Commit | Line | Data |
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238ebcef | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004 Free Software Foundation, Inc. |
ba74ef4e MV |
2 | * |
3 | * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories | |
4 | * and Bellcore. See scm_divide. | |
5 | * | |
f81e080b | 6 | * |
73be1d9e MV |
7 | * This library is free software; you can redistribute it and/or |
8 | * modify it under the terms of the GNU Lesser General Public | |
9 | * License as published by the Free Software Foundation; either | |
10 | * version 2.1 of the License, or (at your option) any later version. | |
0f2d19dd | 11 | * |
73be1d9e MV |
12 | * This library is distributed in the hope that it will be useful, |
13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
15 | * Lesser General Public License for more details. | |
0f2d19dd | 16 | * |
73be1d9e MV |
17 | * You should have received a copy of the GNU Lesser General Public |
18 | * License along with this library; if not, write to the Free Software | |
19 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA | |
20 | */ | |
1bbd0b84 | 21 | |
0f2d19dd | 22 | \f |
ca46fb90 RB |
23 | /* General assumptions: |
24 | * All objects satisfying SCM_COMPLEXP() have a non-zero complex component. | |
25 | * All objects satisfying SCM_BIGP() are too large to fit in a fixnum. | |
26 | * If an object satisfies integer?, it's either an inum, a bignum, or a real. | |
27 | * If floor (r) == r, r is an int, and mpz_set_d will DTRT. | |
f92e85f7 | 28 | * All objects satisfying SCM_FRACTIONP are never an integer. |
ca46fb90 RB |
29 | */ |
30 | ||
31 | /* TODO: | |
32 | ||
33 | - see if special casing bignums and reals in integer-exponent when | |
34 | possible (to use mpz_pow and mpf_pow_ui) is faster. | |
35 | ||
36 | - look in to better short-circuiting of common cases in | |
37 | integer-expt and elsewhere. | |
38 | ||
39 | - see if direct mpz operations can help in ash and elsewhere. | |
40 | ||
41 | */ | |
0f2d19dd | 42 | |
fa605590 KR |
43 | /* tell glibc (2.3) to give prototype for C99 trunc() */ |
44 | #define _GNU_SOURCE | |
45 | ||
ee33d62a RB |
46 | #if HAVE_CONFIG_H |
47 | # include <config.h> | |
48 | #endif | |
49 | ||
0f2d19dd | 50 | #include <math.h> |
3c9a524f | 51 | #include <ctype.h> |
fc194577 | 52 | #include <string.h> |
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 | ||
570b6821 | 186 | SCM_C_INLINE_KEYWORD static 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 MV |
600 | extern unsigned int DINFINITY[2]; |
601 | guile_Inf = (*(X_CAST(double *, DINFINITY))); | |
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 | |
622 | /* OSF */ | |
7351e207 MV |
623 | extern unsigned int DQNAN[2]; |
624 | guile_NaN = (*(X_CAST(double *, DQNAN))); | |
625 | #else | |
626 | guile_NaN = guile_Inf / guile_Inf; | |
627 | #endif | |
628 | ||
629 | #endif | |
630 | } | |
631 | ||
632 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
633 | (void), | |
634 | "Return Inf.") | |
635 | #define FUNC_NAME s_scm_inf | |
636 | { | |
637 | static int initialized = 0; | |
638 | if (! initialized) | |
639 | { | |
640 | guile_ieee_init (); | |
641 | initialized = 1; | |
642 | } | |
55f26379 | 643 | return scm_from_double (guile_Inf); |
7351e207 MV |
644 | } |
645 | #undef FUNC_NAME | |
646 | ||
647 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
648 | (void), | |
649 | "Return NaN.") | |
650 | #define FUNC_NAME s_scm_nan | |
651 | { | |
652 | static int initialized = 0; | |
0aacf84e | 653 | if (!initialized) |
7351e207 MV |
654 | { |
655 | guile_ieee_init (); | |
656 | initialized = 1; | |
657 | } | |
55f26379 | 658 | return scm_from_double (guile_NaN); |
7351e207 MV |
659 | } |
660 | #undef FUNC_NAME | |
661 | ||
4219f20d | 662 | |
a48d60b1 MD |
663 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
664 | (SCM x), | |
665 | "Return the absolute value of @var{x}.") | |
666 | #define FUNC_NAME | |
0f2d19dd | 667 | { |
e11e83f3 | 668 | if (SCM_I_INUMP (x)) |
0aacf84e | 669 | { |
e11e83f3 | 670 | long int xx = SCM_I_INUM (x); |
0aacf84e MD |
671 | if (xx >= 0) |
672 | return x; | |
673 | else if (SCM_POSFIXABLE (-xx)) | |
d956fa6f | 674 | return SCM_I_MAKINUM (-xx); |
0aacf84e MD |
675 | else |
676 | return scm_i_long2big (-xx); | |
4219f20d | 677 | } |
0aacf84e MD |
678 | else if (SCM_BIGP (x)) |
679 | { | |
680 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
681 | if (sgn < 0) | |
682 | return scm_i_clonebig (x, 0); | |
683 | else | |
684 | return x; | |
4219f20d | 685 | } |
0aacf84e | 686 | else if (SCM_REALP (x)) |
ae38324d KR |
687 | { |
688 | /* note that if x is a NaN then xx<0 is false so we return x unchanged */ | |
689 | double xx = SCM_REAL_VALUE (x); | |
690 | if (xx < 0.0) | |
55f26379 | 691 | return scm_from_double (-xx); |
ae38324d KR |
692 | else |
693 | return x; | |
694 | } | |
f92e85f7 MV |
695 | else if (SCM_FRACTIONP (x)) |
696 | { | |
73e4de09 | 697 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) |
f92e85f7 | 698 | return x; |
cba42c93 | 699 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 MV |
700 | SCM_FRACTION_DENOMINATOR (x)); |
701 | } | |
0aacf84e | 702 | else |
a48d60b1 | 703 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 704 | } |
a48d60b1 | 705 | #undef FUNC_NAME |
0f2d19dd | 706 | |
4219f20d | 707 | |
9de33deb | 708 | SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); |
942e5b91 MG |
709 | /* "Return the quotient of the numbers @var{x} and @var{y}." |
710 | */ | |
0f2d19dd | 711 | SCM |
6e8d25a6 | 712 | scm_quotient (SCM x, SCM y) |
0f2d19dd | 713 | { |
e11e83f3 | 714 | if (SCM_I_INUMP (x)) |
0aacf84e | 715 | { |
e11e83f3 MV |
716 | long xx = SCM_I_INUM (x); |
717 | if (SCM_I_INUMP (y)) | |
0aacf84e | 718 | { |
e11e83f3 | 719 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
720 | if (yy == 0) |
721 | scm_num_overflow (s_quotient); | |
722 | else | |
723 | { | |
724 | long z = xx / yy; | |
725 | if (SCM_FIXABLE (z)) | |
d956fa6f | 726 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
727 | else |
728 | return scm_i_long2big (z); | |
729 | } | |
828865c3 | 730 | } |
0aacf84e | 731 | else if (SCM_BIGP (y)) |
ac0c002c | 732 | { |
e11e83f3 | 733 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
734 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
735 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
736 | { | |
737 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
738 | scm_remember_upto_here_1 (y); | |
d956fa6f | 739 | return SCM_I_MAKINUM (-1); |
4dc09ee4 | 740 | } |
0aacf84e | 741 | else |
d956fa6f | 742 | return SCM_I_MAKINUM (0); |
ac0c002c DH |
743 | } |
744 | else | |
0aacf84e | 745 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); |
828865c3 | 746 | } |
0aacf84e MD |
747 | else if (SCM_BIGP (x)) |
748 | { | |
e11e83f3 | 749 | if (SCM_I_INUMP (y)) |
0aacf84e | 750 | { |
e11e83f3 | 751 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
752 | if (yy == 0) |
753 | scm_num_overflow (s_quotient); | |
754 | else if (yy == 1) | |
755 | return x; | |
756 | else | |
757 | { | |
758 | SCM result = scm_i_mkbig (); | |
759 | if (yy < 0) | |
760 | { | |
761 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
762 | SCM_I_BIG_MPZ (x), | |
763 | - yy); | |
764 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
765 | } | |
766 | else | |
767 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
768 | scm_remember_upto_here_1 (x); | |
769 | return scm_i_normbig (result); | |
770 | } | |
771 | } | |
772 | else if (SCM_BIGP (y)) | |
773 | { | |
774 | SCM result = scm_i_mkbig (); | |
775 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
776 | SCM_I_BIG_MPZ (x), | |
777 | SCM_I_BIG_MPZ (y)); | |
778 | scm_remember_upto_here_2 (x, y); | |
779 | return scm_i_normbig (result); | |
780 | } | |
781 | else | |
782 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); | |
f872b822 | 783 | } |
0aacf84e | 784 | else |
89a7e495 | 785 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient); |
0f2d19dd JB |
786 | } |
787 | ||
9de33deb | 788 | SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); |
942e5b91 MG |
789 | /* "Return the remainder of the numbers @var{x} and @var{y}.\n" |
790 | * "@lisp\n" | |
791 | * "(remainder 13 4) @result{} 1\n" | |
792 | * "(remainder -13 4) @result{} -1\n" | |
793 | * "@end lisp" | |
794 | */ | |
0f2d19dd | 795 | SCM |
6e8d25a6 | 796 | scm_remainder (SCM x, SCM y) |
0f2d19dd | 797 | { |
e11e83f3 | 798 | if (SCM_I_INUMP (x)) |
0aacf84e | 799 | { |
e11e83f3 | 800 | if (SCM_I_INUMP (y)) |
0aacf84e | 801 | { |
e11e83f3 | 802 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
803 | if (yy == 0) |
804 | scm_num_overflow (s_remainder); | |
805 | else | |
806 | { | |
e11e83f3 | 807 | long z = SCM_I_INUM (x) % yy; |
d956fa6f | 808 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
809 | } |
810 | } | |
811 | else if (SCM_BIGP (y)) | |
ac0c002c | 812 | { |
e11e83f3 | 813 | if ((SCM_I_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
4dc09ee4 KR |
814 | && (mpz_cmp_ui (SCM_I_BIG_MPZ (y), |
815 | - SCM_MOST_NEGATIVE_FIXNUM) == 0)) | |
816 | { | |
817 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
818 | scm_remember_upto_here_1 (y); | |
d956fa6f | 819 | return SCM_I_MAKINUM (0); |
4dc09ee4 | 820 | } |
0aacf84e MD |
821 | else |
822 | return x; | |
ac0c002c DH |
823 | } |
824 | else | |
0aacf84e | 825 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); |
89a7e495 | 826 | } |
0aacf84e MD |
827 | else if (SCM_BIGP (x)) |
828 | { | |
e11e83f3 | 829 | if (SCM_I_INUMP (y)) |
0aacf84e | 830 | { |
e11e83f3 | 831 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
832 | if (yy == 0) |
833 | scm_num_overflow (s_remainder); | |
834 | else | |
835 | { | |
836 | SCM result = scm_i_mkbig (); | |
837 | if (yy < 0) | |
838 | yy = - yy; | |
839 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
840 | scm_remember_upto_here_1 (x); | |
841 | return scm_i_normbig (result); | |
842 | } | |
843 | } | |
844 | else if (SCM_BIGP (y)) | |
845 | { | |
846 | SCM result = scm_i_mkbig (); | |
847 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
848 | SCM_I_BIG_MPZ (x), | |
849 | SCM_I_BIG_MPZ (y)); | |
850 | scm_remember_upto_here_2 (x, y); | |
851 | return scm_i_normbig (result); | |
852 | } | |
853 | else | |
854 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); | |
f872b822 | 855 | } |
0aacf84e | 856 | else |
89a7e495 | 857 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder); |
0f2d19dd JB |
858 | } |
859 | ||
89a7e495 | 860 | |
9de33deb | 861 | SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); |
942e5b91 MG |
862 | /* "Return the modulo of the numbers @var{x} and @var{y}.\n" |
863 | * "@lisp\n" | |
864 | * "(modulo 13 4) @result{} 1\n" | |
865 | * "(modulo -13 4) @result{} 3\n" | |
866 | * "@end lisp" | |
867 | */ | |
0f2d19dd | 868 | SCM |
6e8d25a6 | 869 | scm_modulo (SCM x, SCM y) |
0f2d19dd | 870 | { |
e11e83f3 | 871 | if (SCM_I_INUMP (x)) |
0aacf84e | 872 | { |
e11e83f3 MV |
873 | long xx = SCM_I_INUM (x); |
874 | if (SCM_I_INUMP (y)) | |
0aacf84e | 875 | { |
e11e83f3 | 876 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
877 | if (yy == 0) |
878 | scm_num_overflow (s_modulo); | |
879 | else | |
880 | { | |
881 | /* FIXME: I think this may be a bug on some arches -- results | |
882 | of % with negative second arg are undefined... */ | |
883 | long z = xx % yy; | |
884 | long result; | |
885 | ||
886 | if (yy < 0) | |
887 | { | |
888 | if (z > 0) | |
889 | result = z + yy; | |
890 | else | |
891 | result = z; | |
892 | } | |
893 | else | |
894 | { | |
895 | if (z < 0) | |
896 | result = z + yy; | |
897 | else | |
898 | result = z; | |
899 | } | |
d956fa6f | 900 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
901 | } |
902 | } | |
903 | else if (SCM_BIGP (y)) | |
904 | { | |
905 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
906 | { |
907 | mpz_t z_x; | |
908 | SCM result; | |
909 | ||
910 | if (sgn_y < 0) | |
911 | { | |
912 | SCM pos_y = scm_i_clonebig (y, 0); | |
913 | /* do this after the last scm_op */ | |
914 | mpz_init_set_si (z_x, xx); | |
915 | result = pos_y; /* re-use this bignum */ | |
916 | mpz_mod (SCM_I_BIG_MPZ (result), | |
917 | z_x, | |
918 | SCM_I_BIG_MPZ (pos_y)); | |
919 | scm_remember_upto_here_1 (pos_y); | |
920 | } | |
921 | else | |
922 | { | |
923 | result = scm_i_mkbig (); | |
924 | /* do this after the last scm_op */ | |
925 | mpz_init_set_si (z_x, xx); | |
926 | mpz_mod (SCM_I_BIG_MPZ (result), | |
927 | z_x, | |
928 | SCM_I_BIG_MPZ (y)); | |
929 | scm_remember_upto_here_1 (y); | |
930 | } | |
ca46fb90 | 931 | |
0aacf84e MD |
932 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
933 | mpz_add (SCM_I_BIG_MPZ (result), | |
934 | SCM_I_BIG_MPZ (y), | |
935 | SCM_I_BIG_MPZ (result)); | |
936 | scm_remember_upto_here_1 (y); | |
937 | /* and do this before the next one */ | |
938 | mpz_clear (z_x); | |
939 | return scm_i_normbig (result); | |
940 | } | |
941 | } | |
942 | else | |
943 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
f872b822 | 944 | } |
0aacf84e MD |
945 | else if (SCM_BIGP (x)) |
946 | { | |
e11e83f3 | 947 | if (SCM_I_INUMP (y)) |
0aacf84e | 948 | { |
e11e83f3 | 949 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
950 | if (yy == 0) |
951 | scm_num_overflow (s_modulo); | |
952 | else | |
953 | { | |
954 | SCM result = scm_i_mkbig (); | |
955 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
956 | SCM_I_BIG_MPZ (x), | |
957 | (yy < 0) ? - yy : yy); | |
958 | scm_remember_upto_here_1 (x); | |
959 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
960 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
961 | SCM_I_BIG_MPZ (result), | |
962 | - yy); | |
963 | return scm_i_normbig (result); | |
964 | } | |
965 | } | |
966 | else if (SCM_BIGP (y)) | |
967 | { | |
0aacf84e MD |
968 | { |
969 | SCM result = scm_i_mkbig (); | |
970 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
971 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
972 | mpz_mod (SCM_I_BIG_MPZ (result), | |
973 | SCM_I_BIG_MPZ (x), | |
974 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 975 | |
0aacf84e MD |
976 | scm_remember_upto_here_1 (x); |
977 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
978 | mpz_add (SCM_I_BIG_MPZ (result), | |
979 | SCM_I_BIG_MPZ (y), | |
980 | SCM_I_BIG_MPZ (result)); | |
981 | scm_remember_upto_here_2 (y, pos_y); | |
982 | return scm_i_normbig (result); | |
983 | } | |
984 | } | |
985 | else | |
986 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
828865c3 | 987 | } |
0aacf84e | 988 | else |
09fb7599 | 989 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); |
0f2d19dd JB |
990 | } |
991 | ||
9de33deb | 992 | SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd); |
942e5b91 MG |
993 | /* "Return the greatest common divisor of all arguments.\n" |
994 | * "If called without arguments, 0 is returned." | |
995 | */ | |
0f2d19dd | 996 | SCM |
6e8d25a6 | 997 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 998 | { |
ca46fb90 | 999 | if (SCM_UNBNDP (y)) |
0aacf84e | 1000 | return SCM_UNBNDP (x) ? SCM_INUM0 : x; |
ca46fb90 | 1001 | |
e11e83f3 | 1002 | if (SCM_I_INUMP (x)) |
ca46fb90 | 1003 | { |
e11e83f3 | 1004 | if (SCM_I_INUMP (y)) |
ca46fb90 | 1005 | { |
e11e83f3 MV |
1006 | long xx = SCM_I_INUM (x); |
1007 | long yy = SCM_I_INUM (y); | |
ca46fb90 RB |
1008 | long u = xx < 0 ? -xx : xx; |
1009 | long v = yy < 0 ? -yy : yy; | |
1010 | long result; | |
0aacf84e MD |
1011 | if (xx == 0) |
1012 | result = v; | |
1013 | else if (yy == 0) | |
1014 | result = u; | |
1015 | else | |
1016 | { | |
1017 | long k = 1; | |
1018 | long t; | |
1019 | /* Determine a common factor 2^k */ | |
1020 | while (!(1 & (u | v))) | |
1021 | { | |
1022 | k <<= 1; | |
1023 | u >>= 1; | |
1024 | v >>= 1; | |
1025 | } | |
1026 | /* Now, any factor 2^n can be eliminated */ | |
1027 | if (u & 1) | |
1028 | t = -v; | |
1029 | else | |
1030 | { | |
1031 | t = u; | |
1032 | b3: | |
1033 | t = SCM_SRS (t, 1); | |
1034 | } | |
1035 | if (!(1 & t)) | |
1036 | goto b3; | |
1037 | if (t > 0) | |
1038 | u = t; | |
1039 | else | |
1040 | v = -t; | |
1041 | t = u - v; | |
1042 | if (t != 0) | |
1043 | goto b3; | |
1044 | result = u * k; | |
1045 | } | |
1046 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 1047 | ? SCM_I_MAKINUM (result) |
0aacf84e | 1048 | : scm_i_long2big (result)); |
ca46fb90 RB |
1049 | } |
1050 | else if (SCM_BIGP (y)) | |
1051 | { | |
0bff4dce KR |
1052 | SCM_SWAP (x, y); |
1053 | goto big_inum; | |
ca46fb90 RB |
1054 | } |
1055 | else | |
1056 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 1057 | } |
ca46fb90 RB |
1058 | else if (SCM_BIGP (x)) |
1059 | { | |
e11e83f3 | 1060 | if (SCM_I_INUMP (y)) |
ca46fb90 RB |
1061 | { |
1062 | unsigned long result; | |
0bff4dce KR |
1063 | long yy; |
1064 | big_inum: | |
e11e83f3 | 1065 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
1066 | if (yy == 0) |
1067 | return scm_abs (x); | |
0aacf84e MD |
1068 | if (yy < 0) |
1069 | yy = -yy; | |
ca46fb90 RB |
1070 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
1071 | scm_remember_upto_here_1 (x); | |
0aacf84e | 1072 | return (SCM_POSFIXABLE (result) |
d956fa6f | 1073 | ? SCM_I_MAKINUM (result) |
c71b0706 | 1074 | : scm_from_ulong (result)); |
ca46fb90 RB |
1075 | } |
1076 | else if (SCM_BIGP (y)) | |
1077 | { | |
1078 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
1079 | mpz_gcd (SCM_I_BIG_MPZ (result), |
1080 | SCM_I_BIG_MPZ (x), | |
1081 | SCM_I_BIG_MPZ (y)); | |
1082 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
1083 | return scm_i_normbig (result); |
1084 | } | |
1085 | else | |
1086 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 1087 | } |
ca46fb90 | 1088 | else |
09fb7599 | 1089 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
1090 | } |
1091 | ||
9de33deb | 1092 | SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm); |
942e5b91 MG |
1093 | /* "Return the least common multiple of the arguments.\n" |
1094 | * "If called without arguments, 1 is returned." | |
1095 | */ | |
0f2d19dd | 1096 | SCM |
6e8d25a6 | 1097 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 1098 | { |
ca46fb90 RB |
1099 | if (SCM_UNBNDP (n2)) |
1100 | { | |
1101 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
1102 | return SCM_I_MAKINUM (1L); |
1103 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 1104 | } |
09fb7599 | 1105 | |
e11e83f3 | 1106 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 1107 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 1108 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 1109 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 1110 | |
e11e83f3 | 1111 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 1112 | { |
e11e83f3 | 1113 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1114 | { |
1115 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 1116 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
1117 | return d; |
1118 | else | |
1119 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
1120 | } | |
1121 | else | |
1122 | { | |
1123 | /* inum n1, big n2 */ | |
1124 | inumbig: | |
1125 | { | |
1126 | SCM result = scm_i_mkbig (); | |
e11e83f3 | 1127 | long nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
1128 | if (nn1 == 0) return SCM_INUM0; |
1129 | if (nn1 < 0) nn1 = - nn1; | |
1130 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
1131 | scm_remember_upto_here_1 (n2); | |
1132 | return result; | |
1133 | } | |
1134 | } | |
1135 | } | |
1136 | else | |
1137 | { | |
1138 | /* big n1 */ | |
e11e83f3 | 1139 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1140 | { |
1141 | SCM_SWAP (n1, n2); | |
1142 | goto inumbig; | |
1143 | } | |
1144 | else | |
1145 | { | |
1146 | SCM result = scm_i_mkbig (); | |
1147 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
1148 | SCM_I_BIG_MPZ (n1), | |
1149 | SCM_I_BIG_MPZ (n2)); | |
1150 | scm_remember_upto_here_2(n1, n2); | |
1151 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
1152 | return result; | |
1153 | } | |
f872b822 | 1154 | } |
0f2d19dd JB |
1155 | } |
1156 | ||
8a525303 GB |
1157 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
1158 | ||
1159 | Logand: | |
1160 | X Y Result Method: | |
1161 | (len) | |
1162 | + + + x (map digit:logand X Y) | |
1163 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
1164 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
1165 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
1166 | ||
1167 | Logior: | |
1168 | X Y Result Method: | |
1169 | ||
1170 | + + + (map digit:logior X Y) | |
1171 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
1172 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
1173 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
1174 | ||
1175 | Logxor: | |
1176 | X Y Result Method: | |
1177 | ||
1178 | + + + (map digit:logxor X Y) | |
1179 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
1180 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
1181 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
1182 | ||
1183 | Logtest: | |
1184 | X Y Result | |
1185 | ||
1186 | + + (any digit:logand X Y) | |
1187 | + - (any digit:logand X (lognot (+ -1 Y))) | |
1188 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
1189 | - - #t | |
1190 | ||
1191 | */ | |
1192 | ||
c3ee7520 | 1193 | SCM_DEFINE1 (scm_logand, "logand", scm_tc7_asubr, |
1bbd0b84 | 1194 | (SCM n1, SCM n2), |
3c3db128 GH |
1195 | "Return the bitwise AND of the integer arguments.\n\n" |
1196 | "@lisp\n" | |
1197 | "(logand) @result{} -1\n" | |
1198 | "(logand 7) @result{} 7\n" | |
535f2a51 | 1199 | "(logand #b111 #b011 #b001) @result{} 1\n" |
3c3db128 | 1200 | "@end lisp") |
1bbd0b84 | 1201 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 1202 | { |
9a00c9fc DH |
1203 | long int nn1; |
1204 | ||
0aacf84e MD |
1205 | if (SCM_UNBNDP (n2)) |
1206 | { | |
1207 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 1208 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
1209 | else if (!SCM_NUMBERP (n1)) |
1210 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1211 | else if (SCM_NUMBERP (n1)) | |
1212 | return n1; | |
1213 | else | |
1214 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1215 | } |
09fb7599 | 1216 | |
e11e83f3 | 1217 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1218 | { |
e11e83f3 MV |
1219 | nn1 = SCM_I_INUM (n1); |
1220 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1221 | { |
e11e83f3 | 1222 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1223 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
1224 | } |
1225 | else if SCM_BIGP (n2) | |
1226 | { | |
1227 | intbig: | |
1228 | if (n1 == 0) | |
1229 | return SCM_INUM0; | |
1230 | { | |
1231 | SCM result_z = scm_i_mkbig (); | |
1232 | mpz_t nn1_z; | |
1233 | mpz_init_set_si (nn1_z, nn1); | |
1234 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1235 | scm_remember_upto_here_1 (n2); | |
1236 | mpz_clear (nn1_z); | |
1237 | return scm_i_normbig (result_z); | |
1238 | } | |
1239 | } | |
1240 | else | |
1241 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1242 | } | |
1243 | else if (SCM_BIGP (n1)) | |
1244 | { | |
e11e83f3 | 1245 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1246 | { |
1247 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1248 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1249 | goto intbig; |
1250 | } | |
1251 | else if (SCM_BIGP (n2)) | |
1252 | { | |
1253 | SCM result_z = scm_i_mkbig (); | |
1254 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
1255 | SCM_I_BIG_MPZ (n1), | |
1256 | SCM_I_BIG_MPZ (n2)); | |
1257 | scm_remember_upto_here_2 (n1, n2); | |
1258 | return scm_i_normbig (result_z); | |
1259 | } | |
1260 | else | |
1261 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1262 | } |
0aacf84e | 1263 | else |
09fb7599 | 1264 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1265 | } |
1bbd0b84 | 1266 | #undef FUNC_NAME |
0f2d19dd | 1267 | |
09fb7599 | 1268 | |
c3ee7520 | 1269 | SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr, |
1bbd0b84 | 1270 | (SCM n1, SCM n2), |
3c3db128 GH |
1271 | "Return the bitwise OR of the integer arguments.\n\n" |
1272 | "@lisp\n" | |
1273 | "(logior) @result{} 0\n" | |
1274 | "(logior 7) @result{} 7\n" | |
1275 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1e6808ea | 1276 | "@end lisp") |
1bbd0b84 | 1277 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 1278 | { |
9a00c9fc DH |
1279 | long int nn1; |
1280 | ||
0aacf84e MD |
1281 | if (SCM_UNBNDP (n2)) |
1282 | { | |
1283 | if (SCM_UNBNDP (n1)) | |
1284 | return SCM_INUM0; | |
1285 | else if (SCM_NUMBERP (n1)) | |
1286 | return n1; | |
1287 | else | |
1288 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1289 | } |
09fb7599 | 1290 | |
e11e83f3 | 1291 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1292 | { |
e11e83f3 MV |
1293 | nn1 = SCM_I_INUM (n1); |
1294 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1295 | { |
e11e83f3 | 1296 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1297 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
1298 | } |
1299 | else if (SCM_BIGP (n2)) | |
1300 | { | |
1301 | intbig: | |
1302 | if (nn1 == 0) | |
1303 | return n2; | |
1304 | { | |
1305 | SCM result_z = scm_i_mkbig (); | |
1306 | mpz_t nn1_z; | |
1307 | mpz_init_set_si (nn1_z, nn1); | |
1308 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1309 | scm_remember_upto_here_1 (n2); | |
1310 | mpz_clear (nn1_z); | |
1311 | return result_z; | |
1312 | } | |
1313 | } | |
1314 | else | |
1315 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1316 | } | |
1317 | else if (SCM_BIGP (n1)) | |
1318 | { | |
e11e83f3 | 1319 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1320 | { |
1321 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1322 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1323 | goto intbig; |
1324 | } | |
1325 | else if (SCM_BIGP (n2)) | |
1326 | { | |
1327 | SCM result_z = scm_i_mkbig (); | |
1328 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
1329 | SCM_I_BIG_MPZ (n1), | |
1330 | SCM_I_BIG_MPZ (n2)); | |
1331 | scm_remember_upto_here_2 (n1, n2); | |
1332 | return result_z; | |
1333 | } | |
1334 | else | |
1335 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1336 | } |
0aacf84e | 1337 | else |
09fb7599 | 1338 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1339 | } |
1bbd0b84 | 1340 | #undef FUNC_NAME |
0f2d19dd | 1341 | |
09fb7599 | 1342 | |
c3ee7520 | 1343 | SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr, |
1bbd0b84 | 1344 | (SCM n1, SCM n2), |
3c3db128 GH |
1345 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1346 | "set in the result if it is set in an odd number of arguments.\n" | |
1347 | "@lisp\n" | |
1348 | "(logxor) @result{} 0\n" | |
1349 | "(logxor 7) @result{} 7\n" | |
1350 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1351 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1352 | "@end lisp") |
1bbd0b84 | 1353 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1354 | { |
9a00c9fc DH |
1355 | long int nn1; |
1356 | ||
0aacf84e MD |
1357 | if (SCM_UNBNDP (n2)) |
1358 | { | |
1359 | if (SCM_UNBNDP (n1)) | |
1360 | return SCM_INUM0; | |
1361 | else if (SCM_NUMBERP (n1)) | |
1362 | return n1; | |
1363 | else | |
1364 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1365 | } |
09fb7599 | 1366 | |
e11e83f3 | 1367 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1368 | { |
e11e83f3 MV |
1369 | nn1 = SCM_I_INUM (n1); |
1370 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1371 | { |
e11e83f3 | 1372 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1373 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
1374 | } |
1375 | else if (SCM_BIGP (n2)) | |
1376 | { | |
1377 | intbig: | |
1378 | { | |
1379 | SCM result_z = scm_i_mkbig (); | |
1380 | mpz_t nn1_z; | |
1381 | mpz_init_set_si (nn1_z, nn1); | |
1382 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1383 | scm_remember_upto_here_1 (n2); | |
1384 | mpz_clear (nn1_z); | |
1385 | return scm_i_normbig (result_z); | |
1386 | } | |
1387 | } | |
1388 | else | |
1389 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1390 | } | |
1391 | else if (SCM_BIGP (n1)) | |
1392 | { | |
e11e83f3 | 1393 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1394 | { |
1395 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1396 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1397 | goto intbig; |
1398 | } | |
1399 | else if (SCM_BIGP (n2)) | |
1400 | { | |
1401 | SCM result_z = scm_i_mkbig (); | |
1402 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
1403 | SCM_I_BIG_MPZ (n1), | |
1404 | SCM_I_BIG_MPZ (n2)); | |
1405 | scm_remember_upto_here_2 (n1, n2); | |
1406 | return scm_i_normbig (result_z); | |
1407 | } | |
1408 | else | |
1409 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1410 | } |
0aacf84e | 1411 | else |
09fb7599 | 1412 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1413 | } |
1bbd0b84 | 1414 | #undef FUNC_NAME |
0f2d19dd | 1415 | |
09fb7599 | 1416 | |
a1ec6916 | 1417 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea MG |
1418 | (SCM j, SCM k), |
1419 | "@lisp\n" | |
b380b885 MD |
1420 | "(logtest j k) @equiv{} (not (zero? (logand j k)))\n\n" |
1421 | "(logtest #b0100 #b1011) @result{} #f\n" | |
1422 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1423 | "@end lisp") |
1bbd0b84 | 1424 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1425 | { |
1e6808ea | 1426 | long int nj; |
9a00c9fc | 1427 | |
e11e83f3 | 1428 | if (SCM_I_INUMP (j)) |
0aacf84e | 1429 | { |
e11e83f3 MV |
1430 | nj = SCM_I_INUM (j); |
1431 | if (SCM_I_INUMP (k)) | |
0aacf84e | 1432 | { |
e11e83f3 | 1433 | long nk = SCM_I_INUM (k); |
73e4de09 | 1434 | return scm_from_bool (nj & nk); |
0aacf84e MD |
1435 | } |
1436 | else if (SCM_BIGP (k)) | |
1437 | { | |
1438 | intbig: | |
1439 | if (nj == 0) | |
1440 | return SCM_BOOL_F; | |
1441 | { | |
1442 | SCM result; | |
1443 | mpz_t nj_z; | |
1444 | mpz_init_set_si (nj_z, nj); | |
1445 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
1446 | scm_remember_upto_here_1 (k); | |
73e4de09 | 1447 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
1448 | mpz_clear (nj_z); |
1449 | return result; | |
1450 | } | |
1451 | } | |
1452 | else | |
1453 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1454 | } | |
1455 | else if (SCM_BIGP (j)) | |
1456 | { | |
e11e83f3 | 1457 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
1458 | { |
1459 | SCM_SWAP (j, k); | |
e11e83f3 | 1460 | nj = SCM_I_INUM (j); |
0aacf84e MD |
1461 | goto intbig; |
1462 | } | |
1463 | else if (SCM_BIGP (k)) | |
1464 | { | |
1465 | SCM result; | |
1466 | mpz_t result_z; | |
1467 | mpz_init (result_z); | |
1468 | mpz_and (result_z, | |
1469 | SCM_I_BIG_MPZ (j), | |
1470 | SCM_I_BIG_MPZ (k)); | |
1471 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 1472 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
1473 | mpz_clear (result_z); |
1474 | return result; | |
1475 | } | |
1476 | else | |
1477 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1478 | } | |
1479 | else | |
1480 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 1481 | } |
1bbd0b84 | 1482 | #undef FUNC_NAME |
0f2d19dd | 1483 | |
c1bfcf60 | 1484 | |
a1ec6916 | 1485 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1486 | (SCM index, SCM j), |
1e6808ea | 1487 | "@lisp\n" |
b380b885 MD |
1488 | "(logbit? index j) @equiv{} (logtest (integer-expt 2 index) j)\n\n" |
1489 | "(logbit? 0 #b1101) @result{} #t\n" | |
1490 | "(logbit? 1 #b1101) @result{} #f\n" | |
1491 | "(logbit? 2 #b1101) @result{} #t\n" | |
1492 | "(logbit? 3 #b1101) @result{} #t\n" | |
1493 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1494 | "@end lisp") |
1bbd0b84 | 1495 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1496 | { |
78166ad5 | 1497 | unsigned long int iindex; |
5efd3c7d | 1498 | iindex = scm_to_ulong (index); |
78166ad5 | 1499 | |
e11e83f3 | 1500 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
1501 | { |
1502 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 1503 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 1504 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 1505 | } |
0aacf84e MD |
1506 | else if (SCM_BIGP (j)) |
1507 | { | |
1508 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
1509 | scm_remember_upto_here_1 (j); | |
73e4de09 | 1510 | return scm_from_bool (val); |
0aacf84e MD |
1511 | } |
1512 | else | |
78166ad5 | 1513 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 1514 | } |
1bbd0b84 | 1515 | #undef FUNC_NAME |
0f2d19dd | 1516 | |
78166ad5 | 1517 | |
a1ec6916 | 1518 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1519 | (SCM n), |
4d814788 | 1520 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
1521 | "argument.\n" |
1522 | "\n" | |
b380b885 MD |
1523 | "@lisp\n" |
1524 | "(number->string (lognot #b10000000) 2)\n" | |
1525 | " @result{} \"-10000001\"\n" | |
1526 | "(number->string (lognot #b0) 2)\n" | |
1527 | " @result{} \"-1\"\n" | |
1e6808ea | 1528 | "@end lisp") |
1bbd0b84 | 1529 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1530 | { |
e11e83f3 | 1531 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
1532 | /* No overflow here, just need to toggle all the bits making up the inum. |
1533 | Enhancement: No need to strip the tag and add it back, could just xor | |
1534 | a block of 1 bits, if that worked with the various debug versions of | |
1535 | the SCM typedef. */ | |
e11e83f3 | 1536 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
1537 | |
1538 | } else if (SCM_BIGP (n)) { | |
1539 | SCM result = scm_i_mkbig (); | |
1540 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
1541 | scm_remember_upto_here_1 (n); | |
1542 | return result; | |
1543 | ||
1544 | } else { | |
1545 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1546 | } | |
0f2d19dd | 1547 | } |
1bbd0b84 | 1548 | #undef FUNC_NAME |
0f2d19dd | 1549 | |
518b7508 KR |
1550 | /* returns 0 if IN is not an integer. OUT must already be |
1551 | initialized. */ | |
1552 | static int | |
1553 | coerce_to_big (SCM in, mpz_t out) | |
1554 | { | |
1555 | if (SCM_BIGP (in)) | |
1556 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
1557 | else if (SCM_I_INUMP (in)) |
1558 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
1559 | else |
1560 | return 0; | |
1561 | ||
1562 | return 1; | |
1563 | } | |
1564 | ||
d885e204 | 1565 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
1566 | (SCM n, SCM k, SCM m), |
1567 | "Return @var{n} raised to the integer exponent\n" | |
1568 | "@var{k}, modulo @var{m}.\n" | |
1569 | "\n" | |
1570 | "@lisp\n" | |
1571 | "(modulo-expt 2 3 5)\n" | |
1572 | " @result{} 3\n" | |
1573 | "@end lisp") | |
d885e204 | 1574 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
1575 | { |
1576 | mpz_t n_tmp; | |
1577 | mpz_t k_tmp; | |
1578 | mpz_t m_tmp; | |
1579 | ||
1580 | /* There are two classes of error we might encounter -- | |
1581 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
1582 | and | |
1583 | 2) wrong-type errors, which of course we'll report by calling | |
1584 | SCM_WRONG_TYPE_ARG. | |
1585 | We don't report those errors immediately, however; instead we do | |
1586 | some cleanup first. These variables tell us which error (if | |
1587 | any) we should report after cleaning up. | |
1588 | */ | |
1589 | int report_overflow = 0; | |
1590 | ||
1591 | int position_of_wrong_type = 0; | |
1592 | SCM value_of_wrong_type = SCM_INUM0; | |
1593 | ||
1594 | SCM result = SCM_UNDEFINED; | |
1595 | ||
1596 | mpz_init (n_tmp); | |
1597 | mpz_init (k_tmp); | |
1598 | mpz_init (m_tmp); | |
1599 | ||
bc36d050 | 1600 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
1601 | { |
1602 | report_overflow = 1; | |
1603 | goto cleanup; | |
1604 | } | |
1605 | ||
1606 | if (!coerce_to_big (n, n_tmp)) | |
1607 | { | |
1608 | value_of_wrong_type = n; | |
1609 | position_of_wrong_type = 1; | |
1610 | goto cleanup; | |
1611 | } | |
1612 | ||
1613 | if (!coerce_to_big (k, k_tmp)) | |
1614 | { | |
1615 | value_of_wrong_type = k; | |
1616 | position_of_wrong_type = 2; | |
1617 | goto cleanup; | |
1618 | } | |
1619 | ||
1620 | if (!coerce_to_big (m, m_tmp)) | |
1621 | { | |
1622 | value_of_wrong_type = m; | |
1623 | position_of_wrong_type = 3; | |
1624 | goto cleanup; | |
1625 | } | |
1626 | ||
1627 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
1628 | will get a divide-by-zero exception when an inverse 1/n mod m | |
1629 | doesn't exist (or is not unique). Since exceptions are hard to | |
1630 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
1631 | a simple failure code, which is easy to handle. */ | |
1632 | ||
1633 | if (-1 == mpz_sgn (k_tmp)) | |
1634 | { | |
1635 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
1636 | { | |
1637 | report_overflow = 1; | |
1638 | goto cleanup; | |
1639 | } | |
1640 | mpz_neg (k_tmp, k_tmp); | |
1641 | } | |
1642 | ||
1643 | result = scm_i_mkbig (); | |
1644 | mpz_powm (SCM_I_BIG_MPZ (result), | |
1645 | n_tmp, | |
1646 | k_tmp, | |
1647 | m_tmp); | |
b7b8c575 KR |
1648 | |
1649 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
1650 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
1651 | ||
518b7508 KR |
1652 | cleanup: |
1653 | mpz_clear (m_tmp); | |
1654 | mpz_clear (k_tmp); | |
1655 | mpz_clear (n_tmp); | |
1656 | ||
1657 | if (report_overflow) | |
1658 | scm_num_overflow (FUNC_NAME); | |
1659 | ||
1660 | if (position_of_wrong_type) | |
1661 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
1662 | value_of_wrong_type); | |
1663 | ||
1664 | return scm_i_normbig (result); | |
1665 | } | |
1666 | #undef FUNC_NAME | |
1667 | ||
a1ec6916 | 1668 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1669 | (SCM n, SCM k), |
0bafe73b | 1670 | "Return @var{n} raised to the exact integer exponent\n" |
1e6808ea MG |
1671 | "@var{k}.\n" |
1672 | "\n" | |
b380b885 MD |
1673 | "@lisp\n" |
1674 | "(integer-expt 2 5)\n" | |
1675 | " @result{} 32\n" | |
1676 | "(integer-expt -3 3)\n" | |
1677 | " @result{} -27\n" | |
1678 | "@end lisp") | |
1bbd0b84 | 1679 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1680 | { |
1c35cb19 RB |
1681 | long i2 = 0; |
1682 | SCM z_i2 = SCM_BOOL_F; | |
1683 | int i2_is_big = 0; | |
d956fa6f | 1684 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 1685 | |
d57ed702 | 1686 | /* 0^0 == 1 according to R5RS */ |
bc36d050 | 1687 | if (scm_is_eq (n, SCM_INUM0) || scm_is_eq (n, acc)) |
73e4de09 | 1688 | return scm_is_false (scm_zero_p(k)) ? n : acc; |
bc36d050 | 1689 | else if (scm_is_eq (n, SCM_I_MAKINUM (-1L))) |
73e4de09 | 1690 | return scm_is_false (scm_even_p (k)) ? n : acc; |
ca46fb90 | 1691 | |
e11e83f3 MV |
1692 | if (SCM_I_INUMP (k)) |
1693 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
1694 | else if (SCM_BIGP (k)) |
1695 | { | |
1696 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
1697 | scm_remember_upto_here_1 (k); |
1698 | i2_is_big = 1; | |
1699 | } | |
2830fd91 | 1700 | else |
ca46fb90 RB |
1701 | SCM_WRONG_TYPE_ARG (2, k); |
1702 | ||
1703 | if (i2_is_big) | |
f872b822 | 1704 | { |
ca46fb90 RB |
1705 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
1706 | { | |
1707 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
1708 | n = scm_divide (n, SCM_UNDEFINED); | |
1709 | } | |
1710 | while (1) | |
1711 | { | |
1712 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
1713 | { | |
ca46fb90 RB |
1714 | return acc; |
1715 | } | |
1716 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
1717 | { | |
ca46fb90 RB |
1718 | return scm_product (acc, n); |
1719 | } | |
1720 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
1721 | acc = scm_product (acc, n); | |
1722 | n = scm_product (n, n); | |
1723 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
1724 | } | |
f872b822 | 1725 | } |
ca46fb90 | 1726 | else |
f872b822 | 1727 | { |
ca46fb90 RB |
1728 | if (i2 < 0) |
1729 | { | |
1730 | i2 = -i2; | |
1731 | n = scm_divide (n, SCM_UNDEFINED); | |
1732 | } | |
1733 | while (1) | |
1734 | { | |
1735 | if (0 == i2) | |
1736 | return acc; | |
1737 | if (1 == i2) | |
1738 | return scm_product (acc, n); | |
1739 | if (i2 & 1) | |
1740 | acc = scm_product (acc, n); | |
1741 | n = scm_product (n, n); | |
1742 | i2 >>= 1; | |
1743 | } | |
f872b822 | 1744 | } |
0f2d19dd | 1745 | } |
1bbd0b84 | 1746 | #undef FUNC_NAME |
0f2d19dd | 1747 | |
a1ec6916 | 1748 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1749 | (SCM n, SCM cnt), |
32f19569 KR |
1750 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
1751 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 1752 | "\n" |
e7644cb2 | 1753 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
1754 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
1755 | "infinity. (Note that this is not the same rounding as\n" | |
1756 | "@code{quotient} does.)\n" | |
1757 | "\n" | |
1758 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
1759 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
1760 | "shift dropping bits.\n" | |
1e6808ea | 1761 | "\n" |
b380b885 | 1762 | "@lisp\n" |
1e6808ea MG |
1763 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1764 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
1765 | "\n" |
1766 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
1767 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 1768 | "@end lisp") |
1bbd0b84 | 1769 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1770 | { |
3ab9f56e | 1771 | long bits_to_shift; |
5efd3c7d | 1772 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 RB |
1773 | |
1774 | if (bits_to_shift < 0) | |
1775 | { | |
1776 | /* Shift right by abs(cnt) bits. This is realized as a division | |
1777 | by div:=2^abs(cnt). However, to guarantee the floor | |
1778 | rounding, negative values require some special treatment. | |
1779 | */ | |
d956fa6f | 1780 | SCM div = scm_integer_expt (SCM_I_MAKINUM (2), |
5efd3c7d | 1781 | scm_from_long (-bits_to_shift)); |
f92e85f7 MV |
1782 | |
1783 | /* scm_quotient assumes its arguments are integers, but it's legal to (ash 1/2 -1) */ | |
73e4de09 | 1784 | if (scm_is_false (scm_negative_p (n))) |
ca46fb90 RB |
1785 | return scm_quotient (n, div); |
1786 | else | |
d956fa6f MV |
1787 | return scm_sum (SCM_I_MAKINUM (-1L), |
1788 | scm_quotient (scm_sum (SCM_I_MAKINUM (1L), n), div)); | |
ca46fb90 RB |
1789 | } |
1790 | else | |
3ab9f56e | 1791 | /* Shift left is done by multiplication with 2^CNT */ |
d956fa6f | 1792 | return scm_product (n, scm_integer_expt (SCM_I_MAKINUM (2), cnt)); |
0f2d19dd | 1793 | } |
1bbd0b84 | 1794 | #undef FUNC_NAME |
0f2d19dd | 1795 | |
3c9f20f8 | 1796 | |
a1ec6916 | 1797 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 1798 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
1799 | "Return the integer composed of the @var{start} (inclusive)\n" |
1800 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
1801 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
1802 | "\n" | |
b380b885 MD |
1803 | "@lisp\n" |
1804 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
1805 | " @result{} \"1010\"\n" | |
1806 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
1807 | " @result{} \"10110\"\n" | |
1808 | "@end lisp") | |
1bbd0b84 | 1809 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 1810 | { |
7f848242 | 1811 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
1812 | istart = scm_to_ulong (start); |
1813 | iend = scm_to_ulong (end); | |
c1bfcf60 | 1814 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 1815 | |
7f848242 KR |
1816 | /* how many bits to keep */ |
1817 | bits = iend - istart; | |
1818 | ||
e11e83f3 | 1819 | if (SCM_I_INUMP (n)) |
0aacf84e | 1820 | { |
e11e83f3 | 1821 | long int in = SCM_I_INUM (n); |
7f848242 KR |
1822 | |
1823 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 1824 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 1825 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 1826 | |
0aacf84e MD |
1827 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
1828 | { | |
1829 | /* Since we emulate two's complement encoded numbers, this | |
1830 | * special case requires us to produce a result that has | |
7f848242 | 1831 | * more bits than can be stored in a fixnum. |
0aacf84e | 1832 | */ |
7f848242 KR |
1833 | SCM result = scm_i_long2big (in); |
1834 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1835 | bits); | |
1836 | return result; | |
0aacf84e | 1837 | } |
ac0c002c | 1838 | |
7f848242 | 1839 | /* mask down to requisite bits */ |
857ae6af | 1840 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 1841 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
1842 | } |
1843 | else if (SCM_BIGP (n)) | |
ac0c002c | 1844 | { |
7f848242 KR |
1845 | SCM result; |
1846 | if (bits == 1) | |
1847 | { | |
d956fa6f | 1848 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
1849 | } |
1850 | else | |
1851 | { | |
1852 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
1853 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
1854 | such bits into a ulong. */ | |
1855 | result = scm_i_mkbig (); | |
1856 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
1857 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
1858 | result = scm_i_normbig (result); | |
1859 | } | |
1860 | scm_remember_upto_here_1 (n); | |
1861 | return result; | |
ac0c002c | 1862 | } |
0aacf84e | 1863 | else |
78166ad5 | 1864 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 1865 | } |
1bbd0b84 | 1866 | #undef FUNC_NAME |
0f2d19dd | 1867 | |
7f848242 | 1868 | |
e4755e5c JB |
1869 | static const char scm_logtab[] = { |
1870 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
1871 | }; | |
1cc91f1b | 1872 | |
a1ec6916 | 1873 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 1874 | (SCM n), |
1e6808ea MG |
1875 | "Return the number of bits in integer @var{n}. If integer is\n" |
1876 | "positive, the 1-bits in its binary representation are counted.\n" | |
1877 | "If negative, the 0-bits in its two's-complement binary\n" | |
1878 | "representation are counted. If 0, 0 is returned.\n" | |
1879 | "\n" | |
b380b885 MD |
1880 | "@lisp\n" |
1881 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
1882 | " @result{} 4\n" |
1883 | "(logcount 0)\n" | |
1884 | " @result{} 0\n" | |
1885 | "(logcount -2)\n" | |
1886 | " @result{} 1\n" | |
1887 | "@end lisp") | |
1888 | #define FUNC_NAME s_scm_logcount | |
1889 | { | |
e11e83f3 | 1890 | if (SCM_I_INUMP (n)) |
f872b822 | 1891 | { |
ca46fb90 | 1892 | unsigned long int c = 0; |
e11e83f3 | 1893 | long int nn = SCM_I_INUM (n); |
ca46fb90 RB |
1894 | if (nn < 0) |
1895 | nn = -1 - nn; | |
1896 | while (nn) | |
1897 | { | |
1898 | c += scm_logtab[15 & nn]; | |
1899 | nn >>= 4; | |
1900 | } | |
d956fa6f | 1901 | return SCM_I_MAKINUM (c); |
f872b822 | 1902 | } |
ca46fb90 | 1903 | else if (SCM_BIGP (n)) |
f872b822 | 1904 | { |
ca46fb90 | 1905 | unsigned long count; |
713a4259 KR |
1906 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
1907 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 1908 | else |
713a4259 KR |
1909 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
1910 | scm_remember_upto_here_1 (n); | |
d956fa6f | 1911 | return SCM_I_MAKINUM (count); |
f872b822 | 1912 | } |
ca46fb90 RB |
1913 | else |
1914 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 1915 | } |
ca46fb90 | 1916 | #undef FUNC_NAME |
0f2d19dd JB |
1917 | |
1918 | ||
ca46fb90 RB |
1919 | static const char scm_ilentab[] = { |
1920 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
1921 | }; | |
1922 | ||
0f2d19dd | 1923 | |
ca46fb90 RB |
1924 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
1925 | (SCM n), | |
1926 | "Return the number of bits necessary to represent @var{n}.\n" | |
1927 | "\n" | |
1928 | "@lisp\n" | |
1929 | "(integer-length #b10101010)\n" | |
1930 | " @result{} 8\n" | |
1931 | "(integer-length 0)\n" | |
1932 | " @result{} 0\n" | |
1933 | "(integer-length #b1111)\n" | |
1934 | " @result{} 4\n" | |
1935 | "@end lisp") | |
1936 | #define FUNC_NAME s_scm_integer_length | |
1937 | { | |
e11e83f3 | 1938 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
1939 | { |
1940 | unsigned long int c = 0; | |
1941 | unsigned int l = 4; | |
e11e83f3 | 1942 | long int nn = SCM_I_INUM (n); |
0aacf84e MD |
1943 | if (nn < 0) |
1944 | nn = -1 - nn; | |
1945 | while (nn) | |
1946 | { | |
1947 | c += 4; | |
1948 | l = scm_ilentab [15 & nn]; | |
1949 | nn >>= 4; | |
1950 | } | |
d956fa6f | 1951 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
1952 | } |
1953 | else if (SCM_BIGP (n)) | |
1954 | { | |
1955 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
1956 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
1957 | 1 too big, so check for that and adjust. */ | |
1958 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
1959 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
1960 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
1961 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
1962 | size--; | |
1963 | scm_remember_upto_here_1 (n); | |
d956fa6f | 1964 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
1965 | } |
1966 | else | |
ca46fb90 | 1967 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
1968 | } |
1969 | #undef FUNC_NAME | |
0f2d19dd JB |
1970 | |
1971 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
1972 | #define SCM_MAX_DBL_PREC 60 |
1973 | #define SCM_MAX_DBL_RADIX 36 | |
1974 | ||
1975 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
1976 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
1977 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
1978 | ||
1979 | static | |
1980 | void init_dblprec(int *prec, int radix) { | |
1981 | /* determine floating point precision by adding successively | |
1982 | smaller increments to 1.0 until it is considered == 1.0 */ | |
1983 | double f = ((double)1.0)/radix; | |
1984 | double fsum = 1.0 + f; | |
1985 | ||
1986 | *prec = 0; | |
1987 | while (fsum != 1.0) | |
1988 | { | |
1989 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
1990 | fsum = 1.0; | |
1991 | else | |
1992 | { | |
1993 | f /= radix; | |
1994 | fsum = f + 1.0; | |
1995 | } | |
1996 | } | |
1997 | (*prec) -= 1; | |
1998 | } | |
1999 | ||
2000 | static | |
2001 | void init_fx_radix(double *fx_list, int radix) | |
2002 | { | |
2003 | /* initialize a per-radix list of tolerances. When added | |
2004 | to a number < 1.0, we can determine if we should raund | |
2005 | up and quit converting a number to a string. */ | |
2006 | int i; | |
2007 | fx_list[0] = 0.0; | |
2008 | fx_list[1] = 0.5; | |
2009 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
2010 | fx_list[i] = (fx_list[i-1] / radix); | |
2011 | } | |
2012 | ||
2013 | /* use this array as a way to generate a single digit */ | |
2014 | static const char*number_chars="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; | |
0f2d19dd | 2015 | |
1be6b49c | 2016 | static size_t |
0b799eea | 2017 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 2018 | { |
0b799eea MV |
2019 | int efmt, dpt, d, i, wp; |
2020 | double *fx; | |
2021 | #ifdef DBL_MIN_10_EXP | |
2022 | double f_cpy; | |
2023 | int exp_cpy; | |
2024 | #endif /* DBL_MIN_10_EXP */ | |
2025 | size_t ch = 0; | |
2026 | int exp = 0; | |
2027 | ||
2028 | if(radix < 2 || | |
2029 | radix > SCM_MAX_DBL_RADIX) | |
2030 | { | |
2031 | /* revert to existing behavior */ | |
2032 | radix = 10; | |
2033 | } | |
2034 | ||
2035 | wp = scm_dblprec[radix-2]; | |
2036 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 2037 | |
f872b822 | 2038 | if (f == 0.0) |
abb7e44d MV |
2039 | { |
2040 | #ifdef HAVE_COPYSIGN | |
2041 | double sgn = copysign (1.0, f); | |
2042 | ||
2043 | if (sgn < 0.0) | |
2044 | a[ch++] = '-'; | |
2045 | #endif | |
abb7e44d MV |
2046 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
2047 | } | |
7351e207 MV |
2048 | |
2049 | if (xisinf (f)) | |
2050 | { | |
2051 | if (f < 0) | |
2052 | strcpy (a, "-inf.0"); | |
2053 | else | |
2054 | strcpy (a, "+inf.0"); | |
2055 | return ch+6; | |
2056 | } | |
2057 | else if (xisnan (f)) | |
2058 | { | |
2059 | strcpy (a, "+nan.0"); | |
2060 | return ch+6; | |
2061 | } | |
2062 | ||
f872b822 MD |
2063 | if (f < 0.0) |
2064 | { | |
2065 | f = -f; | |
2066 | a[ch++] = '-'; | |
2067 | } | |
7351e207 | 2068 | |
f872b822 MD |
2069 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
2070 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
2071 | /* just do the checking...if it passes, we do the conversion for our |
2072 | radix again below */ | |
2073 | f_cpy = f; | |
2074 | exp_cpy = exp; | |
2075 | ||
2076 | while (f_cpy < 1.0) | |
f872b822 | 2077 | { |
0b799eea MV |
2078 | f_cpy *= 10.0; |
2079 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
2080 | { |
2081 | a[ch++] = '#'; | |
2082 | a[ch++] = '.'; | |
2083 | a[ch++] = '#'; | |
2084 | return ch; | |
2085 | } | |
f872b822 | 2086 | } |
0b799eea | 2087 | while (f_cpy > 10.0) |
f872b822 | 2088 | { |
0b799eea MV |
2089 | f_cpy *= 0.10; |
2090 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
2091 | { |
2092 | a[ch++] = '#'; | |
2093 | a[ch++] = '.'; | |
2094 | a[ch++] = '#'; | |
2095 | return ch; | |
2096 | } | |
f872b822 | 2097 | } |
0b799eea MV |
2098 | #endif |
2099 | ||
f872b822 MD |
2100 | while (f < 1.0) |
2101 | { | |
0b799eea | 2102 | f *= radix; |
f872b822 MD |
2103 | exp--; |
2104 | } | |
0b799eea | 2105 | while (f > radix) |
f872b822 | 2106 | { |
0b799eea | 2107 | f /= radix; |
f872b822 MD |
2108 | exp++; |
2109 | } | |
0b799eea MV |
2110 | |
2111 | if (f + fx[wp] >= radix) | |
f872b822 MD |
2112 | { |
2113 | f = 1.0; | |
2114 | exp++; | |
2115 | } | |
0f2d19dd | 2116 | zero: |
0b799eea MV |
2117 | #ifdef ENGNOT |
2118 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 2119 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
2120 | exp -= dpt++; |
2121 | efmt = 1; | |
f872b822 MD |
2122 | #else |
2123 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 2124 | if (!efmt) |
cda139a7 MD |
2125 | { |
2126 | if (exp < 0) | |
2127 | { | |
2128 | a[ch++] = '0'; | |
2129 | a[ch++] = '.'; | |
2130 | dpt = exp; | |
f872b822 MD |
2131 | while (++dpt) |
2132 | a[ch++] = '0'; | |
cda139a7 MD |
2133 | } |
2134 | else | |
f872b822 | 2135 | dpt = exp + 1; |
cda139a7 | 2136 | } |
0f2d19dd JB |
2137 | else |
2138 | dpt = 1; | |
f872b822 MD |
2139 | #endif |
2140 | ||
2141 | do | |
2142 | { | |
2143 | d = f; | |
2144 | f -= d; | |
0b799eea | 2145 | a[ch++] = number_chars[d]; |
f872b822 MD |
2146 | if (f < fx[wp]) |
2147 | break; | |
2148 | if (f + fx[wp] >= 1.0) | |
2149 | { | |
0b799eea | 2150 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
2151 | break; |
2152 | } | |
0b799eea | 2153 | f *= radix; |
f872b822 MD |
2154 | if (!(--dpt)) |
2155 | a[ch++] = '.'; | |
0f2d19dd | 2156 | } |
f872b822 | 2157 | while (wp--); |
0f2d19dd JB |
2158 | |
2159 | if (dpt > 0) | |
cda139a7 | 2160 | { |
f872b822 | 2161 | #ifndef ENGNOT |
cda139a7 MD |
2162 | if ((dpt > 4) && (exp > 6)) |
2163 | { | |
f872b822 | 2164 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 2165 | for (i = ch++; i > d; i--) |
f872b822 | 2166 | a[i] = a[i - 1]; |
cda139a7 MD |
2167 | a[d] = '.'; |
2168 | efmt = 1; | |
2169 | } | |
2170 | else | |
f872b822 | 2171 | #endif |
cda139a7 | 2172 | { |
f872b822 MD |
2173 | while (--dpt) |
2174 | a[ch++] = '0'; | |
cda139a7 MD |
2175 | a[ch++] = '.'; |
2176 | } | |
2177 | } | |
f872b822 MD |
2178 | if (a[ch - 1] == '.') |
2179 | a[ch++] = '0'; /* trailing zero */ | |
2180 | if (efmt && exp) | |
2181 | { | |
2182 | a[ch++] = 'e'; | |
2183 | if (exp < 0) | |
2184 | { | |
2185 | exp = -exp; | |
2186 | a[ch++] = '-'; | |
2187 | } | |
0b799eea MV |
2188 | for (i = radix; i <= exp; i *= radix); |
2189 | for (i /= radix; i; i /= radix) | |
f872b822 | 2190 | { |
0b799eea | 2191 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
2192 | exp %= i; |
2193 | } | |
0f2d19dd | 2194 | } |
0f2d19dd JB |
2195 | return ch; |
2196 | } | |
2197 | ||
1be6b49c | 2198 | static size_t |
0b799eea | 2199 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 2200 | { |
1be6b49c | 2201 | size_t i; |
3c9a524f | 2202 | if (SCM_REALP (flt)) |
0b799eea | 2203 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 2204 | else |
f872b822 | 2205 | { |
0b799eea | 2206 | i = idbl2str (SCM_COMPLEX_REAL (flt), str, radix); |
f3ae5d60 MD |
2207 | if (SCM_COMPLEX_IMAG (flt) != 0.0) |
2208 | { | |
7351e207 MV |
2209 | double imag = SCM_COMPLEX_IMAG (flt); |
2210 | /* Don't output a '+' for negative numbers or for Inf and | |
2211 | NaN. They will provide their own sign. */ | |
2212 | if (0 <= imag && !xisinf (imag) && !xisnan (imag)) | |
f3ae5d60 | 2213 | str[i++] = '+'; |
0b799eea | 2214 | i += idbl2str (imag, &str[i], radix); |
f3ae5d60 MD |
2215 | str[i++] = 'i'; |
2216 | } | |
f872b822 | 2217 | } |
0f2d19dd JB |
2218 | return i; |
2219 | } | |
0f2d19dd | 2220 | |
5c11cc9d | 2221 | /* convert a long to a string (unterminated). returns the number of |
1bbd0b84 GB |
2222 | characters in the result. |
2223 | rad is output base | |
2224 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2225 | size_t |
1bbd0b84 | 2226 | scm_iint2str (long num, int rad, char *p) |
0f2d19dd | 2227 | { |
1be6b49c ML |
2228 | size_t j = 1; |
2229 | size_t i; | |
5c11cc9d GH |
2230 | unsigned long n = (num < 0) ? -num : num; |
2231 | ||
f872b822 | 2232 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2233 | j++; |
2234 | ||
2235 | i = j; | |
2236 | if (num < 0) | |
f872b822 | 2237 | { |
f872b822 | 2238 | *p++ = '-'; |
5c11cc9d GH |
2239 | j++; |
2240 | n = -num; | |
f872b822 | 2241 | } |
5c11cc9d GH |
2242 | else |
2243 | n = num; | |
f872b822 MD |
2244 | while (i--) |
2245 | { | |
5c11cc9d GH |
2246 | int d = n % rad; |
2247 | ||
f872b822 MD |
2248 | n /= rad; |
2249 | p[i] = d + ((d < 10) ? '0' : 'a' - 10); | |
2250 | } | |
0f2d19dd JB |
2251 | return j; |
2252 | } | |
2253 | ||
a1ec6916 | 2254 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2255 | (SCM n, SCM radix), |
2256 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2257 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2258 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2259 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2260 | { |
1bbd0b84 | 2261 | int base; |
98cb6e75 | 2262 | |
0aacf84e | 2263 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 2264 | base = 10; |
0aacf84e | 2265 | else |
5efd3c7d | 2266 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 2267 | |
e11e83f3 | 2268 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2269 | { |
2270 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 2271 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 2272 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
2273 | } |
2274 | else if (SCM_BIGP (n)) | |
2275 | { | |
2276 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
2277 | scm_remember_upto_here_1 (n); | |
cc95e00a | 2278 | return scm_take_locale_string (str); |
0aacf84e | 2279 | } |
f92e85f7 MV |
2280 | else if (SCM_FRACTIONP (n)) |
2281 | { | |
2282 | scm_i_fraction_reduce (n); | |
2283 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), | |
cc95e00a | 2284 | scm_from_locale_string ("/"), |
f92e85f7 MV |
2285 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
2286 | } | |
0aacf84e MD |
2287 | else if (SCM_INEXACTP (n)) |
2288 | { | |
2289 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 2290 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
2291 | } |
2292 | else | |
bb628794 | 2293 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 2294 | } |
1bbd0b84 | 2295 | #undef FUNC_NAME |
0f2d19dd JB |
2296 | |
2297 | ||
ca46fb90 RB |
2298 | /* These print routines used to be stubbed here so that scm_repl.c |
2299 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 2300 | |
0f2d19dd | 2301 | int |
e81d98ec | 2302 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2303 | { |
56e55ac7 | 2304 | char num_buf[FLOBUFLEN]; |
0b799eea | 2305 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
2306 | return !0; |
2307 | } | |
2308 | ||
f3ae5d60 | 2309 | int |
e81d98ec | 2310 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 2311 | |
f3ae5d60 | 2312 | { |
56e55ac7 | 2313 | char num_buf[FLOBUFLEN]; |
0b799eea | 2314 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
2315 | return !0; |
2316 | } | |
1cc91f1b | 2317 | |
f92e85f7 MV |
2318 | int |
2319 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
2320 | { | |
2321 | SCM str; | |
2322 | scm_i_fraction_reduce (sexp); | |
2323 | str = scm_number_to_string (sexp, SCM_UNDEFINED); | |
cc95e00a | 2324 | scm_lfwrite (scm_i_string_chars (str), scm_i_string_length (str), port); |
f92e85f7 MV |
2325 | scm_remember_upto_here_1 (str); |
2326 | return !0; | |
2327 | } | |
2328 | ||
0f2d19dd | 2329 | int |
e81d98ec | 2330 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2331 | { |
ca46fb90 RB |
2332 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
2333 | scm_remember_upto_here_1 (exp); | |
2334 | scm_lfwrite (str, (size_t) strlen (str), port); | |
2335 | free (str); | |
0f2d19dd JB |
2336 | return !0; |
2337 | } | |
2338 | /*** END nums->strs ***/ | |
2339 | ||
3c9a524f | 2340 | |
0f2d19dd | 2341 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2342 | |
3c9a524f DH |
2343 | /* The following functions implement the conversion from strings to numbers. |
2344 | * The implementation somehow follows the grammar for numbers as it is given | |
2345 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2346 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2347 | * points should be noted about the implementation: | |
2348 | * * Each function keeps a local index variable 'idx' that points at the | |
2349 | * current position within the parsed string. The global index is only | |
2350 | * updated if the function could parse the corresponding syntactic unit | |
2351 | * successfully. | |
2352 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2353 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2354 | * global exactness information is only updated after each part has been | |
2355 | * successfully parsed. | |
2356 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2357 | * Only if these fixnums would overflow, the result variables are updated | |
2358 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2359 | * the temporary variables holding the fixnums are cleared, and the process | |
2360 | * starts over again. If for example fixnums were able to store five decimal | |
2361 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2362 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2363 | * only every five digits two bignum operations were performed. | |
2364 | */ | |
2365 | ||
2366 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2367 | ||
2368 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2369 | ||
2370 | /* In non ASCII-style encodings the following macro might not work. */ | |
71df73ac KR |
2371 | #define XDIGIT2UINT(d) \ |
2372 | (isdigit ((int) (unsigned char) d) \ | |
2373 | ? (d) - '0' \ | |
2374 | : tolower ((int) (unsigned char) d) - 'a' + 10) | |
3c9a524f | 2375 | |
2a8fecee | 2376 | static SCM |
3c9a524f DH |
2377 | mem2uinteger (const char* mem, size_t len, unsigned int *p_idx, |
2378 | unsigned int radix, enum t_exactness *p_exactness) | |
2a8fecee | 2379 | { |
3c9a524f DH |
2380 | unsigned int idx = *p_idx; |
2381 | unsigned int hash_seen = 0; | |
2382 | scm_t_bits shift = 1; | |
2383 | scm_t_bits add = 0; | |
2384 | unsigned int digit_value; | |
2385 | SCM result; | |
2386 | char c; | |
2387 | ||
2388 | if (idx == len) | |
2389 | return SCM_BOOL_F; | |
2a8fecee | 2390 | |
3c9a524f | 2391 | c = mem[idx]; |
71df73ac | 2392 | if (!isxdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2393 | return SCM_BOOL_F; |
2394 | digit_value = XDIGIT2UINT (c); | |
2395 | if (digit_value >= radix) | |
2396 | return SCM_BOOL_F; | |
2397 | ||
2398 | idx++; | |
d956fa6f | 2399 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 2400 | while (idx != len) |
f872b822 | 2401 | { |
3c9a524f | 2402 | char c = mem[idx]; |
71df73ac | 2403 | if (isxdigit ((int) (unsigned char) c)) |
f872b822 | 2404 | { |
3c9a524f | 2405 | if (hash_seen) |
1fe5e088 | 2406 | break; |
3c9a524f DH |
2407 | digit_value = XDIGIT2UINT (c); |
2408 | if (digit_value >= radix) | |
1fe5e088 | 2409 | break; |
f872b822 | 2410 | } |
3c9a524f DH |
2411 | else if (c == '#') |
2412 | { | |
2413 | hash_seen = 1; | |
2414 | digit_value = 0; | |
2415 | } | |
2416 | else | |
2417 | break; | |
2418 | ||
2419 | idx++; | |
2420 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2421 | { | |
d956fa6f | 2422 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2423 | if (add > 0) |
d956fa6f | 2424 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2425 | |
2426 | shift = radix; | |
2427 | add = digit_value; | |
2428 | } | |
2429 | else | |
2430 | { | |
2431 | shift = shift * radix; | |
2432 | add = add * radix + digit_value; | |
2433 | } | |
2434 | }; | |
2435 | ||
2436 | if (shift > 1) | |
d956fa6f | 2437 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2438 | if (add > 0) |
d956fa6f | 2439 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2440 | |
2441 | *p_idx = idx; | |
2442 | if (hash_seen) | |
2443 | *p_exactness = INEXACT; | |
2444 | ||
2445 | return result; | |
2a8fecee JB |
2446 | } |
2447 | ||
2448 | ||
3c9a524f DH |
2449 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2450 | * covers the parts of the rules that start at a potential point. The value | |
2451 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2452 | * in variable result. The content of *p_exactness indicates, whether a hash |
2453 | * has already been seen in the digits before the point. | |
3c9a524f | 2454 | */ |
1cc91f1b | 2455 | |
3c9a524f DH |
2456 | /* In non ASCII-style encodings the following macro might not work. */ |
2457 | #define DIGIT2UINT(d) ((d) - '0') | |
2458 | ||
2459 | static SCM | |
79d34f68 | 2460 | mem2decimal_from_point (SCM result, const char* mem, size_t len, |
3c9a524f | 2461 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2462 | { |
3c9a524f DH |
2463 | unsigned int idx = *p_idx; |
2464 | enum t_exactness x = *p_exactness; | |
3c9a524f DH |
2465 | |
2466 | if (idx == len) | |
79d34f68 | 2467 | return result; |
3c9a524f DH |
2468 | |
2469 | if (mem[idx] == '.') | |
2470 | { | |
2471 | scm_t_bits shift = 1; | |
2472 | scm_t_bits add = 0; | |
2473 | unsigned int digit_value; | |
d956fa6f | 2474 | SCM big_shift = SCM_I_MAKINUM (1); |
3c9a524f DH |
2475 | |
2476 | idx++; | |
2477 | while (idx != len) | |
2478 | { | |
2479 | char c = mem[idx]; | |
71df73ac | 2480 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2481 | { |
2482 | if (x == INEXACT) | |
2483 | return SCM_BOOL_F; | |
2484 | else | |
2485 | digit_value = DIGIT2UINT (c); | |
2486 | } | |
2487 | else if (c == '#') | |
2488 | { | |
2489 | x = INEXACT; | |
2490 | digit_value = 0; | |
2491 | } | |
2492 | else | |
2493 | break; | |
2494 | ||
2495 | idx++; | |
2496 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2497 | { | |
d956fa6f MV |
2498 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2499 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 2500 | if (add > 0) |
d956fa6f | 2501 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2502 | |
2503 | shift = 10; | |
2504 | add = digit_value; | |
2505 | } | |
2506 | else | |
2507 | { | |
2508 | shift = shift * 10; | |
2509 | add = add * 10 + digit_value; | |
2510 | } | |
2511 | }; | |
2512 | ||
2513 | if (add > 0) | |
2514 | { | |
d956fa6f MV |
2515 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2516 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
2517 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
2518 | } |
2519 | ||
d8592269 | 2520 | result = scm_divide (result, big_shift); |
79d34f68 | 2521 | |
3c9a524f DH |
2522 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2523 | x = INEXACT; | |
f872b822 | 2524 | } |
3c9a524f | 2525 | |
3c9a524f | 2526 | if (idx != len) |
f872b822 | 2527 | { |
3c9a524f DH |
2528 | int sign = 1; |
2529 | unsigned int start; | |
2530 | char c; | |
2531 | int exponent; | |
2532 | SCM e; | |
2533 | ||
2534 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2535 | ||
2536 | switch (mem[idx]) | |
f872b822 | 2537 | { |
3c9a524f DH |
2538 | case 'd': case 'D': |
2539 | case 'e': case 'E': | |
2540 | case 'f': case 'F': | |
2541 | case 'l': case 'L': | |
2542 | case 's': case 'S': | |
2543 | idx++; | |
2544 | start = idx; | |
2545 | c = mem[idx]; | |
2546 | if (c == '-') | |
2547 | { | |
2548 | idx++; | |
2549 | sign = -1; | |
2550 | c = mem[idx]; | |
2551 | } | |
2552 | else if (c == '+') | |
2553 | { | |
2554 | idx++; | |
2555 | sign = 1; | |
2556 | c = mem[idx]; | |
2557 | } | |
2558 | else | |
2559 | sign = 1; | |
2560 | ||
71df73ac | 2561 | if (!isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2562 | return SCM_BOOL_F; |
2563 | ||
2564 | idx++; | |
2565 | exponent = DIGIT2UINT (c); | |
2566 | while (idx != len) | |
f872b822 | 2567 | { |
3c9a524f | 2568 | char c = mem[idx]; |
71df73ac | 2569 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2570 | { |
2571 | idx++; | |
2572 | if (exponent <= SCM_MAXEXP) | |
2573 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2574 | } | |
2575 | else | |
2576 | break; | |
f872b822 | 2577 | } |
3c9a524f DH |
2578 | |
2579 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2580 | { |
3c9a524f | 2581 | size_t exp_len = idx - start; |
cc95e00a | 2582 | SCM exp_string = scm_from_locale_stringn (&mem[start], exp_len); |
3c9a524f DH |
2583 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
2584 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2585 | } |
3c9a524f | 2586 | |
d956fa6f | 2587 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
2588 | if (sign == 1) |
2589 | result = scm_product (result, e); | |
2590 | else | |
f92e85f7 | 2591 | result = scm_divide2real (result, e); |
3c9a524f DH |
2592 | |
2593 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2594 | x = INEXACT; | |
2595 | ||
f872b822 | 2596 | break; |
3c9a524f | 2597 | |
f872b822 | 2598 | default: |
3c9a524f | 2599 | break; |
f872b822 | 2600 | } |
0f2d19dd | 2601 | } |
3c9a524f DH |
2602 | |
2603 | *p_idx = idx; | |
2604 | if (x == INEXACT) | |
2605 | *p_exactness = x; | |
2606 | ||
2607 | return result; | |
0f2d19dd | 2608 | } |
0f2d19dd | 2609 | |
3c9a524f DH |
2610 | |
2611 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2612 | ||
2613 | static SCM | |
2614 | mem2ureal (const char* mem, size_t len, unsigned int *p_idx, | |
2615 | unsigned int radix, enum t_exactness *p_exactness) | |
0f2d19dd | 2616 | { |
3c9a524f | 2617 | unsigned int idx = *p_idx; |
164d2481 | 2618 | SCM result; |
3c9a524f DH |
2619 | |
2620 | if (idx == len) | |
2621 | return SCM_BOOL_F; | |
2622 | ||
7351e207 MV |
2623 | if (idx+5 <= len && !strncmp (mem+idx, "inf.0", 5)) |
2624 | { | |
2625 | *p_idx = idx+5; | |
2626 | return scm_inf (); | |
2627 | } | |
2628 | ||
2629 | if (idx+4 < len && !strncmp (mem+idx, "nan.", 4)) | |
2630 | { | |
2631 | enum t_exactness x = EXACT; | |
2632 | ||
d8592269 MV |
2633 | /* Cobble up the fractional part. We might want to set the |
2634 | NaN's mantissa from it. */ | |
7351e207 MV |
2635 | idx += 4; |
2636 | mem2uinteger (mem, len, &idx, 10, &x); | |
2637 | *p_idx = idx; | |
2638 | return scm_nan (); | |
2639 | } | |
2640 | ||
3c9a524f DH |
2641 | if (mem[idx] == '.') |
2642 | { | |
2643 | if (radix != 10) | |
2644 | return SCM_BOOL_F; | |
2645 | else if (idx + 1 == len) | |
2646 | return SCM_BOOL_F; | |
71df73ac | 2647 | else if (!isdigit ((int) (unsigned char) mem[idx + 1])) |
3c9a524f DH |
2648 | return SCM_BOOL_F; |
2649 | else | |
d956fa6f | 2650 | result = mem2decimal_from_point (SCM_I_MAKINUM (0), mem, len, |
164d2481 | 2651 | p_idx, p_exactness); |
f872b822 | 2652 | } |
3c9a524f DH |
2653 | else |
2654 | { | |
2655 | enum t_exactness x = EXACT; | |
2656 | SCM uinteger; | |
3c9a524f DH |
2657 | |
2658 | uinteger = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2659 | if (scm_is_false (uinteger)) |
3c9a524f DH |
2660 | return SCM_BOOL_F; |
2661 | ||
2662 | if (idx == len) | |
2663 | result = uinteger; | |
2664 | else if (mem[idx] == '/') | |
f872b822 | 2665 | { |
3c9a524f DH |
2666 | SCM divisor; |
2667 | ||
2668 | idx++; | |
2669 | ||
2670 | divisor = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2671 | if (scm_is_false (divisor)) |
3c9a524f DH |
2672 | return SCM_BOOL_F; |
2673 | ||
f92e85f7 | 2674 | /* both are int/big here, I assume */ |
cba42c93 | 2675 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 2676 | } |
3c9a524f DH |
2677 | else if (radix == 10) |
2678 | { | |
2679 | result = mem2decimal_from_point (uinteger, mem, len, &idx, &x); | |
73e4de09 | 2680 | if (scm_is_false (result)) |
3c9a524f DH |
2681 | return SCM_BOOL_F; |
2682 | } | |
2683 | else | |
2684 | result = uinteger; | |
2685 | ||
2686 | *p_idx = idx; | |
2687 | if (x == INEXACT) | |
2688 | *p_exactness = x; | |
f872b822 | 2689 | } |
164d2481 MV |
2690 | |
2691 | /* When returning an inexact zero, make sure it is represented as a | |
2692 | floating point value so that we can change its sign. | |
2693 | */ | |
bc36d050 | 2694 | if (scm_is_eq (result, SCM_I_MAKINUM(0)) && *p_exactness == INEXACT) |
55f26379 | 2695 | result = scm_from_double (0.0); |
164d2481 MV |
2696 | |
2697 | return result; | |
3c9a524f | 2698 | } |
0f2d19dd | 2699 | |
0f2d19dd | 2700 | |
3c9a524f | 2701 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2702 | |
3c9a524f DH |
2703 | static SCM |
2704 | mem2complex (const char* mem, size_t len, unsigned int idx, | |
2705 | unsigned int radix, enum t_exactness *p_exactness) | |
2706 | { | |
2707 | char c; | |
2708 | int sign = 0; | |
2709 | SCM ureal; | |
2710 | ||
2711 | if (idx == len) | |
2712 | return SCM_BOOL_F; | |
2713 | ||
2714 | c = mem[idx]; | |
2715 | if (c == '+') | |
2716 | { | |
2717 | idx++; | |
2718 | sign = 1; | |
2719 | } | |
2720 | else if (c == '-') | |
2721 | { | |
2722 | idx++; | |
2723 | sign = -1; | |
0f2d19dd | 2724 | } |
0f2d19dd | 2725 | |
3c9a524f DH |
2726 | if (idx == len) |
2727 | return SCM_BOOL_F; | |
2728 | ||
2729 | ureal = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2730 | if (scm_is_false (ureal)) |
f872b822 | 2731 | { |
3c9a524f DH |
2732 | /* input must be either +i or -i */ |
2733 | ||
2734 | if (sign == 0) | |
2735 | return SCM_BOOL_F; | |
2736 | ||
2737 | if (mem[idx] == 'i' || mem[idx] == 'I') | |
f872b822 | 2738 | { |
3c9a524f DH |
2739 | idx++; |
2740 | if (idx != len) | |
2741 | return SCM_BOOL_F; | |
2742 | ||
d956fa6f | 2743 | return scm_make_rectangular (SCM_I_MAKINUM (0), SCM_I_MAKINUM (sign)); |
f872b822 | 2744 | } |
3c9a524f DH |
2745 | else |
2746 | return SCM_BOOL_F; | |
0f2d19dd | 2747 | } |
3c9a524f DH |
2748 | else |
2749 | { | |
73e4de09 | 2750 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 2751 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 2752 | |
3c9a524f DH |
2753 | if (idx == len) |
2754 | return ureal; | |
2755 | ||
2756 | c = mem[idx]; | |
2757 | switch (c) | |
f872b822 | 2758 | { |
3c9a524f DH |
2759 | case 'i': case 'I': |
2760 | /* either +<ureal>i or -<ureal>i */ | |
2761 | ||
2762 | idx++; | |
2763 | if (sign == 0) | |
2764 | return SCM_BOOL_F; | |
2765 | if (idx != len) | |
2766 | return SCM_BOOL_F; | |
d956fa6f | 2767 | return scm_make_rectangular (SCM_I_MAKINUM (0), ureal); |
3c9a524f DH |
2768 | |
2769 | case '@': | |
2770 | /* polar input: <real>@<real>. */ | |
2771 | ||
2772 | idx++; | |
2773 | if (idx == len) | |
2774 | return SCM_BOOL_F; | |
2775 | else | |
f872b822 | 2776 | { |
3c9a524f DH |
2777 | int sign; |
2778 | SCM angle; | |
2779 | SCM result; | |
2780 | ||
2781 | c = mem[idx]; | |
2782 | if (c == '+') | |
2783 | { | |
2784 | idx++; | |
2785 | sign = 1; | |
2786 | } | |
2787 | else if (c == '-') | |
2788 | { | |
2789 | idx++; | |
2790 | sign = -1; | |
2791 | } | |
2792 | else | |
2793 | sign = 1; | |
2794 | ||
2795 | angle = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2796 | if (scm_is_false (angle)) |
3c9a524f DH |
2797 | return SCM_BOOL_F; |
2798 | if (idx != len) | |
2799 | return SCM_BOOL_F; | |
2800 | ||
73e4de09 | 2801 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
2802 | angle = scm_difference (angle, SCM_UNDEFINED); |
2803 | ||
2804 | result = scm_make_polar (ureal, angle); | |
2805 | return result; | |
f872b822 | 2806 | } |
3c9a524f DH |
2807 | case '+': |
2808 | case '-': | |
2809 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 2810 | |
3c9a524f DH |
2811 | idx++; |
2812 | if (idx == len) | |
2813 | return SCM_BOOL_F; | |
2814 | else | |
2815 | { | |
2816 | int sign = (c == '+') ? 1 : -1; | |
2817 | SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness); | |
0f2d19dd | 2818 | |
73e4de09 | 2819 | if (scm_is_false (imag)) |
d956fa6f | 2820 | imag = SCM_I_MAKINUM (sign); |
73e4de09 | 2821 | else if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
1fe5e088 | 2822 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 2823 | |
3c9a524f DH |
2824 | if (idx == len) |
2825 | return SCM_BOOL_F; | |
2826 | if (mem[idx] != 'i' && mem[idx] != 'I') | |
2827 | return SCM_BOOL_F; | |
0f2d19dd | 2828 | |
3c9a524f DH |
2829 | idx++; |
2830 | if (idx != len) | |
2831 | return SCM_BOOL_F; | |
0f2d19dd | 2832 | |
1fe5e088 | 2833 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
2834 | } |
2835 | default: | |
2836 | return SCM_BOOL_F; | |
2837 | } | |
2838 | } | |
0f2d19dd | 2839 | } |
0f2d19dd JB |
2840 | |
2841 | ||
3c9a524f DH |
2842 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
2843 | ||
2844 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 2845 | |
0f2d19dd | 2846 | SCM |
3c9a524f | 2847 | scm_i_mem2number (const char* mem, size_t len, unsigned int default_radix) |
0f2d19dd | 2848 | { |
3c9a524f DH |
2849 | unsigned int idx = 0; |
2850 | unsigned int radix = NO_RADIX; | |
2851 | enum t_exactness forced_x = NO_EXACTNESS; | |
2852 | enum t_exactness implicit_x = EXACT; | |
2853 | SCM result; | |
2854 | ||
2855 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
2856 | while (idx + 2 < len && mem[idx] == '#') | |
2857 | { | |
2858 | switch (mem[idx + 1]) | |
2859 | { | |
2860 | case 'b': case 'B': | |
2861 | if (radix != NO_RADIX) | |
2862 | return SCM_BOOL_F; | |
2863 | radix = DUAL; | |
2864 | break; | |
2865 | case 'd': case 'D': | |
2866 | if (radix != NO_RADIX) | |
2867 | return SCM_BOOL_F; | |
2868 | radix = DEC; | |
2869 | break; | |
2870 | case 'i': case 'I': | |
2871 | if (forced_x != NO_EXACTNESS) | |
2872 | return SCM_BOOL_F; | |
2873 | forced_x = INEXACT; | |
2874 | break; | |
2875 | case 'e': case 'E': | |
2876 | if (forced_x != NO_EXACTNESS) | |
2877 | return SCM_BOOL_F; | |
2878 | forced_x = EXACT; | |
2879 | break; | |
2880 | case 'o': case 'O': | |
2881 | if (radix != NO_RADIX) | |
2882 | return SCM_BOOL_F; | |
2883 | radix = OCT; | |
2884 | break; | |
2885 | case 'x': case 'X': | |
2886 | if (radix != NO_RADIX) | |
2887 | return SCM_BOOL_F; | |
2888 | radix = HEX; | |
2889 | break; | |
2890 | default: | |
f872b822 | 2891 | return SCM_BOOL_F; |
3c9a524f DH |
2892 | } |
2893 | idx += 2; | |
2894 | } | |
2895 | ||
2896 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
2897 | if (radix == NO_RADIX) | |
2898 | result = mem2complex (mem, len, idx, default_radix, &implicit_x); | |
2899 | else | |
2900 | result = mem2complex (mem, len, idx, (unsigned int) radix, &implicit_x); | |
2901 | ||
73e4de09 | 2902 | if (scm_is_false (result)) |
3c9a524f | 2903 | return SCM_BOOL_F; |
f872b822 | 2904 | |
3c9a524f | 2905 | switch (forced_x) |
f872b822 | 2906 | { |
3c9a524f DH |
2907 | case EXACT: |
2908 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
2909 | return scm_inexact_to_exact (result); |
2910 | else | |
2911 | return result; | |
2912 | case INEXACT: | |
2913 | if (SCM_INEXACTP (result)) | |
2914 | return result; | |
2915 | else | |
2916 | return scm_exact_to_inexact (result); | |
2917 | case NO_EXACTNESS: | |
2918 | default: | |
2919 | if (implicit_x == INEXACT) | |
2920 | { | |
2921 | if (SCM_INEXACTP (result)) | |
2922 | return result; | |
2923 | else | |
2924 | return scm_exact_to_inexact (result); | |
2925 | } | |
2926 | else | |
2927 | return result; | |
f872b822 | 2928 | } |
0f2d19dd JB |
2929 | } |
2930 | ||
2931 | ||
a1ec6916 | 2932 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 2933 | (SCM string, SCM radix), |
1e6808ea | 2934 | "Return a number of the maximally precise representation\n" |
942e5b91 | 2935 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
2936 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
2937 | "is a default radix that may be overridden by an explicit radix\n" | |
2938 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
2939 | "supplied, then the default radix is 10. If string is not a\n" | |
2940 | "syntactically valid notation for a number, then\n" | |
2941 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 2942 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
2943 | { |
2944 | SCM answer; | |
5efd3c7d | 2945 | unsigned int base; |
a6d9e5ab | 2946 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
2947 | |
2948 | if (SCM_UNBNDP (radix)) | |
2949 | base = 10; | |
2950 | else | |
2951 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
2952 | ||
cc95e00a MV |
2953 | answer = scm_i_mem2number (scm_i_string_chars (string), |
2954 | scm_i_string_length (string), | |
d8592269 | 2955 | base); |
8824ac88 MV |
2956 | scm_remember_upto_here_1 (string); |
2957 | return answer; | |
0f2d19dd | 2958 | } |
1bbd0b84 | 2959 | #undef FUNC_NAME |
3c9a524f DH |
2960 | |
2961 | ||
0f2d19dd JB |
2962 | /*** END strs->nums ***/ |
2963 | ||
5986c47d | 2964 | |
0f2d19dd | 2965 | SCM |
1bbd0b84 | 2966 | scm_bigequal (SCM x, SCM y) |
0f2d19dd | 2967 | { |
47ae1f0e | 2968 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
ca46fb90 | 2969 | scm_remember_upto_here_2 (x, y); |
73e4de09 | 2970 | return scm_from_bool (0 == result); |
0f2d19dd JB |
2971 | } |
2972 | ||
0f2d19dd | 2973 | SCM |
f3ae5d60 | 2974 | scm_real_equalp (SCM x, SCM y) |
0f2d19dd | 2975 | { |
73e4de09 | 2976 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0f2d19dd JB |
2977 | } |
2978 | ||
f3ae5d60 MD |
2979 | SCM |
2980 | scm_complex_equalp (SCM x, SCM y) | |
2981 | { | |
73e4de09 | 2982 | return scm_from_bool (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) |
f3ae5d60 MD |
2983 | && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); |
2984 | } | |
0f2d19dd | 2985 | |
f92e85f7 MV |
2986 | SCM |
2987 | scm_i_fraction_equalp (SCM x, SCM y) | |
2988 | { | |
2989 | scm_i_fraction_reduce (x); | |
2990 | scm_i_fraction_reduce (y); | |
73e4de09 | 2991 | if (scm_is_false (scm_equal_p (SCM_FRACTION_NUMERATOR (x), |
02164269 | 2992 | SCM_FRACTION_NUMERATOR (y))) |
73e4de09 | 2993 | || scm_is_false (scm_equal_p (SCM_FRACTION_DENOMINATOR (x), |
02164269 MV |
2994 | SCM_FRACTION_DENOMINATOR (y)))) |
2995 | return SCM_BOOL_F; | |
2996 | else | |
2997 | return SCM_BOOL_T; | |
f92e85f7 | 2998 | } |
0f2d19dd JB |
2999 | |
3000 | ||
8507ec80 MV |
3001 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
3002 | (SCM x), | |
3003 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
3004 | "otherwise.") | |
3005 | #define FUNC_NAME s_scm_number_p | |
3006 | { | |
3007 | return scm_from_bool (SCM_NUMBERP (x)); | |
3008 | } | |
3009 | #undef FUNC_NAME | |
3010 | ||
3011 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 3012 | (SCM x), |
942e5b91 | 3013 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 3014 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
3015 | "values form subsets of the set of complex numbers, i. e. the\n" |
3016 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
3017 | "rational or integer number.") | |
8507ec80 | 3018 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 3019 | { |
8507ec80 MV |
3020 | /* all numbers are complex. */ |
3021 | return scm_number_p (x); | |
0f2d19dd | 3022 | } |
1bbd0b84 | 3023 | #undef FUNC_NAME |
0f2d19dd | 3024 | |
f92e85f7 MV |
3025 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
3026 | (SCM x), | |
3027 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
3028 | "otherwise. Note that the set of integer values forms a subset of\n" | |
3029 | "the set of real numbers, i. e. the predicate will also be\n" | |
3030 | "fulfilled if @var{x} is an integer number.") | |
3031 | #define FUNC_NAME s_scm_real_p | |
3032 | { | |
3033 | /* we can't represent irrational numbers. */ | |
3034 | return scm_rational_p (x); | |
3035 | } | |
3036 | #undef FUNC_NAME | |
3037 | ||
3038 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 3039 | (SCM x), |
942e5b91 | 3040 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 3041 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 3042 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
3043 | "fulfilled if @var{x} is an integer number.") |
3044 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 3045 | { |
e11e83f3 | 3046 | if (SCM_I_INUMP (x)) |
0f2d19dd | 3047 | return SCM_BOOL_T; |
0aacf84e | 3048 | else if (SCM_IMP (x)) |
0f2d19dd | 3049 | return SCM_BOOL_F; |
0aacf84e | 3050 | else if (SCM_BIGP (x)) |
0f2d19dd | 3051 | return SCM_BOOL_T; |
f92e85f7 MV |
3052 | else if (SCM_FRACTIONP (x)) |
3053 | return SCM_BOOL_T; | |
3054 | else if (SCM_REALP (x)) | |
3055 | /* due to their limited precision, all floating point numbers are | |
3056 | rational as well. */ | |
3057 | return SCM_BOOL_T; | |
0aacf84e | 3058 | else |
bb628794 | 3059 | return SCM_BOOL_F; |
0f2d19dd | 3060 | } |
1bbd0b84 | 3061 | #undef FUNC_NAME |
0f2d19dd | 3062 | |
a1ec6916 | 3063 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 3064 | (SCM x), |
942e5b91 MG |
3065 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
3066 | "else.") | |
1bbd0b84 | 3067 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd JB |
3068 | { |
3069 | double r; | |
e11e83f3 | 3070 | if (SCM_I_INUMP (x)) |
f872b822 MD |
3071 | return SCM_BOOL_T; |
3072 | if (SCM_IMP (x)) | |
3073 | return SCM_BOOL_F; | |
f872b822 MD |
3074 | if (SCM_BIGP (x)) |
3075 | return SCM_BOOL_T; | |
3c9a524f | 3076 | if (!SCM_INEXACTP (x)) |
f872b822 | 3077 | return SCM_BOOL_F; |
3c9a524f | 3078 | if (SCM_COMPLEXP (x)) |
f872b822 | 3079 | return SCM_BOOL_F; |
5986c47d | 3080 | r = SCM_REAL_VALUE (x); |
1e35a229 | 3081 | /* +/-inf passes r==floor(r), making those #t */ |
f872b822 MD |
3082 | if (r == floor (r)) |
3083 | return SCM_BOOL_T; | |
0f2d19dd JB |
3084 | return SCM_BOOL_F; |
3085 | } | |
1bbd0b84 | 3086 | #undef FUNC_NAME |
0f2d19dd JB |
3087 | |
3088 | ||
a1ec6916 | 3089 | SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, |
1bbd0b84 | 3090 | (SCM x), |
942e5b91 MG |
3091 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" |
3092 | "else.") | |
1bbd0b84 | 3093 | #define FUNC_NAME s_scm_inexact_p |
0f2d19dd | 3094 | { |
eb927cb9 MV |
3095 | if (SCM_INEXACTP (x)) |
3096 | return SCM_BOOL_T; | |
3097 | if (SCM_NUMBERP (x)) | |
3098 | return SCM_BOOL_F; | |
3099 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 3100 | } |
1bbd0b84 | 3101 | #undef FUNC_NAME |
0f2d19dd JB |
3102 | |
3103 | ||
152f82bf | 3104 | SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p); |
942e5b91 | 3105 | /* "Return @code{#t} if all parameters are numerically equal." */ |
0f2d19dd | 3106 | SCM |
6e8d25a6 | 3107 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 3108 | { |
d8b95e27 | 3109 | again: |
e11e83f3 | 3110 | if (SCM_I_INUMP (x)) |
0aacf84e | 3111 | { |
e11e83f3 MV |
3112 | long xx = SCM_I_INUM (x); |
3113 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3114 | { |
e11e83f3 | 3115 | long yy = SCM_I_INUM (y); |
73e4de09 | 3116 | return scm_from_bool (xx == yy); |
0aacf84e MD |
3117 | } |
3118 | else if (SCM_BIGP (y)) | |
3119 | return SCM_BOOL_F; | |
3120 | else if (SCM_REALP (y)) | |
73e4de09 | 3121 | return scm_from_bool ((double) xx == SCM_REAL_VALUE (y)); |
0aacf84e | 3122 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3123 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3124 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
3125 | else if (SCM_FRACTIONP (y)) |
3126 | return SCM_BOOL_F; | |
0aacf84e MD |
3127 | else |
3128 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3129 | } |
0aacf84e MD |
3130 | else if (SCM_BIGP (x)) |
3131 | { | |
e11e83f3 | 3132 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3133 | return SCM_BOOL_F; |
3134 | else if (SCM_BIGP (y)) | |
3135 | { | |
3136 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3137 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3138 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3139 | } |
3140 | else if (SCM_REALP (y)) | |
3141 | { | |
3142 | int cmp; | |
3143 | if (xisnan (SCM_REAL_VALUE (y))) | |
3144 | return SCM_BOOL_F; | |
3145 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3146 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3147 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3148 | } |
3149 | else if (SCM_COMPLEXP (y)) | |
3150 | { | |
3151 | int cmp; | |
3152 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
3153 | return SCM_BOOL_F; | |
3154 | if (xisnan (SCM_COMPLEX_REAL (y))) | |
3155 | return SCM_BOOL_F; | |
3156 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
3157 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3158 | return scm_from_bool (0 == cmp); |
0aacf84e | 3159 | } |
f92e85f7 MV |
3160 | else if (SCM_FRACTIONP (y)) |
3161 | return SCM_BOOL_F; | |
0aacf84e MD |
3162 | else |
3163 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3164 | } |
0aacf84e MD |
3165 | else if (SCM_REALP (x)) |
3166 | { | |
e11e83f3 MV |
3167 | if (SCM_I_INUMP (y)) |
3168 | return scm_from_bool (SCM_REAL_VALUE (x) == (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3169 | else if (SCM_BIGP (y)) |
3170 | { | |
3171 | int cmp; | |
3172 | if (xisnan (SCM_REAL_VALUE (x))) | |
3173 | return SCM_BOOL_F; | |
3174 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3175 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3176 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3177 | } |
3178 | else if (SCM_REALP (y)) | |
73e4de09 | 3179 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 3180 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3181 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3182 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3183 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3184 | { |
3185 | double xx = SCM_REAL_VALUE (x); | |
3186 | if (xisnan (xx)) | |
3187 | return SCM_BOOL_F; | |
3188 | if (xisinf (xx)) | |
73e4de09 | 3189 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3190 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3191 | goto again; | |
3192 | } | |
0aacf84e MD |
3193 | else |
3194 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3195 | } |
0aacf84e MD |
3196 | else if (SCM_COMPLEXP (x)) |
3197 | { | |
e11e83f3 MV |
3198 | if (SCM_I_INUMP (y)) |
3199 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
3200 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3201 | else if (SCM_BIGP (y)) | |
3202 | { | |
3203 | int cmp; | |
3204 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
3205 | return SCM_BOOL_F; | |
3206 | if (xisnan (SCM_COMPLEX_REAL (x))) | |
3207 | return SCM_BOOL_F; | |
3208 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
3209 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3210 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3211 | } |
3212 | else if (SCM_REALP (y)) | |
73e4de09 | 3213 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
3214 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3215 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 3216 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3217 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3218 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3219 | { |
3220 | double xx; | |
3221 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
3222 | return SCM_BOOL_F; | |
3223 | xx = SCM_COMPLEX_REAL (x); | |
3224 | if (xisnan (xx)) | |
3225 | return SCM_BOOL_F; | |
3226 | if (xisinf (xx)) | |
73e4de09 | 3227 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3228 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3229 | goto again; | |
3230 | } | |
f92e85f7 MV |
3231 | else |
3232 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
3233 | } | |
3234 | else if (SCM_FRACTIONP (x)) | |
3235 | { | |
e11e83f3 | 3236 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
3237 | return SCM_BOOL_F; |
3238 | else if (SCM_BIGP (y)) | |
3239 | return SCM_BOOL_F; | |
3240 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
3241 | { |
3242 | double yy = SCM_REAL_VALUE (y); | |
3243 | if (xisnan (yy)) | |
3244 | return SCM_BOOL_F; | |
3245 | if (xisinf (yy)) | |
73e4de09 | 3246 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3247 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3248 | goto again; | |
3249 | } | |
f92e85f7 | 3250 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
3251 | { |
3252 | double yy; | |
3253 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
3254 | return SCM_BOOL_F; | |
3255 | yy = SCM_COMPLEX_REAL (y); | |
3256 | if (xisnan (yy)) | |
3257 | return SCM_BOOL_F; | |
3258 | if (xisinf (yy)) | |
73e4de09 | 3259 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3260 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3261 | goto again; | |
3262 | } | |
f92e85f7 MV |
3263 | else if (SCM_FRACTIONP (y)) |
3264 | return scm_i_fraction_equalp (x, y); | |
0aacf84e MD |
3265 | else |
3266 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3267 | } |
0aacf84e | 3268 | else |
f4c627b3 | 3269 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p); |
0f2d19dd JB |
3270 | } |
3271 | ||
3272 | ||
a5f0b599 KR |
3273 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
3274 | done are good for inums, but for bignums an answer can almost always be | |
3275 | had by just examining a few high bits of the operands, as done by GMP in | |
3276 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
3277 | of the float exponent to take into account. */ | |
3278 | ||
152f82bf | 3279 | SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p); |
942e5b91 MG |
3280 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3281 | * "increasing." | |
3282 | */ | |
0f2d19dd | 3283 | SCM |
6e8d25a6 | 3284 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3285 | { |
a5f0b599 | 3286 | again: |
e11e83f3 | 3287 | if (SCM_I_INUMP (x)) |
0aacf84e | 3288 | { |
e11e83f3 MV |
3289 | long xx = SCM_I_INUM (x); |
3290 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3291 | { |
e11e83f3 | 3292 | long yy = SCM_I_INUM (y); |
73e4de09 | 3293 | return scm_from_bool (xx < yy); |
0aacf84e MD |
3294 | } |
3295 | else if (SCM_BIGP (y)) | |
3296 | { | |
3297 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3298 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3299 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3300 | } |
3301 | else if (SCM_REALP (y)) | |
73e4de09 | 3302 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 3303 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3304 | { |
3305 | /* "x < a/b" becomes "x*b < a" */ | |
3306 | int_frac: | |
3307 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
3308 | y = SCM_FRACTION_NUMERATOR (y); | |
3309 | goto again; | |
3310 | } | |
0aacf84e MD |
3311 | else |
3312 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3313 | } |
0aacf84e MD |
3314 | else if (SCM_BIGP (x)) |
3315 | { | |
e11e83f3 | 3316 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3317 | { |
3318 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3319 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3320 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3321 | } |
3322 | else if (SCM_BIGP (y)) | |
3323 | { | |
3324 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3325 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3326 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
3327 | } |
3328 | else if (SCM_REALP (y)) | |
3329 | { | |
3330 | int cmp; | |
3331 | if (xisnan (SCM_REAL_VALUE (y))) | |
3332 | return SCM_BOOL_F; | |
3333 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3334 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3335 | return scm_from_bool (cmp < 0); |
0aacf84e | 3336 | } |
f92e85f7 | 3337 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 3338 | goto int_frac; |
0aacf84e MD |
3339 | else |
3340 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f4c627b3 | 3341 | } |
0aacf84e MD |
3342 | else if (SCM_REALP (x)) |
3343 | { | |
e11e83f3 MV |
3344 | if (SCM_I_INUMP (y)) |
3345 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3346 | else if (SCM_BIGP (y)) |
3347 | { | |
3348 | int cmp; | |
3349 | if (xisnan (SCM_REAL_VALUE (x))) | |
3350 | return SCM_BOOL_F; | |
3351 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3352 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3353 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
3354 | } |
3355 | else if (SCM_REALP (y)) | |
73e4de09 | 3356 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 3357 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3358 | { |
3359 | double xx = SCM_REAL_VALUE (x); | |
3360 | if (xisnan (xx)) | |
3361 | return SCM_BOOL_F; | |
3362 | if (xisinf (xx)) | |
73e4de09 | 3363 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
3364 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3365 | goto again; | |
3366 | } | |
f92e85f7 MV |
3367 | else |
3368 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
3369 | } | |
3370 | else if (SCM_FRACTIONP (x)) | |
3371 | { | |
e11e83f3 | 3372 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
3373 | { |
3374 | /* "a/b < y" becomes "a < y*b" */ | |
3375 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
3376 | x = SCM_FRACTION_NUMERATOR (x); | |
3377 | goto again; | |
3378 | } | |
f92e85f7 | 3379 | else if (SCM_REALP (y)) |
a5f0b599 KR |
3380 | { |
3381 | double yy = SCM_REAL_VALUE (y); | |
3382 | if (xisnan (yy)) | |
3383 | return SCM_BOOL_F; | |
3384 | if (xisinf (yy)) | |
73e4de09 | 3385 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
3386 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3387 | goto again; | |
3388 | } | |
f92e85f7 | 3389 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3390 | { |
3391 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
3392 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
3393 | SCM_FRACTION_DENOMINATOR (y)); | |
3394 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
3395 | SCM_FRACTION_DENOMINATOR (x)); | |
3396 | x = new_x; | |
3397 | y = new_y; | |
3398 | goto again; | |
3399 | } | |
0aacf84e MD |
3400 | else |
3401 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3402 | } |
0aacf84e | 3403 | else |
f4c627b3 | 3404 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p); |
0f2d19dd JB |
3405 | } |
3406 | ||
3407 | ||
c76b1eaf | 3408 | SCM_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p); |
942e5b91 MG |
3409 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3410 | * "decreasing." | |
c76b1eaf | 3411 | */ |
1bbd0b84 | 3412 | #define FUNC_NAME s_scm_gr_p |
c76b1eaf MD |
3413 | SCM |
3414 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3415 | { |
c76b1eaf MD |
3416 | if (!SCM_NUMBERP (x)) |
3417 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME); | |
3418 | else if (!SCM_NUMBERP (y)) | |
3419 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME); | |
3420 | else | |
3421 | return scm_less_p (y, x); | |
0f2d19dd | 3422 | } |
1bbd0b84 | 3423 | #undef FUNC_NAME |
0f2d19dd JB |
3424 | |
3425 | ||
c76b1eaf | 3426 | SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p); |
942e5b91 | 3427 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3428 | * "non-decreasing." |
3429 | */ | |
1bbd0b84 | 3430 | #define FUNC_NAME s_scm_leq_p |
c76b1eaf MD |
3431 | SCM |
3432 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3433 | { |
c76b1eaf MD |
3434 | if (!SCM_NUMBERP (x)) |
3435 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3436 | else if (!SCM_NUMBERP (y)) | |
3437 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3438 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3439 | return SCM_BOOL_F; |
c76b1eaf | 3440 | else |
73e4de09 | 3441 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 3442 | } |
1bbd0b84 | 3443 | #undef FUNC_NAME |
0f2d19dd JB |
3444 | |
3445 | ||
c76b1eaf | 3446 | SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p); |
942e5b91 | 3447 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3448 | * "non-increasing." |
3449 | */ | |
1bbd0b84 | 3450 | #define FUNC_NAME s_scm_geq_p |
c76b1eaf MD |
3451 | SCM |
3452 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3453 | { |
c76b1eaf MD |
3454 | if (!SCM_NUMBERP (x)) |
3455 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3456 | else if (!SCM_NUMBERP (y)) | |
3457 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3458 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3459 | return SCM_BOOL_F; |
c76b1eaf | 3460 | else |
73e4de09 | 3461 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 3462 | } |
1bbd0b84 | 3463 | #undef FUNC_NAME |
0f2d19dd JB |
3464 | |
3465 | ||
152f82bf | 3466 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3467 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3468 | * "zero." | |
3469 | */ | |
0f2d19dd | 3470 | SCM |
6e8d25a6 | 3471 | scm_zero_p (SCM z) |
0f2d19dd | 3472 | { |
e11e83f3 | 3473 | if (SCM_I_INUMP (z)) |
bc36d050 | 3474 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 3475 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 3476 | return SCM_BOOL_F; |
0aacf84e | 3477 | else if (SCM_REALP (z)) |
73e4de09 | 3478 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 3479 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 3480 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 3481 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
3482 | else if (SCM_FRACTIONP (z)) |
3483 | return SCM_BOOL_F; | |
0aacf84e | 3484 | else |
c2ff8ab0 | 3485 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); |
0f2d19dd JB |
3486 | } |
3487 | ||
3488 | ||
152f82bf | 3489 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3490 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3491 | * "zero." | |
3492 | */ | |
0f2d19dd | 3493 | SCM |
6e8d25a6 | 3494 | scm_positive_p (SCM x) |
0f2d19dd | 3495 | { |
e11e83f3 MV |
3496 | if (SCM_I_INUMP (x)) |
3497 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
3498 | else if (SCM_BIGP (x)) |
3499 | { | |
3500 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3501 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3502 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3503 | } |
3504 | else if (SCM_REALP (x)) | |
73e4de09 | 3505 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
3506 | else if (SCM_FRACTIONP (x)) |
3507 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3508 | else |
c2ff8ab0 | 3509 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); |
0f2d19dd JB |
3510 | } |
3511 | ||
3512 | ||
152f82bf | 3513 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3514 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3515 | * "zero." | |
3516 | */ | |
0f2d19dd | 3517 | SCM |
6e8d25a6 | 3518 | scm_negative_p (SCM x) |
0f2d19dd | 3519 | { |
e11e83f3 MV |
3520 | if (SCM_I_INUMP (x)) |
3521 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
3522 | else if (SCM_BIGP (x)) |
3523 | { | |
3524 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3525 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3526 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3527 | } |
3528 | else if (SCM_REALP (x)) | |
73e4de09 | 3529 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
3530 | else if (SCM_FRACTIONP (x)) |
3531 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3532 | else |
c2ff8ab0 | 3533 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); |
0f2d19dd JB |
3534 | } |
3535 | ||
3536 | ||
2a06f791 KR |
3537 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
3538 | required by r5rs. On that basis, for exact/inexact combinations the | |
3539 | exact is converted to inexact to compare and possibly return. This is | |
3540 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
3541 | its test, such trouble is not required for min and max. */ | |
3542 | ||
9de33deb | 3543 | SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max); |
942e5b91 MG |
3544 | /* "Return the maximum of all parameter values." |
3545 | */ | |
0f2d19dd | 3546 | SCM |
6e8d25a6 | 3547 | scm_max (SCM x, SCM y) |
0f2d19dd | 3548 | { |
0aacf84e MD |
3549 | if (SCM_UNBNDP (y)) |
3550 | { | |
3551 | if (SCM_UNBNDP (x)) | |
3552 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 3553 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3554 | return x; |
3555 | else | |
3556 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3557 | } |
f4c627b3 | 3558 | |
e11e83f3 | 3559 | if (SCM_I_INUMP (x)) |
0aacf84e | 3560 | { |
e11e83f3 MV |
3561 | long xx = SCM_I_INUM (x); |
3562 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3563 | { |
e11e83f3 | 3564 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3565 | return (xx < yy) ? y : x; |
3566 | } | |
3567 | else if (SCM_BIGP (y)) | |
3568 | { | |
3569 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3570 | scm_remember_upto_here_1 (y); | |
3571 | return (sgn < 0) ? x : y; | |
3572 | } | |
3573 | else if (SCM_REALP (y)) | |
3574 | { | |
3575 | double z = xx; | |
3576 | /* if y==NaN then ">" is false and we return NaN */ | |
55f26379 | 3577 | return (z > SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3578 | } |
f92e85f7 MV |
3579 | else if (SCM_FRACTIONP (y)) |
3580 | { | |
e4bc5d6c | 3581 | use_less: |
73e4de09 | 3582 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 3583 | } |
0aacf84e MD |
3584 | else |
3585 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3586 | } |
0aacf84e MD |
3587 | else if (SCM_BIGP (x)) |
3588 | { | |
e11e83f3 | 3589 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3590 | { |
3591 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3592 | scm_remember_upto_here_1 (x); | |
3593 | return (sgn < 0) ? y : x; | |
3594 | } | |
3595 | else if (SCM_BIGP (y)) | |
3596 | { | |
3597 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3598 | scm_remember_upto_here_2 (x, y); | |
3599 | return (cmp > 0) ? x : y; | |
3600 | } | |
3601 | else if (SCM_REALP (y)) | |
3602 | { | |
2a06f791 KR |
3603 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
3604 | double xx, yy; | |
3605 | big_real: | |
3606 | xx = scm_i_big2dbl (x); | |
3607 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3608 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 3609 | } |
f92e85f7 MV |
3610 | else if (SCM_FRACTIONP (y)) |
3611 | { | |
e4bc5d6c | 3612 | goto use_less; |
f92e85f7 | 3613 | } |
0aacf84e MD |
3614 | else |
3615 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 3616 | } |
0aacf84e MD |
3617 | else if (SCM_REALP (x)) |
3618 | { | |
e11e83f3 | 3619 | if (SCM_I_INUMP (y)) |
0aacf84e | 3620 | { |
e11e83f3 | 3621 | double z = SCM_I_INUM (y); |
0aacf84e | 3622 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3623 | return (SCM_REAL_VALUE (x) < z) ? scm_from_double (z) : x; |
0aacf84e MD |
3624 | } |
3625 | else if (SCM_BIGP (y)) | |
3626 | { | |
b6f8f763 | 3627 | SCM_SWAP (x, y); |
2a06f791 | 3628 | goto big_real; |
0aacf84e MD |
3629 | } |
3630 | else if (SCM_REALP (y)) | |
3631 | { | |
3632 | /* if x==NaN then our explicit check means we return NaN | |
3633 | if y==NaN then ">" is false and we return NaN | |
3634 | calling isnan is unavoidable, since it's the only way to know | |
3635 | which of x or y causes any compares to be false */ | |
3636 | double xx = SCM_REAL_VALUE (x); | |
3637 | return (xisnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y; | |
3638 | } | |
f92e85f7 MV |
3639 | else if (SCM_FRACTIONP (y)) |
3640 | { | |
3641 | double yy = scm_i_fraction2double (y); | |
3642 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3643 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
3644 | } |
3645 | else | |
3646 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3647 | } | |
3648 | else if (SCM_FRACTIONP (x)) | |
3649 | { | |
e11e83f3 | 3650 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3651 | { |
e4bc5d6c | 3652 | goto use_less; |
f92e85f7 MV |
3653 | } |
3654 | else if (SCM_BIGP (y)) | |
3655 | { | |
e4bc5d6c | 3656 | goto use_less; |
f92e85f7 MV |
3657 | } |
3658 | else if (SCM_REALP (y)) | |
3659 | { | |
3660 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3661 | return (xx < SCM_REAL_VALUE (y)) ? y : scm_from_double (xx); |
f92e85f7 MV |
3662 | } |
3663 | else if (SCM_FRACTIONP (y)) | |
3664 | { | |
e4bc5d6c | 3665 | goto use_less; |
f92e85f7 | 3666 | } |
0aacf84e MD |
3667 | else |
3668 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3669 | } |
0aacf84e | 3670 | else |
f4c627b3 | 3671 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
3672 | } |
3673 | ||
3674 | ||
9de33deb | 3675 | SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min); |
942e5b91 MG |
3676 | /* "Return the minium of all parameter values." |
3677 | */ | |
0f2d19dd | 3678 | SCM |
6e8d25a6 | 3679 | scm_min (SCM x, SCM y) |
0f2d19dd | 3680 | { |
0aacf84e MD |
3681 | if (SCM_UNBNDP (y)) |
3682 | { | |
3683 | if (SCM_UNBNDP (x)) | |
3684 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 3685 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3686 | return x; |
3687 | else | |
3688 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 3689 | } |
f4c627b3 | 3690 | |
e11e83f3 | 3691 | if (SCM_I_INUMP (x)) |
0aacf84e | 3692 | { |
e11e83f3 MV |
3693 | long xx = SCM_I_INUM (x); |
3694 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3695 | { |
e11e83f3 | 3696 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3697 | return (xx < yy) ? x : y; |
3698 | } | |
3699 | else if (SCM_BIGP (y)) | |
3700 | { | |
3701 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3702 | scm_remember_upto_here_1 (y); | |
3703 | return (sgn < 0) ? y : x; | |
3704 | } | |
3705 | else if (SCM_REALP (y)) | |
3706 | { | |
3707 | double z = xx; | |
3708 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 3709 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3710 | } |
f92e85f7 MV |
3711 | else if (SCM_FRACTIONP (y)) |
3712 | { | |
e4bc5d6c | 3713 | use_less: |
73e4de09 | 3714 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 3715 | } |
0aacf84e MD |
3716 | else |
3717 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3718 | } |
0aacf84e MD |
3719 | else if (SCM_BIGP (x)) |
3720 | { | |
e11e83f3 | 3721 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3722 | { |
3723 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3724 | scm_remember_upto_here_1 (x); | |
3725 | return (sgn < 0) ? x : y; | |
3726 | } | |
3727 | else if (SCM_BIGP (y)) | |
3728 | { | |
3729 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3730 | scm_remember_upto_here_2 (x, y); | |
3731 | return (cmp > 0) ? y : x; | |
3732 | } | |
3733 | else if (SCM_REALP (y)) | |
3734 | { | |
2a06f791 KR |
3735 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
3736 | double xx, yy; | |
3737 | big_real: | |
3738 | xx = scm_i_big2dbl (x); | |
3739 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3740 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 3741 | } |
f92e85f7 MV |
3742 | else if (SCM_FRACTIONP (y)) |
3743 | { | |
e4bc5d6c | 3744 | goto use_less; |
f92e85f7 | 3745 | } |
0aacf84e MD |
3746 | else |
3747 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 3748 | } |
0aacf84e MD |
3749 | else if (SCM_REALP (x)) |
3750 | { | |
e11e83f3 | 3751 | if (SCM_I_INUMP (y)) |
0aacf84e | 3752 | { |
e11e83f3 | 3753 | double z = SCM_I_INUM (y); |
0aacf84e | 3754 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3755 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
3756 | } |
3757 | else if (SCM_BIGP (y)) | |
3758 | { | |
b6f8f763 | 3759 | SCM_SWAP (x, y); |
2a06f791 | 3760 | goto big_real; |
0aacf84e MD |
3761 | } |
3762 | else if (SCM_REALP (y)) | |
3763 | { | |
3764 | /* if x==NaN then our explicit check means we return NaN | |
3765 | if y==NaN then "<" is false and we return NaN | |
3766 | calling isnan is unavoidable, since it's the only way to know | |
3767 | which of x or y causes any compares to be false */ | |
3768 | double xx = SCM_REAL_VALUE (x); | |
3769 | return (xisnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y; | |
3770 | } | |
f92e85f7 MV |
3771 | else if (SCM_FRACTIONP (y)) |
3772 | { | |
3773 | double yy = scm_i_fraction2double (y); | |
3774 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3775 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 3776 | } |
0aacf84e MD |
3777 | else |
3778 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3779 | } |
f92e85f7 MV |
3780 | else if (SCM_FRACTIONP (x)) |
3781 | { | |
e11e83f3 | 3782 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3783 | { |
e4bc5d6c | 3784 | goto use_less; |
f92e85f7 MV |
3785 | } |
3786 | else if (SCM_BIGP (y)) | |
3787 | { | |
e4bc5d6c | 3788 | goto use_less; |
f92e85f7 MV |
3789 | } |
3790 | else if (SCM_REALP (y)) | |
3791 | { | |
3792 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3793 | return (SCM_REAL_VALUE (y) < xx) ? y : scm_from_double (xx); |
f92e85f7 MV |
3794 | } |
3795 | else if (SCM_FRACTIONP (y)) | |
3796 | { | |
e4bc5d6c | 3797 | goto use_less; |
f92e85f7 MV |
3798 | } |
3799 | else | |
3800 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3801 | } | |
0aacf84e | 3802 | else |
f4c627b3 | 3803 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
3804 | } |
3805 | ||
3806 | ||
9de33deb | 3807 | SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum); |
942e5b91 MG |
3808 | /* "Return the sum of all parameter values. Return 0 if called without\n" |
3809 | * "any parameters." | |
3810 | */ | |
0f2d19dd | 3811 | SCM |
6e8d25a6 | 3812 | scm_sum (SCM x, SCM y) |
0f2d19dd | 3813 | { |
ca46fb90 RB |
3814 | if (SCM_UNBNDP (y)) |
3815 | { | |
3816 | if (SCM_NUMBERP (x)) return x; | |
3817 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 3818 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 3819 | } |
c209c88e | 3820 | |
e11e83f3 | 3821 | if (SCM_I_INUMP (x)) |
ca46fb90 | 3822 | { |
e11e83f3 | 3823 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3824 | { |
e11e83f3 MV |
3825 | long xx = SCM_I_INUM (x); |
3826 | long yy = SCM_I_INUM (y); | |
ca46fb90 | 3827 | long int z = xx + yy; |
d956fa6f | 3828 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_long2big (z); |
ca46fb90 RB |
3829 | } |
3830 | else if (SCM_BIGP (y)) | |
3831 | { | |
3832 | SCM_SWAP (x, y); | |
3833 | goto add_big_inum; | |
3834 | } | |
3835 | else if (SCM_REALP (y)) | |
3836 | { | |
e11e83f3 | 3837 | long int xx = SCM_I_INUM (x); |
55f26379 | 3838 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
3839 | } |
3840 | else if (SCM_COMPLEXP (y)) | |
3841 | { | |
e11e83f3 | 3842 | long int xx = SCM_I_INUM (x); |
8507ec80 | 3843 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
3844 | SCM_COMPLEX_IMAG (y)); |
3845 | } | |
f92e85f7 | 3846 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 3847 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
3848 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
3849 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
3850 | else |
3851 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
3852 | } else if (SCM_BIGP (x)) |
3853 | { | |
e11e83f3 | 3854 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3855 | { |
3856 | long int inum; | |
3857 | int bigsgn; | |
3858 | add_big_inum: | |
e11e83f3 | 3859 | inum = SCM_I_INUM (y); |
0aacf84e MD |
3860 | if (inum == 0) |
3861 | return x; | |
3862 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3863 | if (inum < 0) | |
3864 | { | |
3865 | SCM result = scm_i_mkbig (); | |
3866 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
3867 | scm_remember_upto_here_1 (x); | |
3868 | /* we know the result will have to be a bignum */ | |
3869 | if (bigsgn == -1) | |
3870 | return result; | |
3871 | return scm_i_normbig (result); | |
3872 | } | |
3873 | else | |
3874 | { | |
3875 | SCM result = scm_i_mkbig (); | |
3876 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
3877 | scm_remember_upto_here_1 (x); | |
3878 | /* we know the result will have to be a bignum */ | |
3879 | if (bigsgn == 1) | |
3880 | return result; | |
3881 | return scm_i_normbig (result); | |
3882 | } | |
3883 | } | |
3884 | else if (SCM_BIGP (y)) | |
3885 | { | |
3886 | SCM result = scm_i_mkbig (); | |
3887 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3888 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3889 | mpz_add (SCM_I_BIG_MPZ (result), | |
3890 | SCM_I_BIG_MPZ (x), | |
3891 | SCM_I_BIG_MPZ (y)); | |
3892 | scm_remember_upto_here_2 (x, y); | |
3893 | /* we know the result will have to be a bignum */ | |
3894 | if (sgn_x == sgn_y) | |
3895 | return result; | |
3896 | return scm_i_normbig (result); | |
3897 | } | |
3898 | else if (SCM_REALP (y)) | |
3899 | { | |
3900 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
3901 | scm_remember_upto_here_1 (x); | |
55f26379 | 3902 | return scm_from_double (result); |
0aacf84e MD |
3903 | } |
3904 | else if (SCM_COMPLEXP (y)) | |
3905 | { | |
3906 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
3907 | + SCM_COMPLEX_REAL (y)); | |
3908 | scm_remember_upto_here_1 (x); | |
8507ec80 | 3909 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 3910 | } |
f92e85f7 | 3911 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 3912 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
3913 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
3914 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
3915 | else |
3916 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 3917 | } |
0aacf84e MD |
3918 | else if (SCM_REALP (x)) |
3919 | { | |
e11e83f3 | 3920 | if (SCM_I_INUMP (y)) |
55f26379 | 3921 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
3922 | else if (SCM_BIGP (y)) |
3923 | { | |
3924 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
3925 | scm_remember_upto_here_1 (y); | |
55f26379 | 3926 | return scm_from_double (result); |
0aacf84e MD |
3927 | } |
3928 | else if (SCM_REALP (y)) | |
55f26379 | 3929 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 3930 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 3931 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 3932 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 3933 | else if (SCM_FRACTIONP (y)) |
55f26379 | 3934 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
3935 | else |
3936 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 3937 | } |
0aacf84e MD |
3938 | else if (SCM_COMPLEXP (x)) |
3939 | { | |
e11e83f3 | 3940 | if (SCM_I_INUMP (y)) |
8507ec80 | 3941 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
3942 | SCM_COMPLEX_IMAG (x)); |
3943 | else if (SCM_BIGP (y)) | |
3944 | { | |
3945 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
3946 | + SCM_COMPLEX_REAL (x)); | |
3947 | scm_remember_upto_here_1 (y); | |
8507ec80 | 3948 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
3949 | } |
3950 | else if (SCM_REALP (y)) | |
8507ec80 | 3951 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
3952 | SCM_COMPLEX_IMAG (x)); |
3953 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 3954 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 3955 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 3956 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 3957 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
3958 | SCM_COMPLEX_IMAG (x)); |
3959 | else | |
3960 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
3961 | } | |
3962 | else if (SCM_FRACTIONP (x)) | |
3963 | { | |
e11e83f3 | 3964 | if (SCM_I_INUMP (y)) |
cba42c93 | 3965 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
3966 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
3967 | SCM_FRACTION_DENOMINATOR (x)); | |
3968 | else if (SCM_BIGP (y)) | |
cba42c93 | 3969 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
3970 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
3971 | SCM_FRACTION_DENOMINATOR (x)); | |
3972 | else if (SCM_REALP (y)) | |
55f26379 | 3973 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 3974 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 3975 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
3976 | SCM_COMPLEX_IMAG (y)); |
3977 | else if (SCM_FRACTIONP (y)) | |
3978 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 3979 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
3980 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
3981 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
3982 | else |
3983 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 3984 | } |
0aacf84e | 3985 | else |
98cb6e75 | 3986 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
3987 | } |
3988 | ||
3989 | ||
9de33deb | 3990 | SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference); |
609c3d30 MG |
3991 | /* If called with one argument @var{z1}, -@var{z1} returned. Otherwise |
3992 | * the sum of all but the first argument are subtracted from the first | |
3993 | * argument. */ | |
c05e97b7 | 3994 | #define FUNC_NAME s_difference |
0f2d19dd | 3995 | SCM |
6e8d25a6 | 3996 | scm_difference (SCM x, SCM y) |
0f2d19dd | 3997 | { |
ca46fb90 RB |
3998 | if (SCM_UNBNDP (y)) |
3999 | { | |
4000 | if (SCM_UNBNDP (x)) | |
4001 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
4002 | else | |
e11e83f3 | 4003 | if (SCM_I_INUMP (x)) |
ca46fb90 | 4004 | { |
e11e83f3 | 4005 | long xx = -SCM_I_INUM (x); |
ca46fb90 | 4006 | if (SCM_FIXABLE (xx)) |
d956fa6f | 4007 | return SCM_I_MAKINUM (xx); |
ca46fb90 RB |
4008 | else |
4009 | return scm_i_long2big (xx); | |
4010 | } | |
4011 | else if (SCM_BIGP (x)) | |
4012 | /* FIXME: do we really need to normalize here? */ | |
4013 | return scm_i_normbig (scm_i_clonebig (x, 0)); | |
4014 | else if (SCM_REALP (x)) | |
55f26379 | 4015 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 4016 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 4017 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 4018 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 4019 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4020 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 4021 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
4022 | else |
4023 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 4024 | } |
ca46fb90 | 4025 | |
e11e83f3 | 4026 | if (SCM_I_INUMP (x)) |
0aacf84e | 4027 | { |
e11e83f3 | 4028 | if (SCM_I_INUMP (y)) |
0aacf84e | 4029 | { |
e11e83f3 MV |
4030 | long int xx = SCM_I_INUM (x); |
4031 | long int yy = SCM_I_INUM (y); | |
0aacf84e MD |
4032 | long int z = xx - yy; |
4033 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4034 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4035 | else |
4036 | return scm_i_long2big (z); | |
4037 | } | |
4038 | else if (SCM_BIGP (y)) | |
4039 | { | |
4040 | /* inum-x - big-y */ | |
e11e83f3 | 4041 | long xx = SCM_I_INUM (x); |
ca46fb90 | 4042 | |
0aacf84e MD |
4043 | if (xx == 0) |
4044 | return scm_i_clonebig (y, 0); | |
4045 | else | |
4046 | { | |
4047 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4048 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4049 | |
0aacf84e MD |
4050 | if (xx >= 0) |
4051 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
4052 | else | |
4053 | { | |
4054 | /* x - y == -(y + -x) */ | |
4055 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
4056 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4057 | } | |
4058 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 4059 | |
0aacf84e MD |
4060 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
4061 | /* we know the result will have to be a bignum */ | |
4062 | return result; | |
4063 | else | |
4064 | return scm_i_normbig (result); | |
4065 | } | |
4066 | } | |
4067 | else if (SCM_REALP (y)) | |
4068 | { | |
e11e83f3 | 4069 | long int xx = SCM_I_INUM (x); |
55f26379 | 4070 | return scm_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
4071 | } |
4072 | else if (SCM_COMPLEXP (y)) | |
4073 | { | |
e11e83f3 | 4074 | long int xx = SCM_I_INUM (x); |
8507ec80 | 4075 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4076 | - SCM_COMPLEX_IMAG (y)); |
4077 | } | |
f92e85f7 MV |
4078 | else if (SCM_FRACTIONP (y)) |
4079 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 4080 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4081 | SCM_FRACTION_NUMERATOR (y)), |
4082 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4083 | else |
4084 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 4085 | } |
0aacf84e MD |
4086 | else if (SCM_BIGP (x)) |
4087 | { | |
e11e83f3 | 4088 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4089 | { |
4090 | /* big-x - inum-y */ | |
e11e83f3 | 4091 | long yy = SCM_I_INUM (y); |
0aacf84e | 4092 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 4093 | |
0aacf84e MD |
4094 | scm_remember_upto_here_1 (x); |
4095 | if (sgn_x == 0) | |
c71b0706 MV |
4096 | return (SCM_FIXABLE (-yy) ? |
4097 | SCM_I_MAKINUM (-yy) : scm_from_long (-yy)); | |
0aacf84e MD |
4098 | else |
4099 | { | |
4100 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4101 | |
708f22c6 KR |
4102 | if (yy >= 0) |
4103 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
4104 | else | |
4105 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 4106 | scm_remember_upto_here_1 (x); |
ca46fb90 | 4107 | |
0aacf84e MD |
4108 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
4109 | /* we know the result will have to be a bignum */ | |
4110 | return result; | |
4111 | else | |
4112 | return scm_i_normbig (result); | |
4113 | } | |
4114 | } | |
4115 | else if (SCM_BIGP (y)) | |
4116 | { | |
4117 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4118 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4119 | SCM result = scm_i_mkbig (); | |
4120 | mpz_sub (SCM_I_BIG_MPZ (result), | |
4121 | SCM_I_BIG_MPZ (x), | |
4122 | SCM_I_BIG_MPZ (y)); | |
4123 | scm_remember_upto_here_2 (x, y); | |
4124 | /* we know the result will have to be a bignum */ | |
4125 | if ((sgn_x == 1) && (sgn_y == -1)) | |
4126 | return result; | |
4127 | if ((sgn_x == -1) && (sgn_y == 1)) | |
4128 | return result; | |
4129 | return scm_i_normbig (result); | |
4130 | } | |
4131 | else if (SCM_REALP (y)) | |
4132 | { | |
4133 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
4134 | scm_remember_upto_here_1 (x); | |
55f26379 | 4135 | return scm_from_double (result); |
0aacf84e MD |
4136 | } |
4137 | else if (SCM_COMPLEXP (y)) | |
4138 | { | |
4139 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4140 | - SCM_COMPLEX_REAL (y)); | |
4141 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4142 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4143 | } |
f92e85f7 | 4144 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4145 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4146 | SCM_FRACTION_NUMERATOR (y)), |
4147 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 4148 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 4149 | } |
0aacf84e MD |
4150 | else if (SCM_REALP (x)) |
4151 | { | |
e11e83f3 | 4152 | if (SCM_I_INUMP (y)) |
55f26379 | 4153 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
4154 | else if (SCM_BIGP (y)) |
4155 | { | |
4156 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4157 | scm_remember_upto_here_1 (x); | |
55f26379 | 4158 | return scm_from_double (result); |
0aacf84e MD |
4159 | } |
4160 | else if (SCM_REALP (y)) | |
55f26379 | 4161 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 4162 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4163 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4164 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4165 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4166 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
4167 | else |
4168 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4169 | } |
0aacf84e MD |
4170 | else if (SCM_COMPLEXP (x)) |
4171 | { | |
e11e83f3 | 4172 | if (SCM_I_INUMP (y)) |
8507ec80 | 4173 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
4174 | SCM_COMPLEX_IMAG (x)); |
4175 | else if (SCM_BIGP (y)) | |
4176 | { | |
4177 | double real_part = (SCM_COMPLEX_REAL (x) | |
4178 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
4179 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4180 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
4181 | } |
4182 | else if (SCM_REALP (y)) | |
8507ec80 | 4183 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
4184 | SCM_COMPLEX_IMAG (x)); |
4185 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4186 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4187 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4188 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4189 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
4190 | SCM_COMPLEX_IMAG (x)); |
4191 | else | |
4192 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
4193 | } | |
4194 | else if (SCM_FRACTIONP (x)) | |
4195 | { | |
e11e83f3 | 4196 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4197 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 4198 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4199 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4200 | SCM_FRACTION_DENOMINATOR (x)); | |
4201 | else if (SCM_BIGP (y)) | |
cba42c93 | 4202 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4203 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4204 | SCM_FRACTION_DENOMINATOR (x)); | |
4205 | else if (SCM_REALP (y)) | |
55f26379 | 4206 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 4207 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4208 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4209 | -SCM_COMPLEX_IMAG (y)); |
4210 | else if (SCM_FRACTIONP (y)) | |
4211 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 4212 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4213 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4214 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4215 | else |
4216 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4217 | } |
0aacf84e | 4218 | else |
98cb6e75 | 4219 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 4220 | } |
c05e97b7 | 4221 | #undef FUNC_NAME |
0f2d19dd | 4222 | |
ca46fb90 | 4223 | |
9de33deb | 4224 | SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product); |
942e5b91 MG |
4225 | /* "Return the product of all arguments. If called without arguments,\n" |
4226 | * "1 is returned." | |
4227 | */ | |
0f2d19dd | 4228 | SCM |
6e8d25a6 | 4229 | scm_product (SCM x, SCM y) |
0f2d19dd | 4230 | { |
0aacf84e MD |
4231 | if (SCM_UNBNDP (y)) |
4232 | { | |
4233 | if (SCM_UNBNDP (x)) | |
d956fa6f | 4234 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
4235 | else if (SCM_NUMBERP (x)) |
4236 | return x; | |
4237 | else | |
4238 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 4239 | } |
ca46fb90 | 4240 | |
e11e83f3 | 4241 | if (SCM_I_INUMP (x)) |
0aacf84e MD |
4242 | { |
4243 | long xx; | |
f4c627b3 | 4244 | |
0aacf84e | 4245 | intbig: |
e11e83f3 | 4246 | xx = SCM_I_INUM (x); |
f4c627b3 | 4247 | |
0aacf84e MD |
4248 | switch (xx) |
4249 | { | |
ca46fb90 RB |
4250 | case 0: return x; break; |
4251 | case 1: return y; break; | |
0aacf84e | 4252 | } |
f4c627b3 | 4253 | |
e11e83f3 | 4254 | if (SCM_I_INUMP (y)) |
0aacf84e | 4255 | { |
e11e83f3 | 4256 | long yy = SCM_I_INUM (y); |
0aacf84e | 4257 | long kk = xx * yy; |
d956fa6f | 4258 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 4259 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
4260 | return k; |
4261 | else | |
4262 | { | |
4263 | SCM result = scm_i_long2big (xx); | |
4264 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); | |
4265 | return scm_i_normbig (result); | |
4266 | } | |
4267 | } | |
4268 | else if (SCM_BIGP (y)) | |
4269 | { | |
4270 | SCM result = scm_i_mkbig (); | |
4271 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
4272 | scm_remember_upto_here_1 (y); | |
4273 | return result; | |
4274 | } | |
4275 | else if (SCM_REALP (y)) | |
55f26379 | 4276 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 4277 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4278 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 4279 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4280 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4281 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4282 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4283 | else |
4284 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4285 | } |
0aacf84e MD |
4286 | else if (SCM_BIGP (x)) |
4287 | { | |
e11e83f3 | 4288 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4289 | { |
4290 | SCM_SWAP (x, y); | |
4291 | goto intbig; | |
4292 | } | |
4293 | else if (SCM_BIGP (y)) | |
4294 | { | |
4295 | SCM result = scm_i_mkbig (); | |
4296 | mpz_mul (SCM_I_BIG_MPZ (result), | |
4297 | SCM_I_BIG_MPZ (x), | |
4298 | SCM_I_BIG_MPZ (y)); | |
4299 | scm_remember_upto_here_2 (x, y); | |
4300 | return result; | |
4301 | } | |
4302 | else if (SCM_REALP (y)) | |
4303 | { | |
4304 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
4305 | scm_remember_upto_here_1 (x); | |
55f26379 | 4306 | return scm_from_double (result); |
0aacf84e MD |
4307 | } |
4308 | else if (SCM_COMPLEXP (y)) | |
4309 | { | |
4310 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4311 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4312 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4313 | z * SCM_COMPLEX_IMAG (y)); |
4314 | } | |
f92e85f7 | 4315 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4316 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4317 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4318 | else |
4319 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4320 | } |
0aacf84e MD |
4321 | else if (SCM_REALP (x)) |
4322 | { | |
e11e83f3 | 4323 | if (SCM_I_INUMP (y)) |
55f26379 | 4324 | return scm_from_double (SCM_I_INUM (y) * SCM_REAL_VALUE (x)); |
0aacf84e MD |
4325 | else if (SCM_BIGP (y)) |
4326 | { | |
4327 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
4328 | scm_remember_upto_here_1 (y); | |
55f26379 | 4329 | return scm_from_double (result); |
0aacf84e MD |
4330 | } |
4331 | else if (SCM_REALP (y)) | |
55f26379 | 4332 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 4333 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4334 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 4335 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4336 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4337 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
4338 | else |
4339 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4340 | } |
0aacf84e MD |
4341 | else if (SCM_COMPLEXP (x)) |
4342 | { | |
e11e83f3 | 4343 | if (SCM_I_INUMP (y)) |
8507ec80 | 4344 | return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x), |
e11e83f3 | 4345 | SCM_I_INUM (y) * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4346 | else if (SCM_BIGP (y)) |
4347 | { | |
4348 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4349 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4350 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 4351 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4352 | } |
4353 | else if (SCM_REALP (y)) | |
8507ec80 | 4354 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
4355 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
4356 | else if (SCM_COMPLEXP (y)) | |
4357 | { | |
8507ec80 | 4358 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
4359 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
4360 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
4361 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
4362 | } | |
f92e85f7 MV |
4363 | else if (SCM_FRACTIONP (y)) |
4364 | { | |
4365 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4366 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
4367 | yy * SCM_COMPLEX_IMAG (x)); |
4368 | } | |
4369 | else | |
4370 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
4371 | } | |
4372 | else if (SCM_FRACTIONP (x)) | |
4373 | { | |
e11e83f3 | 4374 | if (SCM_I_INUMP (y)) |
cba42c93 | 4375 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4376 | SCM_FRACTION_DENOMINATOR (x)); |
4377 | else if (SCM_BIGP (y)) | |
cba42c93 | 4378 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4379 | SCM_FRACTION_DENOMINATOR (x)); |
4380 | else if (SCM_REALP (y)) | |
55f26379 | 4381 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
4382 | else if (SCM_COMPLEXP (y)) |
4383 | { | |
4384 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 4385 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4386 | xx * SCM_COMPLEX_IMAG (y)); |
4387 | } | |
4388 | else if (SCM_FRACTIONP (y)) | |
4389 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 4390 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4391 | SCM_FRACTION_NUMERATOR (y)), |
4392 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
4393 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4394 | else |
4395 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4396 | } |
0aacf84e | 4397 | else |
f4c627b3 | 4398 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
4399 | } |
4400 | ||
7351e207 MV |
4401 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
4402 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
4403 | #define ALLOW_DIVIDE_BY_ZERO | |
4404 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
4405 | #endif | |
0f2d19dd | 4406 | |
ba74ef4e MV |
4407 | /* The code below for complex division is adapted from the GNU |
4408 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
4409 | this copyright: */ | |
4410 | ||
4411 | /**************************************************************** | |
4412 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
4413 | ||
4414 | Permission to use, copy, modify, and distribute this software | |
4415 | and its documentation for any purpose and without fee is hereby | |
4416 | granted, provided that the above copyright notice appear in all | |
4417 | copies and that both that the copyright notice and this | |
4418 | permission notice and warranty disclaimer appear in supporting | |
4419 | documentation, and that the names of AT&T Bell Laboratories or | |
4420 | Bellcore or any of their entities not be used in advertising or | |
4421 | publicity pertaining to distribution of the software without | |
4422 | specific, written prior permission. | |
4423 | ||
4424 | AT&T and Bellcore disclaim all warranties with regard to this | |
4425 | software, including all implied warranties of merchantability | |
4426 | and fitness. In no event shall AT&T or Bellcore be liable for | |
4427 | any special, indirect or consequential damages or any damages | |
4428 | whatsoever resulting from loss of use, data or profits, whether | |
4429 | in an action of contract, negligence or other tortious action, | |
4430 | arising out of or in connection with the use or performance of | |
4431 | this software. | |
4432 | ****************************************************************/ | |
4433 | ||
9de33deb | 4434 | SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide); |
609c3d30 MG |
4435 | /* Divide the first argument by the product of the remaining |
4436 | arguments. If called with one argument @var{z1}, 1/@var{z1} is | |
4437 | returned. */ | |
c05e97b7 | 4438 | #define FUNC_NAME s_divide |
f92e85f7 MV |
4439 | static SCM |
4440 | scm_i_divide (SCM x, SCM y, int inexact) | |
0f2d19dd | 4441 | { |
f8de44c1 DH |
4442 | double a; |
4443 | ||
0aacf84e MD |
4444 | if (SCM_UNBNDP (y)) |
4445 | { | |
4446 | if (SCM_UNBNDP (x)) | |
4447 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 4448 | else if (SCM_I_INUMP (x)) |
0aacf84e | 4449 | { |
e11e83f3 | 4450 | long xx = SCM_I_INUM (x); |
0aacf84e MD |
4451 | if (xx == 1 || xx == -1) |
4452 | return x; | |
7351e207 | 4453 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4454 | else if (xx == 0) |
4455 | scm_num_overflow (s_divide); | |
7351e207 | 4456 | #endif |
0aacf84e | 4457 | else |
f92e85f7 MV |
4458 | { |
4459 | if (inexact) | |
55f26379 | 4460 | return scm_from_double (1.0 / (double) xx); |
cba42c93 | 4461 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4462 | } |
0aacf84e MD |
4463 | } |
4464 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
4465 | { |
4466 | if (inexact) | |
55f26379 | 4467 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cba42c93 | 4468 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4469 | } |
0aacf84e MD |
4470 | else if (SCM_REALP (x)) |
4471 | { | |
4472 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 4473 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4474 | if (xx == 0.0) |
4475 | scm_num_overflow (s_divide); | |
4476 | else | |
7351e207 | 4477 | #endif |
55f26379 | 4478 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
4479 | } |
4480 | else if (SCM_COMPLEXP (x)) | |
4481 | { | |
4482 | double r = SCM_COMPLEX_REAL (x); | |
4483 | double i = SCM_COMPLEX_IMAG (x); | |
4484 | if (r <= i) | |
4485 | { | |
4486 | double t = r / i; | |
4487 | double d = i * (1.0 + t * t); | |
8507ec80 | 4488 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
4489 | } |
4490 | else | |
4491 | { | |
4492 | double t = i / r; | |
4493 | double d = r * (1.0 + t * t); | |
8507ec80 | 4494 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
4495 | } |
4496 | } | |
f92e85f7 | 4497 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4498 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 4499 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
4500 | else |
4501 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 4502 | } |
f8de44c1 | 4503 | |
e11e83f3 | 4504 | if (SCM_I_INUMP (x)) |
0aacf84e | 4505 | { |
e11e83f3 MV |
4506 | long xx = SCM_I_INUM (x); |
4507 | if (SCM_I_INUMP (y)) | |
0aacf84e | 4508 | { |
e11e83f3 | 4509 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
4510 | if (yy == 0) |
4511 | { | |
7351e207 | 4512 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4513 | scm_num_overflow (s_divide); |
7351e207 | 4514 | #else |
55f26379 | 4515 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 4516 | #endif |
0aacf84e MD |
4517 | } |
4518 | else if (xx % yy != 0) | |
f92e85f7 MV |
4519 | { |
4520 | if (inexact) | |
55f26379 | 4521 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 4522 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4523 | } |
0aacf84e MD |
4524 | else |
4525 | { | |
4526 | long z = xx / yy; | |
4527 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4528 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4529 | else |
4530 | return scm_i_long2big (z); | |
4531 | } | |
f872b822 | 4532 | } |
0aacf84e | 4533 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
4534 | { |
4535 | if (inexact) | |
55f26379 | 4536 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 4537 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4538 | } |
0aacf84e MD |
4539 | else if (SCM_REALP (y)) |
4540 | { | |
4541 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4542 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4543 | if (yy == 0.0) |
4544 | scm_num_overflow (s_divide); | |
4545 | else | |
7351e207 | 4546 | #endif |
55f26379 | 4547 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 4548 | } |
0aacf84e MD |
4549 | else if (SCM_COMPLEXP (y)) |
4550 | { | |
4551 | a = xx; | |
4552 | complex_div: /* y _must_ be a complex number */ | |
4553 | { | |
4554 | double r = SCM_COMPLEX_REAL (y); | |
4555 | double i = SCM_COMPLEX_IMAG (y); | |
4556 | if (r <= i) | |
4557 | { | |
4558 | double t = r / i; | |
4559 | double d = i * (1.0 + t * t); | |
8507ec80 | 4560 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
4561 | } |
4562 | else | |
4563 | { | |
4564 | double t = i / r; | |
4565 | double d = r * (1.0 + t * t); | |
8507ec80 | 4566 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
4567 | } |
4568 | } | |
4569 | } | |
f92e85f7 MV |
4570 | else if (SCM_FRACTIONP (y)) |
4571 | /* a / b/c = ac / b */ | |
cba42c93 | 4572 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4573 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4574 | else |
4575 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4576 | } |
0aacf84e MD |
4577 | else if (SCM_BIGP (x)) |
4578 | { | |
e11e83f3 | 4579 | if (SCM_I_INUMP (y)) |
0aacf84e | 4580 | { |
e11e83f3 | 4581 | long int yy = SCM_I_INUM (y); |
0aacf84e MD |
4582 | if (yy == 0) |
4583 | { | |
7351e207 | 4584 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4585 | scm_num_overflow (s_divide); |
7351e207 | 4586 | #else |
0aacf84e MD |
4587 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4588 | scm_remember_upto_here_1 (x); | |
4589 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 4590 | #endif |
0aacf84e MD |
4591 | } |
4592 | else if (yy == 1) | |
4593 | return x; | |
4594 | else | |
4595 | { | |
4596 | /* FIXME: HMM, what are the relative performance issues here? | |
4597 | We need to test. Is it faster on average to test | |
4598 | divisible_p, then perform whichever operation, or is it | |
4599 | faster to perform the integer div opportunistically and | |
4600 | switch to real if there's a remainder? For now we take the | |
4601 | middle ground: test, then if divisible, use the faster div | |
4602 | func. */ | |
4603 | ||
4604 | long abs_yy = yy < 0 ? -yy : yy; | |
4605 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); | |
4606 | ||
4607 | if (divisible_p) | |
4608 | { | |
4609 | SCM result = scm_i_mkbig (); | |
4610 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
4611 | scm_remember_upto_here_1 (x); | |
4612 | if (yy < 0) | |
4613 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4614 | return scm_i_normbig (result); | |
4615 | } | |
4616 | else | |
f92e85f7 MV |
4617 | { |
4618 | if (inexact) | |
55f26379 | 4619 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 4620 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4621 | } |
0aacf84e MD |
4622 | } |
4623 | } | |
4624 | else if (SCM_BIGP (y)) | |
4625 | { | |
4626 | int y_is_zero = (mpz_sgn (SCM_I_BIG_MPZ (y)) == 0); | |
4627 | if (y_is_zero) | |
4628 | { | |
ca46fb90 | 4629 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4630 | scm_num_overflow (s_divide); |
f872b822 | 4631 | #else |
0aacf84e MD |
4632 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4633 | scm_remember_upto_here_1 (x); | |
4634 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
f872b822 | 4635 | #endif |
0aacf84e MD |
4636 | } |
4637 | else | |
4638 | { | |
4639 | /* big_x / big_y */ | |
4640 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), | |
4641 | SCM_I_BIG_MPZ (y)); | |
4642 | if (divisible_p) | |
4643 | { | |
4644 | SCM result = scm_i_mkbig (); | |
4645 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
4646 | SCM_I_BIG_MPZ (x), | |
4647 | SCM_I_BIG_MPZ (y)); | |
4648 | scm_remember_upto_here_2 (x, y); | |
4649 | return scm_i_normbig (result); | |
4650 | } | |
4651 | else | |
4652 | { | |
f92e85f7 MV |
4653 | if (inexact) |
4654 | { | |
4655 | double dbx = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4656 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4657 | scm_remember_upto_here_2 (x, y); | |
55f26379 | 4658 | return scm_from_double (dbx / dby); |
f92e85f7 | 4659 | } |
cba42c93 | 4660 | else return scm_i_make_ratio (x, y); |
0aacf84e MD |
4661 | } |
4662 | } | |
4663 | } | |
4664 | else if (SCM_REALP (y)) | |
4665 | { | |
4666 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4667 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4668 | if (yy == 0.0) |
4669 | scm_num_overflow (s_divide); | |
4670 | else | |
7351e207 | 4671 | #endif |
55f26379 | 4672 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
4673 | } |
4674 | else if (SCM_COMPLEXP (y)) | |
4675 | { | |
4676 | a = scm_i_big2dbl (x); | |
4677 | goto complex_div; | |
4678 | } | |
f92e85f7 | 4679 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4680 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4681 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4682 | else |
4683 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4684 | } |
0aacf84e MD |
4685 | else if (SCM_REALP (x)) |
4686 | { | |
4687 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 4688 | if (SCM_I_INUMP (y)) |
0aacf84e | 4689 | { |
e11e83f3 | 4690 | long int yy = SCM_I_INUM (y); |
7351e207 | 4691 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4692 | if (yy == 0) |
4693 | scm_num_overflow (s_divide); | |
4694 | else | |
7351e207 | 4695 | #endif |
55f26379 | 4696 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
4697 | } |
4698 | else if (SCM_BIGP (y)) | |
4699 | { | |
4700 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4701 | scm_remember_upto_here_1 (y); | |
55f26379 | 4702 | return scm_from_double (rx / dby); |
0aacf84e MD |
4703 | } |
4704 | else if (SCM_REALP (y)) | |
4705 | { | |
4706 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4707 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4708 | if (yy == 0.0) |
4709 | scm_num_overflow (s_divide); | |
4710 | else | |
7351e207 | 4711 | #endif |
55f26379 | 4712 | return scm_from_double (rx / yy); |
0aacf84e MD |
4713 | } |
4714 | else if (SCM_COMPLEXP (y)) | |
4715 | { | |
4716 | a = rx; | |
4717 | goto complex_div; | |
4718 | } | |
f92e85f7 | 4719 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4720 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
4721 | else |
4722 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4723 | } |
0aacf84e MD |
4724 | else if (SCM_COMPLEXP (x)) |
4725 | { | |
4726 | double rx = SCM_COMPLEX_REAL (x); | |
4727 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 4728 | if (SCM_I_INUMP (y)) |
0aacf84e | 4729 | { |
e11e83f3 | 4730 | long int yy = SCM_I_INUM (y); |
7351e207 | 4731 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4732 | if (yy == 0) |
4733 | scm_num_overflow (s_divide); | |
4734 | else | |
7351e207 | 4735 | #endif |
0aacf84e MD |
4736 | { |
4737 | double d = yy; | |
8507ec80 | 4738 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
4739 | } |
4740 | } | |
4741 | else if (SCM_BIGP (y)) | |
4742 | { | |
4743 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4744 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4745 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
4746 | } |
4747 | else if (SCM_REALP (y)) | |
4748 | { | |
4749 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4750 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4751 | if (yy == 0.0) |
4752 | scm_num_overflow (s_divide); | |
4753 | else | |
7351e207 | 4754 | #endif |
8507ec80 | 4755 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
4756 | } |
4757 | else if (SCM_COMPLEXP (y)) | |
4758 | { | |
4759 | double ry = SCM_COMPLEX_REAL (y); | |
4760 | double iy = SCM_COMPLEX_IMAG (y); | |
4761 | if (ry <= iy) | |
4762 | { | |
4763 | double t = ry / iy; | |
4764 | double d = iy * (1.0 + t * t); | |
8507ec80 | 4765 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
4766 | } |
4767 | else | |
4768 | { | |
4769 | double t = iy / ry; | |
4770 | double d = ry * (1.0 + t * t); | |
8507ec80 | 4771 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
4772 | } |
4773 | } | |
f92e85f7 MV |
4774 | else if (SCM_FRACTIONP (y)) |
4775 | { | |
4776 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4777 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 4778 | } |
0aacf84e MD |
4779 | else |
4780 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4781 | } |
f92e85f7 MV |
4782 | else if (SCM_FRACTIONP (x)) |
4783 | { | |
e11e83f3 | 4784 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4785 | { |
e11e83f3 | 4786 | long int yy = SCM_I_INUM (y); |
f92e85f7 MV |
4787 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
4788 | if (yy == 0) | |
4789 | scm_num_overflow (s_divide); | |
4790 | else | |
4791 | #endif | |
cba42c93 | 4792 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4793 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4794 | } | |
4795 | else if (SCM_BIGP (y)) | |
4796 | { | |
cba42c93 | 4797 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4798 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4799 | } | |
4800 | else if (SCM_REALP (y)) | |
4801 | { | |
4802 | double yy = SCM_REAL_VALUE (y); | |
4803 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
4804 | if (yy == 0.0) | |
4805 | scm_num_overflow (s_divide); | |
4806 | else | |
4807 | #endif | |
55f26379 | 4808 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
4809 | } |
4810 | else if (SCM_COMPLEXP (y)) | |
4811 | { | |
4812 | a = scm_i_fraction2double (x); | |
4813 | goto complex_div; | |
4814 | } | |
4815 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 4816 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4817 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
4818 | else | |
4819 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
4820 | } | |
0aacf84e | 4821 | else |
f8de44c1 | 4822 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 4823 | } |
f92e85f7 MV |
4824 | |
4825 | SCM | |
4826 | scm_divide (SCM x, SCM y) | |
4827 | { | |
4828 | return scm_i_divide (x, y, 0); | |
4829 | } | |
4830 | ||
4831 | static SCM scm_divide2real (SCM x, SCM y) | |
4832 | { | |
4833 | return scm_i_divide (x, y, 1); | |
4834 | } | |
c05e97b7 | 4835 | #undef FUNC_NAME |
0f2d19dd | 4836 | |
fa605590 | 4837 | |
0f2d19dd | 4838 | double |
6e8d25a6 | 4839 | scm_asinh (double x) |
0f2d19dd | 4840 | { |
fa605590 KR |
4841 | #if HAVE_ASINH |
4842 | return asinh (x); | |
4843 | #else | |
4844 | #define asinh scm_asinh | |
f872b822 | 4845 | return log (x + sqrt (x * x + 1)); |
fa605590 | 4846 | #endif |
0f2d19dd | 4847 | } |
fa605590 KR |
4848 | SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_dsubr, (SCM (*)()) asinh, g_asinh); |
4849 | /* "Return the inverse hyperbolic sine of @var{x}." | |
4850 | */ | |
0f2d19dd JB |
4851 | |
4852 | ||
0f2d19dd | 4853 | double |
6e8d25a6 | 4854 | scm_acosh (double x) |
0f2d19dd | 4855 | { |
fa605590 KR |
4856 | #if HAVE_ACOSH |
4857 | return acosh (x); | |
4858 | #else | |
4859 | #define acosh scm_acosh | |
f872b822 | 4860 | return log (x + sqrt (x * x - 1)); |
fa605590 | 4861 | #endif |
0f2d19dd | 4862 | } |
fa605590 KR |
4863 | SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_dsubr, (SCM (*)()) acosh, g_acosh); |
4864 | /* "Return the inverse hyperbolic cosine of @var{x}." | |
4865 | */ | |
0f2d19dd JB |
4866 | |
4867 | ||
0f2d19dd | 4868 | double |
6e8d25a6 | 4869 | scm_atanh (double x) |
0f2d19dd | 4870 | { |
fa605590 KR |
4871 | #if HAVE_ATANH |
4872 | return atanh (x); | |
4873 | #else | |
4874 | #define atanh scm_atanh | |
f872b822 | 4875 | return 0.5 * log ((1 + x) / (1 - x)); |
fa605590 | 4876 | #endif |
0f2d19dd | 4877 | } |
fa605590 KR |
4878 | SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_dsubr, (SCM (*)()) atanh, g_atanh); |
4879 | /* "Return the inverse hyperbolic tangent of @var{x}." | |
4880 | */ | |
0f2d19dd JB |
4881 | |
4882 | ||
0f2d19dd | 4883 | double |
3101f40f | 4884 | scm_c_truncate (double x) |
0f2d19dd | 4885 | { |
fa605590 KR |
4886 | #if HAVE_TRUNC |
4887 | return trunc (x); | |
4888 | #else | |
f872b822 MD |
4889 | if (x < 0.0) |
4890 | return -floor (-x); | |
4891 | return floor (x); | |
fa605590 | 4892 | #endif |
0f2d19dd | 4893 | } |
0f2d19dd | 4894 | |
3101f40f MV |
4895 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
4896 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
4897 | Then half-way cases are identified and adjusted down if the | |
4898 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
4899 | |
4900 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
4901 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
4902 | ||
4903 | An odd "result" value is identified with result/2 != floor(result/2). | |
4904 | This is done with plus_half, since that value is ready for use sooner in | |
4905 | a pipelined cpu, and we're already requiring plus_half == result. | |
4906 | ||
4907 | Note however that we need to be careful when x is big and already an | |
4908 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
4909 | us to return such a value, incorrectly. For instance if the hardware is | |
4910 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
4911 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
4912 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
4913 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
4914 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
4915 | ||
4916 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
4917 | x is already an integer. If it is then clearly that's the desired result | |
4918 | already. And if it's not then the exponent must be small enough to allow | |
4919 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
4920 | ||
0f2d19dd | 4921 | double |
3101f40f | 4922 | scm_c_round (double x) |
0f2d19dd | 4923 | { |
6187f48b KR |
4924 | double plus_half, result; |
4925 | ||
4926 | if (x == floor (x)) | |
4927 | return x; | |
4928 | ||
4929 | plus_half = x + 0.5; | |
4930 | result = floor (plus_half); | |
3101f40f | 4931 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
4932 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
4933 | ? result - 1 | |
4934 | : result); | |
0f2d19dd JB |
4935 | } |
4936 | ||
f92e85f7 MV |
4937 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
4938 | (SCM x), | |
4939 | "Round the number @var{x} towards zero.") | |
4940 | #define FUNC_NAME s_scm_truncate_number | |
4941 | { | |
73e4de09 | 4942 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
4943 | return scm_floor (x); |
4944 | else | |
4945 | return scm_ceiling (x); | |
4946 | } | |
4947 | #undef FUNC_NAME | |
4948 | ||
4949 | static SCM exactly_one_half; | |
4950 | ||
4951 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, | |
4952 | (SCM x), | |
4953 | "Round the number @var{x} towards the nearest integer. " | |
4954 | "When it is exactly halfway between two integers, " | |
4955 | "round towards the even one.") | |
4956 | #define FUNC_NAME s_scm_round_number | |
4957 | { | |
e11e83f3 | 4958 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
4959 | return x; |
4960 | else if (SCM_REALP (x)) | |
3101f40f | 4961 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 4962 | else |
bae30667 KR |
4963 | { |
4964 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
4965 | single quotient+remainder division then examining to see which way | |
4966 | the rounding should go. */ | |
4967 | SCM plus_half = scm_sum (x, exactly_one_half); | |
4968 | SCM result = scm_floor (plus_half); | |
3101f40f | 4969 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
4970 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
4971 | && scm_is_true (scm_odd_p (result))) | |
d956fa6f | 4972 | return scm_difference (result, SCM_I_MAKINUM (1)); |
bae30667 KR |
4973 | else |
4974 | return result; | |
4975 | } | |
f92e85f7 MV |
4976 | } |
4977 | #undef FUNC_NAME | |
4978 | ||
4979 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
4980 | (SCM x), | |
4981 | "Round the number @var{x} towards minus infinity.") | |
4982 | #define FUNC_NAME s_scm_floor | |
4983 | { | |
e11e83f3 | 4984 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
4985 | return x; |
4986 | else if (SCM_REALP (x)) | |
55f26379 | 4987 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
4988 | else if (SCM_FRACTIONP (x)) |
4989 | { | |
4990 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
4991 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 4992 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
4993 | { |
4994 | /* For positive x, rounding towards zero is correct. */ | |
4995 | return q; | |
4996 | } | |
4997 | else | |
4998 | { | |
4999 | /* For negative x, we need to return q-1 unless x is an | |
5000 | integer. But fractions are never integer, per our | |
5001 | assumptions. */ | |
d956fa6f | 5002 | return scm_difference (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5003 | } |
5004 | } | |
5005 | else | |
5006 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
5007 | } | |
5008 | #undef FUNC_NAME | |
5009 | ||
5010 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
5011 | (SCM x), | |
5012 | "Round the number @var{x} towards infinity.") | |
5013 | #define FUNC_NAME s_scm_ceiling | |
5014 | { | |
e11e83f3 | 5015 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5016 | return x; |
5017 | else if (SCM_REALP (x)) | |
55f26379 | 5018 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5019 | else if (SCM_FRACTIONP (x)) |
5020 | { | |
5021 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5022 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5023 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
5024 | { |
5025 | /* For negative x, rounding towards zero is correct. */ | |
5026 | return q; | |
5027 | } | |
5028 | else | |
5029 | { | |
5030 | /* For positive x, we need to return q+1 unless x is an | |
5031 | integer. But fractions are never integer, per our | |
5032 | assumptions. */ | |
d956fa6f | 5033 | return scm_sum (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5034 | } |
5035 | } | |
5036 | else | |
5037 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
5038 | } | |
5039 | #undef FUNC_NAME | |
0f2d19dd | 5040 | |
14b18ed6 | 5041 | SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_dsubr, (SCM (*)()) sqrt, g_i_sqrt); |
942e5b91 MG |
5042 | /* "Return the square root of the real number @var{x}." |
5043 | */ | |
14b18ed6 | 5044 | SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_dsubr, (SCM (*)()) fabs, g_i_abs); |
942e5b91 MG |
5045 | /* "Return the absolute value of the real number @var{x}." |
5046 | */ | |
14b18ed6 | 5047 | SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_dsubr, (SCM (*)()) exp, g_i_exp); |
942e5b91 MG |
5048 | /* "Return the @var{x}th power of e." |
5049 | */ | |
14b18ed6 | 5050 | SCM_GPROC1 (s_i_log, "$log", scm_tc7_dsubr, (SCM (*)()) log, g_i_log); |
b3fcac34 | 5051 | /* "Return the natural logarithm of the real number @var{x}." |
942e5b91 | 5052 | */ |
14b18ed6 | 5053 | SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_dsubr, (SCM (*)()) sin, g_i_sin); |
942e5b91 MG |
5054 | /* "Return the sine of the real number @var{x}." |
5055 | */ | |
14b18ed6 | 5056 | SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_dsubr, (SCM (*)()) cos, g_i_cos); |
942e5b91 MG |
5057 | /* "Return the cosine of the real number @var{x}." |
5058 | */ | |
14b18ed6 | 5059 | SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_dsubr, (SCM (*)()) tan, g_i_tan); |
942e5b91 MG |
5060 | /* "Return the tangent of the real number @var{x}." |
5061 | */ | |
14b18ed6 | 5062 | SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_dsubr, (SCM (*)()) asin, g_i_asin); |
942e5b91 MG |
5063 | /* "Return the arc sine of the real number @var{x}." |
5064 | */ | |
14b18ed6 | 5065 | SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_dsubr, (SCM (*)()) acos, g_i_acos); |
942e5b91 MG |
5066 | /* "Return the arc cosine of the real number @var{x}." |
5067 | */ | |
14b18ed6 | 5068 | SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_dsubr, (SCM (*)()) atan, g_i_atan); |
942e5b91 MG |
5069 | /* "Return the arc tangent of the real number @var{x}." |
5070 | */ | |
14b18ed6 | 5071 | SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_dsubr, (SCM (*)()) sinh, g_i_sinh); |
942e5b91 MG |
5072 | /* "Return the hyperbolic sine of the real number @var{x}." |
5073 | */ | |
14b18ed6 | 5074 | SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_dsubr, (SCM (*)()) cosh, g_i_cosh); |
942e5b91 MG |
5075 | /* "Return the hyperbolic cosine of the real number @var{x}." |
5076 | */ | |
14b18ed6 | 5077 | SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_dsubr, (SCM (*)()) tanh, g_i_tanh); |
942e5b91 MG |
5078 | /* "Return the hyperbolic tangent of the real number @var{x}." |
5079 | */ | |
f872b822 MD |
5080 | |
5081 | struct dpair | |
5082 | { | |
5083 | double x, y; | |
5084 | }; | |
5085 | ||
27c37006 NJ |
5086 | static void scm_two_doubles (SCM x, |
5087 | SCM y, | |
3eeba8d4 JB |
5088 | const char *sstring, |
5089 | struct dpair * xy); | |
f872b822 MD |
5090 | |
5091 | static void | |
27c37006 NJ |
5092 | scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy) |
5093 | { | |
e11e83f3 MV |
5094 | if (SCM_I_INUMP (x)) |
5095 | xy->x = SCM_I_INUM (x); | |
0aacf84e | 5096 | else if (SCM_BIGP (x)) |
1be6b49c | 5097 | xy->x = scm_i_big2dbl (x); |
0aacf84e | 5098 | else if (SCM_REALP (x)) |
27c37006 | 5099 | xy->x = SCM_REAL_VALUE (x); |
f92e85f7 MV |
5100 | else if (SCM_FRACTIONP (x)) |
5101 | xy->x = scm_i_fraction2double (x); | |
0aacf84e | 5102 | else |
27c37006 | 5103 | scm_wrong_type_arg (sstring, SCM_ARG1, x); |
98cb6e75 | 5104 | |
e11e83f3 MV |
5105 | if (SCM_I_INUMP (y)) |
5106 | xy->y = SCM_I_INUM (y); | |
0aacf84e | 5107 | else if (SCM_BIGP (y)) |
1be6b49c | 5108 | xy->y = scm_i_big2dbl (y); |
0aacf84e | 5109 | else if (SCM_REALP (y)) |
27c37006 | 5110 | xy->y = SCM_REAL_VALUE (y); |
f92e85f7 MV |
5111 | else if (SCM_FRACTIONP (y)) |
5112 | xy->y = scm_i_fraction2double (y); | |
0aacf84e | 5113 | else |
27c37006 | 5114 | scm_wrong_type_arg (sstring, SCM_ARG2, y); |
0f2d19dd JB |
5115 | } |
5116 | ||
5117 | ||
a1ec6916 | 5118 | SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0, |
27c37006 NJ |
5119 | (SCM x, SCM y), |
5120 | "Return @var{x} raised to the power of @var{y}. This\n" | |
0137a31b | 5121 | "procedure does not accept complex arguments.") |
1bbd0b84 | 5122 | #define FUNC_NAME s_scm_sys_expt |
0f2d19dd JB |
5123 | { |
5124 | struct dpair xy; | |
27c37006 | 5125 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5126 | return scm_from_double (pow (xy.x, xy.y)); |
0f2d19dd | 5127 | } |
1bbd0b84 | 5128 | #undef FUNC_NAME |
0f2d19dd JB |
5129 | |
5130 | ||
a1ec6916 | 5131 | SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0, |
27c37006 NJ |
5132 | (SCM x, SCM y), |
5133 | "Return the arc tangent of the two arguments @var{x} and\n" | |
5134 | "@var{y}. This is similar to calculating the arc tangent of\n" | |
5135 | "@var{x} / @var{y}, except that the signs of both arguments\n" | |
0137a31b MG |
5136 | "are used to determine the quadrant of the result. This\n" |
5137 | "procedure does not accept complex arguments.") | |
1bbd0b84 | 5138 | #define FUNC_NAME s_scm_sys_atan2 |
0f2d19dd JB |
5139 | { |
5140 | struct dpair xy; | |
27c37006 | 5141 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5142 | return scm_from_double (atan2 (xy.x, xy.y)); |
0f2d19dd | 5143 | } |
1bbd0b84 | 5144 | #undef FUNC_NAME |
0f2d19dd | 5145 | |
8507ec80 MV |
5146 | SCM |
5147 | scm_c_make_rectangular (double re, double im) | |
5148 | { | |
5149 | if (im == 0.0) | |
5150 | return scm_from_double (re); | |
5151 | else | |
5152 | { | |
5153 | SCM z; | |
5154 | SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (sizeof (scm_t_complex), | |
5155 | "complex")); | |
5156 | SCM_COMPLEX_REAL (z) = re; | |
5157 | SCM_COMPLEX_IMAG (z) = im; | |
5158 | return z; | |
5159 | } | |
5160 | } | |
0f2d19dd | 5161 | |
a1ec6916 | 5162 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
bb628794 | 5163 | (SCM real, SCM imaginary), |
942e5b91 MG |
5164 | "Return a complex number constructed of the given @var{real} and\n" |
5165 | "@var{imaginary} parts.") | |
1bbd0b84 | 5166 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd JB |
5167 | { |
5168 | struct dpair xy; | |
bb628794 | 5169 | scm_two_doubles (real, imaginary, FUNC_NAME, &xy); |
8507ec80 | 5170 | return scm_c_make_rectangular (xy.x, xy.y); |
0f2d19dd | 5171 | } |
1bbd0b84 | 5172 | #undef FUNC_NAME |
0f2d19dd | 5173 | |
8507ec80 MV |
5174 | SCM |
5175 | scm_c_make_polar (double mag, double ang) | |
5176 | { | |
5177 | double s, c; | |
5178 | #if HAVE_SINCOS | |
5179 | sincos (ang, &s, &c); | |
5180 | #else | |
5181 | s = sin (ang); | |
5182 | c = cos (ang); | |
5183 | #endif | |
5184 | return scm_c_make_rectangular (mag * c, mag * s); | |
5185 | } | |
0f2d19dd | 5186 | |
a1ec6916 | 5187 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 5188 | (SCM x, SCM y), |
942e5b91 | 5189 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 5190 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd JB |
5191 | { |
5192 | struct dpair xy; | |
27c37006 | 5193 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
8507ec80 | 5194 | return scm_c_make_polar (xy.x, xy.y); |
0f2d19dd | 5195 | } |
1bbd0b84 | 5196 | #undef FUNC_NAME |
0f2d19dd JB |
5197 | |
5198 | ||
152f82bf | 5199 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
5200 | /* "Return the real part of the number @var{z}." |
5201 | */ | |
0f2d19dd | 5202 | SCM |
6e8d25a6 | 5203 | scm_real_part (SCM z) |
0f2d19dd | 5204 | { |
e11e83f3 | 5205 | if (SCM_I_INUMP (z)) |
c2ff8ab0 | 5206 | return z; |
0aacf84e | 5207 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5208 | return z; |
0aacf84e | 5209 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5210 | return z; |
0aacf84e | 5211 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5212 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
f92e85f7 | 5213 | else if (SCM_FRACTIONP (z)) |
2fa2d879 | 5214 | return z; |
0aacf84e | 5215 | else |
c2ff8ab0 | 5216 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); |
0f2d19dd JB |
5217 | } |
5218 | ||
5219 | ||
152f82bf | 5220 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
5221 | /* "Return the imaginary part of the number @var{z}." |
5222 | */ | |
0f2d19dd | 5223 | SCM |
6e8d25a6 | 5224 | scm_imag_part (SCM z) |
0f2d19dd | 5225 | { |
e11e83f3 | 5226 | if (SCM_I_INUMP (z)) |
f872b822 | 5227 | return SCM_INUM0; |
0aacf84e | 5228 | else if (SCM_BIGP (z)) |
f872b822 | 5229 | return SCM_INUM0; |
0aacf84e | 5230 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5231 | return scm_flo0; |
0aacf84e | 5232 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5233 | return scm_from_double (SCM_COMPLEX_IMAG (z)); |
f92e85f7 MV |
5234 | else if (SCM_FRACTIONP (z)) |
5235 | return SCM_INUM0; | |
0aacf84e | 5236 | else |
c2ff8ab0 | 5237 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); |
0f2d19dd JB |
5238 | } |
5239 | ||
f92e85f7 MV |
5240 | SCM_GPROC (s_numerator, "numerator", 1, 0, 0, scm_numerator, g_numerator); |
5241 | /* "Return the numerator of the number @var{z}." | |
5242 | */ | |
5243 | SCM | |
5244 | scm_numerator (SCM z) | |
5245 | { | |
e11e83f3 | 5246 | if (SCM_I_INUMP (z)) |
f92e85f7 MV |
5247 | return z; |
5248 | else if (SCM_BIGP (z)) | |
5249 | return z; | |
5250 | else if (SCM_FRACTIONP (z)) | |
5251 | { | |
5252 | scm_i_fraction_reduce (z); | |
5253 | return SCM_FRACTION_NUMERATOR (z); | |
5254 | } | |
5255 | else if (SCM_REALP (z)) | |
5256 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
5257 | else | |
5258 | SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator); | |
5259 | } | |
5260 | ||
5261 | ||
5262 | SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator); | |
5263 | /* "Return the denominator of the number @var{z}." | |
5264 | */ | |
5265 | SCM | |
5266 | scm_denominator (SCM z) | |
5267 | { | |
e11e83f3 | 5268 | if (SCM_I_INUMP (z)) |
d956fa6f | 5269 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5270 | else if (SCM_BIGP (z)) |
d956fa6f | 5271 | return SCM_I_MAKINUM (1); |
f92e85f7 MV |
5272 | else if (SCM_FRACTIONP (z)) |
5273 | { | |
5274 | scm_i_fraction_reduce (z); | |
5275 | return SCM_FRACTION_DENOMINATOR (z); | |
5276 | } | |
5277 | else if (SCM_REALP (z)) | |
5278 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
5279 | else | |
5280 | SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator); | |
5281 | } | |
0f2d19dd | 5282 | |
9de33deb | 5283 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
5284 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
5285 | * "@code{abs} for real arguments, but also allows complex numbers." | |
5286 | */ | |
0f2d19dd | 5287 | SCM |
6e8d25a6 | 5288 | scm_magnitude (SCM z) |
0f2d19dd | 5289 | { |
e11e83f3 | 5290 | if (SCM_I_INUMP (z)) |
0aacf84e | 5291 | { |
e11e83f3 | 5292 | long int zz = SCM_I_INUM (z); |
0aacf84e MD |
5293 | if (zz >= 0) |
5294 | return z; | |
5295 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 5296 | return SCM_I_MAKINUM (-zz); |
0aacf84e MD |
5297 | else |
5298 | return scm_i_long2big (-zz); | |
5986c47d | 5299 | } |
0aacf84e MD |
5300 | else if (SCM_BIGP (z)) |
5301 | { | |
5302 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5303 | scm_remember_upto_here_1 (z); | |
5304 | if (sgn < 0) | |
5305 | return scm_i_clonebig (z, 0); | |
5306 | else | |
5307 | return z; | |
5986c47d | 5308 | } |
0aacf84e | 5309 | else if (SCM_REALP (z)) |
55f26379 | 5310 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 5311 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5312 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
5313 | else if (SCM_FRACTIONP (z)) |
5314 | { | |
73e4de09 | 5315 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5316 | return z; |
cba42c93 | 5317 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
5318 | SCM_FRACTION_DENOMINATOR (z)); |
5319 | } | |
0aacf84e | 5320 | else |
c2ff8ab0 | 5321 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); |
0f2d19dd JB |
5322 | } |
5323 | ||
5324 | ||
9de33deb | 5325 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
5326 | /* "Return the angle of the complex number @var{z}." |
5327 | */ | |
0f2d19dd | 5328 | SCM |
6e8d25a6 | 5329 | scm_angle (SCM z) |
0f2d19dd | 5330 | { |
c8ae173e | 5331 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
55f26379 | 5332 | scm_flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
5333 | But if atan2 follows the floating point rounding mode, then the value |
5334 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 5335 | if (SCM_I_INUMP (z)) |
0aacf84e | 5336 | { |
e11e83f3 | 5337 | if (SCM_I_INUM (z) >= 0) |
c8ae173e | 5338 | return scm_flo0; |
0aacf84e | 5339 | else |
55f26379 | 5340 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 5341 | } |
0aacf84e MD |
5342 | else if (SCM_BIGP (z)) |
5343 | { | |
5344 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5345 | scm_remember_upto_here_1 (z); | |
5346 | if (sgn < 0) | |
55f26379 | 5347 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 5348 | else |
c8ae173e | 5349 | return scm_flo0; |
0f2d19dd | 5350 | } |
0aacf84e | 5351 | else if (SCM_REALP (z)) |
c8ae173e KR |
5352 | { |
5353 | if (SCM_REAL_VALUE (z) >= 0) | |
5354 | return scm_flo0; | |
5355 | else | |
55f26379 | 5356 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 5357 | } |
0aacf84e | 5358 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5359 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
5360 | else if (SCM_FRACTIONP (z)) |
5361 | { | |
73e4de09 | 5362 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5363 | return scm_flo0; |
55f26379 | 5364 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 5365 | } |
0aacf84e | 5366 | else |
f4c627b3 | 5367 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); |
0f2d19dd JB |
5368 | } |
5369 | ||
5370 | ||
3c9a524f DH |
5371 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
5372 | /* Convert the number @var{x} to its inexact representation.\n" | |
5373 | */ | |
5374 | SCM | |
5375 | scm_exact_to_inexact (SCM z) | |
5376 | { | |
e11e83f3 | 5377 | if (SCM_I_INUMP (z)) |
55f26379 | 5378 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 5379 | else if (SCM_BIGP (z)) |
55f26379 | 5380 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 5381 | else if (SCM_FRACTIONP (z)) |
55f26379 | 5382 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
5383 | else if (SCM_INEXACTP (z)) |
5384 | return z; | |
5385 | else | |
5386 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
5387 | } | |
5388 | ||
5389 | ||
a1ec6916 | 5390 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 5391 | (SCM z), |
1e6808ea | 5392 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 5393 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 5394 | { |
e11e83f3 | 5395 | if (SCM_I_INUMP (z)) |
f872b822 | 5396 | return z; |
0aacf84e | 5397 | else if (SCM_BIGP (z)) |
f872b822 | 5398 | return z; |
0aacf84e MD |
5399 | else if (SCM_REALP (z)) |
5400 | { | |
f92e85f7 MV |
5401 | if (xisinf (SCM_REAL_VALUE (z)) || xisnan (SCM_REAL_VALUE (z))) |
5402 | SCM_OUT_OF_RANGE (1, z); | |
2be24db4 | 5403 | else |
f92e85f7 MV |
5404 | { |
5405 | mpq_t frac; | |
5406 | SCM q; | |
5407 | ||
5408 | mpq_init (frac); | |
5409 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 5410 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
5411 | scm_i_mpz2num (mpq_denref (frac))); |
5412 | ||
cba42c93 | 5413 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
5414 | for frac... |
5415 | */ | |
5416 | mpq_clear (frac); | |
5417 | return q; | |
5418 | } | |
c2ff8ab0 | 5419 | } |
f92e85f7 MV |
5420 | else if (SCM_FRACTIONP (z)) |
5421 | return z; | |
0aacf84e | 5422 | else |
c2ff8ab0 | 5423 | SCM_WRONG_TYPE_ARG (1, z); |
0f2d19dd | 5424 | } |
1bbd0b84 | 5425 | #undef FUNC_NAME |
0f2d19dd | 5426 | |
f92e85f7 MV |
5427 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
5428 | (SCM x, SCM err), | |
5429 | "Return an exact number that is within @var{err} of @var{x}.") | |
5430 | #define FUNC_NAME s_scm_rationalize | |
5431 | { | |
e11e83f3 | 5432 | if (SCM_I_INUMP (x)) |
f92e85f7 MV |
5433 | return x; |
5434 | else if (SCM_BIGP (x)) | |
5435 | return x; | |
5436 | else if ((SCM_REALP (x)) || SCM_FRACTIONP (x)) | |
5437 | { | |
5438 | /* Use continued fractions to find closest ratio. All | |
5439 | arithmetic is done with exact numbers. | |
5440 | */ | |
5441 | ||
5442 | SCM ex = scm_inexact_to_exact (x); | |
5443 | SCM int_part = scm_floor (ex); | |
d956fa6f MV |
5444 | SCM tt = SCM_I_MAKINUM (1); |
5445 | SCM a1 = SCM_I_MAKINUM (0), a2 = SCM_I_MAKINUM (1), a = SCM_I_MAKINUM (0); | |
5446 | SCM b1 = SCM_I_MAKINUM (1), b2 = SCM_I_MAKINUM (0), b = SCM_I_MAKINUM (0); | |
f92e85f7 MV |
5447 | SCM rx; |
5448 | int i = 0; | |
5449 | ||
73e4de09 | 5450 | if (scm_is_true (scm_num_eq_p (ex, int_part))) |
f92e85f7 MV |
5451 | return ex; |
5452 | ||
5453 | ex = scm_difference (ex, int_part); /* x = x-int_part */ | |
5454 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
5455 | ||
5456 | /* We stop after a million iterations just to be absolutely sure | |
5457 | that we don't go into an infinite loop. The process normally | |
5458 | converges after less than a dozen iterations. | |
5459 | */ | |
5460 | ||
5461 | err = scm_abs (err); | |
5462 | while (++i < 1000000) | |
5463 | { | |
5464 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
5465 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
5466 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
5467 | scm_is_false | |
f92e85f7 MV |
5468 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
5469 | err))) /* abs(x-a/b) <= err */ | |
02164269 MV |
5470 | { |
5471 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
73e4de09 MV |
5472 | if (scm_is_false (scm_exact_p (x)) |
5473 | || scm_is_false (scm_exact_p (err))) | |
02164269 MV |
5474 | return scm_exact_to_inexact (res); |
5475 | else | |
5476 | return res; | |
5477 | } | |
f92e85f7 MV |
5478 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
5479 | SCM_UNDEFINED); | |
5480 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
5481 | a2 = a1; | |
5482 | b2 = b1; | |
5483 | a1 = a; | |
5484 | b1 = b; | |
5485 | } | |
5486 | scm_num_overflow (s_scm_rationalize); | |
5487 | } | |
5488 | else | |
5489 | SCM_WRONG_TYPE_ARG (1, x); | |
5490 | } | |
5491 | #undef FUNC_NAME | |
5492 | ||
73e4de09 MV |
5493 | /* conversion functions */ |
5494 | ||
5495 | int | |
5496 | scm_is_integer (SCM val) | |
5497 | { | |
5498 | return scm_is_true (scm_integer_p (val)); | |
5499 | } | |
5500 | ||
5501 | int | |
5502 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
5503 | { | |
e11e83f3 | 5504 | if (SCM_I_INUMP (val)) |
73e4de09 | 5505 | { |
e11e83f3 | 5506 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5507 | return n >= min && n <= max; |
5508 | } | |
5509 | else if (SCM_BIGP (val)) | |
5510 | { | |
5511 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
5512 | return 0; | |
5513 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
5514 | { |
5515 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
5516 | { | |
5517 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
5518 | return n >= min && n <= max; | |
5519 | } | |
5520 | else | |
5521 | return 0; | |
5522 | } | |
73e4de09 MV |
5523 | else |
5524 | { | |
d956fa6f MV |
5525 | scm_t_intmax n; |
5526 | size_t count; | |
73e4de09 | 5527 | |
d956fa6f MV |
5528 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5529 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
5530 | return 0; | |
5531 | ||
5532 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5533 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5534 | |
d956fa6f | 5535 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 5536 | { |
d956fa6f MV |
5537 | if (n < 0) |
5538 | return 0; | |
73e4de09 | 5539 | } |
73e4de09 MV |
5540 | else |
5541 | { | |
d956fa6f MV |
5542 | n = -n; |
5543 | if (n >= 0) | |
5544 | return 0; | |
73e4de09 | 5545 | } |
d956fa6f MV |
5546 | |
5547 | return n >= min && n <= max; | |
73e4de09 MV |
5548 | } |
5549 | } | |
73e4de09 MV |
5550 | else |
5551 | return 0; | |
5552 | } | |
5553 | ||
5554 | int | |
5555 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
5556 | { | |
e11e83f3 | 5557 | if (SCM_I_INUMP (val)) |
73e4de09 | 5558 | { |
e11e83f3 | 5559 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5560 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
5561 | } | |
5562 | else if (SCM_BIGP (val)) | |
5563 | { | |
5564 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
5565 | return 0; | |
5566 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
5567 | { |
5568 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
5569 | { | |
5570 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
5571 | return n >= min && n <= max; | |
5572 | } | |
5573 | else | |
5574 | return 0; | |
5575 | } | |
73e4de09 MV |
5576 | else |
5577 | { | |
d956fa6f MV |
5578 | scm_t_uintmax n; |
5579 | size_t count; | |
73e4de09 | 5580 | |
d956fa6f MV |
5581 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
5582 | return 0; | |
73e4de09 | 5583 | |
d956fa6f MV |
5584 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5585 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 5586 | return 0; |
d956fa6f MV |
5587 | |
5588 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5589 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5590 | |
d956fa6f | 5591 | return n >= min && n <= max; |
73e4de09 MV |
5592 | } |
5593 | } | |
73e4de09 MV |
5594 | else |
5595 | return 0; | |
5596 | } | |
5597 | ||
bfd7932e MV |
5598 | #define TYPE scm_t_intmax |
5599 | #define TYPE_MIN min | |
5600 | #define TYPE_MAX max | |
5601 | #define SIZEOF_TYPE 0 | |
5602 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
5603 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
5604 | #include "libguile/conv-integer.i.c" | |
5605 | ||
5606 | #define TYPE scm_t_uintmax | |
5607 | #define TYPE_MIN min | |
5608 | #define TYPE_MAX max | |
5609 | #define SIZEOF_TYPE 0 | |
5610 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
5611 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
5612 | #include "libguile/conv-uinteger.i.c" | |
5613 | ||
5614 | #define TYPE scm_t_int8 | |
5615 | #define TYPE_MIN SCM_T_INT8_MIN | |
5616 | #define TYPE_MAX SCM_T_INT8_MAX | |
5617 | #define SIZEOF_TYPE 1 | |
5618 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
5619 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
5620 | #include "libguile/conv-integer.i.c" | |
5621 | ||
5622 | #define TYPE scm_t_uint8 | |
5623 | #define TYPE_MIN 0 | |
5624 | #define TYPE_MAX SCM_T_UINT8_MAX | |
5625 | #define SIZEOF_TYPE 1 | |
5626 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
5627 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
5628 | #include "libguile/conv-uinteger.i.c" | |
5629 | ||
5630 | #define TYPE scm_t_int16 | |
5631 | #define TYPE_MIN SCM_T_INT16_MIN | |
5632 | #define TYPE_MAX SCM_T_INT16_MAX | |
5633 | #define SIZEOF_TYPE 2 | |
5634 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
5635 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
5636 | #include "libguile/conv-integer.i.c" | |
5637 | ||
5638 | #define TYPE scm_t_uint16 | |
5639 | #define TYPE_MIN 0 | |
5640 | #define TYPE_MAX SCM_T_UINT16_MAX | |
5641 | #define SIZEOF_TYPE 2 | |
5642 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
5643 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
5644 | #include "libguile/conv-uinteger.i.c" | |
5645 | ||
5646 | #define TYPE scm_t_int32 | |
5647 | #define TYPE_MIN SCM_T_INT32_MIN | |
5648 | #define TYPE_MAX SCM_T_INT32_MAX | |
5649 | #define SIZEOF_TYPE 4 | |
5650 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
5651 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
5652 | #include "libguile/conv-integer.i.c" | |
5653 | ||
5654 | #define TYPE scm_t_uint32 | |
5655 | #define TYPE_MIN 0 | |
5656 | #define TYPE_MAX SCM_T_UINT32_MAX | |
5657 | #define SIZEOF_TYPE 4 | |
5658 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
5659 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
5660 | #include "libguile/conv-uinteger.i.c" | |
5661 | ||
5662 | #if SCM_HAVE_T_INT64 | |
5663 | ||
5664 | #define TYPE scm_t_int64 | |
5665 | #define TYPE_MIN SCM_T_INT64_MIN | |
5666 | #define TYPE_MAX SCM_T_INT64_MAX | |
5667 | #define SIZEOF_TYPE 8 | |
5668 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
5669 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
5670 | #include "libguile/conv-integer.i.c" | |
5671 | ||
5672 | #define TYPE scm_t_uint64 | |
5673 | #define TYPE_MIN 0 | |
5674 | #define TYPE_MAX SCM_T_UINT64_MAX | |
5675 | #define SIZEOF_TYPE 8 | |
5676 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
5677 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
5678 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 5679 | |
bfd7932e | 5680 | #endif |
73e4de09 | 5681 | |
cd036260 MV |
5682 | void |
5683 | scm_to_mpz (SCM val, mpz_t rop) | |
5684 | { | |
5685 | if (SCM_I_INUMP (val)) | |
5686 | mpz_set_si (rop, SCM_I_INUM (val)); | |
5687 | else if (SCM_BIGP (val)) | |
5688 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
5689 | else | |
5690 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
5691 | } | |
5692 | ||
5693 | SCM | |
5694 | scm_from_mpz (mpz_t val) | |
5695 | { | |
5696 | return scm_i_mpz2num (val); | |
5697 | } | |
5698 | ||
73e4de09 MV |
5699 | int |
5700 | scm_is_real (SCM val) | |
5701 | { | |
5702 | return scm_is_true (scm_real_p (val)); | |
5703 | } | |
5704 | ||
55f26379 MV |
5705 | int |
5706 | scm_is_rational (SCM val) | |
5707 | { | |
5708 | return scm_is_true (scm_rational_p (val)); | |
5709 | } | |
5710 | ||
73e4de09 MV |
5711 | double |
5712 | scm_to_double (SCM val) | |
5713 | { | |
55f26379 MV |
5714 | if (SCM_I_INUMP (val)) |
5715 | return SCM_I_INUM (val); | |
5716 | else if (SCM_BIGP (val)) | |
5717 | return scm_i_big2dbl (val); | |
5718 | else if (SCM_FRACTIONP (val)) | |
5719 | return scm_i_fraction2double (val); | |
5720 | else if (SCM_REALP (val)) | |
5721 | return SCM_REAL_VALUE (val); | |
5722 | else | |
5723 | scm_wrong_type_arg (NULL, 0, val); | |
73e4de09 MV |
5724 | } |
5725 | ||
5726 | SCM | |
5727 | scm_from_double (double val) | |
5728 | { | |
55f26379 MV |
5729 | SCM z = scm_double_cell (scm_tc16_real, 0, 0, 0); |
5730 | SCM_REAL_VALUE (z) = val; | |
5731 | return z; | |
73e4de09 MV |
5732 | } |
5733 | ||
55f26379 MV |
5734 | #if SCM_ENABLE_DISCOURAGED == 1 |
5735 | ||
5736 | float | |
5737 | scm_num2float (SCM num, unsigned long int pos, const char *s_caller) | |
5738 | { | |
5739 | if (SCM_BIGP (num)) | |
5740 | { | |
5741 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5742 | if (!xisinf (res)) | |
5743 | return res; | |
5744 | else | |
5745 | scm_out_of_range (NULL, num); | |
5746 | } | |
5747 | else | |
5748 | return scm_to_double (num); | |
5749 | } | |
5750 | ||
5751 | double | |
5752 | scm_num2double (SCM num, unsigned long int pos, const char *s_caller) | |
5753 | { | |
5754 | if (SCM_BIGP (num)) | |
5755 | { | |
5756 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5757 | if (!xisinf (res)) | |
5758 | return res; | |
5759 | else | |
5760 | scm_out_of_range (NULL, num); | |
5761 | } | |
5762 | else | |
5763 | return scm_to_double (num); | |
5764 | } | |
5765 | ||
5766 | #endif | |
5767 | ||
8507ec80 MV |
5768 | int |
5769 | scm_is_complex (SCM val) | |
5770 | { | |
5771 | return scm_is_true (scm_complex_p (val)); | |
5772 | } | |
5773 | ||
5774 | double | |
5775 | scm_c_real_part (SCM z) | |
5776 | { | |
5777 | if (SCM_COMPLEXP (z)) | |
5778 | return SCM_COMPLEX_REAL (z); | |
5779 | else | |
5780 | { | |
5781 | /* Use the scm_real_part to get proper error checking and | |
5782 | dispatching. | |
5783 | */ | |
5784 | return scm_to_double (scm_real_part (z)); | |
5785 | } | |
5786 | } | |
5787 | ||
5788 | double | |
5789 | scm_c_imag_part (SCM z) | |
5790 | { | |
5791 | if (SCM_COMPLEXP (z)) | |
5792 | return SCM_COMPLEX_IMAG (z); | |
5793 | else | |
5794 | { | |
5795 | /* Use the scm_imag_part to get proper error checking and | |
5796 | dispatching. The result will almost always be 0.0, but not | |
5797 | always. | |
5798 | */ | |
5799 | return scm_to_double (scm_imag_part (z)); | |
5800 | } | |
5801 | } | |
5802 | ||
5803 | double | |
5804 | scm_c_magnitude (SCM z) | |
5805 | { | |
5806 | return scm_to_double (scm_magnitude (z)); | |
5807 | } | |
5808 | ||
5809 | double | |
5810 | scm_c_angle (SCM z) | |
5811 | { | |
5812 | return scm_to_double (scm_angle (z)); | |
5813 | } | |
5814 | ||
5815 | int | |
5816 | scm_is_number (SCM z) | |
5817 | { | |
5818 | return scm_is_true (scm_number_p (z)); | |
5819 | } | |
5820 | ||
0f2d19dd JB |
5821 | void |
5822 | scm_init_numbers () | |
0f2d19dd | 5823 | { |
0b799eea MV |
5824 | int i; |
5825 | ||
713a4259 KR |
5826 | mpz_init_set_si (z_negative_one, -1); |
5827 | ||
a261c0e9 DH |
5828 | /* It may be possible to tune the performance of some algorithms by using |
5829 | * the following constants to avoid the creation of bignums. Please, before | |
5830 | * using these values, remember the two rules of program optimization: | |
5831 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 5832 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 5833 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 5834 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 5835 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 5836 | |
f3ae5d60 MD |
5837 | scm_add_feature ("complex"); |
5838 | scm_add_feature ("inexact"); | |
55f26379 | 5839 | scm_flo0 = scm_from_double (0.0); |
0b799eea MV |
5840 | |
5841 | /* determine floating point precision */ | |
55f26379 | 5842 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
5843 | { |
5844 | init_dblprec(&scm_dblprec[i-2],i); | |
5845 | init_fx_radix(fx_per_radix[i-2],i); | |
5846 | } | |
f872b822 | 5847 | #ifdef DBL_DIG |
0b799eea MV |
5848 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
5849 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; | |
5850 | #endif | |
1be6b49c | 5851 | |
d956fa6f MV |
5852 | exactly_one_half = scm_permanent_object (scm_divide (SCM_I_MAKINUM (1), |
5853 | SCM_I_MAKINUM (2))); | |
a0599745 | 5854 | #include "libguile/numbers.x" |
0f2d19dd | 5855 | } |
89e00824 ML |
5856 | |
5857 | /* | |
5858 | Local Variables: | |
5859 | c-file-style: "gnu" | |
5860 | End: | |
5861 | */ |