < len && mem[idx] == '#') | |
2953 | { | |
2954 | switch (mem[idx + 1]) | |
2955 | { | |
2956 | case 'b': case 'B': | |
2957 | if (radix != NO_RADIX) | |
2958 | return SCM_BOOL_F; | |
2959 | radix = DUAL; | |
2960 | break; | |
2961 | case 'd': case 'D': | |
2962 | if (radix != NO_RADIX) | |
2963 | return SCM_BOOL_F; | |
2964 | radix = DEC; | |
2965 | break; | |
2966 | case 'i': case 'I': | |
2967 | if (forced_x != NO_EXACTNESS) | |
2968 | return SCM_BOOL_F; | |
2969 | forced_x = INEXACT; | |
2970 | break; | |
2971 | case 'e': case 'E': | |
2972 | if (forced_x != NO_EXACTNESS) | |
2973 | return SCM_BOOL_F; | |
2974 | forced_x = EXACT; | |
2975 | break; | |
2976 | case 'o': case 'O': | |
2977 | if (radix != NO_RADIX) | |
2978 | return SCM_BOOL_F; | |
2979 | radix = OCT; | |
2980 | break; | |
2981 | case 'x': case 'X': | |
2982 | if (radix != NO_RADIX) | |
2983 | return SCM_BOOL_F; | |
2984 | radix = HEX; | |
2985 | break; | |
2986 | default: | |
f872b822 | 2987 | return SCM_BOOL_F; |
3c9a524f DH |
2988 | } |
2989 | idx += 2; | |
2990 | } | |
2991 | ||
2992 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
2993 | if (radix == NO_RADIX) | |
2994 | result = mem2complex (mem, len, idx, default_radix, &implicit_x); | |
2995 | else | |
2996 | result = mem2complex (mem, len, idx, (unsigned int) radix, &implicit_x); | |
2997 | ||
73e4de09 | 2998 | if (scm_is_false (result)) |
3c9a524f | 2999 | return SCM_BOOL_F; |
f872b822 | 3000 | |
3c9a524f | 3001 | switch (forced_x) |
f872b822 | 3002 | { |
3c9a524f DH |
3003 | case EXACT: |
3004 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
3005 | return scm_inexact_to_exact (result); |
3006 | else | |
3007 | return result; | |
3008 | case INEXACT: | |
3009 | if (SCM_INEXACTP (result)) | |
3010 | return result; | |
3011 | else | |
3012 | return scm_exact_to_inexact (result); | |
3013 | case NO_EXACTNESS: | |
3014 | default: | |
3015 | if (implicit_x == INEXACT) | |
3016 | { | |
3017 | if (SCM_INEXACTP (result)) | |
3018 | return result; | |
3019 | else | |
3020 | return scm_exact_to_inexact (result); | |
3021 | } | |
3022 | else | |
3023 | return result; | |
f872b822 | 3024 | } |
0f2d19dd JB |
3025 | } |
3026 | ||
3027 | ||
a1ec6916 | 3028 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 3029 | (SCM string, SCM radix), |
1e6808ea | 3030 | "Return a number of the maximally precise representation\n" |
942e5b91 | 3031 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
3032 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
3033 | "is a default radix that may be overridden by an explicit radix\n" | |
3034 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
3035 | "supplied, then the default radix is 10. If string is not a\n" | |
3036 | "syntactically valid notation for a number, then\n" | |
3037 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 3038 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
3039 | { |
3040 | SCM answer; | |
5efd3c7d | 3041 | unsigned int base; |
a6d9e5ab | 3042 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
3043 | |
3044 | if (SCM_UNBNDP (radix)) | |
3045 | base = 10; | |
3046 | else | |
3047 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
3048 | ||
2b829bbb KR |
3049 | answer = scm_c_locale_stringn_to_number (scm_i_string_chars (string), |
3050 | scm_i_string_length (string), | |
3051 | base); | |
8824ac88 MV |
3052 | scm_remember_upto_here_1 (string); |
3053 | return answer; | |
0f2d19dd | 3054 | } |
1bbd0b84 | 3055 | #undef FUNC_NAME |
3c9a524f DH |
3056 | |
3057 | ||
0f2d19dd JB |
3058 | /*** END strs->nums ***/ |
3059 | ||
5986c47d | 3060 | |
0f2d19dd | 3061 | SCM |
1bbd0b84 | 3062 | scm_bigequal (SCM x, SCM y) |
0f2d19dd | 3063 | { |
47ae1f0e | 3064 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
ca46fb90 | 3065 | scm_remember_upto_here_2 (x, y); |
73e4de09 | 3066 | return scm_from_bool (0 == result); |
0f2d19dd JB |
3067 | } |
3068 | ||
0f2d19dd | 3069 | SCM |
f3ae5d60 | 3070 | scm_real_equalp (SCM x, SCM y) |
0f2d19dd | 3071 | { |
73e4de09 | 3072 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0f2d19dd JB |
3073 | } |
3074 | ||
f3ae5d60 MD |
3075 | SCM |
3076 | scm_complex_equalp (SCM x, SCM y) | |
3077 | { | |
73e4de09 | 3078 | return scm_from_bool (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) |
f3ae5d60 MD |
3079 | && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); |
3080 | } | |
0f2d19dd | 3081 | |
f92e85f7 MV |
3082 | SCM |
3083 | scm_i_fraction_equalp (SCM x, SCM y) | |
3084 | { | |
3085 | scm_i_fraction_reduce (x); | |
3086 | scm_i_fraction_reduce (y); | |
73e4de09 | 3087 | if (scm_is_false (scm_equal_p (SCM_FRACTION_NUMERATOR (x), |
02164269 | 3088 | SCM_FRACTION_NUMERATOR (y))) |
73e4de09 | 3089 | || scm_is_false (scm_equal_p (SCM_FRACTION_DENOMINATOR (x), |
02164269 MV |
3090 | SCM_FRACTION_DENOMINATOR (y)))) |
3091 | return SCM_BOOL_F; | |
3092 | else | |
3093 | return SCM_BOOL_T; | |
f92e85f7 | 3094 | } |
0f2d19dd JB |
3095 | |
3096 | ||
8507ec80 MV |
3097 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
3098 | (SCM x), | |
3099 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
3100 | "otherwise.") | |
3101 | #define FUNC_NAME s_scm_number_p | |
3102 | { | |
3103 | return scm_from_bool (SCM_NUMBERP (x)); | |
3104 | } | |
3105 | #undef FUNC_NAME | |
3106 | ||
3107 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 3108 | (SCM x), |
942e5b91 | 3109 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 3110 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
3111 | "values form subsets of the set of complex numbers, i. e. the\n" |
3112 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
3113 | "rational or integer number.") | |
8507ec80 | 3114 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 3115 | { |
8507ec80 MV |
3116 | /* all numbers are complex. */ |
3117 | return scm_number_p (x); | |
0f2d19dd | 3118 | } |
1bbd0b84 | 3119 | #undef FUNC_NAME |
0f2d19dd | 3120 | |
f92e85f7 MV |
3121 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
3122 | (SCM x), | |
3123 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
3124 | "otherwise. Note that the set of integer values forms a subset of\n" | |
3125 | "the set of real numbers, i. e. the predicate will also be\n" | |
3126 | "fulfilled if @var{x} is an integer number.") | |
3127 | #define FUNC_NAME s_scm_real_p | |
3128 | { | |
3129 | /* we can't represent irrational numbers. */ | |
3130 | return scm_rational_p (x); | |
3131 | } | |
3132 | #undef FUNC_NAME | |
3133 | ||
3134 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 3135 | (SCM x), |
942e5b91 | 3136 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 3137 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 3138 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
3139 | "fulfilled if @var{x} is an integer number.") |
3140 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 3141 | { |
e11e83f3 | 3142 | if (SCM_I_INUMP (x)) |
0f2d19dd | 3143 | return SCM_BOOL_T; |
0aacf84e | 3144 | else if (SCM_IMP (x)) |
0f2d19dd | 3145 | return SCM_BOOL_F; |
0aacf84e | 3146 | else if (SCM_BIGP (x)) |
0f2d19dd | 3147 | return SCM_BOOL_T; |
f92e85f7 MV |
3148 | else if (SCM_FRACTIONP (x)) |
3149 | return SCM_BOOL_T; | |
3150 | else if (SCM_REALP (x)) | |
3151 | /* due to their limited precision, all floating point numbers are | |
3152 | rational as well. */ | |
3153 | return SCM_BOOL_T; | |
0aacf84e | 3154 | else |
bb628794 | 3155 | return SCM_BOOL_F; |
0f2d19dd | 3156 | } |
1bbd0b84 | 3157 | #undef FUNC_NAME |
0f2d19dd | 3158 | |
a1ec6916 | 3159 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 3160 | (SCM x), |
942e5b91 MG |
3161 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
3162 | "else.") | |
1bbd0b84 | 3163 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd JB |
3164 | { |
3165 | double r; | |
e11e83f3 | 3166 | if (SCM_I_INUMP (x)) |
f872b822 MD |
3167 | return SCM_BOOL_T; |
3168 | if (SCM_IMP (x)) | |
3169 | return SCM_BOOL_F; | |
f872b822 MD |
3170 | if (SCM_BIGP (x)) |
3171 | return SCM_BOOL_T; | |
3c9a524f | 3172 | if (!SCM_INEXACTP (x)) |
f872b822 | 3173 | return SCM_BOOL_F; |
3c9a524f | 3174 | if (SCM_COMPLEXP (x)) |
f872b822 | 3175 | return SCM_BOOL_F; |
5986c47d | 3176 | r = SCM_REAL_VALUE (x); |
1e35a229 | 3177 | /* +/-inf passes r==floor(r), making those #t */ |
f872b822 MD |
3178 | if (r == floor (r)) |
3179 | return SCM_BOOL_T; | |
0f2d19dd JB |
3180 | return SCM_BOOL_F; |
3181 | } | |
1bbd0b84 | 3182 | #undef FUNC_NAME |
0f2d19dd JB |
3183 | |
3184 | ||
a1ec6916 | 3185 | SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, |
1bbd0b84 | 3186 | (SCM x), |
942e5b91 MG |
3187 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" |
3188 | "else.") | |
1bbd0b84 | 3189 | #define FUNC_NAME s_scm_inexact_p |
0f2d19dd | 3190 | { |
eb927cb9 MV |
3191 | if (SCM_INEXACTP (x)) |
3192 | return SCM_BOOL_T; | |
3193 | if (SCM_NUMBERP (x)) | |
3194 | return SCM_BOOL_F; | |
3195 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 3196 | } |
1bbd0b84 | 3197 | #undef FUNC_NAME |
0f2d19dd JB |
3198 | |
3199 | ||
152f82bf | 3200 | SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p); |
942e5b91 | 3201 | /* "Return @code{#t} if all parameters are numerically equal." */ |
0f2d19dd | 3202 | SCM |
6e8d25a6 | 3203 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 3204 | { |
d8b95e27 | 3205 | again: |
e11e83f3 | 3206 | if (SCM_I_INUMP (x)) |
0aacf84e | 3207 | { |
e11e83f3 MV |
3208 | long xx = SCM_I_INUM (x); |
3209 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3210 | { |
e11e83f3 | 3211 | long yy = SCM_I_INUM (y); |
73e4de09 | 3212 | return scm_from_bool (xx == yy); |
0aacf84e MD |
3213 | } |
3214 | else if (SCM_BIGP (y)) | |
3215 | return SCM_BOOL_F; | |
3216 | else if (SCM_REALP (y)) | |
e8c5b1f2 KR |
3217 | { |
3218 | /* On a 32-bit system an inum fits a double, we can cast the inum | |
3219 | to a double and compare. | |
3220 | ||
3221 | But on a 64-bit system an inum is bigger than a double and | |
3222 | casting it to a double (call that dxx) will round. dxx is at | |
3223 | worst 1 bigger or smaller than xx, so if dxx==yy we know yy is | |
3224 | an integer and fits a long. So we cast yy to a long and | |
3225 | compare with plain xx. | |
3226 | ||
3227 | An alternative (for any size system actually) would be to check | |
3228 | yy is an integer (with floor) and is in range of an inum | |
3229 | (compare against appropriate powers of 2) then test | |
3230 | xx==(long)yy. It's just a matter of which casts/comparisons | |
3231 | might be fastest or easiest for the cpu. */ | |
3232 | ||
3233 | double yy = SCM_REAL_VALUE (y); | |
3a1b45fd MV |
3234 | return scm_from_bool ((double) xx == yy |
3235 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
3236 | || xx == (long) yy)); | |
e8c5b1f2 | 3237 | } |
0aacf84e | 3238 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3239 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3240 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
3241 | else if (SCM_FRACTIONP (y)) |
3242 | return SCM_BOOL_F; | |
0aacf84e MD |
3243 | else |
3244 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3245 | } |
0aacf84e MD |
3246 | else if (SCM_BIGP (x)) |
3247 | { | |
e11e83f3 | 3248 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3249 | return SCM_BOOL_F; |
3250 | else if (SCM_BIGP (y)) | |
3251 | { | |
3252 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3253 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3254 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3255 | } |
3256 | else if (SCM_REALP (y)) | |
3257 | { | |
3258 | int cmp; | |
3259 | if (xisnan (SCM_REAL_VALUE (y))) | |
3260 | return SCM_BOOL_F; | |
3261 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3262 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3263 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3264 | } |
3265 | else if (SCM_COMPLEXP (y)) | |
3266 | { | |
3267 | int cmp; | |
3268 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
3269 | return SCM_BOOL_F; | |
3270 | if (xisnan (SCM_COMPLEX_REAL (y))) | |
3271 | return SCM_BOOL_F; | |
3272 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
3273 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3274 | return scm_from_bool (0 == cmp); |
0aacf84e | 3275 | } |
f92e85f7 MV |
3276 | else if (SCM_FRACTIONP (y)) |
3277 | return SCM_BOOL_F; | |
0aacf84e MD |
3278 | else |
3279 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3280 | } |
0aacf84e MD |
3281 | else if (SCM_REALP (x)) |
3282 | { | |
e8c5b1f2 | 3283 | double xx = SCM_REAL_VALUE (x); |
e11e83f3 | 3284 | if (SCM_I_INUMP (y)) |
e8c5b1f2 KR |
3285 | { |
3286 | /* see comments with inum/real above */ | |
3287 | long yy = SCM_I_INUM (y); | |
3a1b45fd MV |
3288 | return scm_from_bool (xx == (double) yy |
3289 | && (DBL_MANT_DIG >= SCM_I_FIXNUM_BIT-1 | |
3290 | || (long) xx == yy)); | |
e8c5b1f2 | 3291 | } |
0aacf84e MD |
3292 | else if (SCM_BIGP (y)) |
3293 | { | |
3294 | int cmp; | |
3295 | if (xisnan (SCM_REAL_VALUE (x))) | |
3296 | return SCM_BOOL_F; | |
3297 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3298 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3299 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3300 | } |
3301 | else if (SCM_REALP (y)) | |
73e4de09 | 3302 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 3303 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3304 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3305 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3306 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3307 | { |
3308 | double xx = SCM_REAL_VALUE (x); | |
3309 | if (xisnan (xx)) | |
3310 | return SCM_BOOL_F; | |
3311 | if (xisinf (xx)) | |
73e4de09 | 3312 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3313 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3314 | goto again; | |
3315 | } | |
0aacf84e MD |
3316 | else |
3317 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3318 | } |
0aacf84e MD |
3319 | else if (SCM_COMPLEXP (x)) |
3320 | { | |
e11e83f3 MV |
3321 | if (SCM_I_INUMP (y)) |
3322 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
3323 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3324 | else if (SCM_BIGP (y)) | |
3325 | { | |
3326 | int cmp; | |
3327 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
3328 | return SCM_BOOL_F; | |
3329 | if (xisnan (SCM_COMPLEX_REAL (x))) | |
3330 | return SCM_BOOL_F; | |
3331 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
3332 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3333 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3334 | } |
3335 | else if (SCM_REALP (y)) | |
73e4de09 | 3336 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
3337 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3338 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 3339 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3340 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3341 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3342 | { |
3343 | double xx; | |
3344 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
3345 | return SCM_BOOL_F; | |
3346 | xx = SCM_COMPLEX_REAL (x); | |
3347 | if (xisnan (xx)) | |
3348 | return SCM_BOOL_F; | |
3349 | if (xisinf (xx)) | |
73e4de09 | 3350 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3351 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3352 | goto again; | |
3353 | } | |
f92e85f7 MV |
3354 | else |
3355 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
3356 | } | |
3357 | else if (SCM_FRACTIONP (x)) | |
3358 | { | |
e11e83f3 | 3359 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
3360 | return SCM_BOOL_F; |
3361 | else if (SCM_BIGP (y)) | |
3362 | return SCM_BOOL_F; | |
3363 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
3364 | { |
3365 | double yy = SCM_REAL_VALUE (y); | |
3366 | if (xisnan (yy)) | |
3367 | return SCM_BOOL_F; | |
3368 | if (xisinf (yy)) | |
73e4de09 | 3369 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3370 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3371 | goto again; | |
3372 | } | |
f92e85f7 | 3373 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
3374 | { |
3375 | double yy; | |
3376 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
3377 | return SCM_BOOL_F; | |
3378 | yy = SCM_COMPLEX_REAL (y); | |
3379 | if (xisnan (yy)) | |
3380 | return SCM_BOOL_F; | |
3381 | if (xisinf (yy)) | |
73e4de09 | 3382 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3383 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3384 | goto again; | |
3385 | } | |
f92e85f7 MV |
3386 | else if (SCM_FRACTIONP (y)) |
3387 | return scm_i_fraction_equalp (x, y); | |
0aacf84e MD |
3388 | else |
3389 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3390 | } |
0aacf84e | 3391 | else |
f4c627b3 | 3392 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p); |
0f2d19dd JB |
3393 | } |
3394 | ||
3395 | ||
a5f0b599 KR |
3396 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
3397 | done are good for inums, but for bignums an answer can almost always be | |
3398 | had by just examining a few high bits of the operands, as done by GMP in | |
3399 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
3400 | of the float exponent to take into account. */ | |
3401 | ||
152f82bf | 3402 | SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p); |
942e5b91 MG |
3403 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3404 | * "increasing." | |
3405 | */ | |
0f2d19dd | 3406 | SCM |
6e8d25a6 | 3407 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3408 | { |
a5f0b599 | 3409 | again: |
e11e83f3 | 3410 | if (SCM_I_INUMP (x)) |
0aacf84e | 3411 | { |
e11e83f3 MV |
3412 | long xx = SCM_I_INUM (x); |
3413 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3414 | { |
e11e83f3 | 3415 | long yy = SCM_I_INUM (y); |
73e4de09 | 3416 | return scm_from_bool (xx < yy); |
0aacf84e MD |
3417 | } |
3418 | else if (SCM_BIGP (y)) | |
3419 | { | |
3420 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3421 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3422 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3423 | } |
3424 | else if (SCM_REALP (y)) | |
73e4de09 | 3425 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 3426 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3427 | { |
3428 | /* "x < a/b" becomes "x*b < a" */ | |
3429 | int_frac: | |
3430 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
3431 | y = SCM_FRACTION_NUMERATOR (y); | |
3432 | goto again; | |
3433 | } | |
0aacf84e MD |
3434 | else |
3435 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3436 | } |
0aacf84e MD |
3437 | else if (SCM_BIGP (x)) |
3438 | { | |
e11e83f3 | 3439 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3440 | { |
3441 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3442 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3443 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3444 | } |
3445 | else if (SCM_BIGP (y)) | |
3446 | { | |
3447 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3448 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3449 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
3450 | } |
3451 | else if (SCM_REALP (y)) | |
3452 | { | |
3453 | int cmp; | |
3454 | if (xisnan (SCM_REAL_VALUE (y))) | |
3455 | return SCM_BOOL_F; | |
3456 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3457 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3458 | return scm_from_bool (cmp < 0); |
0aacf84e | 3459 | } |
f92e85f7 | 3460 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 3461 | goto int_frac; |
0aacf84e MD |
3462 | else |
3463 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f4c627b3 | 3464 | } |
0aacf84e MD |
3465 | else if (SCM_REALP (x)) |
3466 | { | |
e11e83f3 MV |
3467 | if (SCM_I_INUMP (y)) |
3468 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3469 | else if (SCM_BIGP (y)) |
3470 | { | |
3471 | int cmp; | |
3472 | if (xisnan (SCM_REAL_VALUE (x))) | |
3473 | return SCM_BOOL_F; | |
3474 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3475 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3476 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
3477 | } |
3478 | else if (SCM_REALP (y)) | |
73e4de09 | 3479 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 3480 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3481 | { |
3482 | double xx = SCM_REAL_VALUE (x); | |
3483 | if (xisnan (xx)) | |
3484 | return SCM_BOOL_F; | |
3485 | if (xisinf (xx)) | |
73e4de09 | 3486 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
3487 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3488 | goto again; | |
3489 | } | |
f92e85f7 MV |
3490 | else |
3491 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
3492 | } | |
3493 | else if (SCM_FRACTIONP (x)) | |
3494 | { | |
e11e83f3 | 3495 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
3496 | { |
3497 | /* "a/b < y" becomes "a < y*b" */ | |
3498 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
3499 | x = SCM_FRACTION_NUMERATOR (x); | |
3500 | goto again; | |
3501 | } | |
f92e85f7 | 3502 | else if (SCM_REALP (y)) |
a5f0b599 KR |
3503 | { |
3504 | double yy = SCM_REAL_VALUE (y); | |
3505 | if (xisnan (yy)) | |
3506 | return SCM_BOOL_F; | |
3507 | if (xisinf (yy)) | |
73e4de09 | 3508 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
3509 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3510 | goto again; | |
3511 | } | |
f92e85f7 | 3512 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3513 | { |
3514 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
3515 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
3516 | SCM_FRACTION_DENOMINATOR (y)); | |
3517 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
3518 | SCM_FRACTION_DENOMINATOR (x)); | |
3519 | x = new_x; | |
3520 | y = new_y; | |
3521 | goto again; | |
3522 | } | |
0aacf84e MD |
3523 | else |
3524 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3525 | } |
0aacf84e | 3526 | else |
f4c627b3 | 3527 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p); |
0f2d19dd JB |
3528 | } |
3529 | ||
3530 | ||
c76b1eaf | 3531 | SCM_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p); |
942e5b91 MG |
3532 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3533 | * "decreasing." | |
c76b1eaf | 3534 | */ |
1bbd0b84 | 3535 | #define FUNC_NAME s_scm_gr_p |
c76b1eaf MD |
3536 | SCM |
3537 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3538 | { |
c76b1eaf MD |
3539 | if (!SCM_NUMBERP (x)) |
3540 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME); | |
3541 | else if (!SCM_NUMBERP (y)) | |
3542 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME); | |
3543 | else | |
3544 | return scm_less_p (y, x); | |
0f2d19dd | 3545 | } |
1bbd0b84 | 3546 | #undef FUNC_NAME |
0f2d19dd JB |
3547 | |
3548 | ||
c76b1eaf | 3549 | SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p); |
942e5b91 | 3550 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3551 | * "non-decreasing." |
3552 | */ | |
1bbd0b84 | 3553 | #define FUNC_NAME s_scm_leq_p |
c76b1eaf MD |
3554 | SCM |
3555 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3556 | { |
c76b1eaf MD |
3557 | if (!SCM_NUMBERP (x)) |
3558 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3559 | else if (!SCM_NUMBERP (y)) | |
3560 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3561 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3562 | return SCM_BOOL_F; |
c76b1eaf | 3563 | else |
73e4de09 | 3564 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 3565 | } |
1bbd0b84 | 3566 | #undef FUNC_NAME |
0f2d19dd JB |
3567 | |
3568 | ||
c76b1eaf | 3569 | SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p); |
942e5b91 | 3570 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3571 | * "non-increasing." |
3572 | */ | |
1bbd0b84 | 3573 | #define FUNC_NAME s_scm_geq_p |
c76b1eaf MD |
3574 | SCM |
3575 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3576 | { |
c76b1eaf MD |
3577 | if (!SCM_NUMBERP (x)) |
3578 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3579 | else if (!SCM_NUMBERP (y)) | |
3580 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3581 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3582 | return SCM_BOOL_F; |
c76b1eaf | 3583 | else |
73e4de09 | 3584 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 3585 | } |
1bbd0b84 | 3586 | #undef FUNC_NAME |
0f2d19dd JB |
3587 | |
3588 | ||
152f82bf | 3589 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3590 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3591 | * "zero." | |
3592 | */ | |
0f2d19dd | 3593 | SCM |
6e8d25a6 | 3594 | scm_zero_p (SCM z) |
0f2d19dd | 3595 | { |
e11e83f3 | 3596 | if (SCM_I_INUMP (z)) |
bc36d050 | 3597 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 3598 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 3599 | return SCM_BOOL_F; |
0aacf84e | 3600 | else if (SCM_REALP (z)) |
73e4de09 | 3601 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 3602 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 3603 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 3604 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
3605 | else if (SCM_FRACTIONP (z)) |
3606 | return SCM_BOOL_F; | |
0aacf84e | 3607 | else |
c2ff8ab0 | 3608 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); |
0f2d19dd JB |
3609 | } |
3610 | ||
3611 | ||
152f82bf | 3612 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3613 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3614 | * "zero." | |
3615 | */ | |
0f2d19dd | 3616 | SCM |
6e8d25a6 | 3617 | scm_positive_p (SCM x) |
0f2d19dd | 3618 | { |
e11e83f3 MV |
3619 | if (SCM_I_INUMP (x)) |
3620 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
3621 | else if (SCM_BIGP (x)) |
3622 | { | |
3623 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3624 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3625 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3626 | } |
3627 | else if (SCM_REALP (x)) | |
73e4de09 | 3628 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
3629 | else if (SCM_FRACTIONP (x)) |
3630 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3631 | else |
c2ff8ab0 | 3632 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); |
0f2d19dd JB |
3633 | } |
3634 | ||
3635 | ||
152f82bf | 3636 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3637 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3638 | * "zero." | |
3639 | */ | |
0f2d19dd | 3640 | SCM |
6e8d25a6 | 3641 | scm_negative_p (SCM x) |
0f2d19dd | 3642 | { |
e11e83f3 MV |
3643 | if (SCM_I_INUMP (x)) |
3644 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
3645 | else if (SCM_BIGP (x)) |
3646 | { | |
3647 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3648 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3649 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3650 | } |
3651 | else if (SCM_REALP (x)) | |
73e4de09 | 3652 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
3653 | else if (SCM_FRACTIONP (x)) |
3654 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3655 | else |
c2ff8ab0 | 3656 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); |
0f2d19dd JB |
3657 | } |
3658 | ||
3659 | ||
2a06f791 KR |
3660 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
3661 | required by r5rs. On that basis, for exact/inexact combinations the | |
3662 | exact is converted to inexact to compare and possibly return. This is | |
3663 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
3664 | its test, such trouble is not required for min and max. */ | |
3665 | ||
9de33deb | 3666 | SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max); |
942e5b91 MG |
3667 | /* "Return the maximum of all parameter values." |
3668 | */ | |
0f2d19dd | 3669 | SCM |
6e8d25a6 | 3670 | scm_max (SCM x, SCM y) |
0f2d19dd | 3671 | { |
0aacf84e MD |
3672 | if (SCM_UNBNDP (y)) |
3673 | { | |
3674 | if (SCM_UNBNDP (x)) | |
3675 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 3676 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3677 | return x; |
3678 | else | |
3679 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3680 | } |
f4c627b3 | 3681 | |
e11e83f3 | 3682 | if (SCM_I_INUMP (x)) |
0aacf84e | 3683 | { |
e11e83f3 MV |
3684 | long xx = SCM_I_INUM (x); |
3685 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3686 | { |
e11e83f3 | 3687 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3688 | return (xx < yy) ? y : x; |
3689 | } | |
3690 | else if (SCM_BIGP (y)) | |
3691 | { | |
3692 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3693 | scm_remember_upto_here_1 (y); | |
3694 | return (sgn < 0) ? x : y; | |
3695 | } | |
3696 | else if (SCM_REALP (y)) | |
3697 | { | |
3698 | double z = xx; | |
3699 | /* if y==NaN then ">" is false and we return NaN */ | |
55f26379 | 3700 | return (z > SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3701 | } |
f92e85f7 MV |
3702 | else if (SCM_FRACTIONP (y)) |
3703 | { | |
e4bc5d6c | 3704 | use_less: |
73e4de09 | 3705 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 3706 | } |
0aacf84e MD |
3707 | else |
3708 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3709 | } |
0aacf84e MD |
3710 | else if (SCM_BIGP (x)) |
3711 | { | |
e11e83f3 | 3712 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3713 | { |
3714 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3715 | scm_remember_upto_here_1 (x); | |
3716 | return (sgn < 0) ? y : x; | |
3717 | } | |
3718 | else if (SCM_BIGP (y)) | |
3719 | { | |
3720 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3721 | scm_remember_upto_here_2 (x, y); | |
3722 | return (cmp > 0) ? x : y; | |
3723 | } | |
3724 | else if (SCM_REALP (y)) | |
3725 | { | |
2a06f791 KR |
3726 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
3727 | double xx, yy; | |
3728 | big_real: | |
3729 | xx = scm_i_big2dbl (x); | |
3730 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3731 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 3732 | } |
f92e85f7 MV |
3733 | else if (SCM_FRACTIONP (y)) |
3734 | { | |
e4bc5d6c | 3735 | goto use_less; |
f92e85f7 | 3736 | } |
0aacf84e MD |
3737 | else |
3738 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 3739 | } |
0aacf84e MD |
3740 | else if (SCM_REALP (x)) |
3741 | { | |
e11e83f3 | 3742 | if (SCM_I_INUMP (y)) |
0aacf84e | 3743 | { |
e11e83f3 | 3744 | double z = SCM_I_INUM (y); |
0aacf84e | 3745 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3746 | return (SCM_REAL_VALUE (x) < z) ? scm_from_double (z) : x; |
0aacf84e MD |
3747 | } |
3748 | else if (SCM_BIGP (y)) | |
3749 | { | |
b6f8f763 | 3750 | SCM_SWAP (x, y); |
2a06f791 | 3751 | goto big_real; |
0aacf84e MD |
3752 | } |
3753 | else if (SCM_REALP (y)) | |
3754 | { | |
3755 | /* if x==NaN then our explicit check means we return NaN | |
3756 | if y==NaN then ">" is false and we return NaN | |
3757 | calling isnan is unavoidable, since it's the only way to know | |
3758 | which of x or y causes any compares to be false */ | |
3759 | double xx = SCM_REAL_VALUE (x); | |
3760 | return (xisnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y; | |
3761 | } | |
f92e85f7 MV |
3762 | else if (SCM_FRACTIONP (y)) |
3763 | { | |
3764 | double yy = scm_i_fraction2double (y); | |
3765 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3766 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
3767 | } |
3768 | else | |
3769 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3770 | } | |
3771 | else if (SCM_FRACTIONP (x)) | |
3772 | { | |
e11e83f3 | 3773 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3774 | { |
e4bc5d6c | 3775 | goto use_less; |
f92e85f7 MV |
3776 | } |
3777 | else if (SCM_BIGP (y)) | |
3778 | { | |
e4bc5d6c | 3779 | goto use_less; |
f92e85f7 MV |
3780 | } |
3781 | else if (SCM_REALP (y)) | |
3782 | { | |
3783 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3784 | return (xx < SCM_REAL_VALUE (y)) ? y : scm_from_double (xx); |
f92e85f7 MV |
3785 | } |
3786 | else if (SCM_FRACTIONP (y)) | |
3787 | { | |
e4bc5d6c | 3788 | goto use_less; |
f92e85f7 | 3789 | } |
0aacf84e MD |
3790 | else |
3791 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3792 | } |
0aacf84e | 3793 | else |
f4c627b3 | 3794 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
3795 | } |
3796 | ||
3797 | ||
9de33deb | 3798 | SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min); |
942e5b91 MG |
3799 | /* "Return the minium of all parameter values." |
3800 | */ | |
0f2d19dd | 3801 | SCM |
6e8d25a6 | 3802 | scm_min (SCM x, SCM y) |
0f2d19dd | 3803 | { |
0aacf84e MD |
3804 | if (SCM_UNBNDP (y)) |
3805 | { | |
3806 | if (SCM_UNBNDP (x)) | |
3807 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 3808 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3809 | return x; |
3810 | else | |
3811 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 3812 | } |
f4c627b3 | 3813 | |
e11e83f3 | 3814 | if (SCM_I_INUMP (x)) |
0aacf84e | 3815 | { |
e11e83f3 MV |
3816 | long xx = SCM_I_INUM (x); |
3817 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3818 | { |
e11e83f3 | 3819 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3820 | return (xx < yy) ? x : y; |
3821 | } | |
3822 | else if (SCM_BIGP (y)) | |
3823 | { | |
3824 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3825 | scm_remember_upto_here_1 (y); | |
3826 | return (sgn < 0) ? y : x; | |
3827 | } | |
3828 | else if (SCM_REALP (y)) | |
3829 | { | |
3830 | double z = xx; | |
3831 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 3832 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3833 | } |
f92e85f7 MV |
3834 | else if (SCM_FRACTIONP (y)) |
3835 | { | |
e4bc5d6c | 3836 | use_less: |
73e4de09 | 3837 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 3838 | } |
0aacf84e MD |
3839 | else |
3840 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3841 | } |
0aacf84e MD |
3842 | else if (SCM_BIGP (x)) |
3843 | { | |
e11e83f3 | 3844 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3845 | { |
3846 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3847 | scm_remember_upto_here_1 (x); | |
3848 | return (sgn < 0) ? x : y; | |
3849 | } | |
3850 | else if (SCM_BIGP (y)) | |
3851 | { | |
3852 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3853 | scm_remember_upto_here_2 (x, y); | |
3854 | return (cmp > 0) ? y : x; | |
3855 | } | |
3856 | else if (SCM_REALP (y)) | |
3857 | { | |
2a06f791 KR |
3858 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
3859 | double xx, yy; | |
3860 | big_real: | |
3861 | xx = scm_i_big2dbl (x); | |
3862 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3863 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 3864 | } |
f92e85f7 MV |
3865 | else if (SCM_FRACTIONP (y)) |
3866 | { | |
e4bc5d6c | 3867 | goto use_less; |
f92e85f7 | 3868 | } |
0aacf84e MD |
3869 | else |
3870 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 3871 | } |
0aacf84e MD |
3872 | else if (SCM_REALP (x)) |
3873 | { | |
e11e83f3 | 3874 | if (SCM_I_INUMP (y)) |
0aacf84e | 3875 | { |
e11e83f3 | 3876 | double z = SCM_I_INUM (y); |
0aacf84e | 3877 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3878 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
3879 | } |
3880 | else if (SCM_BIGP (y)) | |
3881 | { | |
b6f8f763 | 3882 | SCM_SWAP (x, y); |
2a06f791 | 3883 | goto big_real; |
0aacf84e MD |
3884 | } |
3885 | else if (SCM_REALP (y)) | |
3886 | { | |
3887 | /* if x==NaN then our explicit check means we return NaN | |
3888 | if y==NaN then "<" is false and we return NaN | |
3889 | calling isnan is unavoidable, since it's the only way to know | |
3890 | which of x or y causes any compares to be false */ | |
3891 | double xx = SCM_REAL_VALUE (x); | |
3892 | return (xisnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y; | |
3893 | } | |
f92e85f7 MV |
3894 | else if (SCM_FRACTIONP (y)) |
3895 | { | |
3896 | double yy = scm_i_fraction2double (y); | |
3897 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3898 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 3899 | } |
0aacf84e MD |
3900 | else |
3901 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3902 | } |
f92e85f7 MV |
3903 | else if (SCM_FRACTIONP (x)) |
3904 | { | |
e11e83f3 | 3905 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3906 | { |
e4bc5d6c | 3907 | goto use_less; |
f92e85f7 MV |
3908 | } |
3909 | else if (SCM_BIGP (y)) | |
3910 | { | |
e4bc5d6c | 3911 | goto use_less; |
f92e85f7 MV |
3912 | } |
3913 | else if (SCM_REALP (y)) | |
3914 | { | |
3915 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3916 | return (SCM_REAL_VALUE (y) < xx) ? y : scm_from_double (xx); |
f92e85f7 MV |
3917 | } |
3918 | else if (SCM_FRACTIONP (y)) | |
3919 | { | |
e4bc5d6c | 3920 | goto use_less; |
f92e85f7 MV |
3921 | } |
3922 | else | |
3923 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3924 | } | |
0aacf84e | 3925 | else |
f4c627b3 | 3926 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
3927 | } |
3928 | ||
3929 | ||
9de33deb | 3930 | SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum); |
942e5b91 MG |
3931 | /* "Return the sum of all parameter values. Return 0 if called without\n" |
3932 | * "any parameters." | |
3933 | */ | |
0f2d19dd | 3934 | SCM |
6e8d25a6 | 3935 | scm_sum (SCM x, SCM y) |
0f2d19dd | 3936 | { |
ca46fb90 RB |
3937 | if (SCM_UNBNDP (y)) |
3938 | { | |
3939 | if (SCM_NUMBERP (x)) return x; | |
3940 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 3941 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 3942 | } |
c209c88e | 3943 | |
e11e83f3 | 3944 | if (SCM_I_INUMP (x)) |
ca46fb90 | 3945 | { |
e11e83f3 | 3946 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3947 | { |
e11e83f3 MV |
3948 | long xx = SCM_I_INUM (x); |
3949 | long yy = SCM_I_INUM (y); | |
ca46fb90 | 3950 | long int z = xx + yy; |
d956fa6f | 3951 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_long2big (z); |
ca46fb90 RB |
3952 | } |
3953 | else if (SCM_BIGP (y)) | |
3954 | { | |
3955 | SCM_SWAP (x, y); | |
3956 | goto add_big_inum; | |
3957 | } | |
3958 | else if (SCM_REALP (y)) | |
3959 | { | |
e11e83f3 | 3960 | long int xx = SCM_I_INUM (x); |
55f26379 | 3961 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
3962 | } |
3963 | else if (SCM_COMPLEXP (y)) | |
3964 | { | |
e11e83f3 | 3965 | long int xx = SCM_I_INUM (x); |
8507ec80 | 3966 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
3967 | SCM_COMPLEX_IMAG (y)); |
3968 | } | |
f92e85f7 | 3969 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 3970 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
3971 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
3972 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
3973 | else |
3974 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
3975 | } else if (SCM_BIGP (x)) |
3976 | { | |
e11e83f3 | 3977 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3978 | { |
3979 | long int inum; | |
3980 | int bigsgn; | |
3981 | add_big_inum: | |
e11e83f3 | 3982 | inum = SCM_I_INUM (y); |
0aacf84e MD |
3983 | if (inum == 0) |
3984 | return x; | |
3985 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3986 | if (inum < 0) | |
3987 | { | |
3988 | SCM result = scm_i_mkbig (); | |
3989 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
3990 | scm_remember_upto_here_1 (x); | |
3991 | /* we know the result will have to be a bignum */ | |
3992 | if (bigsgn == -1) | |
3993 | return result; | |
3994 | return scm_i_normbig (result); | |
3995 | } | |
3996 | else | |
3997 | { | |
3998 | SCM result = scm_i_mkbig (); | |
3999 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
4000 | scm_remember_upto_here_1 (x); | |
4001 | /* we know the result will have to be a bignum */ | |
4002 | if (bigsgn == 1) | |
4003 | return result; | |
4004 | return scm_i_normbig (result); | |
4005 | } | |
4006 | } | |
4007 | else if (SCM_BIGP (y)) | |
4008 | { | |
4009 | SCM result = scm_i_mkbig (); | |
4010 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4011 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4012 | mpz_add (SCM_I_BIG_MPZ (result), | |
4013 | SCM_I_BIG_MPZ (x), | |
4014 | SCM_I_BIG_MPZ (y)); | |
4015 | scm_remember_upto_here_2 (x, y); | |
4016 | /* we know the result will have to be a bignum */ | |
4017 | if (sgn_x == sgn_y) | |
4018 | return result; | |
4019 | return scm_i_normbig (result); | |
4020 | } | |
4021 | else if (SCM_REALP (y)) | |
4022 | { | |
4023 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
4024 | scm_remember_upto_here_1 (x); | |
55f26379 | 4025 | return scm_from_double (result); |
0aacf84e MD |
4026 | } |
4027 | else if (SCM_COMPLEXP (y)) | |
4028 | { | |
4029 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4030 | + SCM_COMPLEX_REAL (y)); | |
4031 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4032 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4033 | } |
f92e85f7 | 4034 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4035 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
4036 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
4037 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4038 | else |
4039 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 4040 | } |
0aacf84e MD |
4041 | else if (SCM_REALP (x)) |
4042 | { | |
e11e83f3 | 4043 | if (SCM_I_INUMP (y)) |
55f26379 | 4044 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
4045 | else if (SCM_BIGP (y)) |
4046 | { | |
4047 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
4048 | scm_remember_upto_here_1 (y); | |
55f26379 | 4049 | return scm_from_double (result); |
0aacf84e MD |
4050 | } |
4051 | else if (SCM_REALP (y)) | |
55f26379 | 4052 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 4053 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4054 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4055 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4056 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4057 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
4058 | else |
4059 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 4060 | } |
0aacf84e MD |
4061 | else if (SCM_COMPLEXP (x)) |
4062 | { | |
e11e83f3 | 4063 | if (SCM_I_INUMP (y)) |
8507ec80 | 4064 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
4065 | SCM_COMPLEX_IMAG (x)); |
4066 | else if (SCM_BIGP (y)) | |
4067 | { | |
4068 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
4069 | + SCM_COMPLEX_REAL (x)); | |
4070 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4071 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4072 | } |
4073 | else if (SCM_REALP (y)) | |
8507ec80 | 4074 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
4075 | SCM_COMPLEX_IMAG (x)); |
4076 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4077 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4078 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4079 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4080 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
4081 | SCM_COMPLEX_IMAG (x)); |
4082 | else | |
4083 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
4084 | } | |
4085 | else if (SCM_FRACTIONP (x)) | |
4086 | { | |
e11e83f3 | 4087 | if (SCM_I_INUMP (y)) |
cba42c93 | 4088 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4089 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4090 | SCM_FRACTION_DENOMINATOR (x)); | |
4091 | else if (SCM_BIGP (y)) | |
cba42c93 | 4092 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4093 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4094 | SCM_FRACTION_DENOMINATOR (x)); | |
4095 | else if (SCM_REALP (y)) | |
55f26379 | 4096 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 4097 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4098 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
4099 | SCM_COMPLEX_IMAG (y)); |
4100 | else if (SCM_FRACTIONP (y)) | |
4101 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 4102 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4103 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4104 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4105 | else |
4106 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 4107 | } |
0aacf84e | 4108 | else |
98cb6e75 | 4109 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
4110 | } |
4111 | ||
4112 | ||
40882e3d KR |
4113 | SCM_DEFINE (scm_oneplus, "1+", 1, 0, 0, |
4114 | (SCM x), | |
4115 | "Return @math{@var{x}+1}.") | |
4116 | #define FUNC_NAME s_scm_oneplus | |
4117 | { | |
4118 | return scm_sum (x, SCM_I_MAKINUM (1)); | |
4119 | } | |
4120 | #undef FUNC_NAME | |
4121 | ||
4122 | ||
9de33deb | 4123 | SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference); |
609c3d30 MG |
4124 | /* If called with one argument @var{z1}, -@var{z1} returned. Otherwise |
4125 | * the sum of all but the first argument are subtracted from the first | |
4126 | * argument. */ | |
c05e97b7 | 4127 | #define FUNC_NAME s_difference |
0f2d19dd | 4128 | SCM |
6e8d25a6 | 4129 | scm_difference (SCM x, SCM y) |
0f2d19dd | 4130 | { |
ca46fb90 RB |
4131 | if (SCM_UNBNDP (y)) |
4132 | { | |
4133 | if (SCM_UNBNDP (x)) | |
4134 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
4135 | else | |
e11e83f3 | 4136 | if (SCM_I_INUMP (x)) |
ca46fb90 | 4137 | { |
e11e83f3 | 4138 | long xx = -SCM_I_INUM (x); |
ca46fb90 | 4139 | if (SCM_FIXABLE (xx)) |
d956fa6f | 4140 | return SCM_I_MAKINUM (xx); |
ca46fb90 RB |
4141 | else |
4142 | return scm_i_long2big (xx); | |
4143 | } | |
4144 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
4145 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
4146 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
4147 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
4148 | else if (SCM_REALP (x)) | |
55f26379 | 4149 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 4150 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 4151 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 4152 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 4153 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4154 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 4155 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
4156 | else |
4157 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 4158 | } |
ca46fb90 | 4159 | |
e11e83f3 | 4160 | if (SCM_I_INUMP (x)) |
0aacf84e | 4161 | { |
e11e83f3 | 4162 | if (SCM_I_INUMP (y)) |
0aacf84e | 4163 | { |
e11e83f3 MV |
4164 | long int xx = SCM_I_INUM (x); |
4165 | long int yy = SCM_I_INUM (y); | |
0aacf84e MD |
4166 | long int z = xx - yy; |
4167 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4168 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4169 | else |
4170 | return scm_i_long2big (z); | |
4171 | } | |
4172 | else if (SCM_BIGP (y)) | |
4173 | { | |
4174 | /* inum-x - big-y */ | |
e11e83f3 | 4175 | long xx = SCM_I_INUM (x); |
ca46fb90 | 4176 | |
0aacf84e MD |
4177 | if (xx == 0) |
4178 | return scm_i_clonebig (y, 0); | |
4179 | else | |
4180 | { | |
4181 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4182 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4183 | |
0aacf84e MD |
4184 | if (xx >= 0) |
4185 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
4186 | else | |
4187 | { | |
4188 | /* x - y == -(y + -x) */ | |
4189 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
4190 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4191 | } | |
4192 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 4193 | |
0aacf84e MD |
4194 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
4195 | /* we know the result will have to be a bignum */ | |
4196 | return result; | |
4197 | else | |
4198 | return scm_i_normbig (result); | |
4199 | } | |
4200 | } | |
4201 | else if (SCM_REALP (y)) | |
4202 | { | |
e11e83f3 | 4203 | long int xx = SCM_I_INUM (x); |
55f26379 | 4204 | return scm_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
4205 | } |
4206 | else if (SCM_COMPLEXP (y)) | |
4207 | { | |
e11e83f3 | 4208 | long int xx = SCM_I_INUM (x); |
8507ec80 | 4209 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4210 | - SCM_COMPLEX_IMAG (y)); |
4211 | } | |
f92e85f7 MV |
4212 | else if (SCM_FRACTIONP (y)) |
4213 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 4214 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4215 | SCM_FRACTION_NUMERATOR (y)), |
4216 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4217 | else |
4218 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 4219 | } |
0aacf84e MD |
4220 | else if (SCM_BIGP (x)) |
4221 | { | |
e11e83f3 | 4222 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4223 | { |
4224 | /* big-x - inum-y */ | |
e11e83f3 | 4225 | long yy = SCM_I_INUM (y); |
0aacf84e | 4226 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 4227 | |
0aacf84e MD |
4228 | scm_remember_upto_here_1 (x); |
4229 | if (sgn_x == 0) | |
c71b0706 MV |
4230 | return (SCM_FIXABLE (-yy) ? |
4231 | SCM_I_MAKINUM (-yy) : scm_from_long (-yy)); | |
0aacf84e MD |
4232 | else |
4233 | { | |
4234 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4235 | |
708f22c6 KR |
4236 | if (yy >= 0) |
4237 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
4238 | else | |
4239 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 4240 | scm_remember_upto_here_1 (x); |
ca46fb90 | 4241 | |
0aacf84e MD |
4242 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
4243 | /* we know the result will have to be a bignum */ | |
4244 | return result; | |
4245 | else | |
4246 | return scm_i_normbig (result); | |
4247 | } | |
4248 | } | |
4249 | else if (SCM_BIGP (y)) | |
4250 | { | |
4251 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4252 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4253 | SCM result = scm_i_mkbig (); | |
4254 | mpz_sub (SCM_I_BIG_MPZ (result), | |
4255 | SCM_I_BIG_MPZ (x), | |
4256 | SCM_I_BIG_MPZ (y)); | |
4257 | scm_remember_upto_here_2 (x, y); | |
4258 | /* we know the result will have to be a bignum */ | |
4259 | if ((sgn_x == 1) && (sgn_y == -1)) | |
4260 | return result; | |
4261 | if ((sgn_x == -1) && (sgn_y == 1)) | |
4262 | return result; | |
4263 | return scm_i_normbig (result); | |
4264 | } | |
4265 | else if (SCM_REALP (y)) | |
4266 | { | |
4267 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
4268 | scm_remember_upto_here_1 (x); | |
55f26379 | 4269 | return scm_from_double (result); |
0aacf84e MD |
4270 | } |
4271 | else if (SCM_COMPLEXP (y)) | |
4272 | { | |
4273 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4274 | - SCM_COMPLEX_REAL (y)); | |
4275 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4276 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4277 | } |
f92e85f7 | 4278 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4279 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4280 | SCM_FRACTION_NUMERATOR (y)), |
4281 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 4282 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 4283 | } |
0aacf84e MD |
4284 | else if (SCM_REALP (x)) |
4285 | { | |
e11e83f3 | 4286 | if (SCM_I_INUMP (y)) |
55f26379 | 4287 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
4288 | else if (SCM_BIGP (y)) |
4289 | { | |
4290 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4291 | scm_remember_upto_here_1 (x); | |
55f26379 | 4292 | return scm_from_double (result); |
0aacf84e MD |
4293 | } |
4294 | else if (SCM_REALP (y)) | |
55f26379 | 4295 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 4296 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4297 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4298 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4299 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4300 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
4301 | else |
4302 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4303 | } |
0aacf84e MD |
4304 | else if (SCM_COMPLEXP (x)) |
4305 | { | |
e11e83f3 | 4306 | if (SCM_I_INUMP (y)) |
8507ec80 | 4307 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
4308 | SCM_COMPLEX_IMAG (x)); |
4309 | else if (SCM_BIGP (y)) | |
4310 | { | |
4311 | double real_part = (SCM_COMPLEX_REAL (x) | |
4312 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
4313 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4314 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
4315 | } |
4316 | else if (SCM_REALP (y)) | |
8507ec80 | 4317 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
4318 | SCM_COMPLEX_IMAG (x)); |
4319 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4320 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4321 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4322 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4323 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
4324 | SCM_COMPLEX_IMAG (x)); |
4325 | else | |
4326 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
4327 | } | |
4328 | else if (SCM_FRACTIONP (x)) | |
4329 | { | |
e11e83f3 | 4330 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4331 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 4332 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4333 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4334 | SCM_FRACTION_DENOMINATOR (x)); | |
4335 | else if (SCM_BIGP (y)) | |
cba42c93 | 4336 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4337 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4338 | SCM_FRACTION_DENOMINATOR (x)); | |
4339 | else if (SCM_REALP (y)) | |
55f26379 | 4340 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 4341 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4342 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4343 | -SCM_COMPLEX_IMAG (y)); |
4344 | else if (SCM_FRACTIONP (y)) | |
4345 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 4346 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4347 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4348 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4349 | else |
4350 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4351 | } |
0aacf84e | 4352 | else |
98cb6e75 | 4353 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 4354 | } |
c05e97b7 | 4355 | #undef FUNC_NAME |
0f2d19dd | 4356 | |
ca46fb90 | 4357 | |
40882e3d KR |
4358 | SCM_DEFINE (scm_oneminus, "1-", 1, 0, 0, |
4359 | (SCM x), | |
4360 | "Return @math{@var{x}-1}.") | |
4361 | #define FUNC_NAME s_scm_oneminus | |
4362 | { | |
4363 | return scm_difference (x, SCM_I_MAKINUM (1)); | |
4364 | } | |
4365 | #undef FUNC_NAME | |
4366 | ||
4367 | ||
9de33deb | 4368 | SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product); |
942e5b91 MG |
4369 | /* "Return the product of all arguments. If called without arguments,\n" |
4370 | * "1 is returned." | |
4371 | */ | |
0f2d19dd | 4372 | SCM |
6e8d25a6 | 4373 | scm_product (SCM x, SCM y) |
0f2d19dd | 4374 | { |
0aacf84e MD |
4375 | if (SCM_UNBNDP (y)) |
4376 | { | |
4377 | if (SCM_UNBNDP (x)) | |
d956fa6f | 4378 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
4379 | else if (SCM_NUMBERP (x)) |
4380 | return x; | |
4381 | else | |
4382 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 4383 | } |
ca46fb90 | 4384 | |
e11e83f3 | 4385 | if (SCM_I_INUMP (x)) |
0aacf84e MD |
4386 | { |
4387 | long xx; | |
f4c627b3 | 4388 | |
0aacf84e | 4389 | intbig: |
e11e83f3 | 4390 | xx = SCM_I_INUM (x); |
f4c627b3 | 4391 | |
0aacf84e MD |
4392 | switch (xx) |
4393 | { | |
ca46fb90 RB |
4394 | case 0: return x; break; |
4395 | case 1: return y; break; | |
0aacf84e | 4396 | } |
f4c627b3 | 4397 | |
e11e83f3 | 4398 | if (SCM_I_INUMP (y)) |
0aacf84e | 4399 | { |
e11e83f3 | 4400 | long yy = SCM_I_INUM (y); |
0aacf84e | 4401 | long kk = xx * yy; |
d956fa6f | 4402 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 4403 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
4404 | return k; |
4405 | else | |
4406 | { | |
4407 | SCM result = scm_i_long2big (xx); | |
4408 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); | |
4409 | return scm_i_normbig (result); | |
4410 | } | |
4411 | } | |
4412 | else if (SCM_BIGP (y)) | |
4413 | { | |
4414 | SCM result = scm_i_mkbig (); | |
4415 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
4416 | scm_remember_upto_here_1 (y); | |
4417 | return result; | |
4418 | } | |
4419 | else if (SCM_REALP (y)) | |
55f26379 | 4420 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 4421 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4422 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 4423 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4424 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4425 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4426 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4427 | else |
4428 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4429 | } |
0aacf84e MD |
4430 | else if (SCM_BIGP (x)) |
4431 | { | |
e11e83f3 | 4432 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4433 | { |
4434 | SCM_SWAP (x, y); | |
4435 | goto intbig; | |
4436 | } | |
4437 | else if (SCM_BIGP (y)) | |
4438 | { | |
4439 | SCM result = scm_i_mkbig (); | |
4440 | mpz_mul (SCM_I_BIG_MPZ (result), | |
4441 | SCM_I_BIG_MPZ (x), | |
4442 | SCM_I_BIG_MPZ (y)); | |
4443 | scm_remember_upto_here_2 (x, y); | |
4444 | return result; | |
4445 | } | |
4446 | else if (SCM_REALP (y)) | |
4447 | { | |
4448 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
4449 | scm_remember_upto_here_1 (x); | |
55f26379 | 4450 | return scm_from_double (result); |
0aacf84e MD |
4451 | } |
4452 | else if (SCM_COMPLEXP (y)) | |
4453 | { | |
4454 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4455 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4456 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4457 | z * SCM_COMPLEX_IMAG (y)); |
4458 | } | |
f92e85f7 | 4459 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4460 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4461 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4462 | else |
4463 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4464 | } |
0aacf84e MD |
4465 | else if (SCM_REALP (x)) |
4466 | { | |
e11e83f3 | 4467 | if (SCM_I_INUMP (y)) |
55f26379 | 4468 | return scm_from_double (SCM_I_INUM (y) * SCM_REAL_VALUE (x)); |
0aacf84e MD |
4469 | else if (SCM_BIGP (y)) |
4470 | { | |
4471 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
4472 | scm_remember_upto_here_1 (y); | |
55f26379 | 4473 | return scm_from_double (result); |
0aacf84e MD |
4474 | } |
4475 | else if (SCM_REALP (y)) | |
55f26379 | 4476 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 4477 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4478 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 4479 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4480 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4481 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
4482 | else |
4483 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4484 | } |
0aacf84e MD |
4485 | else if (SCM_COMPLEXP (x)) |
4486 | { | |
e11e83f3 | 4487 | if (SCM_I_INUMP (y)) |
8507ec80 | 4488 | return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x), |
e11e83f3 | 4489 | SCM_I_INUM (y) * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4490 | else if (SCM_BIGP (y)) |
4491 | { | |
4492 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4493 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4494 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 4495 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4496 | } |
4497 | else if (SCM_REALP (y)) | |
8507ec80 | 4498 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
4499 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
4500 | else if (SCM_COMPLEXP (y)) | |
4501 | { | |
8507ec80 | 4502 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
4503 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
4504 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
4505 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
4506 | } | |
f92e85f7 MV |
4507 | else if (SCM_FRACTIONP (y)) |
4508 | { | |
4509 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4510 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
4511 | yy * SCM_COMPLEX_IMAG (x)); |
4512 | } | |
4513 | else | |
4514 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
4515 | } | |
4516 | else if (SCM_FRACTIONP (x)) | |
4517 | { | |
e11e83f3 | 4518 | if (SCM_I_INUMP (y)) |
cba42c93 | 4519 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4520 | SCM_FRACTION_DENOMINATOR (x)); |
4521 | else if (SCM_BIGP (y)) | |
cba42c93 | 4522 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4523 | SCM_FRACTION_DENOMINATOR (x)); |
4524 | else if (SCM_REALP (y)) | |
55f26379 | 4525 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
4526 | else if (SCM_COMPLEXP (y)) |
4527 | { | |
4528 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 4529 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4530 | xx * SCM_COMPLEX_IMAG (y)); |
4531 | } | |
4532 | else if (SCM_FRACTIONP (y)) | |
4533 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 4534 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4535 | SCM_FRACTION_NUMERATOR (y)), |
4536 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
4537 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4538 | else |
4539 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4540 | } |
0aacf84e | 4541 | else |
f4c627b3 | 4542 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
4543 | } |
4544 | ||
7351e207 MV |
4545 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
4546 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
4547 | #define ALLOW_DIVIDE_BY_ZERO | |
4548 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
4549 | #endif | |
0f2d19dd | 4550 | |
ba74ef4e MV |
4551 | /* The code below for complex division is adapted from the GNU |
4552 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
4553 | this copyright: */ | |
4554 | ||
4555 | /**************************************************************** | |
4556 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
4557 | ||
4558 | Permission to use, copy, modify, and distribute this software | |
4559 | and its documentation for any purpose and without fee is hereby | |
4560 | granted, provided that the above copyright notice appear in all | |
4561 | copies and that both that the copyright notice and this | |
4562 | permission notice and warranty disclaimer appear in supporting | |
4563 | documentation, and that the names of AT&T Bell Laboratories or | |
4564 | Bellcore or any of their entities not be used in advertising or | |
4565 | publicity pertaining to distribution of the software without | |
4566 | specific, written prior permission. | |
4567 | ||
4568 | AT&T and Bellcore disclaim all warranties with regard to this | |
4569 | software, including all implied warranties of merchantability | |
4570 | and fitness. In no event shall AT&T or Bellcore be liable for | |
4571 | any special, indirect or consequential damages or any damages | |
4572 | whatsoever resulting from loss of use, data or profits, whether | |
4573 | in an action of contract, negligence or other tortious action, | |
4574 | arising out of or in connection with the use or performance of | |
4575 | this software. | |
4576 | ****************************************************************/ | |
4577 | ||
9de33deb | 4578 | SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide); |
609c3d30 MG |
4579 | /* Divide the first argument by the product of the remaining |
4580 | arguments. If called with one argument @var{z1}, 1/@var{z1} is | |
4581 | returned. */ | |
c05e97b7 | 4582 | #define FUNC_NAME s_divide |
f92e85f7 MV |
4583 | static SCM |
4584 | scm_i_divide (SCM x, SCM y, int inexact) | |
0f2d19dd | 4585 | { |
f8de44c1 DH |
4586 | double a; |
4587 | ||
0aacf84e MD |
4588 | if (SCM_UNBNDP (y)) |
4589 | { | |
4590 | if (SCM_UNBNDP (x)) | |
4591 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 4592 | else if (SCM_I_INUMP (x)) |
0aacf84e | 4593 | { |
e11e83f3 | 4594 | long xx = SCM_I_INUM (x); |
0aacf84e MD |
4595 | if (xx == 1 || xx == -1) |
4596 | return x; | |
7351e207 | 4597 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4598 | else if (xx == 0) |
4599 | scm_num_overflow (s_divide); | |
7351e207 | 4600 | #endif |
0aacf84e | 4601 | else |
f92e85f7 MV |
4602 | { |
4603 | if (inexact) | |
55f26379 | 4604 | return scm_from_double (1.0 / (double) xx); |
cba42c93 | 4605 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4606 | } |
0aacf84e MD |
4607 | } |
4608 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
4609 | { |
4610 | if (inexact) | |
55f26379 | 4611 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cba42c93 | 4612 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4613 | } |
0aacf84e MD |
4614 | else if (SCM_REALP (x)) |
4615 | { | |
4616 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 4617 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4618 | if (xx == 0.0) |
4619 | scm_num_overflow (s_divide); | |
4620 | else | |
7351e207 | 4621 | #endif |
55f26379 | 4622 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
4623 | } |
4624 | else if (SCM_COMPLEXP (x)) | |
4625 | { | |
4626 | double r = SCM_COMPLEX_REAL (x); | |
4627 | double i = SCM_COMPLEX_IMAG (x); | |
4c6e36a6 | 4628 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
4629 | { |
4630 | double t = r / i; | |
4631 | double d = i * (1.0 + t * t); | |
8507ec80 | 4632 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
4633 | } |
4634 | else | |
4635 | { | |
4636 | double t = i / r; | |
4637 | double d = r * (1.0 + t * t); | |
8507ec80 | 4638 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
4639 | } |
4640 | } | |
f92e85f7 | 4641 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4642 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 4643 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
4644 | else |
4645 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 4646 | } |
f8de44c1 | 4647 | |
e11e83f3 | 4648 | if (SCM_I_INUMP (x)) |
0aacf84e | 4649 | { |
e11e83f3 MV |
4650 | long xx = SCM_I_INUM (x); |
4651 | if (SCM_I_INUMP (y)) | |
0aacf84e | 4652 | { |
e11e83f3 | 4653 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
4654 | if (yy == 0) |
4655 | { | |
7351e207 | 4656 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4657 | scm_num_overflow (s_divide); |
7351e207 | 4658 | #else |
55f26379 | 4659 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 4660 | #endif |
0aacf84e MD |
4661 | } |
4662 | else if (xx % yy != 0) | |
f92e85f7 MV |
4663 | { |
4664 | if (inexact) | |
55f26379 | 4665 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 4666 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4667 | } |
0aacf84e MD |
4668 | else |
4669 | { | |
4670 | long z = xx / yy; | |
4671 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4672 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4673 | else |
4674 | return scm_i_long2big (z); | |
4675 | } | |
f872b822 | 4676 | } |
0aacf84e | 4677 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
4678 | { |
4679 | if (inexact) | |
55f26379 | 4680 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 4681 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4682 | } |
0aacf84e MD |
4683 | else if (SCM_REALP (y)) |
4684 | { | |
4685 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4686 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4687 | if (yy == 0.0) |
4688 | scm_num_overflow (s_divide); | |
4689 | else | |
7351e207 | 4690 | #endif |
55f26379 | 4691 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 4692 | } |
0aacf84e MD |
4693 | else if (SCM_COMPLEXP (y)) |
4694 | { | |
4695 | a = xx; | |
4696 | complex_div: /* y _must_ be a complex number */ | |
4697 | { | |
4698 | double r = SCM_COMPLEX_REAL (y); | |
4699 | double i = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 4700 | if (fabs(r) <= fabs(i)) |
0aacf84e MD |
4701 | { |
4702 | double t = r / i; | |
4703 | double d = i * (1.0 + t * t); | |
8507ec80 | 4704 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
4705 | } |
4706 | else | |
4707 | { | |
4708 | double t = i / r; | |
4709 | double d = r * (1.0 + t * t); | |
8507ec80 | 4710 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
4711 | } |
4712 | } | |
4713 | } | |
f92e85f7 MV |
4714 | else if (SCM_FRACTIONP (y)) |
4715 | /* a / b/c = ac / b */ | |
cba42c93 | 4716 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4717 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4718 | else |
4719 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4720 | } |
0aacf84e MD |
4721 | else if (SCM_BIGP (x)) |
4722 | { | |
e11e83f3 | 4723 | if (SCM_I_INUMP (y)) |
0aacf84e | 4724 | { |
e11e83f3 | 4725 | long int yy = SCM_I_INUM (y); |
0aacf84e MD |
4726 | if (yy == 0) |
4727 | { | |
7351e207 | 4728 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4729 | scm_num_overflow (s_divide); |
7351e207 | 4730 | #else |
0aacf84e MD |
4731 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4732 | scm_remember_upto_here_1 (x); | |
4733 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 4734 | #endif |
0aacf84e MD |
4735 | } |
4736 | else if (yy == 1) | |
4737 | return x; | |
4738 | else | |
4739 | { | |
4740 | /* FIXME: HMM, what are the relative performance issues here? | |
4741 | We need to test. Is it faster on average to test | |
4742 | divisible_p, then perform whichever operation, or is it | |
4743 | faster to perform the integer div opportunistically and | |
4744 | switch to real if there's a remainder? For now we take the | |
4745 | middle ground: test, then if divisible, use the faster div | |
4746 | func. */ | |
4747 | ||
4748 | long abs_yy = yy < 0 ? -yy : yy; | |
4749 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); | |
4750 | ||
4751 | if (divisible_p) | |
4752 | { | |
4753 | SCM result = scm_i_mkbig (); | |
4754 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
4755 | scm_remember_upto_here_1 (x); | |
4756 | if (yy < 0) | |
4757 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4758 | return scm_i_normbig (result); | |
4759 | } | |
4760 | else | |
f92e85f7 MV |
4761 | { |
4762 | if (inexact) | |
55f26379 | 4763 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 4764 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4765 | } |
0aacf84e MD |
4766 | } |
4767 | } | |
4768 | else if (SCM_BIGP (y)) | |
4769 | { | |
4770 | int y_is_zero = (mpz_sgn (SCM_I_BIG_MPZ (y)) == 0); | |
4771 | if (y_is_zero) | |
4772 | { | |
ca46fb90 | 4773 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4774 | scm_num_overflow (s_divide); |
f872b822 | 4775 | #else |
0aacf84e MD |
4776 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4777 | scm_remember_upto_here_1 (x); | |
4778 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
f872b822 | 4779 | #endif |
0aacf84e MD |
4780 | } |
4781 | else | |
4782 | { | |
4783 | /* big_x / big_y */ | |
23f2b9a3 KR |
4784 | if (inexact) |
4785 | { | |
4786 | /* It's easily possible for the ratio x/y to fit a double | |
4787 | but one or both x and y be too big to fit a double, | |
4788 | hence the use of mpq_get_d rather than converting and | |
4789 | dividing. */ | |
4790 | mpq_t q; | |
4791 | *mpq_numref(q) = *SCM_I_BIG_MPZ (x); | |
4792 | *mpq_denref(q) = *SCM_I_BIG_MPZ (y); | |
4793 | return scm_from_double (mpq_get_d (q)); | |
4794 | } | |
4795 | else | |
4796 | { | |
4797 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), | |
4798 | SCM_I_BIG_MPZ (y)); | |
4799 | if (divisible_p) | |
4800 | { | |
4801 | SCM result = scm_i_mkbig (); | |
4802 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
4803 | SCM_I_BIG_MPZ (x), | |
4804 | SCM_I_BIG_MPZ (y)); | |
4805 | scm_remember_upto_here_2 (x, y); | |
4806 | return scm_i_normbig (result); | |
4807 | } | |
4808 | else | |
4809 | return scm_i_make_ratio (x, y); | |
4810 | } | |
0aacf84e MD |
4811 | } |
4812 | } | |
4813 | else if (SCM_REALP (y)) | |
4814 | { | |
4815 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4816 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4817 | if (yy == 0.0) |
4818 | scm_num_overflow (s_divide); | |
4819 | else | |
7351e207 | 4820 | #endif |
55f26379 | 4821 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
4822 | } |
4823 | else if (SCM_COMPLEXP (y)) | |
4824 | { | |
4825 | a = scm_i_big2dbl (x); | |
4826 | goto complex_div; | |
4827 | } | |
f92e85f7 | 4828 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4829 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4830 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4831 | else |
4832 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4833 | } |
0aacf84e MD |
4834 | else if (SCM_REALP (x)) |
4835 | { | |
4836 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 4837 | if (SCM_I_INUMP (y)) |
0aacf84e | 4838 | { |
e11e83f3 | 4839 | long int yy = SCM_I_INUM (y); |
7351e207 | 4840 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4841 | if (yy == 0) |
4842 | scm_num_overflow (s_divide); | |
4843 | else | |
7351e207 | 4844 | #endif |
55f26379 | 4845 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
4846 | } |
4847 | else if (SCM_BIGP (y)) | |
4848 | { | |
4849 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4850 | scm_remember_upto_here_1 (y); | |
55f26379 | 4851 | return scm_from_double (rx / dby); |
0aacf84e MD |
4852 | } |
4853 | else if (SCM_REALP (y)) | |
4854 | { | |
4855 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4856 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4857 | if (yy == 0.0) |
4858 | scm_num_overflow (s_divide); | |
4859 | else | |
7351e207 | 4860 | #endif |
55f26379 | 4861 | return scm_from_double (rx / yy); |
0aacf84e MD |
4862 | } |
4863 | else if (SCM_COMPLEXP (y)) | |
4864 | { | |
4865 | a = rx; | |
4866 | goto complex_div; | |
4867 | } | |
f92e85f7 | 4868 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4869 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
4870 | else |
4871 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4872 | } |
0aacf84e MD |
4873 | else if (SCM_COMPLEXP (x)) |
4874 | { | |
4875 | double rx = SCM_COMPLEX_REAL (x); | |
4876 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 4877 | if (SCM_I_INUMP (y)) |
0aacf84e | 4878 | { |
e11e83f3 | 4879 | long int yy = SCM_I_INUM (y); |
7351e207 | 4880 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4881 | if (yy == 0) |
4882 | scm_num_overflow (s_divide); | |
4883 | else | |
7351e207 | 4884 | #endif |
0aacf84e MD |
4885 | { |
4886 | double d = yy; | |
8507ec80 | 4887 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
4888 | } |
4889 | } | |
4890 | else if (SCM_BIGP (y)) | |
4891 | { | |
4892 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4893 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4894 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
4895 | } |
4896 | else if (SCM_REALP (y)) | |
4897 | { | |
4898 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4899 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4900 | if (yy == 0.0) |
4901 | scm_num_overflow (s_divide); | |
4902 | else | |
7351e207 | 4903 | #endif |
8507ec80 | 4904 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
4905 | } |
4906 | else if (SCM_COMPLEXP (y)) | |
4907 | { | |
4908 | double ry = SCM_COMPLEX_REAL (y); | |
4909 | double iy = SCM_COMPLEX_IMAG (y); | |
4c6e36a6 | 4910 | if (fabs(ry) <= fabs(iy)) |
0aacf84e MD |
4911 | { |
4912 | double t = ry / iy; | |
4913 | double d = iy * (1.0 + t * t); | |
8507ec80 | 4914 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
4915 | } |
4916 | else | |
4917 | { | |
4918 | double t = iy / ry; | |
4919 | double d = ry * (1.0 + t * t); | |
8507ec80 | 4920 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
4921 | } |
4922 | } | |
f92e85f7 MV |
4923 | else if (SCM_FRACTIONP (y)) |
4924 | { | |
4925 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4926 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 4927 | } |
0aacf84e MD |
4928 | else |
4929 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4930 | } |
f92e85f7 MV |
4931 | else if (SCM_FRACTIONP (x)) |
4932 | { | |
e11e83f3 | 4933 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4934 | { |
e11e83f3 | 4935 | long int yy = SCM_I_INUM (y); |
f92e85f7 MV |
4936 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
4937 | if (yy == 0) | |
4938 | scm_num_overflow (s_divide); | |
4939 | else | |
4940 | #endif | |
cba42c93 | 4941 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4942 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4943 | } | |
4944 | else if (SCM_BIGP (y)) | |
4945 | { | |
cba42c93 | 4946 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4947 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4948 | } | |
4949 | else if (SCM_REALP (y)) | |
4950 | { | |
4951 | double yy = SCM_REAL_VALUE (y); | |
4952 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
4953 | if (yy == 0.0) | |
4954 | scm_num_overflow (s_divide); | |
4955 | else | |
4956 | #endif | |
55f26379 | 4957 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
4958 | } |
4959 | else if (SCM_COMPLEXP (y)) | |
4960 | { | |
4961 | a = scm_i_fraction2double (x); | |
4962 | goto complex_div; | |
4963 | } | |
4964 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 4965 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4966 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
4967 | else | |
4968 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
4969 | } | |
0aacf84e | 4970 | else |
f8de44c1 | 4971 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 4972 | } |
f92e85f7 MV |
4973 | |
4974 | SCM | |
4975 | scm_divide (SCM x, SCM y) | |
4976 | { | |
4977 | return scm_i_divide (x, y, 0); | |
4978 | } | |
4979 | ||
4980 | static SCM scm_divide2real (SCM x, SCM y) | |
4981 | { | |
4982 | return scm_i_divide (x, y, 1); | |
4983 | } | |
c05e97b7 | 4984 | #undef FUNC_NAME |
0f2d19dd | 4985 | |
fa605590 | 4986 | |
0f2d19dd | 4987 | double |
6e8d25a6 | 4988 | scm_asinh (double x) |
0f2d19dd | 4989 | { |
fa605590 KR |
4990 | #if HAVE_ASINH |
4991 | return asinh (x); | |
4992 | #else | |
4993 | #define asinh scm_asinh | |
f872b822 | 4994 | return log (x + sqrt (x * x + 1)); |
fa605590 | 4995 | #endif |
0f2d19dd | 4996 | } |
fa605590 KR |
4997 | SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_dsubr, (SCM (*)()) asinh, g_asinh); |
4998 | /* "Return the inverse hyperbolic sine of @var{x}." | |
4999 | */ | |
0f2d19dd JB |
5000 | |
5001 | ||
0f2d19dd | 5002 | double |
6e8d25a6 | 5003 | scm_acosh (double x) |
0f2d19dd | 5004 | { |
fa605590 KR |
5005 | #if HAVE_ACOSH |
5006 | return acosh (x); | |
5007 | #else | |
5008 | #define acosh scm_acosh | |
f872b822 | 5009 | return log (x + sqrt (x * x - 1)); |
fa605590 | 5010 | #endif |
0f2d19dd | 5011 | } |
fa605590 KR |
5012 | SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_dsubr, (SCM (*)()) acosh, g_acosh); |
5013 | /* "Return the inverse hyperbolic cosine of @var{x}." | |
5014 | */ | |
0f2d19dd JB |
5015 | |
5016 | ||
0f2d19dd | 5017 | double |
6e8d25a6 | 5018 | scm_atanh (double x) |
0f2d19dd | 5019 | { |
fa605590 KR |
5020 | #if HAVE_ATANH |
5021 | return atanh (x); | |
5022 | #else | |
5023 | #define atanh scm_atanh | |
f872b822 | 5024 | return 0.5 * log ((1 + x) / (1 - x)); |
fa605590 | 5025 | #endif |
0f2d19dd | 5026 | } |
fa605590 KR |
5027 | SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_dsubr, (SCM (*)()) atanh, g_atanh); |
5028 | /* "Return the inverse hyperbolic tangent of @var{x}." | |
5029 | */ | |
0f2d19dd JB |
5030 | |
5031 | ||
0f2d19dd | 5032 | double |
3101f40f | 5033 | scm_c_truncate (double x) |
0f2d19dd | 5034 | { |
fa605590 KR |
5035 | #if HAVE_TRUNC |
5036 | return trunc (x); | |
5037 | #else | |
f872b822 MD |
5038 | if (x < 0.0) |
5039 | return -floor (-x); | |
5040 | return floor (x); | |
fa605590 | 5041 | #endif |
0f2d19dd | 5042 | } |
0f2d19dd | 5043 | |
3101f40f MV |
5044 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
5045 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
5046 | Then half-way cases are identified and adjusted down if the | |
5047 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
5048 | |
5049 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
5050 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
5051 | ||
5052 | An odd "result" value is identified with result/2 != floor(result/2). | |
5053 | This is done with plus_half, since that value is ready for use sooner in | |
5054 | a pipelined cpu, and we're already requiring plus_half == result. | |
5055 | ||
5056 | Note however that we need to be careful when x is big and already an | |
5057 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
5058 | us to return such a value, incorrectly. For instance if the hardware is | |
5059 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
5060 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
5061 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
5062 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
5063 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
5064 | ||
5065 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
5066 | x is already an integer. If it is then clearly that's the desired result | |
5067 | already. And if it's not then the exponent must be small enough to allow | |
5068 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
5069 | ||
0f2d19dd | 5070 | double |
3101f40f | 5071 | scm_c_round (double x) |
0f2d19dd | 5072 | { |
6187f48b KR |
5073 | double plus_half, result; |
5074 | ||
5075 | if (x == floor (x)) | |
5076 | return x; | |
5077 | ||
5078 | plus_half = x + 0.5; | |
5079 | result = floor (plus_half); | |
3101f40f | 5080 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
5081 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
5082 | ? result - 1 | |
5083 | : result); | |
0f2d19dd JB |
5084 | } |
5085 | ||
f92e85f7 MV |
5086 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
5087 | (SCM x), | |
5088 | "Round the number @var{x} towards zero.") | |
5089 | #define FUNC_NAME s_scm_truncate_number | |
5090 | { | |
73e4de09 | 5091 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5092 | return scm_floor (x); |
5093 | else | |
5094 | return scm_ceiling (x); | |
5095 | } | |
5096 | #undef FUNC_NAME | |
5097 | ||
5098 | static SCM exactly_one_half; | |
5099 | ||
5100 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, | |
5101 | (SCM x), | |
5102 | "Round the number @var{x} towards the nearest integer. " | |
5103 | "When it is exactly halfway between two integers, " | |
5104 | "round towards the even one.") | |
5105 | #define FUNC_NAME s_scm_round_number | |
5106 | { | |
e11e83f3 | 5107 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
5108 | return x; |
5109 | else if (SCM_REALP (x)) | |
3101f40f | 5110 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 5111 | else |
bae30667 KR |
5112 | { |
5113 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
5114 | single quotient+remainder division then examining to see which way | |
5115 | the rounding should go. */ | |
5116 | SCM plus_half = scm_sum (x, exactly_one_half); | |
5117 | SCM result = scm_floor (plus_half); | |
3101f40f | 5118 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
5119 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
5120 | && scm_is_true (scm_odd_p (result))) | |
d956fa6f | 5121 | return scm_difference (result, SCM_I_MAKINUM (1)); |
bae30667 KR |
5122 | else |
5123 | return result; | |
5124 | } | |
f92e85f7 MV |
5125 | } |
5126 | #undef FUNC_NAME | |
5127 | ||
5128 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
5129 | (SCM x), | |
5130 | "Round the number @var{x} towards minus infinity.") | |
5131 | #define FUNC_NAME s_scm_floor | |
5132 | { | |
e11e83f3 | 5133 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5134 | return x; |
5135 | else if (SCM_REALP (x)) | |
55f26379 | 5136 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5137 | else if (SCM_FRACTIONP (x)) |
5138 | { | |
5139 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5140 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5141 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5142 | { |
5143 | /* For positive x, rounding towards zero is correct. */ | |
5144 | return q; | |
5145 | } | |
5146 | else | |
5147 | { | |
5148 | /* For negative x, we need to return q-1 unless x is an | |
5149 | integer. But fractions are never integer, per our | |
5150 | assumptions. */ | |
d956fa6f | 5151 | return scm_difference (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5152 | } |
5153 | } | |
5154 | else | |
5155 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
5156 | } | |
5157 | #undef FUNC_NAME | |
5158 | ||
5159 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
5160 | (SCM x), | |
5161 | "Round the number @var{x} towards infinity.") | |
5162 | #define FUNC_NAME s_scm_ceiling | |
5163 | { | |
e11e83f3 | 5164 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5165 | return x; |
5166 | else if (SCM_REALP (x)) | |
55f26379 | 5167 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5168 | else if (SCM_FRACTIONP (x)) |
5169 | { | |
5170 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5171 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5172 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
5173 | { |
5174 | /* For negative x, rounding towards zero is correct. */ | |
5175 | return q; | |
5176 | } | |
5177 | else | |
5178 | { | |
5179 | /* For positive x, we need to return q+1 unless x is an | |
5180 | integer. But fractions are never integer, per our | |
5181 | assumptions. */ | |
d956fa6f | 5182 | return scm_sum (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5183 | } |
5184 | } | |
5185 | else | |
5186 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
5187 | } | |
5188 | #undef FUNC_NAME | |
0f2d19dd | 5189 | |
14b18ed6 | 5190 | SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_dsubr, (SCM (*)()) sqrt, g_i_sqrt); |
942e5b91 MG |
5191 | /* "Return the square root of the real number @var{x}." |
5192 | */ | |
14b18ed6 | 5193 | SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_dsubr, (SCM (*)()) fabs, g_i_abs); |
942e5b91 MG |
5194 | /* "Return the absolute value of the real number @var{x}." |
5195 | */ | |
14b18ed6 | 5196 | SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_dsubr, (SCM (*)()) exp, g_i_exp); |
942e5b91 MG |
5197 | /* "Return the @var{x}th power of e." |
5198 | */ | |
14b18ed6 | 5199 | SCM_GPROC1 (s_i_log, "$log", scm_tc7_dsubr, (SCM (*)()) log, g_i_log); |
b3fcac34 | 5200 | /* "Return the natural logarithm of the real number @var{x}." |
942e5b91 | 5201 | */ |
14b18ed6 | 5202 | SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_dsubr, (SCM (*)()) sin, g_i_sin); |
942e5b91 MG |
5203 | /* "Return the sine of the real number @var{x}." |
5204 | */ | |
14b18ed6 | 5205 | SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_dsubr, (SCM (*)()) cos, g_i_cos); |
942e5b91 MG |
5206 | /* "Return the cosine of the real number @var{x}." |
5207 | */ | |
14b18ed6 | 5208 | SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_dsubr, (SCM (*)()) tan, g_i_tan); |
942e5b91 MG |
5209 | /* "Return the tangent of the real number @var{x}." |
5210 | */ | |
14b18ed6 | 5211 | SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_dsubr, (SCM (*)()) asin, g_i_asin); |
942e5b91 MG |
5212 | /* "Return the arc sine of the real number @var{x}." |
5213 | */ | |
14b18ed6 | 5214 | SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_dsubr, (SCM (*)()) acos, g_i_acos); |
942e5b91 MG |
5215 | /* "Return the arc cosine of the real number @var{x}." |
5216 | */ | |
14b18ed6 | 5217 | SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_dsubr, (SCM (*)()) atan, g_i_atan); |
942e5b91 MG |
5218 | /* "Return the arc tangent of the real number @var{x}." |
5219 | */ | |
14b18ed6 | 5220 | SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_dsubr, (SCM (*)()) sinh, g_i_sinh); |
942e5b91 MG |
5221 | /* "Return the hyperbolic sine of the real number @var{x}." |
5222 | */ | |
14b18ed6 | 5223 | SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_dsubr, (SCM (*)()) cosh, g_i_cosh); |
942e5b91 MG |
5224 | /* "Return the hyperbolic cosine of the real number @var{x}." |
5225 | */ | |
14b18ed6 | 5226 | SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_dsubr, (SCM (*)()) tanh, g_i_tanh); |
942e5b91 MG |
5227 | /* "Return the hyperbolic tangent of the real number @var{x}." |
5228 | */ | |
f872b822 MD |
5229 | |
5230 | struct dpair | |
5231 | { | |
5232 | double x, y; | |
5233 | }; | |
5234 | ||
27c37006 NJ |
5235 | static void scm_two_doubles (SCM x, |
5236 | SCM y, | |
3eeba8d4 JB |
5237 | const char *sstring, |
5238 | struct dpair * xy); | |
f872b822 MD |
5239 | |
5240 | static void | |
27c37006 NJ |
5241 | scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy) |
5242 | { | |
e11e83f3 MV |
5243 | if (SCM_I_INUMP (x)) |
5244 | xy->x = SCM_I_INUM (x); | |
0aacf84e | 5245 | else if (SCM_BIGP (x)) |
1be6b49c | 5246 | xy->x = scm_i_big2dbl (x); |
0aacf84e | 5247 | else if (SCM_REALP (x)) |
27c37006 | 5248 | xy->x = SCM_REAL_VALUE (x); |
f92e85f7 MV |
5249 | else if (SCM_FRACTIONP (x)) |
5250 | xy->x = scm_i_fraction2double (x); | |
0aacf84e | 5251 | else |
27c37006 | 5252 | scm_wrong_type_arg (sstring, SCM_ARG1, x); |
98cb6e75 | 5253 | |
e11e83f3 MV |
5254 | if (SCM_I_INUMP (y)) |
5255 | xy->y = SCM_I_INUM (y); | |
0aacf84e | 5256 | else if (SCM_BIGP (y)) |
1be6b49c | 5257 | xy->y = scm_i_big2dbl (y); |
0aacf84e | 5258 | else if (SCM_REALP (y)) |
27c37006 | 5259 | xy->y = SCM_REAL_VALUE (y); |
f92e85f7 MV |
5260 | else if (SCM_FRACTIONP (y)) |
5261 | xy->y = scm_i_fraction2double (y); | |
0aacf84e | 5262 | else |
27c37006 | 5263 | scm_wrong_type_arg (sstring, SCM_ARG2, y); |
0f2d19dd JB |
5264 | } |
5265 | ||
5266 | ||
a1ec6916 | 5267 | SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0, |
27c37006 NJ |
5268 | (SCM x, SCM y), |
5269 | "Return @var{x} raised to the power of @var{y}. This\n" | |
0137a31b | 5270 | "procedure does not accept complex arguments.") |
1bbd0b84 | 5271 | #define FUNC_NAME s_scm_sys_expt |
0f2d19dd JB |
5272 | { |
5273 | struct dpair xy; | |
27c37006 | 5274 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5275 | return scm_from_double (pow (xy.x, xy.y)); |
0f2d19dd | 5276 | } |
1bbd0b84 | 5277 | #undef FUNC_NAME |
0f2d19dd JB |
5278 | |
5279 | ||
a1ec6916 | 5280 | SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0, |
27c37006 NJ |
5281 | (SCM x, SCM y), |
5282 | "Return the arc tangent of the two arguments @var{x} and\n" | |
5283 | "@var{y}. This is similar to calculating the arc tangent of\n" | |
5284 | "@var{x} / @var{y}, except that the signs of both arguments\n" | |
0137a31b MG |
5285 | "are used to determine the quadrant of the result. This\n" |
5286 | "procedure does not accept complex arguments.") | |
1bbd0b84 | 5287 | #define FUNC_NAME s_scm_sys_atan2 |
0f2d19dd JB |
5288 | { |
5289 | struct dpair xy; | |
27c37006 | 5290 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5291 | return scm_from_double (atan2 (xy.x, xy.y)); |
0f2d19dd | 5292 | } |
1bbd0b84 | 5293 | #undef FUNC_NAME |
0f2d19dd | 5294 | |
8507ec80 MV |
5295 | SCM |
5296 | scm_c_make_rectangular (double re, double im) | |
5297 | { | |
5298 | if (im == 0.0) | |
5299 | return scm_from_double (re); | |
5300 | else | |
5301 | { | |
5302 | SCM z; | |
5303 | SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (sizeof (scm_t_complex), | |
5304 | "complex")); | |
5305 | SCM_COMPLEX_REAL (z) = re; | |
5306 | SCM_COMPLEX_IMAG (z) = im; | |
5307 | return z; | |
5308 | } | |
5309 | } | |
0f2d19dd | 5310 | |
a1ec6916 | 5311 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
bb628794 | 5312 | (SCM real, SCM imaginary), |
942e5b91 MG |
5313 | "Return a complex number constructed of the given @var{real} and\n" |
5314 | "@var{imaginary} parts.") | |
1bbd0b84 | 5315 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd JB |
5316 | { |
5317 | struct dpair xy; | |
bb628794 | 5318 | scm_two_doubles (real, imaginary, FUNC_NAME, &xy); |
8507ec80 | 5319 | return scm_c_make_rectangular (xy.x, xy.y); |
0f2d19dd | 5320 | } |
1bbd0b84 | 5321 | #undef FUNC_NAME |
0f2d19dd | 5322 | |
8507ec80 MV |
5323 | SCM |
5324 | scm_c_make_polar (double mag, double ang) | |
5325 | { | |
5326 | double s, c; | |
5327 | #if HAVE_SINCOS | |
5328 | sincos (ang, &s, &c); | |
5329 | #else | |
5330 | s = sin (ang); | |
5331 | c = cos (ang); | |
5332 | #endif | |
5333 | return scm_c_make_rectangular (mag * c, mag * s); | |
5334 | } | |
0f2d19dd | 5335 | |
a1ec6916 | 5336 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 5337 | (SCM x, SCM y), |
942e5b91 | 5338 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 5339 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd JB |
5340 | { |
5341 | struct dpair xy; | |
27c37006 | 5342 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
8507ec80 | 5343 | return scm_c_make_polar (xy.x, xy.y); |
0f2d19dd | 5344 | } |
1bbd0b84 | 5345 | #undef FUNC_NAME |
0f2d19dd JB |
5346 | |
5347 | ||
152f82bf | 5348 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
5349 | /* "Return the real part of the number @var{z}." |
5350 | */ | |
0f2d19dd | 5351 | SCM |
6e8d25a6 | 5352 | scm_real_part (SCM z) |
0f2d19dd | 5353 | { |
e11e83f3 | 5354 | if (SCM_I_INUMP (z)) |
c2ff8ab0 | 5355 | return z; |
0aacf84e | 5356 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5357 | return z; |
0aacf84e | 5358 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5359 | return z; |
0aacf84e | 5360 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5361 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
f92e85f7 | 5362 | else if (SCM_FRACTIONP (z)) |
2fa2d879 | 5363 | return z; |
0aacf84e | 5364 | else |
c2ff8ab0 | 5365 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); |
0f2d19dd JB |
5366 | } |
5367 | ||
5368 | ||
152f82bf | 5369 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
5370 | /* "Return the imaginary part of the number @var{z}." |
5371 | */ | |
0f2d19dd | 5372 | SCM |
6e8d25a6 | 5373 | scm_imag_part (SCM z) |
0f2d19dd | 5374 | { |
e11e83f3 | 5375 | if (SCM_I_INUMP (z)) |
f872b822 | 5376 | return SCM_INUM0; |
0aacf84e | 5377 | else if (SCM_BIGP (z)) |
f872b822 | 5378 | return SCM_INUM0; |
0aacf84e | 5379 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5380 | return scm_flo0; |
0aacf84e | 5381 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5382 | return scm_from_double (SCM_COMPLEX_IMAG (z)); |
f92e85f7 MV |
5383 | else if (SCM_FRACTIONP (z)) |
5384 | return SCM_INUM0; | |
0aacf84e | 5385 | else |
c2ff8ab0 | 5386 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); |
0f2d19dd JB |
5387 | } |
5388 | ||
f92e85f7 MV |
5389 | SCM_GPROC (s_numerator, "numerator", 1, 0, 0, scm_numerator, g_numerator); |
5390 | /* "Return the numerator of the number @var{z}." | |
5391 | */ | |
5392 | SCM | |
5393 | scm_numerator (SCM z) | |
5394 | { | |
e11e83f3 | 5395 | if (SCM_I_INUMP (z)) |
f92e85f7 MV |
5396 | return z; |
5397 | else if (SCM_BIGP (z)) | |
5398 | return z; | |
5399 | else if (SCM_FRACTIONP (z)) | |
5400 | { | |
5401 | scm_i_fraction_reduce (z); | |
5402 | return SCM_FRACTION_NUMERATOR (z); | |
5403 | } | |
5404 | else if (SCM_REALP (z)) | |
5405 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
5406 | else | |
5407 | SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator); | |
5408 | } | |
5409 | ||
5410 | ||
5411 | SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator); | |
5412 | /* "Return the denominator of the number @var{z}." | |
5413 | */ | |
5414 | SCM | |
5415 | scm_denominator (SCM z) | |
5416 | { | |
e11e83f3 | 5417 | if (SCM_I_INUMP (z)) |
d956fa6f | 5418 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5419 | else if (SCM_BIGP (z)) |
d956fa6f | 5420 | return SCM_I_MAKINUM (1); |
f92e85f7 MV |
5421 | else if (SCM_FRACTIONP (z)) |
5422 | { | |
5423 | scm_i_fraction_reduce (z); | |
5424 | return SCM_FRACTION_DENOMINATOR (z); | |
5425 | } | |
5426 | else if (SCM_REALP (z)) | |
5427 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
5428 | else | |
5429 | SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator); | |
5430 | } | |
0f2d19dd | 5431 | |
9de33deb | 5432 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
5433 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
5434 | * "@code{abs} for real arguments, but also allows complex numbers." | |
5435 | */ | |
0f2d19dd | 5436 | SCM |
6e8d25a6 | 5437 | scm_magnitude (SCM z) |
0f2d19dd | 5438 | { |
e11e83f3 | 5439 | if (SCM_I_INUMP (z)) |
0aacf84e | 5440 | { |
e11e83f3 | 5441 | long int zz = SCM_I_INUM (z); |
0aacf84e MD |
5442 | if (zz >= 0) |
5443 | return z; | |
5444 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 5445 | return SCM_I_MAKINUM (-zz); |
0aacf84e MD |
5446 | else |
5447 | return scm_i_long2big (-zz); | |
5986c47d | 5448 | } |
0aacf84e MD |
5449 | else if (SCM_BIGP (z)) |
5450 | { | |
5451 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5452 | scm_remember_upto_here_1 (z); | |
5453 | if (sgn < 0) | |
5454 | return scm_i_clonebig (z, 0); | |
5455 | else | |
5456 | return z; | |
5986c47d | 5457 | } |
0aacf84e | 5458 | else if (SCM_REALP (z)) |
55f26379 | 5459 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 5460 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5461 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
5462 | else if (SCM_FRACTIONP (z)) |
5463 | { | |
73e4de09 | 5464 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5465 | return z; |
cba42c93 | 5466 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
5467 | SCM_FRACTION_DENOMINATOR (z)); |
5468 | } | |
0aacf84e | 5469 | else |
c2ff8ab0 | 5470 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); |
0f2d19dd JB |
5471 | } |
5472 | ||
5473 | ||
9de33deb | 5474 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
5475 | /* "Return the angle of the complex number @var{z}." |
5476 | */ | |
0f2d19dd | 5477 | SCM |
6e8d25a6 | 5478 | scm_angle (SCM z) |
0f2d19dd | 5479 | { |
c8ae173e | 5480 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
55f26379 | 5481 | scm_flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
5482 | But if atan2 follows the floating point rounding mode, then the value |
5483 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 5484 | if (SCM_I_INUMP (z)) |
0aacf84e | 5485 | { |
e11e83f3 | 5486 | if (SCM_I_INUM (z) >= 0) |
c8ae173e | 5487 | return scm_flo0; |
0aacf84e | 5488 | else |
55f26379 | 5489 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 5490 | } |
0aacf84e MD |
5491 | else if (SCM_BIGP (z)) |
5492 | { | |
5493 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5494 | scm_remember_upto_here_1 (z); | |
5495 | if (sgn < 0) | |
55f26379 | 5496 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 5497 | else |
c8ae173e | 5498 | return scm_flo0; |
0f2d19dd | 5499 | } |
0aacf84e | 5500 | else if (SCM_REALP (z)) |
c8ae173e KR |
5501 | { |
5502 | if (SCM_REAL_VALUE (z) >= 0) | |
5503 | return scm_flo0; | |
5504 | else | |
55f26379 | 5505 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 5506 | } |
0aacf84e | 5507 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5508 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
5509 | else if (SCM_FRACTIONP (z)) |
5510 | { | |
73e4de09 | 5511 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5512 | return scm_flo0; |
55f26379 | 5513 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 5514 | } |
0aacf84e | 5515 | else |
f4c627b3 | 5516 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); |
0f2d19dd JB |
5517 | } |
5518 | ||
5519 | ||
3c9a524f DH |
5520 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
5521 | /* Convert the number @var{x} to its inexact representation.\n" | |
5522 | */ | |
5523 | SCM | |
5524 | scm_exact_to_inexact (SCM z) | |
5525 | { | |
e11e83f3 | 5526 | if (SCM_I_INUMP (z)) |
55f26379 | 5527 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 5528 | else if (SCM_BIGP (z)) |
55f26379 | 5529 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 5530 | else if (SCM_FRACTIONP (z)) |
55f26379 | 5531 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
5532 | else if (SCM_INEXACTP (z)) |
5533 | return z; | |
5534 | else | |
5535 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
5536 | } | |
5537 | ||
5538 | ||
a1ec6916 | 5539 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 5540 | (SCM z), |
1e6808ea | 5541 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 5542 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 5543 | { |
e11e83f3 | 5544 | if (SCM_I_INUMP (z)) |
f872b822 | 5545 | return z; |
0aacf84e | 5546 | else if (SCM_BIGP (z)) |
f872b822 | 5547 | return z; |
0aacf84e MD |
5548 | else if (SCM_REALP (z)) |
5549 | { | |
f92e85f7 MV |
5550 | if (xisinf (SCM_REAL_VALUE (z)) || xisnan (SCM_REAL_VALUE (z))) |
5551 | SCM_OUT_OF_RANGE (1, z); | |
2be24db4 | 5552 | else |
f92e85f7 MV |
5553 | { |
5554 | mpq_t frac; | |
5555 | SCM q; | |
5556 | ||
5557 | mpq_init (frac); | |
5558 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 5559 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
5560 | scm_i_mpz2num (mpq_denref (frac))); |
5561 | ||
cba42c93 | 5562 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
5563 | for frac... |
5564 | */ | |
5565 | mpq_clear (frac); | |
5566 | return q; | |
5567 | } | |
c2ff8ab0 | 5568 | } |
f92e85f7 MV |
5569 | else if (SCM_FRACTIONP (z)) |
5570 | return z; | |
0aacf84e | 5571 | else |
c2ff8ab0 | 5572 | SCM_WRONG_TYPE_ARG (1, z); |
0f2d19dd | 5573 | } |
1bbd0b84 | 5574 | #undef FUNC_NAME |
0f2d19dd | 5575 | |
f92e85f7 MV |
5576 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
5577 | (SCM x, SCM err), | |
5578 | "Return an exact number that is within @var{err} of @var{x}.") | |
5579 | #define FUNC_NAME s_scm_rationalize | |
5580 | { | |
e11e83f3 | 5581 | if (SCM_I_INUMP (x)) |
f92e85f7 MV |
5582 | return x; |
5583 | else if (SCM_BIGP (x)) | |
5584 | return x; | |
5585 | else if ((SCM_REALP (x)) || SCM_FRACTIONP (x)) | |
5586 | { | |
5587 | /* Use continued fractions to find closest ratio. All | |
5588 | arithmetic is done with exact numbers. | |
5589 | */ | |
5590 | ||
5591 | SCM ex = scm_inexact_to_exact (x); | |
5592 | SCM int_part = scm_floor (ex); | |
d956fa6f MV |
5593 | SCM tt = SCM_I_MAKINUM (1); |
5594 | SCM a1 = SCM_I_MAKINUM (0), a2 = SCM_I_MAKINUM (1), a = SCM_I_MAKINUM (0); | |
5595 | SCM b1 = SCM_I_MAKINUM (1), b2 = SCM_I_MAKINUM (0), b = SCM_I_MAKINUM (0); | |
f92e85f7 MV |
5596 | SCM rx; |
5597 | int i = 0; | |
5598 | ||
73e4de09 | 5599 | if (scm_is_true (scm_num_eq_p (ex, int_part))) |
f92e85f7 MV |
5600 | return ex; |
5601 | ||
5602 | ex = scm_difference (ex, int_part); /* x = x-int_part */ | |
5603 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
5604 | ||
5605 | /* We stop after a million iterations just to be absolutely sure | |
5606 | that we don't go into an infinite loop. The process normally | |
5607 | converges after less than a dozen iterations. | |
5608 | */ | |
5609 | ||
5610 | err = scm_abs (err); | |
5611 | while (++i < 1000000) | |
5612 | { | |
5613 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
5614 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
5615 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
5616 | scm_is_false | |
f92e85f7 MV |
5617 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
5618 | err))) /* abs(x-a/b) <= err */ | |
02164269 MV |
5619 | { |
5620 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
73e4de09 MV |
5621 | if (scm_is_false (scm_exact_p (x)) |
5622 | || scm_is_false (scm_exact_p (err))) | |
02164269 MV |
5623 | return scm_exact_to_inexact (res); |
5624 | else | |
5625 | return res; | |
5626 | } | |
f92e85f7 MV |
5627 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
5628 | SCM_UNDEFINED); | |
5629 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
5630 | a2 = a1; | |
5631 | b2 = b1; | |
5632 | a1 = a; | |
5633 | b1 = b; | |
5634 | } | |
5635 | scm_num_overflow (s_scm_rationalize); | |
5636 | } | |
5637 | else | |
5638 | SCM_WRONG_TYPE_ARG (1, x); | |
5639 | } | |
5640 | #undef FUNC_NAME | |
5641 | ||
73e4de09 MV |
5642 | /* conversion functions */ |
5643 | ||
5644 | int | |
5645 | scm_is_integer (SCM val) | |
5646 | { | |
5647 | return scm_is_true (scm_integer_p (val)); | |
5648 | } | |
5649 | ||
5650 | int | |
5651 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
5652 | { | |
e11e83f3 | 5653 | if (SCM_I_INUMP (val)) |
73e4de09 | 5654 | { |
e11e83f3 | 5655 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5656 | return n >= min && n <= max; |
5657 | } | |
5658 | else if (SCM_BIGP (val)) | |
5659 | { | |
5660 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
5661 | return 0; | |
5662 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
5663 | { |
5664 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
5665 | { | |
5666 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
5667 | return n >= min && n <= max; | |
5668 | } | |
5669 | else | |
5670 | return 0; | |
5671 | } | |
73e4de09 MV |
5672 | else |
5673 | { | |
d956fa6f MV |
5674 | scm_t_intmax n; |
5675 | size_t count; | |
73e4de09 | 5676 | |
d956fa6f MV |
5677 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5678 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
5679 | return 0; | |
5680 | ||
5681 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5682 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5683 | |
d956fa6f | 5684 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 5685 | { |
d956fa6f MV |
5686 | if (n < 0) |
5687 | return 0; | |
73e4de09 | 5688 | } |
73e4de09 MV |
5689 | else |
5690 | { | |
d956fa6f MV |
5691 | n = -n; |
5692 | if (n >= 0) | |
5693 | return 0; | |
73e4de09 | 5694 | } |
d956fa6f MV |
5695 | |
5696 | return n >= min && n <= max; | |
73e4de09 MV |
5697 | } |
5698 | } | |
73e4de09 MV |
5699 | else |
5700 | return 0; | |
5701 | } | |
5702 | ||
5703 | int | |
5704 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
5705 | { | |
e11e83f3 | 5706 | if (SCM_I_INUMP (val)) |
73e4de09 | 5707 | { |
e11e83f3 | 5708 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5709 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
5710 | } | |
5711 | else if (SCM_BIGP (val)) | |
5712 | { | |
5713 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
5714 | return 0; | |
5715 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
5716 | { |
5717 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
5718 | { | |
5719 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
5720 | return n >= min && n <= max; | |
5721 | } | |
5722 | else | |
5723 | return 0; | |
5724 | } | |
73e4de09 MV |
5725 | else |
5726 | { | |
d956fa6f MV |
5727 | scm_t_uintmax n; |
5728 | size_t count; | |
73e4de09 | 5729 | |
d956fa6f MV |
5730 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
5731 | return 0; | |
73e4de09 | 5732 | |
d956fa6f MV |
5733 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5734 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 5735 | return 0; |
d956fa6f MV |
5736 | |
5737 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5738 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5739 | |
d956fa6f | 5740 | return n >= min && n <= max; |
73e4de09 MV |
5741 | } |
5742 | } | |
73e4de09 MV |
5743 | else |
5744 | return 0; | |
5745 | } | |
5746 | ||
1713d319 MV |
5747 | static void |
5748 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
5749 | { | |
5750 | scm_error (scm_out_of_range_key, | |
5751 | NULL, | |
5752 | "Value out of range ~S to ~S: ~S", | |
5753 | scm_list_3 (min, max, bad_val), | |
5754 | scm_list_1 (bad_val)); | |
5755 | } | |
5756 | ||
bfd7932e MV |
5757 | #define TYPE scm_t_intmax |
5758 | #define TYPE_MIN min | |
5759 | #define TYPE_MAX max | |
5760 | #define SIZEOF_TYPE 0 | |
5761 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
5762 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
5763 | #include "libguile/conv-integer.i.c" | |
5764 | ||
5765 | #define TYPE scm_t_uintmax | |
5766 | #define TYPE_MIN min | |
5767 | #define TYPE_MAX max | |
5768 | #define SIZEOF_TYPE 0 | |
5769 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
5770 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
5771 | #include "libguile/conv-uinteger.i.c" | |
5772 | ||
5773 | #define TYPE scm_t_int8 | |
5774 | #define TYPE_MIN SCM_T_INT8_MIN | |
5775 | #define TYPE_MAX SCM_T_INT8_MAX | |
5776 | #define SIZEOF_TYPE 1 | |
5777 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
5778 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
5779 | #include "libguile/conv-integer.i.c" | |
5780 | ||
5781 | #define TYPE scm_t_uint8 | |
5782 | #define TYPE_MIN 0 | |
5783 | #define TYPE_MAX SCM_T_UINT8_MAX | |
5784 | #define SIZEOF_TYPE 1 | |
5785 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
5786 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
5787 | #include "libguile/conv-uinteger.i.c" | |
5788 | ||
5789 | #define TYPE scm_t_int16 | |
5790 | #define TYPE_MIN SCM_T_INT16_MIN | |
5791 | #define TYPE_MAX SCM_T_INT16_MAX | |
5792 | #define SIZEOF_TYPE 2 | |
5793 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
5794 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
5795 | #include "libguile/conv-integer.i.c" | |
5796 | ||
5797 | #define TYPE scm_t_uint16 | |
5798 | #define TYPE_MIN 0 | |
5799 | #define TYPE_MAX SCM_T_UINT16_MAX | |
5800 | #define SIZEOF_TYPE 2 | |
5801 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
5802 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
5803 | #include "libguile/conv-uinteger.i.c" | |
5804 | ||
5805 | #define TYPE scm_t_int32 | |
5806 | #define TYPE_MIN SCM_T_INT32_MIN | |
5807 | #define TYPE_MAX SCM_T_INT32_MAX | |
5808 | #define SIZEOF_TYPE 4 | |
5809 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
5810 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
5811 | #include "libguile/conv-integer.i.c" | |
5812 | ||
5813 | #define TYPE scm_t_uint32 | |
5814 | #define TYPE_MIN 0 | |
5815 | #define TYPE_MAX SCM_T_UINT32_MAX | |
5816 | #define SIZEOF_TYPE 4 | |
5817 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
5818 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
5819 | #include "libguile/conv-uinteger.i.c" | |
5820 | ||
5821 | #if SCM_HAVE_T_INT64 | |
5822 | ||
5823 | #define TYPE scm_t_int64 | |
5824 | #define TYPE_MIN SCM_T_INT64_MIN | |
5825 | #define TYPE_MAX SCM_T_INT64_MAX | |
5826 | #define SIZEOF_TYPE 8 | |
5827 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
5828 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
5829 | #include "libguile/conv-integer.i.c" | |
5830 | ||
5831 | #define TYPE scm_t_uint64 | |
5832 | #define TYPE_MIN 0 | |
5833 | #define TYPE_MAX SCM_T_UINT64_MAX | |
5834 | #define SIZEOF_TYPE 8 | |
5835 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
5836 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
5837 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 5838 | |
bfd7932e | 5839 | #endif |
73e4de09 | 5840 | |
cd036260 MV |
5841 | void |
5842 | scm_to_mpz (SCM val, mpz_t rop) | |
5843 | { | |
5844 | if (SCM_I_INUMP (val)) | |
5845 | mpz_set_si (rop, SCM_I_INUM (val)); | |
5846 | else if (SCM_BIGP (val)) | |
5847 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
5848 | else | |
5849 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
5850 | } | |
5851 | ||
5852 | SCM | |
5853 | scm_from_mpz (mpz_t val) | |
5854 | { | |
5855 | return scm_i_mpz2num (val); | |
5856 | } | |
5857 | ||
73e4de09 MV |
5858 | int |
5859 | scm_is_real (SCM val) | |
5860 | { | |
5861 | return scm_is_true (scm_real_p (val)); | |
5862 | } | |
5863 | ||
55f26379 MV |
5864 | int |
5865 | scm_is_rational (SCM val) | |
5866 | { | |
5867 | return scm_is_true (scm_rational_p (val)); | |
5868 | } | |
5869 | ||
73e4de09 MV |
5870 | double |
5871 | scm_to_double (SCM val) | |
5872 | { | |
55f26379 MV |
5873 | if (SCM_I_INUMP (val)) |
5874 | return SCM_I_INUM (val); | |
5875 | else if (SCM_BIGP (val)) | |
5876 | return scm_i_big2dbl (val); | |
5877 | else if (SCM_FRACTIONP (val)) | |
5878 | return scm_i_fraction2double (val); | |
5879 | else if (SCM_REALP (val)) | |
5880 | return SCM_REAL_VALUE (val); | |
5881 | else | |
7a1aba42 | 5882 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
5883 | } |
5884 | ||
5885 | SCM | |
5886 | scm_from_double (double val) | |
5887 | { | |
55f26379 MV |
5888 | SCM z = scm_double_cell (scm_tc16_real, 0, 0, 0); |
5889 | SCM_REAL_VALUE (z) = val; | |
5890 | return z; | |
73e4de09 MV |
5891 | } |
5892 | ||
55f26379 MV |
5893 | #if SCM_ENABLE_DISCOURAGED == 1 |
5894 | ||
5895 | float | |
5896 | scm_num2float (SCM num, unsigned long int pos, const char *s_caller) | |
5897 | { | |
5898 | if (SCM_BIGP (num)) | |
5899 | { | |
5900 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5901 | if (!xisinf (res)) | |
5902 | return res; | |
5903 | else | |
5904 | scm_out_of_range (NULL, num); | |
5905 | } | |
5906 | else | |
5907 | return scm_to_double (num); | |
5908 | } | |
5909 | ||
5910 | double | |
5911 | scm_num2double (SCM num, unsigned long int pos, const char *s_caller) | |
5912 | { | |
5913 | if (SCM_BIGP (num)) | |
5914 | { | |
5915 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5916 | if (!xisinf (res)) | |
5917 | return res; | |
5918 | else | |
5919 | scm_out_of_range (NULL, num); | |
5920 | } | |
5921 | else | |
5922 | return scm_to_double (num); | |
5923 | } | |
5924 | ||
5925 | #endif | |
5926 | ||
8507ec80 MV |
5927 | int |
5928 | scm_is_complex (SCM val) | |
5929 | { | |
5930 | return scm_is_true (scm_complex_p (val)); | |
5931 | } | |
5932 | ||
5933 | double | |
5934 | scm_c_real_part (SCM z) | |
5935 | { | |
5936 | if (SCM_COMPLEXP (z)) | |
5937 | return SCM_COMPLEX_REAL (z); | |
5938 | else | |
5939 | { | |
5940 | /* Use the scm_real_part to get proper error checking and | |
5941 | dispatching. | |
5942 | */ | |
5943 | return scm_to_double (scm_real_part (z)); | |
5944 | } | |
5945 | } | |
5946 | ||
5947 | double | |
5948 | scm_c_imag_part (SCM z) | |
5949 | { | |
5950 | if (SCM_COMPLEXP (z)) | |
5951 | return SCM_COMPLEX_IMAG (z); | |
5952 | else | |
5953 | { | |
5954 | /* Use the scm_imag_part to get proper error checking and | |
5955 | dispatching. The result will almost always be 0.0, but not | |
5956 | always. | |
5957 | */ | |
5958 | return scm_to_double (scm_imag_part (z)); | |
5959 | } | |
5960 | } | |
5961 | ||
5962 | double | |
5963 | scm_c_magnitude (SCM z) | |
5964 | { | |
5965 | return scm_to_double (scm_magnitude (z)); | |
5966 | } | |
5967 | ||
5968 | double | |
5969 | scm_c_angle (SCM z) | |
5970 | { | |
5971 | return scm_to_double (scm_angle (z)); | |
5972 | } | |
5973 | ||
5974 | int | |
5975 | scm_is_number (SCM z) | |
5976 | { | |
5977 | return scm_is_true (scm_number_p (z)); | |
5978 | } | |
5979 | ||
0f2d19dd JB |
5980 | void |
5981 | scm_init_numbers () | |
0f2d19dd | 5982 | { |
0b799eea MV |
5983 | int i; |
5984 | ||
713a4259 KR |
5985 | mpz_init_set_si (z_negative_one, -1); |
5986 | ||
a261c0e9 DH |
5987 | /* It may be possible to tune the performance of some algorithms by using |
5988 | * the following constants to avoid the creation of bignums. Please, before | |
5989 | * using these values, remember the two rules of program optimization: | |
5990 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 5991 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 5992 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 5993 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 5994 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 5995 | |
f3ae5d60 MD |
5996 | scm_add_feature ("complex"); |
5997 | scm_add_feature ("inexact"); | |
55f26379 | 5998 | scm_flo0 = scm_from_double (0.0); |
0b799eea MV |
5999 | |
6000 | /* determine floating point precision */ | |
55f26379 | 6001 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
6002 | { |
6003 | init_dblprec(&scm_dblprec[i-2],i); | |
6004 | init_fx_radix(fx_per_radix[i-2],i); | |
6005 | } | |
f872b822 | 6006 | #ifdef DBL_DIG |
0b799eea MV |
6007 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
6008 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; | |
6009 | #endif | |
1be6b49c | 6010 | |
d956fa6f MV |
6011 | exactly_one_half = scm_permanent_object (scm_divide (SCM_I_MAKINUM (1), |
6012 | SCM_I_MAKINUM (2))); | |
a0599745 | 6013 | #include "libguile/numbers.x" |
0f2d19dd | 6014 | } |
89e00824 ML |
6015 | |
6016 | /* | |
6017 | Local Variables: | |
6018 | c-file-style: "gnu" | |
6019 | End: | |
6020 | */ |