Commit | Line | Data |
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7d92d3d0 | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004,2005 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 | { | |
66b1c775 KR |
881 | /* C99 specifies that "%" is the remainder corresponding to a |
882 | quotient rounded towards zero, and that's also traditional | |
883 | for machine division, so z here should be well defined. */ | |
0aacf84e MD |
884 | long z = xx % yy; |
885 | long result; | |
886 | ||
887 | if (yy < 0) | |
888 | { | |
889 | if (z > 0) | |
890 | result = z + yy; | |
891 | else | |
892 | result = z; | |
893 | } | |
894 | else | |
895 | { | |
896 | if (z < 0) | |
897 | result = z + yy; | |
898 | else | |
899 | result = z; | |
900 | } | |
d956fa6f | 901 | return SCM_I_MAKINUM (result); |
0aacf84e MD |
902 | } |
903 | } | |
904 | else if (SCM_BIGP (y)) | |
905 | { | |
906 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
0aacf84e MD |
907 | { |
908 | mpz_t z_x; | |
909 | SCM result; | |
910 | ||
911 | if (sgn_y < 0) | |
912 | { | |
913 | SCM pos_y = scm_i_clonebig (y, 0); | |
914 | /* do this after the last scm_op */ | |
915 | mpz_init_set_si (z_x, xx); | |
916 | result = pos_y; /* re-use this bignum */ | |
917 | mpz_mod (SCM_I_BIG_MPZ (result), | |
918 | z_x, | |
919 | SCM_I_BIG_MPZ (pos_y)); | |
920 | scm_remember_upto_here_1 (pos_y); | |
921 | } | |
922 | else | |
923 | { | |
924 | result = scm_i_mkbig (); | |
925 | /* do this after the last scm_op */ | |
926 | mpz_init_set_si (z_x, xx); | |
927 | mpz_mod (SCM_I_BIG_MPZ (result), | |
928 | z_x, | |
929 | SCM_I_BIG_MPZ (y)); | |
930 | scm_remember_upto_here_1 (y); | |
931 | } | |
ca46fb90 | 932 | |
0aacf84e MD |
933 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
934 | mpz_add (SCM_I_BIG_MPZ (result), | |
935 | SCM_I_BIG_MPZ (y), | |
936 | SCM_I_BIG_MPZ (result)); | |
937 | scm_remember_upto_here_1 (y); | |
938 | /* and do this before the next one */ | |
939 | mpz_clear (z_x); | |
940 | return scm_i_normbig (result); | |
941 | } | |
942 | } | |
943 | else | |
944 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
f872b822 | 945 | } |
0aacf84e MD |
946 | else if (SCM_BIGP (x)) |
947 | { | |
e11e83f3 | 948 | if (SCM_I_INUMP (y)) |
0aacf84e | 949 | { |
e11e83f3 | 950 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
951 | if (yy == 0) |
952 | scm_num_overflow (s_modulo); | |
953 | else | |
954 | { | |
955 | SCM result = scm_i_mkbig (); | |
956 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
957 | SCM_I_BIG_MPZ (x), | |
958 | (yy < 0) ? - yy : yy); | |
959 | scm_remember_upto_here_1 (x); | |
960 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
961 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
962 | SCM_I_BIG_MPZ (result), | |
963 | - yy); | |
964 | return scm_i_normbig (result); | |
965 | } | |
966 | } | |
967 | else if (SCM_BIGP (y)) | |
968 | { | |
0aacf84e MD |
969 | { |
970 | SCM result = scm_i_mkbig (); | |
971 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
972 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
973 | mpz_mod (SCM_I_BIG_MPZ (result), | |
974 | SCM_I_BIG_MPZ (x), | |
975 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 976 | |
0aacf84e MD |
977 | scm_remember_upto_here_1 (x); |
978 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
979 | mpz_add (SCM_I_BIG_MPZ (result), | |
980 | SCM_I_BIG_MPZ (y), | |
981 | SCM_I_BIG_MPZ (result)); | |
982 | scm_remember_upto_here_2 (y, pos_y); | |
983 | return scm_i_normbig (result); | |
984 | } | |
985 | } | |
986 | else | |
987 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
828865c3 | 988 | } |
0aacf84e | 989 | else |
09fb7599 | 990 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); |
0f2d19dd JB |
991 | } |
992 | ||
9de33deb | 993 | SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd); |
942e5b91 MG |
994 | /* "Return the greatest common divisor of all arguments.\n" |
995 | * "If called without arguments, 0 is returned." | |
996 | */ | |
0f2d19dd | 997 | SCM |
6e8d25a6 | 998 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 999 | { |
ca46fb90 | 1000 | if (SCM_UNBNDP (y)) |
0aacf84e | 1001 | return SCM_UNBNDP (x) ? SCM_INUM0 : x; |
ca46fb90 | 1002 | |
e11e83f3 | 1003 | if (SCM_I_INUMP (x)) |
ca46fb90 | 1004 | { |
e11e83f3 | 1005 | if (SCM_I_INUMP (y)) |
ca46fb90 | 1006 | { |
e11e83f3 MV |
1007 | long xx = SCM_I_INUM (x); |
1008 | long yy = SCM_I_INUM (y); | |
ca46fb90 RB |
1009 | long u = xx < 0 ? -xx : xx; |
1010 | long v = yy < 0 ? -yy : yy; | |
1011 | long result; | |
0aacf84e MD |
1012 | if (xx == 0) |
1013 | result = v; | |
1014 | else if (yy == 0) | |
1015 | result = u; | |
1016 | else | |
1017 | { | |
1018 | long k = 1; | |
1019 | long t; | |
1020 | /* Determine a common factor 2^k */ | |
1021 | while (!(1 & (u | v))) | |
1022 | { | |
1023 | k <<= 1; | |
1024 | u >>= 1; | |
1025 | v >>= 1; | |
1026 | } | |
1027 | /* Now, any factor 2^n can be eliminated */ | |
1028 | if (u & 1) | |
1029 | t = -v; | |
1030 | else | |
1031 | { | |
1032 | t = u; | |
1033 | b3: | |
1034 | t = SCM_SRS (t, 1); | |
1035 | } | |
1036 | if (!(1 & t)) | |
1037 | goto b3; | |
1038 | if (t > 0) | |
1039 | u = t; | |
1040 | else | |
1041 | v = -t; | |
1042 | t = u - v; | |
1043 | if (t != 0) | |
1044 | goto b3; | |
1045 | result = u * k; | |
1046 | } | |
1047 | return (SCM_POSFIXABLE (result) | |
d956fa6f | 1048 | ? SCM_I_MAKINUM (result) |
0aacf84e | 1049 | : scm_i_long2big (result)); |
ca46fb90 RB |
1050 | } |
1051 | else if (SCM_BIGP (y)) | |
1052 | { | |
0bff4dce KR |
1053 | SCM_SWAP (x, y); |
1054 | goto big_inum; | |
ca46fb90 RB |
1055 | } |
1056 | else | |
1057 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 1058 | } |
ca46fb90 RB |
1059 | else if (SCM_BIGP (x)) |
1060 | { | |
e11e83f3 | 1061 | if (SCM_I_INUMP (y)) |
ca46fb90 RB |
1062 | { |
1063 | unsigned long result; | |
0bff4dce KR |
1064 | long yy; |
1065 | big_inum: | |
e11e83f3 | 1066 | yy = SCM_I_INUM (y); |
8c5b0afc KR |
1067 | if (yy == 0) |
1068 | return scm_abs (x); | |
0aacf84e MD |
1069 | if (yy < 0) |
1070 | yy = -yy; | |
ca46fb90 RB |
1071 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
1072 | scm_remember_upto_here_1 (x); | |
0aacf84e | 1073 | return (SCM_POSFIXABLE (result) |
d956fa6f | 1074 | ? SCM_I_MAKINUM (result) |
c71b0706 | 1075 | : scm_from_ulong (result)); |
ca46fb90 RB |
1076 | } |
1077 | else if (SCM_BIGP (y)) | |
1078 | { | |
1079 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
1080 | mpz_gcd (SCM_I_BIG_MPZ (result), |
1081 | SCM_I_BIG_MPZ (x), | |
1082 | SCM_I_BIG_MPZ (y)); | |
1083 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
1084 | return scm_i_normbig (result); |
1085 | } | |
1086 | else | |
1087 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 1088 | } |
ca46fb90 | 1089 | else |
09fb7599 | 1090 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
1091 | } |
1092 | ||
9de33deb | 1093 | SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm); |
942e5b91 MG |
1094 | /* "Return the least common multiple of the arguments.\n" |
1095 | * "If called without arguments, 1 is returned." | |
1096 | */ | |
0f2d19dd | 1097 | SCM |
6e8d25a6 | 1098 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 1099 | { |
ca46fb90 RB |
1100 | if (SCM_UNBNDP (n2)) |
1101 | { | |
1102 | if (SCM_UNBNDP (n1)) | |
d956fa6f MV |
1103 | return SCM_I_MAKINUM (1L); |
1104 | n2 = SCM_I_MAKINUM (1L); | |
09fb7599 | 1105 | } |
09fb7599 | 1106 | |
e11e83f3 | 1107 | SCM_GASSERT2 (SCM_I_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 1108 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
e11e83f3 | 1109 | SCM_GASSERT2 (SCM_I_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 1110 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 1111 | |
e11e83f3 | 1112 | if (SCM_I_INUMP (n1)) |
ca46fb90 | 1113 | { |
e11e83f3 | 1114 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1115 | { |
1116 | SCM d = scm_gcd (n1, n2); | |
bc36d050 | 1117 | if (scm_is_eq (d, SCM_INUM0)) |
ca46fb90 RB |
1118 | return d; |
1119 | else | |
1120 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
1121 | } | |
1122 | else | |
1123 | { | |
1124 | /* inum n1, big n2 */ | |
1125 | inumbig: | |
1126 | { | |
1127 | SCM result = scm_i_mkbig (); | |
e11e83f3 | 1128 | long nn1 = SCM_I_INUM (n1); |
ca46fb90 RB |
1129 | if (nn1 == 0) return SCM_INUM0; |
1130 | if (nn1 < 0) nn1 = - nn1; | |
1131 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
1132 | scm_remember_upto_here_1 (n2); | |
1133 | return result; | |
1134 | } | |
1135 | } | |
1136 | } | |
1137 | else | |
1138 | { | |
1139 | /* big n1 */ | |
e11e83f3 | 1140 | if (SCM_I_INUMP (n2)) |
ca46fb90 RB |
1141 | { |
1142 | SCM_SWAP (n1, n2); | |
1143 | goto inumbig; | |
1144 | } | |
1145 | else | |
1146 | { | |
1147 | SCM result = scm_i_mkbig (); | |
1148 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
1149 | SCM_I_BIG_MPZ (n1), | |
1150 | SCM_I_BIG_MPZ (n2)); | |
1151 | scm_remember_upto_here_2(n1, n2); | |
1152 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
1153 | return result; | |
1154 | } | |
f872b822 | 1155 | } |
0f2d19dd JB |
1156 | } |
1157 | ||
8a525303 GB |
1158 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
1159 | ||
1160 | Logand: | |
1161 | X Y Result Method: | |
1162 | (len) | |
1163 | + + + x (map digit:logand X Y) | |
1164 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
1165 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
1166 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
1167 | ||
1168 | Logior: | |
1169 | X Y Result Method: | |
1170 | ||
1171 | + + + (map digit:logior X Y) | |
1172 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
1173 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
1174 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
1175 | ||
1176 | Logxor: | |
1177 | X Y Result Method: | |
1178 | ||
1179 | + + + (map digit:logxor X Y) | |
1180 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
1181 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
1182 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
1183 | ||
1184 | Logtest: | |
1185 | X Y Result | |
1186 | ||
1187 | + + (any digit:logand X Y) | |
1188 | + - (any digit:logand X (lognot (+ -1 Y))) | |
1189 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
1190 | - - #t | |
1191 | ||
1192 | */ | |
1193 | ||
c3ee7520 | 1194 | SCM_DEFINE1 (scm_logand, "logand", scm_tc7_asubr, |
1bbd0b84 | 1195 | (SCM n1, SCM n2), |
3c3db128 GH |
1196 | "Return the bitwise AND of the integer arguments.\n\n" |
1197 | "@lisp\n" | |
1198 | "(logand) @result{} -1\n" | |
1199 | "(logand 7) @result{} 7\n" | |
535f2a51 | 1200 | "(logand #b111 #b011 #b001) @result{} 1\n" |
3c3db128 | 1201 | "@end lisp") |
1bbd0b84 | 1202 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 1203 | { |
9a00c9fc DH |
1204 | long int nn1; |
1205 | ||
0aacf84e MD |
1206 | if (SCM_UNBNDP (n2)) |
1207 | { | |
1208 | if (SCM_UNBNDP (n1)) | |
d956fa6f | 1209 | return SCM_I_MAKINUM (-1); |
0aacf84e MD |
1210 | else if (!SCM_NUMBERP (n1)) |
1211 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1212 | else if (SCM_NUMBERP (n1)) | |
1213 | return n1; | |
1214 | else | |
1215 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1216 | } |
09fb7599 | 1217 | |
e11e83f3 | 1218 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1219 | { |
e11e83f3 MV |
1220 | nn1 = SCM_I_INUM (n1); |
1221 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1222 | { |
e11e83f3 | 1223 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1224 | return SCM_I_MAKINUM (nn1 & nn2); |
0aacf84e MD |
1225 | } |
1226 | else if SCM_BIGP (n2) | |
1227 | { | |
1228 | intbig: | |
1229 | if (n1 == 0) | |
1230 | return SCM_INUM0; | |
1231 | { | |
1232 | SCM result_z = scm_i_mkbig (); | |
1233 | mpz_t nn1_z; | |
1234 | mpz_init_set_si (nn1_z, nn1); | |
1235 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1236 | scm_remember_upto_here_1 (n2); | |
1237 | mpz_clear (nn1_z); | |
1238 | return scm_i_normbig (result_z); | |
1239 | } | |
1240 | } | |
1241 | else | |
1242 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1243 | } | |
1244 | else if (SCM_BIGP (n1)) | |
1245 | { | |
e11e83f3 | 1246 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1247 | { |
1248 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1249 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1250 | goto intbig; |
1251 | } | |
1252 | else if (SCM_BIGP (n2)) | |
1253 | { | |
1254 | SCM result_z = scm_i_mkbig (); | |
1255 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
1256 | SCM_I_BIG_MPZ (n1), | |
1257 | SCM_I_BIG_MPZ (n2)); | |
1258 | scm_remember_upto_here_2 (n1, n2); | |
1259 | return scm_i_normbig (result_z); | |
1260 | } | |
1261 | else | |
1262 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1263 | } |
0aacf84e | 1264 | else |
09fb7599 | 1265 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1266 | } |
1bbd0b84 | 1267 | #undef FUNC_NAME |
0f2d19dd | 1268 | |
09fb7599 | 1269 | |
c3ee7520 | 1270 | SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr, |
1bbd0b84 | 1271 | (SCM n1, SCM n2), |
3c3db128 GH |
1272 | "Return the bitwise OR of the integer arguments.\n\n" |
1273 | "@lisp\n" | |
1274 | "(logior) @result{} 0\n" | |
1275 | "(logior 7) @result{} 7\n" | |
1276 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1e6808ea | 1277 | "@end lisp") |
1bbd0b84 | 1278 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 1279 | { |
9a00c9fc DH |
1280 | long int nn1; |
1281 | ||
0aacf84e MD |
1282 | if (SCM_UNBNDP (n2)) |
1283 | { | |
1284 | if (SCM_UNBNDP (n1)) | |
1285 | return SCM_INUM0; | |
1286 | else if (SCM_NUMBERP (n1)) | |
1287 | return n1; | |
1288 | else | |
1289 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1290 | } |
09fb7599 | 1291 | |
e11e83f3 | 1292 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1293 | { |
e11e83f3 MV |
1294 | nn1 = SCM_I_INUM (n1); |
1295 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1296 | { |
e11e83f3 | 1297 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1298 | return SCM_I_MAKINUM (nn1 | nn2); |
0aacf84e MD |
1299 | } |
1300 | else if (SCM_BIGP (n2)) | |
1301 | { | |
1302 | intbig: | |
1303 | if (nn1 == 0) | |
1304 | return n2; | |
1305 | { | |
1306 | SCM result_z = scm_i_mkbig (); | |
1307 | mpz_t nn1_z; | |
1308 | mpz_init_set_si (nn1_z, nn1); | |
1309 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1310 | scm_remember_upto_here_1 (n2); | |
1311 | mpz_clear (nn1_z); | |
1312 | return result_z; | |
1313 | } | |
1314 | } | |
1315 | else | |
1316 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1317 | } | |
1318 | else if (SCM_BIGP (n1)) | |
1319 | { | |
e11e83f3 | 1320 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1321 | { |
1322 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1323 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1324 | goto intbig; |
1325 | } | |
1326 | else if (SCM_BIGP (n2)) | |
1327 | { | |
1328 | SCM result_z = scm_i_mkbig (); | |
1329 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
1330 | SCM_I_BIG_MPZ (n1), | |
1331 | SCM_I_BIG_MPZ (n2)); | |
1332 | scm_remember_upto_here_2 (n1, n2); | |
1333 | return result_z; | |
1334 | } | |
1335 | else | |
1336 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1337 | } |
0aacf84e | 1338 | else |
09fb7599 | 1339 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1340 | } |
1bbd0b84 | 1341 | #undef FUNC_NAME |
0f2d19dd | 1342 | |
09fb7599 | 1343 | |
c3ee7520 | 1344 | SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr, |
1bbd0b84 | 1345 | (SCM n1, SCM n2), |
3c3db128 GH |
1346 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1347 | "set in the result if it is set in an odd number of arguments.\n" | |
1348 | "@lisp\n" | |
1349 | "(logxor) @result{} 0\n" | |
1350 | "(logxor 7) @result{} 7\n" | |
1351 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1352 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1353 | "@end lisp") |
1bbd0b84 | 1354 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1355 | { |
9a00c9fc DH |
1356 | long int nn1; |
1357 | ||
0aacf84e MD |
1358 | if (SCM_UNBNDP (n2)) |
1359 | { | |
1360 | if (SCM_UNBNDP (n1)) | |
1361 | return SCM_INUM0; | |
1362 | else if (SCM_NUMBERP (n1)) | |
1363 | return n1; | |
1364 | else | |
1365 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1366 | } |
09fb7599 | 1367 | |
e11e83f3 | 1368 | if (SCM_I_INUMP (n1)) |
0aacf84e | 1369 | { |
e11e83f3 MV |
1370 | nn1 = SCM_I_INUM (n1); |
1371 | if (SCM_I_INUMP (n2)) | |
0aacf84e | 1372 | { |
e11e83f3 | 1373 | long nn2 = SCM_I_INUM (n2); |
d956fa6f | 1374 | return SCM_I_MAKINUM (nn1 ^ nn2); |
0aacf84e MD |
1375 | } |
1376 | else if (SCM_BIGP (n2)) | |
1377 | { | |
1378 | intbig: | |
1379 | { | |
1380 | SCM result_z = scm_i_mkbig (); | |
1381 | mpz_t nn1_z; | |
1382 | mpz_init_set_si (nn1_z, nn1); | |
1383 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1384 | scm_remember_upto_here_1 (n2); | |
1385 | mpz_clear (nn1_z); | |
1386 | return scm_i_normbig (result_z); | |
1387 | } | |
1388 | } | |
1389 | else | |
1390 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1391 | } | |
1392 | else if (SCM_BIGP (n1)) | |
1393 | { | |
e11e83f3 | 1394 | if (SCM_I_INUMP (n2)) |
0aacf84e MD |
1395 | { |
1396 | SCM_SWAP (n1, n2); | |
e11e83f3 | 1397 | nn1 = SCM_I_INUM (n1); |
0aacf84e MD |
1398 | goto intbig; |
1399 | } | |
1400 | else if (SCM_BIGP (n2)) | |
1401 | { | |
1402 | SCM result_z = scm_i_mkbig (); | |
1403 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
1404 | SCM_I_BIG_MPZ (n1), | |
1405 | SCM_I_BIG_MPZ (n2)); | |
1406 | scm_remember_upto_here_2 (n1, n2); | |
1407 | return scm_i_normbig (result_z); | |
1408 | } | |
1409 | else | |
1410 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1411 | } |
0aacf84e | 1412 | else |
09fb7599 | 1413 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1414 | } |
1bbd0b84 | 1415 | #undef FUNC_NAME |
0f2d19dd | 1416 | |
09fb7599 | 1417 | |
a1ec6916 | 1418 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea | 1419 | (SCM j, SCM k), |
ba6e7231 KR |
1420 | "Test whether @var{j} and @var{k} have any 1 bits in common.\n" |
1421 | "This is equivalent to @code{(not (zero? (logand j k)))}, but\n" | |
1422 | "without actually calculating the @code{logand}, just testing\n" | |
1423 | "for non-zero.\n" | |
1424 | "\n" | |
1e6808ea | 1425 | "@lisp\n" |
b380b885 MD |
1426 | "(logtest #b0100 #b1011) @result{} #f\n" |
1427 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1428 | "@end lisp") |
1bbd0b84 | 1429 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1430 | { |
1e6808ea | 1431 | long int nj; |
9a00c9fc | 1432 | |
e11e83f3 | 1433 | if (SCM_I_INUMP (j)) |
0aacf84e | 1434 | { |
e11e83f3 MV |
1435 | nj = SCM_I_INUM (j); |
1436 | if (SCM_I_INUMP (k)) | |
0aacf84e | 1437 | { |
e11e83f3 | 1438 | long nk = SCM_I_INUM (k); |
73e4de09 | 1439 | return scm_from_bool (nj & nk); |
0aacf84e MD |
1440 | } |
1441 | else if (SCM_BIGP (k)) | |
1442 | { | |
1443 | intbig: | |
1444 | if (nj == 0) | |
1445 | return SCM_BOOL_F; | |
1446 | { | |
1447 | SCM result; | |
1448 | mpz_t nj_z; | |
1449 | mpz_init_set_si (nj_z, nj); | |
1450 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
1451 | scm_remember_upto_here_1 (k); | |
73e4de09 | 1452 | result = scm_from_bool (mpz_sgn (nj_z) != 0); |
0aacf84e MD |
1453 | mpz_clear (nj_z); |
1454 | return result; | |
1455 | } | |
1456 | } | |
1457 | else | |
1458 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1459 | } | |
1460 | else if (SCM_BIGP (j)) | |
1461 | { | |
e11e83f3 | 1462 | if (SCM_I_INUMP (k)) |
0aacf84e MD |
1463 | { |
1464 | SCM_SWAP (j, k); | |
e11e83f3 | 1465 | nj = SCM_I_INUM (j); |
0aacf84e MD |
1466 | goto intbig; |
1467 | } | |
1468 | else if (SCM_BIGP (k)) | |
1469 | { | |
1470 | SCM result; | |
1471 | mpz_t result_z; | |
1472 | mpz_init (result_z); | |
1473 | mpz_and (result_z, | |
1474 | SCM_I_BIG_MPZ (j), | |
1475 | SCM_I_BIG_MPZ (k)); | |
1476 | scm_remember_upto_here_2 (j, k); | |
73e4de09 | 1477 | result = scm_from_bool (mpz_sgn (result_z) != 0); |
0aacf84e MD |
1478 | mpz_clear (result_z); |
1479 | return result; | |
1480 | } | |
1481 | else | |
1482 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1483 | } | |
1484 | else | |
1485 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 1486 | } |
1bbd0b84 | 1487 | #undef FUNC_NAME |
0f2d19dd | 1488 | |
c1bfcf60 | 1489 | |
a1ec6916 | 1490 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1491 | (SCM index, SCM j), |
ba6e7231 KR |
1492 | "Test whether bit number @var{index} in @var{j} is set.\n" |
1493 | "@var{index} starts from 0 for the least significant bit.\n" | |
1494 | "\n" | |
1e6808ea | 1495 | "@lisp\n" |
b380b885 MD |
1496 | "(logbit? 0 #b1101) @result{} #t\n" |
1497 | "(logbit? 1 #b1101) @result{} #f\n" | |
1498 | "(logbit? 2 #b1101) @result{} #t\n" | |
1499 | "(logbit? 3 #b1101) @result{} #t\n" | |
1500 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1501 | "@end lisp") |
1bbd0b84 | 1502 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1503 | { |
78166ad5 | 1504 | unsigned long int iindex; |
5efd3c7d | 1505 | iindex = scm_to_ulong (index); |
78166ad5 | 1506 | |
e11e83f3 | 1507 | if (SCM_I_INUMP (j)) |
0d75f6d8 KR |
1508 | { |
1509 | /* bits above what's in an inum follow the sign bit */ | |
20fcc8ed | 1510 | iindex = min (iindex, SCM_LONG_BIT - 1); |
e11e83f3 | 1511 | return scm_from_bool ((1L << iindex) & SCM_I_INUM (j)); |
0d75f6d8 | 1512 | } |
0aacf84e MD |
1513 | else if (SCM_BIGP (j)) |
1514 | { | |
1515 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
1516 | scm_remember_upto_here_1 (j); | |
73e4de09 | 1517 | return scm_from_bool (val); |
0aacf84e MD |
1518 | } |
1519 | else | |
78166ad5 | 1520 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 1521 | } |
1bbd0b84 | 1522 | #undef FUNC_NAME |
0f2d19dd | 1523 | |
78166ad5 | 1524 | |
a1ec6916 | 1525 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1526 | (SCM n), |
4d814788 | 1527 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
1528 | "argument.\n" |
1529 | "\n" | |
b380b885 MD |
1530 | "@lisp\n" |
1531 | "(number->string (lognot #b10000000) 2)\n" | |
1532 | " @result{} \"-10000001\"\n" | |
1533 | "(number->string (lognot #b0) 2)\n" | |
1534 | " @result{} \"-1\"\n" | |
1e6808ea | 1535 | "@end lisp") |
1bbd0b84 | 1536 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1537 | { |
e11e83f3 | 1538 | if (SCM_I_INUMP (n)) { |
f9811f9f KR |
1539 | /* No overflow here, just need to toggle all the bits making up the inum. |
1540 | Enhancement: No need to strip the tag and add it back, could just xor | |
1541 | a block of 1 bits, if that worked with the various debug versions of | |
1542 | the SCM typedef. */ | |
e11e83f3 | 1543 | return SCM_I_MAKINUM (~ SCM_I_INUM (n)); |
f9811f9f KR |
1544 | |
1545 | } else if (SCM_BIGP (n)) { | |
1546 | SCM result = scm_i_mkbig (); | |
1547 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
1548 | scm_remember_upto_here_1 (n); | |
1549 | return result; | |
1550 | ||
1551 | } else { | |
1552 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1553 | } | |
0f2d19dd | 1554 | } |
1bbd0b84 | 1555 | #undef FUNC_NAME |
0f2d19dd | 1556 | |
518b7508 KR |
1557 | /* returns 0 if IN is not an integer. OUT must already be |
1558 | initialized. */ | |
1559 | static int | |
1560 | coerce_to_big (SCM in, mpz_t out) | |
1561 | { | |
1562 | if (SCM_BIGP (in)) | |
1563 | mpz_set (out, SCM_I_BIG_MPZ (in)); | |
e11e83f3 MV |
1564 | else if (SCM_I_INUMP (in)) |
1565 | mpz_set_si (out, SCM_I_INUM (in)); | |
518b7508 KR |
1566 | else |
1567 | return 0; | |
1568 | ||
1569 | return 1; | |
1570 | } | |
1571 | ||
d885e204 | 1572 | SCM_DEFINE (scm_modulo_expt, "modulo-expt", 3, 0, 0, |
518b7508 KR |
1573 | (SCM n, SCM k, SCM m), |
1574 | "Return @var{n} raised to the integer exponent\n" | |
1575 | "@var{k}, modulo @var{m}.\n" | |
1576 | "\n" | |
1577 | "@lisp\n" | |
1578 | "(modulo-expt 2 3 5)\n" | |
1579 | " @result{} 3\n" | |
1580 | "@end lisp") | |
d885e204 | 1581 | #define FUNC_NAME s_scm_modulo_expt |
518b7508 KR |
1582 | { |
1583 | mpz_t n_tmp; | |
1584 | mpz_t k_tmp; | |
1585 | mpz_t m_tmp; | |
1586 | ||
1587 | /* There are two classes of error we might encounter -- | |
1588 | 1) Math errors, which we'll report by calling scm_num_overflow, | |
1589 | and | |
1590 | 2) wrong-type errors, which of course we'll report by calling | |
1591 | SCM_WRONG_TYPE_ARG. | |
1592 | We don't report those errors immediately, however; instead we do | |
1593 | some cleanup first. These variables tell us which error (if | |
1594 | any) we should report after cleaning up. | |
1595 | */ | |
1596 | int report_overflow = 0; | |
1597 | ||
1598 | int position_of_wrong_type = 0; | |
1599 | SCM value_of_wrong_type = SCM_INUM0; | |
1600 | ||
1601 | SCM result = SCM_UNDEFINED; | |
1602 | ||
1603 | mpz_init (n_tmp); | |
1604 | mpz_init (k_tmp); | |
1605 | mpz_init (m_tmp); | |
1606 | ||
bc36d050 | 1607 | if (scm_is_eq (m, SCM_INUM0)) |
518b7508 KR |
1608 | { |
1609 | report_overflow = 1; | |
1610 | goto cleanup; | |
1611 | } | |
1612 | ||
1613 | if (!coerce_to_big (n, n_tmp)) | |
1614 | { | |
1615 | value_of_wrong_type = n; | |
1616 | position_of_wrong_type = 1; | |
1617 | goto cleanup; | |
1618 | } | |
1619 | ||
1620 | if (!coerce_to_big (k, k_tmp)) | |
1621 | { | |
1622 | value_of_wrong_type = k; | |
1623 | position_of_wrong_type = 2; | |
1624 | goto cleanup; | |
1625 | } | |
1626 | ||
1627 | if (!coerce_to_big (m, m_tmp)) | |
1628 | { | |
1629 | value_of_wrong_type = m; | |
1630 | position_of_wrong_type = 3; | |
1631 | goto cleanup; | |
1632 | } | |
1633 | ||
1634 | /* if the exponent K is negative, and we simply call mpz_powm, we | |
1635 | will get a divide-by-zero exception when an inverse 1/n mod m | |
1636 | doesn't exist (or is not unique). Since exceptions are hard to | |
1637 | handle, we'll attempt the inversion "by hand" -- that way, we get | |
1638 | a simple failure code, which is easy to handle. */ | |
1639 | ||
1640 | if (-1 == mpz_sgn (k_tmp)) | |
1641 | { | |
1642 | if (!mpz_invert (n_tmp, n_tmp, m_tmp)) | |
1643 | { | |
1644 | report_overflow = 1; | |
1645 | goto cleanup; | |
1646 | } | |
1647 | mpz_neg (k_tmp, k_tmp); | |
1648 | } | |
1649 | ||
1650 | result = scm_i_mkbig (); | |
1651 | mpz_powm (SCM_I_BIG_MPZ (result), | |
1652 | n_tmp, | |
1653 | k_tmp, | |
1654 | m_tmp); | |
b7b8c575 KR |
1655 | |
1656 | if (mpz_sgn (m_tmp) < 0 && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) | |
1657 | mpz_add (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), m_tmp); | |
1658 | ||
518b7508 KR |
1659 | cleanup: |
1660 | mpz_clear (m_tmp); | |
1661 | mpz_clear (k_tmp); | |
1662 | mpz_clear (n_tmp); | |
1663 | ||
1664 | if (report_overflow) | |
1665 | scm_num_overflow (FUNC_NAME); | |
1666 | ||
1667 | if (position_of_wrong_type) | |
1668 | SCM_WRONG_TYPE_ARG (position_of_wrong_type, | |
1669 | value_of_wrong_type); | |
1670 | ||
1671 | return scm_i_normbig (result); | |
1672 | } | |
1673 | #undef FUNC_NAME | |
1674 | ||
a1ec6916 | 1675 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1676 | (SCM n, SCM k), |
ba6e7231 KR |
1677 | "Return @var{n} raised to the power @var{k}. @var{k} must be an\n" |
1678 | "exact integer, @var{n} can be any number.\n" | |
1679 | "\n" | |
1680 | "Negative @var{k} is supported, and results in @math{1/n^abs(k)}\n" | |
1681 | "in the usual way. @math{@var{n}^0} is 1, as usual, and that\n" | |
1682 | "includes @math{0^0} is 1.\n" | |
1e6808ea | 1683 | "\n" |
b380b885 | 1684 | "@lisp\n" |
ba6e7231 KR |
1685 | "(integer-expt 2 5) @result{} 32\n" |
1686 | "(integer-expt -3 3) @result{} -27\n" | |
1687 | "(integer-expt 5 -3) @result{} 1/125\n" | |
1688 | "(integer-expt 0 0) @result{} 1\n" | |
b380b885 | 1689 | "@end lisp") |
1bbd0b84 | 1690 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1691 | { |
1c35cb19 RB |
1692 | long i2 = 0; |
1693 | SCM z_i2 = SCM_BOOL_F; | |
1694 | int i2_is_big = 0; | |
d956fa6f | 1695 | SCM acc = SCM_I_MAKINUM (1L); |
ca46fb90 | 1696 | |
d57ed702 | 1697 | /* 0^0 == 1 according to R5RS */ |
bc36d050 | 1698 | if (scm_is_eq (n, SCM_INUM0) || scm_is_eq (n, acc)) |
73e4de09 | 1699 | return scm_is_false (scm_zero_p(k)) ? n : acc; |
bc36d050 | 1700 | else if (scm_is_eq (n, SCM_I_MAKINUM (-1L))) |
73e4de09 | 1701 | return scm_is_false (scm_even_p (k)) ? n : acc; |
ca46fb90 | 1702 | |
e11e83f3 MV |
1703 | if (SCM_I_INUMP (k)) |
1704 | i2 = SCM_I_INUM (k); | |
ca46fb90 RB |
1705 | else if (SCM_BIGP (k)) |
1706 | { | |
1707 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
1708 | scm_remember_upto_here_1 (k); |
1709 | i2_is_big = 1; | |
1710 | } | |
2830fd91 | 1711 | else |
ca46fb90 RB |
1712 | SCM_WRONG_TYPE_ARG (2, k); |
1713 | ||
1714 | if (i2_is_big) | |
f872b822 | 1715 | { |
ca46fb90 RB |
1716 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
1717 | { | |
1718 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
1719 | n = scm_divide (n, SCM_UNDEFINED); | |
1720 | } | |
1721 | while (1) | |
1722 | { | |
1723 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
1724 | { | |
ca46fb90 RB |
1725 | return acc; |
1726 | } | |
1727 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
1728 | { | |
ca46fb90 RB |
1729 | return scm_product (acc, n); |
1730 | } | |
1731 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
1732 | acc = scm_product (acc, n); | |
1733 | n = scm_product (n, n); | |
1734 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
1735 | } | |
f872b822 | 1736 | } |
ca46fb90 | 1737 | else |
f872b822 | 1738 | { |
ca46fb90 RB |
1739 | if (i2 < 0) |
1740 | { | |
1741 | i2 = -i2; | |
1742 | n = scm_divide (n, SCM_UNDEFINED); | |
1743 | } | |
1744 | while (1) | |
1745 | { | |
1746 | if (0 == i2) | |
1747 | return acc; | |
1748 | if (1 == i2) | |
1749 | return scm_product (acc, n); | |
1750 | if (i2 & 1) | |
1751 | acc = scm_product (acc, n); | |
1752 | n = scm_product (n, n); | |
1753 | i2 >>= 1; | |
1754 | } | |
f872b822 | 1755 | } |
0f2d19dd | 1756 | } |
1bbd0b84 | 1757 | #undef FUNC_NAME |
0f2d19dd | 1758 | |
a1ec6916 | 1759 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1760 | (SCM n, SCM cnt), |
32f19569 KR |
1761 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
1762 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 1763 | "\n" |
e7644cb2 | 1764 | "This is effectively a multiplication by 2^@var{cnt}, and when\n" |
32f19569 KR |
1765 | "@var{cnt} is negative it's a division, rounded towards negative\n" |
1766 | "infinity. (Note that this is not the same rounding as\n" | |
1767 | "@code{quotient} does.)\n" | |
1768 | "\n" | |
1769 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
1770 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
1771 | "shift dropping bits.\n" | |
1e6808ea | 1772 | "\n" |
b380b885 | 1773 | "@lisp\n" |
1e6808ea MG |
1774 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1775 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
1776 | "\n" |
1777 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
1778 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 1779 | "@end lisp") |
1bbd0b84 | 1780 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1781 | { |
3ab9f56e | 1782 | long bits_to_shift; |
5efd3c7d | 1783 | bits_to_shift = scm_to_long (cnt); |
ca46fb90 | 1784 | |
788aca27 KR |
1785 | if (SCM_I_INUMP (n)) |
1786 | { | |
1787 | long nn = SCM_I_INUM (n); | |
1788 | ||
1789 | if (bits_to_shift > 0) | |
1790 | { | |
1791 | /* Left shift of bits_to_shift >= SCM_I_FIXNUM_BIT-1 will always | |
1792 | overflow a non-zero fixnum. For smaller shifts we check the | |
1793 | bits going into positions above SCM_I_FIXNUM_BIT-1. If they're | |
1794 | all 0s for nn>=0, or all 1s for nn<0 then there's no overflow. | |
1795 | Those bits are "nn >> (SCM_I_FIXNUM_BIT-1 - | |
1796 | bits_to_shift)". */ | |
1797 | ||
1798 | if (nn == 0) | |
1799 | return n; | |
1800 | ||
1801 | if (bits_to_shift < SCM_I_FIXNUM_BIT-1 | |
1802 | && ((unsigned long) | |
1803 | (SCM_SRS (nn, (SCM_I_FIXNUM_BIT-1 - bits_to_shift)) + 1) | |
1804 | <= 1)) | |
1805 | { | |
1806 | return SCM_I_MAKINUM (nn << bits_to_shift); | |
1807 | } | |
1808 | else | |
1809 | { | |
1810 | SCM result = scm_i_long2big (nn); | |
1811 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1812 | bits_to_shift); | |
1813 | return result; | |
1814 | } | |
1815 | } | |
1816 | else | |
1817 | { | |
1818 | bits_to_shift = -bits_to_shift; | |
1819 | if (bits_to_shift >= SCM_LONG_BIT) | |
1820 | return (nn >= 0 ? SCM_I_MAKINUM (0) : SCM_I_MAKINUM(-1)); | |
1821 | else | |
1822 | return SCM_I_MAKINUM (SCM_SRS (nn, bits_to_shift)); | |
1823 | } | |
1824 | ||
1825 | } | |
1826 | else if (SCM_BIGP (n)) | |
ca46fb90 | 1827 | { |
788aca27 KR |
1828 | SCM result; |
1829 | ||
1830 | if (bits_to_shift == 0) | |
1831 | return n; | |
1832 | ||
1833 | result = scm_i_mkbig (); | |
1834 | if (bits_to_shift >= 0) | |
1835 | { | |
1836 | mpz_mul_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1837 | bits_to_shift); | |
1838 | return result; | |
1839 | } | |
ca46fb90 | 1840 | else |
788aca27 KR |
1841 | { |
1842 | /* GMP doesn't have an fdiv_q_2exp variant returning just a long, so | |
1843 | we have to allocate a bignum even if the result is going to be a | |
1844 | fixnum. */ | |
1845 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n), | |
1846 | -bits_to_shift); | |
1847 | return scm_i_normbig (result); | |
1848 | } | |
1849 | ||
ca46fb90 RB |
1850 | } |
1851 | else | |
788aca27 KR |
1852 | { |
1853 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1854 | } | |
0f2d19dd | 1855 | } |
1bbd0b84 | 1856 | #undef FUNC_NAME |
0f2d19dd | 1857 | |
3c9f20f8 | 1858 | |
a1ec6916 | 1859 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 1860 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
1861 | "Return the integer composed of the @var{start} (inclusive)\n" |
1862 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
1863 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
1864 | "\n" | |
b380b885 MD |
1865 | "@lisp\n" |
1866 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
1867 | " @result{} \"1010\"\n" | |
1868 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
1869 | " @result{} \"10110\"\n" | |
1870 | "@end lisp") | |
1bbd0b84 | 1871 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 1872 | { |
7f848242 | 1873 | unsigned long int istart, iend, bits; |
5efd3c7d MV |
1874 | istart = scm_to_ulong (start); |
1875 | iend = scm_to_ulong (end); | |
c1bfcf60 | 1876 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); |
78166ad5 | 1877 | |
7f848242 KR |
1878 | /* how many bits to keep */ |
1879 | bits = iend - istart; | |
1880 | ||
e11e83f3 | 1881 | if (SCM_I_INUMP (n)) |
0aacf84e | 1882 | { |
e11e83f3 | 1883 | long int in = SCM_I_INUM (n); |
7f848242 KR |
1884 | |
1885 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
d77ad560 | 1886 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". */ |
857ae6af | 1887 | in = SCM_SRS (in, min (istart, SCM_I_FIXNUM_BIT-1)); |
ac0c002c | 1888 | |
0aacf84e MD |
1889 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
1890 | { | |
1891 | /* Since we emulate two's complement encoded numbers, this | |
1892 | * special case requires us to produce a result that has | |
7f848242 | 1893 | * more bits than can be stored in a fixnum. |
0aacf84e | 1894 | */ |
7f848242 KR |
1895 | SCM result = scm_i_long2big (in); |
1896 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1897 | bits); | |
1898 | return result; | |
0aacf84e | 1899 | } |
ac0c002c | 1900 | |
7f848242 | 1901 | /* mask down to requisite bits */ |
857ae6af | 1902 | bits = min (bits, SCM_I_FIXNUM_BIT); |
d956fa6f | 1903 | return SCM_I_MAKINUM (in & ((1L << bits) - 1)); |
0aacf84e MD |
1904 | } |
1905 | else if (SCM_BIGP (n)) | |
ac0c002c | 1906 | { |
7f848242 KR |
1907 | SCM result; |
1908 | if (bits == 1) | |
1909 | { | |
d956fa6f | 1910 | result = SCM_I_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); |
7f848242 KR |
1911 | } |
1912 | else | |
1913 | { | |
1914 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
1915 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
1916 | such bits into a ulong. */ | |
1917 | result = scm_i_mkbig (); | |
1918 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
1919 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
1920 | result = scm_i_normbig (result); | |
1921 | } | |
1922 | scm_remember_upto_here_1 (n); | |
1923 | return result; | |
ac0c002c | 1924 | } |
0aacf84e | 1925 | else |
78166ad5 | 1926 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 1927 | } |
1bbd0b84 | 1928 | #undef FUNC_NAME |
0f2d19dd | 1929 | |
7f848242 | 1930 | |
e4755e5c JB |
1931 | static const char scm_logtab[] = { |
1932 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
1933 | }; | |
1cc91f1b | 1934 | |
a1ec6916 | 1935 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 1936 | (SCM n), |
1e6808ea MG |
1937 | "Return the number of bits in integer @var{n}. If integer is\n" |
1938 | "positive, the 1-bits in its binary representation are counted.\n" | |
1939 | "If negative, the 0-bits in its two's-complement binary\n" | |
1940 | "representation are counted. If 0, 0 is returned.\n" | |
1941 | "\n" | |
b380b885 MD |
1942 | "@lisp\n" |
1943 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
1944 | " @result{} 4\n" |
1945 | "(logcount 0)\n" | |
1946 | " @result{} 0\n" | |
1947 | "(logcount -2)\n" | |
1948 | " @result{} 1\n" | |
1949 | "@end lisp") | |
1950 | #define FUNC_NAME s_scm_logcount | |
1951 | { | |
e11e83f3 | 1952 | if (SCM_I_INUMP (n)) |
f872b822 | 1953 | { |
ca46fb90 | 1954 | unsigned long int c = 0; |
e11e83f3 | 1955 | long int nn = SCM_I_INUM (n); |
ca46fb90 RB |
1956 | if (nn < 0) |
1957 | nn = -1 - nn; | |
1958 | while (nn) | |
1959 | { | |
1960 | c += scm_logtab[15 & nn]; | |
1961 | nn >>= 4; | |
1962 | } | |
d956fa6f | 1963 | return SCM_I_MAKINUM (c); |
f872b822 | 1964 | } |
ca46fb90 | 1965 | else if (SCM_BIGP (n)) |
f872b822 | 1966 | { |
ca46fb90 | 1967 | unsigned long count; |
713a4259 KR |
1968 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
1969 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 1970 | else |
713a4259 KR |
1971 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
1972 | scm_remember_upto_here_1 (n); | |
d956fa6f | 1973 | return SCM_I_MAKINUM (count); |
f872b822 | 1974 | } |
ca46fb90 RB |
1975 | else |
1976 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 1977 | } |
ca46fb90 | 1978 | #undef FUNC_NAME |
0f2d19dd JB |
1979 | |
1980 | ||
ca46fb90 RB |
1981 | static const char scm_ilentab[] = { |
1982 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
1983 | }; | |
1984 | ||
0f2d19dd | 1985 | |
ca46fb90 RB |
1986 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
1987 | (SCM n), | |
1988 | "Return the number of bits necessary to represent @var{n}.\n" | |
1989 | "\n" | |
1990 | "@lisp\n" | |
1991 | "(integer-length #b10101010)\n" | |
1992 | " @result{} 8\n" | |
1993 | "(integer-length 0)\n" | |
1994 | " @result{} 0\n" | |
1995 | "(integer-length #b1111)\n" | |
1996 | " @result{} 4\n" | |
1997 | "@end lisp") | |
1998 | #define FUNC_NAME s_scm_integer_length | |
1999 | { | |
e11e83f3 | 2000 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2001 | { |
2002 | unsigned long int c = 0; | |
2003 | unsigned int l = 4; | |
e11e83f3 | 2004 | long int nn = SCM_I_INUM (n); |
0aacf84e MD |
2005 | if (nn < 0) |
2006 | nn = -1 - nn; | |
2007 | while (nn) | |
2008 | { | |
2009 | c += 4; | |
2010 | l = scm_ilentab [15 & nn]; | |
2011 | nn >>= 4; | |
2012 | } | |
d956fa6f | 2013 | return SCM_I_MAKINUM (c - 4 + l); |
0aacf84e MD |
2014 | } |
2015 | else if (SCM_BIGP (n)) | |
2016 | { | |
2017 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
2018 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
2019 | 1 too big, so check for that and adjust. */ | |
2020 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
2021 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
2022 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
2023 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
2024 | size--; | |
2025 | scm_remember_upto_here_1 (n); | |
d956fa6f | 2026 | return SCM_I_MAKINUM (size); |
0aacf84e MD |
2027 | } |
2028 | else | |
ca46fb90 | 2029 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
2030 | } |
2031 | #undef FUNC_NAME | |
0f2d19dd JB |
2032 | |
2033 | /*** NUMBERS -> STRINGS ***/ | |
0b799eea MV |
2034 | #define SCM_MAX_DBL_PREC 60 |
2035 | #define SCM_MAX_DBL_RADIX 36 | |
2036 | ||
2037 | /* this is an array starting with radix 2, and ending with radix SCM_MAX_DBL_RADIX */ | |
2038 | static int scm_dblprec[SCM_MAX_DBL_RADIX - 1]; | |
2039 | static double fx_per_radix[SCM_MAX_DBL_RADIX - 1][SCM_MAX_DBL_PREC]; | |
2040 | ||
2041 | static | |
2042 | void init_dblprec(int *prec, int radix) { | |
2043 | /* determine floating point precision by adding successively | |
2044 | smaller increments to 1.0 until it is considered == 1.0 */ | |
2045 | double f = ((double)1.0)/radix; | |
2046 | double fsum = 1.0 + f; | |
2047 | ||
2048 | *prec = 0; | |
2049 | while (fsum != 1.0) | |
2050 | { | |
2051 | if (++(*prec) > SCM_MAX_DBL_PREC) | |
2052 | fsum = 1.0; | |
2053 | else | |
2054 | { | |
2055 | f /= radix; | |
2056 | fsum = f + 1.0; | |
2057 | } | |
2058 | } | |
2059 | (*prec) -= 1; | |
2060 | } | |
2061 | ||
2062 | static | |
2063 | void init_fx_radix(double *fx_list, int radix) | |
2064 | { | |
2065 | /* initialize a per-radix list of tolerances. When added | |
2066 | to a number < 1.0, we can determine if we should raund | |
2067 | up and quit converting a number to a string. */ | |
2068 | int i; | |
2069 | fx_list[0] = 0.0; | |
2070 | fx_list[1] = 0.5; | |
2071 | for( i = 2 ; i < SCM_MAX_DBL_PREC; ++i ) | |
2072 | fx_list[i] = (fx_list[i-1] / radix); | |
2073 | } | |
2074 | ||
2075 | /* use this array as a way to generate a single digit */ | |
2076 | static const char*number_chars="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; | |
0f2d19dd | 2077 | |
1be6b49c | 2078 | static size_t |
0b799eea | 2079 | idbl2str (double f, char *a, int radix) |
0f2d19dd | 2080 | { |
0b799eea MV |
2081 | int efmt, dpt, d, i, wp; |
2082 | double *fx; | |
2083 | #ifdef DBL_MIN_10_EXP | |
2084 | double f_cpy; | |
2085 | int exp_cpy; | |
2086 | #endif /* DBL_MIN_10_EXP */ | |
2087 | size_t ch = 0; | |
2088 | int exp = 0; | |
2089 | ||
2090 | if(radix < 2 || | |
2091 | radix > SCM_MAX_DBL_RADIX) | |
2092 | { | |
2093 | /* revert to existing behavior */ | |
2094 | radix = 10; | |
2095 | } | |
2096 | ||
2097 | wp = scm_dblprec[radix-2]; | |
2098 | fx = fx_per_radix[radix-2]; | |
0f2d19dd | 2099 | |
f872b822 | 2100 | if (f == 0.0) |
abb7e44d MV |
2101 | { |
2102 | #ifdef HAVE_COPYSIGN | |
2103 | double sgn = copysign (1.0, f); | |
2104 | ||
2105 | if (sgn < 0.0) | |
2106 | a[ch++] = '-'; | |
2107 | #endif | |
abb7e44d MV |
2108 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ |
2109 | } | |
7351e207 MV |
2110 | |
2111 | if (xisinf (f)) | |
2112 | { | |
2113 | if (f < 0) | |
2114 | strcpy (a, "-inf.0"); | |
2115 | else | |
2116 | strcpy (a, "+inf.0"); | |
2117 | return ch+6; | |
2118 | } | |
2119 | else if (xisnan (f)) | |
2120 | { | |
2121 | strcpy (a, "+nan.0"); | |
2122 | return ch+6; | |
2123 | } | |
2124 | ||
f872b822 MD |
2125 | if (f < 0.0) |
2126 | { | |
2127 | f = -f; | |
2128 | a[ch++] = '-'; | |
2129 | } | |
7351e207 | 2130 | |
f872b822 MD |
2131 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
2132 | make-uniform-vector, from causing infinite loops. */ | |
0b799eea MV |
2133 | /* just do the checking...if it passes, we do the conversion for our |
2134 | radix again below */ | |
2135 | f_cpy = f; | |
2136 | exp_cpy = exp; | |
2137 | ||
2138 | while (f_cpy < 1.0) | |
f872b822 | 2139 | { |
0b799eea MV |
2140 | f_cpy *= 10.0; |
2141 | if (exp_cpy-- < DBL_MIN_10_EXP) | |
7351e207 MV |
2142 | { |
2143 | a[ch++] = '#'; | |
2144 | a[ch++] = '.'; | |
2145 | a[ch++] = '#'; | |
2146 | return ch; | |
2147 | } | |
f872b822 | 2148 | } |
0b799eea | 2149 | while (f_cpy > 10.0) |
f872b822 | 2150 | { |
0b799eea MV |
2151 | f_cpy *= 0.10; |
2152 | if (exp_cpy++ > DBL_MAX_10_EXP) | |
7351e207 MV |
2153 | { |
2154 | a[ch++] = '#'; | |
2155 | a[ch++] = '.'; | |
2156 | a[ch++] = '#'; | |
2157 | return ch; | |
2158 | } | |
f872b822 | 2159 | } |
0b799eea MV |
2160 | #endif |
2161 | ||
f872b822 MD |
2162 | while (f < 1.0) |
2163 | { | |
0b799eea | 2164 | f *= radix; |
f872b822 MD |
2165 | exp--; |
2166 | } | |
0b799eea | 2167 | while (f > radix) |
f872b822 | 2168 | { |
0b799eea | 2169 | f /= radix; |
f872b822 MD |
2170 | exp++; |
2171 | } | |
0b799eea MV |
2172 | |
2173 | if (f + fx[wp] >= radix) | |
f872b822 MD |
2174 | { |
2175 | f = 1.0; | |
2176 | exp++; | |
2177 | } | |
0f2d19dd | 2178 | zero: |
0b799eea MV |
2179 | #ifdef ENGNOT |
2180 | /* adding 9999 makes this equivalent to abs(x) % 3 */ | |
f872b822 | 2181 | dpt = (exp + 9999) % 3; |
0f2d19dd JB |
2182 | exp -= dpt++; |
2183 | efmt = 1; | |
f872b822 MD |
2184 | #else |
2185 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 2186 | if (!efmt) |
cda139a7 MD |
2187 | { |
2188 | if (exp < 0) | |
2189 | { | |
2190 | a[ch++] = '0'; | |
2191 | a[ch++] = '.'; | |
2192 | dpt = exp; | |
f872b822 MD |
2193 | while (++dpt) |
2194 | a[ch++] = '0'; | |
cda139a7 MD |
2195 | } |
2196 | else | |
f872b822 | 2197 | dpt = exp + 1; |
cda139a7 | 2198 | } |
0f2d19dd JB |
2199 | else |
2200 | dpt = 1; | |
f872b822 MD |
2201 | #endif |
2202 | ||
2203 | do | |
2204 | { | |
2205 | d = f; | |
2206 | f -= d; | |
0b799eea | 2207 | a[ch++] = number_chars[d]; |
f872b822 MD |
2208 | if (f < fx[wp]) |
2209 | break; | |
2210 | if (f + fx[wp] >= 1.0) | |
2211 | { | |
0b799eea | 2212 | a[ch - 1] = number_chars[d+1]; |
f872b822 MD |
2213 | break; |
2214 | } | |
0b799eea | 2215 | f *= radix; |
f872b822 MD |
2216 | if (!(--dpt)) |
2217 | a[ch++] = '.'; | |
0f2d19dd | 2218 | } |
f872b822 | 2219 | while (wp--); |
0f2d19dd JB |
2220 | |
2221 | if (dpt > 0) | |
cda139a7 | 2222 | { |
f872b822 | 2223 | #ifndef ENGNOT |
cda139a7 MD |
2224 | if ((dpt > 4) && (exp > 6)) |
2225 | { | |
f872b822 | 2226 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 2227 | for (i = ch++; i > d; i--) |
f872b822 | 2228 | a[i] = a[i - 1]; |
cda139a7 MD |
2229 | a[d] = '.'; |
2230 | efmt = 1; | |
2231 | } | |
2232 | else | |
f872b822 | 2233 | #endif |
cda139a7 | 2234 | { |
f872b822 MD |
2235 | while (--dpt) |
2236 | a[ch++] = '0'; | |
cda139a7 MD |
2237 | a[ch++] = '.'; |
2238 | } | |
2239 | } | |
f872b822 MD |
2240 | if (a[ch - 1] == '.') |
2241 | a[ch++] = '0'; /* trailing zero */ | |
2242 | if (efmt && exp) | |
2243 | { | |
2244 | a[ch++] = 'e'; | |
2245 | if (exp < 0) | |
2246 | { | |
2247 | exp = -exp; | |
2248 | a[ch++] = '-'; | |
2249 | } | |
0b799eea MV |
2250 | for (i = radix; i <= exp; i *= radix); |
2251 | for (i /= radix; i; i /= radix) | |
f872b822 | 2252 | { |
0b799eea | 2253 | a[ch++] = number_chars[exp / i]; |
f872b822 MD |
2254 | exp %= i; |
2255 | } | |
0f2d19dd | 2256 | } |
0f2d19dd JB |
2257 | return ch; |
2258 | } | |
2259 | ||
7a1aba42 MV |
2260 | |
2261 | static size_t | |
2262 | icmplx2str (double real, double imag, char *str, int radix) | |
2263 | { | |
2264 | size_t i; | |
2265 | ||
2266 | i = idbl2str (real, str, radix); | |
2267 | if (imag != 0.0) | |
2268 | { | |
2269 | /* Don't output a '+' for negative numbers or for Inf and | |
2270 | NaN. They will provide their own sign. */ | |
2271 | if (0 <= imag && !xisinf (imag) && !xisnan (imag)) | |
2272 | str[i++] = '+'; | |
2273 | i += idbl2str (imag, &str[i], radix); | |
2274 | str[i++] = 'i'; | |
2275 | } | |
2276 | return i; | |
2277 | } | |
2278 | ||
1be6b49c | 2279 | static size_t |
0b799eea | 2280 | iflo2str (SCM flt, char *str, int radix) |
0f2d19dd | 2281 | { |
1be6b49c | 2282 | size_t i; |
3c9a524f | 2283 | if (SCM_REALP (flt)) |
0b799eea | 2284 | i = idbl2str (SCM_REAL_VALUE (flt), str, radix); |
0f2d19dd | 2285 | else |
7a1aba42 MV |
2286 | i = icmplx2str (SCM_COMPLEX_REAL (flt), SCM_COMPLEX_IMAG (flt), |
2287 | str, radix); | |
0f2d19dd JB |
2288 | return i; |
2289 | } | |
0f2d19dd | 2290 | |
2881e77b | 2291 | /* convert a scm_t_intmax to a string (unterminated). returns the number of |
1bbd0b84 GB |
2292 | characters in the result. |
2293 | rad is output base | |
2294 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2295 | size_t |
2881e77b MV |
2296 | scm_iint2str (scm_t_intmax num, int rad, char *p) |
2297 | { | |
2298 | if (num < 0) | |
2299 | { | |
2300 | *p++ = '-'; | |
2301 | return scm_iuint2str (-num, rad, p) + 1; | |
2302 | } | |
2303 | else | |
2304 | return scm_iuint2str (num, rad, p); | |
2305 | } | |
2306 | ||
2307 | /* convert a scm_t_intmax to a string (unterminated). returns the number of | |
2308 | characters in the result. | |
2309 | rad is output base | |
2310 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
2311 | size_t | |
2312 | scm_iuint2str (scm_t_uintmax num, int rad, char *p) | |
0f2d19dd | 2313 | { |
1be6b49c ML |
2314 | size_t j = 1; |
2315 | size_t i; | |
2881e77b | 2316 | scm_t_uintmax n = num; |
5c11cc9d | 2317 | |
f872b822 | 2318 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2319 | j++; |
2320 | ||
2321 | i = j; | |
2881e77b | 2322 | n = num; |
f872b822 MD |
2323 | while (i--) |
2324 | { | |
5c11cc9d GH |
2325 | int d = n % rad; |
2326 | ||
f872b822 MD |
2327 | n /= rad; |
2328 | p[i] = d + ((d < 10) ? '0' : 'a' - 10); | |
2329 | } | |
0f2d19dd JB |
2330 | return j; |
2331 | } | |
2332 | ||
a1ec6916 | 2333 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2334 | (SCM n, SCM radix), |
2335 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2336 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2337 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2338 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2339 | { |
1bbd0b84 | 2340 | int base; |
98cb6e75 | 2341 | |
0aacf84e | 2342 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 2343 | base = 10; |
0aacf84e | 2344 | else |
5efd3c7d | 2345 | base = scm_to_signed_integer (radix, 2, 36); |
98cb6e75 | 2346 | |
e11e83f3 | 2347 | if (SCM_I_INUMP (n)) |
0aacf84e MD |
2348 | { |
2349 | char num_buf [SCM_INTBUFLEN]; | |
e11e83f3 | 2350 | size_t length = scm_iint2str (SCM_I_INUM (n), base, num_buf); |
cc95e00a | 2351 | return scm_from_locale_stringn (num_buf, length); |
0aacf84e MD |
2352 | } |
2353 | else if (SCM_BIGP (n)) | |
2354 | { | |
2355 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
2356 | scm_remember_upto_here_1 (n); | |
cc95e00a | 2357 | return scm_take_locale_string (str); |
0aacf84e | 2358 | } |
f92e85f7 MV |
2359 | else if (SCM_FRACTIONP (n)) |
2360 | { | |
2361 | scm_i_fraction_reduce (n); | |
2362 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), | |
cc95e00a | 2363 | scm_from_locale_string ("/"), |
f92e85f7 MV |
2364 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); |
2365 | } | |
0aacf84e MD |
2366 | else if (SCM_INEXACTP (n)) |
2367 | { | |
2368 | char num_buf [FLOBUFLEN]; | |
cc95e00a | 2369 | return scm_from_locale_stringn (num_buf, iflo2str (n, num_buf, base)); |
0aacf84e MD |
2370 | } |
2371 | else | |
bb628794 | 2372 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 2373 | } |
1bbd0b84 | 2374 | #undef FUNC_NAME |
0f2d19dd JB |
2375 | |
2376 | ||
ca46fb90 RB |
2377 | /* These print routines used to be stubbed here so that scm_repl.c |
2378 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 2379 | |
0f2d19dd | 2380 | int |
e81d98ec | 2381 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2382 | { |
56e55ac7 | 2383 | char num_buf[FLOBUFLEN]; |
0b799eea | 2384 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
0f2d19dd JB |
2385 | return !0; |
2386 | } | |
2387 | ||
b479fe9a MV |
2388 | void |
2389 | scm_i_print_double (double val, SCM port) | |
2390 | { | |
2391 | char num_buf[FLOBUFLEN]; | |
2392 | scm_lfwrite (num_buf, idbl2str (val, num_buf, 10), port); | |
2393 | } | |
2394 | ||
f3ae5d60 | 2395 | int |
e81d98ec | 2396 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 2397 | |
f3ae5d60 | 2398 | { |
56e55ac7 | 2399 | char num_buf[FLOBUFLEN]; |
0b799eea | 2400 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf, 10), port); |
f3ae5d60 MD |
2401 | return !0; |
2402 | } | |
1cc91f1b | 2403 | |
7a1aba42 MV |
2404 | void |
2405 | scm_i_print_complex (double real, double imag, SCM port) | |
2406 | { | |
2407 | char num_buf[FLOBUFLEN]; | |
2408 | scm_lfwrite (num_buf, icmplx2str (real, imag, num_buf, 10), port); | |
2409 | } | |
2410 | ||
f92e85f7 MV |
2411 | int |
2412 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
2413 | { | |
2414 | SCM str; | |
2415 | scm_i_fraction_reduce (sexp); | |
2416 | str = scm_number_to_string (sexp, SCM_UNDEFINED); | |
cc95e00a | 2417 | scm_lfwrite (scm_i_string_chars (str), scm_i_string_length (str), port); |
f92e85f7 MV |
2418 | scm_remember_upto_here_1 (str); |
2419 | return !0; | |
2420 | } | |
2421 | ||
0f2d19dd | 2422 | int |
e81d98ec | 2423 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2424 | { |
ca46fb90 RB |
2425 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
2426 | scm_remember_upto_here_1 (exp); | |
2427 | scm_lfwrite (str, (size_t) strlen (str), port); | |
2428 | free (str); | |
0f2d19dd JB |
2429 | return !0; |
2430 | } | |
2431 | /*** END nums->strs ***/ | |
2432 | ||
3c9a524f | 2433 | |
0f2d19dd | 2434 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2435 | |
3c9a524f DH |
2436 | /* The following functions implement the conversion from strings to numbers. |
2437 | * The implementation somehow follows the grammar for numbers as it is given | |
2438 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2439 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2440 | * points should be noted about the implementation: | |
2441 | * * Each function keeps a local index variable 'idx' that points at the | |
2442 | * current position within the parsed string. The global index is only | |
2443 | * updated if the function could parse the corresponding syntactic unit | |
2444 | * successfully. | |
2445 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2446 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2447 | * global exactness information is only updated after each part has been | |
2448 | * successfully parsed. | |
2449 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2450 | * Only if these fixnums would overflow, the result variables are updated | |
2451 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2452 | * the temporary variables holding the fixnums are cleared, and the process | |
2453 | * starts over again. If for example fixnums were able to store five decimal | |
2454 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2455 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2456 | * only every five digits two bignum operations were performed. | |
2457 | */ | |
2458 | ||
2459 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2460 | ||
2461 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2462 | ||
2463 | /* In non ASCII-style encodings the following macro might not work. */ | |
71df73ac KR |
2464 | #define XDIGIT2UINT(d) \ |
2465 | (isdigit ((int) (unsigned char) d) \ | |
2466 | ? (d) - '0' \ | |
2467 | : tolower ((int) (unsigned char) d) - 'a' + 10) | |
3c9a524f | 2468 | |
2a8fecee | 2469 | static SCM |
3c9a524f DH |
2470 | mem2uinteger (const char* mem, size_t len, unsigned int *p_idx, |
2471 | unsigned int radix, enum t_exactness *p_exactness) | |
2a8fecee | 2472 | { |
3c9a524f DH |
2473 | unsigned int idx = *p_idx; |
2474 | unsigned int hash_seen = 0; | |
2475 | scm_t_bits shift = 1; | |
2476 | scm_t_bits add = 0; | |
2477 | unsigned int digit_value; | |
2478 | SCM result; | |
2479 | char c; | |
2480 | ||
2481 | if (idx == len) | |
2482 | return SCM_BOOL_F; | |
2a8fecee | 2483 | |
3c9a524f | 2484 | c = mem[idx]; |
71df73ac | 2485 | if (!isxdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2486 | return SCM_BOOL_F; |
2487 | digit_value = XDIGIT2UINT (c); | |
2488 | if (digit_value >= radix) | |
2489 | return SCM_BOOL_F; | |
2490 | ||
2491 | idx++; | |
d956fa6f | 2492 | result = SCM_I_MAKINUM (digit_value); |
3c9a524f | 2493 | while (idx != len) |
f872b822 | 2494 | { |
3c9a524f | 2495 | char c = mem[idx]; |
71df73ac | 2496 | if (isxdigit ((int) (unsigned char) c)) |
f872b822 | 2497 | { |
3c9a524f | 2498 | if (hash_seen) |
1fe5e088 | 2499 | break; |
3c9a524f DH |
2500 | digit_value = XDIGIT2UINT (c); |
2501 | if (digit_value >= radix) | |
1fe5e088 | 2502 | break; |
f872b822 | 2503 | } |
3c9a524f DH |
2504 | else if (c == '#') |
2505 | { | |
2506 | hash_seen = 1; | |
2507 | digit_value = 0; | |
2508 | } | |
2509 | else | |
2510 | break; | |
2511 | ||
2512 | idx++; | |
2513 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2514 | { | |
d956fa6f | 2515 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2516 | if (add > 0) |
d956fa6f | 2517 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2518 | |
2519 | shift = radix; | |
2520 | add = digit_value; | |
2521 | } | |
2522 | else | |
2523 | { | |
2524 | shift = shift * radix; | |
2525 | add = add * radix + digit_value; | |
2526 | } | |
2527 | }; | |
2528 | ||
2529 | if (shift > 1) | |
d956fa6f | 2530 | result = scm_product (result, SCM_I_MAKINUM (shift)); |
3c9a524f | 2531 | if (add > 0) |
d956fa6f | 2532 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2533 | |
2534 | *p_idx = idx; | |
2535 | if (hash_seen) | |
2536 | *p_exactness = INEXACT; | |
2537 | ||
2538 | return result; | |
2a8fecee JB |
2539 | } |
2540 | ||
2541 | ||
3c9a524f DH |
2542 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2543 | * covers the parts of the rules that start at a potential point. The value | |
2544 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2545 | * in variable result. The content of *p_exactness indicates, whether a hash |
2546 | * has already been seen in the digits before the point. | |
3c9a524f | 2547 | */ |
1cc91f1b | 2548 | |
3c9a524f DH |
2549 | /* In non ASCII-style encodings the following macro might not work. */ |
2550 | #define DIGIT2UINT(d) ((d) - '0') | |
2551 | ||
2552 | static SCM | |
79d34f68 | 2553 | mem2decimal_from_point (SCM result, const char* mem, size_t len, |
3c9a524f | 2554 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2555 | { |
3c9a524f DH |
2556 | unsigned int idx = *p_idx; |
2557 | enum t_exactness x = *p_exactness; | |
3c9a524f DH |
2558 | |
2559 | if (idx == len) | |
79d34f68 | 2560 | return result; |
3c9a524f DH |
2561 | |
2562 | if (mem[idx] == '.') | |
2563 | { | |
2564 | scm_t_bits shift = 1; | |
2565 | scm_t_bits add = 0; | |
2566 | unsigned int digit_value; | |
d956fa6f | 2567 | SCM big_shift = SCM_I_MAKINUM (1); |
3c9a524f DH |
2568 | |
2569 | idx++; | |
2570 | while (idx != len) | |
2571 | { | |
2572 | char c = mem[idx]; | |
71df73ac | 2573 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2574 | { |
2575 | if (x == INEXACT) | |
2576 | return SCM_BOOL_F; | |
2577 | else | |
2578 | digit_value = DIGIT2UINT (c); | |
2579 | } | |
2580 | else if (c == '#') | |
2581 | { | |
2582 | x = INEXACT; | |
2583 | digit_value = 0; | |
2584 | } | |
2585 | else | |
2586 | break; | |
2587 | ||
2588 | idx++; | |
2589 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2590 | { | |
d956fa6f MV |
2591 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2592 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
3c9a524f | 2593 | if (add > 0) |
d956fa6f | 2594 | result = scm_sum (result, SCM_I_MAKINUM (add)); |
3c9a524f DH |
2595 | |
2596 | shift = 10; | |
2597 | add = digit_value; | |
2598 | } | |
2599 | else | |
2600 | { | |
2601 | shift = shift * 10; | |
2602 | add = add * 10 + digit_value; | |
2603 | } | |
2604 | }; | |
2605 | ||
2606 | if (add > 0) | |
2607 | { | |
d956fa6f MV |
2608 | big_shift = scm_product (big_shift, SCM_I_MAKINUM (shift)); |
2609 | result = scm_product (result, SCM_I_MAKINUM (shift)); | |
2610 | result = scm_sum (result, SCM_I_MAKINUM (add)); | |
3c9a524f DH |
2611 | } |
2612 | ||
d8592269 | 2613 | result = scm_divide (result, big_shift); |
79d34f68 | 2614 | |
3c9a524f DH |
2615 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2616 | x = INEXACT; | |
f872b822 | 2617 | } |
3c9a524f | 2618 | |
3c9a524f | 2619 | if (idx != len) |
f872b822 | 2620 | { |
3c9a524f DH |
2621 | int sign = 1; |
2622 | unsigned int start; | |
2623 | char c; | |
2624 | int exponent; | |
2625 | SCM e; | |
2626 | ||
2627 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2628 | ||
2629 | switch (mem[idx]) | |
f872b822 | 2630 | { |
3c9a524f DH |
2631 | case 'd': case 'D': |
2632 | case 'e': case 'E': | |
2633 | case 'f': case 'F': | |
2634 | case 'l': case 'L': | |
2635 | case 's': case 'S': | |
2636 | idx++; | |
2637 | start = idx; | |
2638 | c = mem[idx]; | |
2639 | if (c == '-') | |
2640 | { | |
2641 | idx++; | |
2642 | sign = -1; | |
2643 | c = mem[idx]; | |
2644 | } | |
2645 | else if (c == '+') | |
2646 | { | |
2647 | idx++; | |
2648 | sign = 1; | |
2649 | c = mem[idx]; | |
2650 | } | |
2651 | else | |
2652 | sign = 1; | |
2653 | ||
71df73ac | 2654 | if (!isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2655 | return SCM_BOOL_F; |
2656 | ||
2657 | idx++; | |
2658 | exponent = DIGIT2UINT (c); | |
2659 | while (idx != len) | |
f872b822 | 2660 | { |
3c9a524f | 2661 | char c = mem[idx]; |
71df73ac | 2662 | if (isdigit ((int) (unsigned char) c)) |
3c9a524f DH |
2663 | { |
2664 | idx++; | |
2665 | if (exponent <= SCM_MAXEXP) | |
2666 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2667 | } | |
2668 | else | |
2669 | break; | |
f872b822 | 2670 | } |
3c9a524f DH |
2671 | |
2672 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2673 | { |
3c9a524f | 2674 | size_t exp_len = idx - start; |
cc95e00a | 2675 | SCM exp_string = scm_from_locale_stringn (&mem[start], exp_len); |
3c9a524f DH |
2676 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); |
2677 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2678 | } |
3c9a524f | 2679 | |
d956fa6f | 2680 | e = scm_integer_expt (SCM_I_MAKINUM (10), SCM_I_MAKINUM (exponent)); |
3c9a524f DH |
2681 | if (sign == 1) |
2682 | result = scm_product (result, e); | |
2683 | else | |
f92e85f7 | 2684 | result = scm_divide2real (result, e); |
3c9a524f DH |
2685 | |
2686 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2687 | x = INEXACT; | |
2688 | ||
f872b822 | 2689 | break; |
3c9a524f | 2690 | |
f872b822 | 2691 | default: |
3c9a524f | 2692 | break; |
f872b822 | 2693 | } |
0f2d19dd | 2694 | } |
3c9a524f DH |
2695 | |
2696 | *p_idx = idx; | |
2697 | if (x == INEXACT) | |
2698 | *p_exactness = x; | |
2699 | ||
2700 | return result; | |
0f2d19dd | 2701 | } |
0f2d19dd | 2702 | |
3c9a524f DH |
2703 | |
2704 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2705 | ||
2706 | static SCM | |
2707 | mem2ureal (const char* mem, size_t len, unsigned int *p_idx, | |
2708 | unsigned int radix, enum t_exactness *p_exactness) | |
0f2d19dd | 2709 | { |
3c9a524f | 2710 | unsigned int idx = *p_idx; |
164d2481 | 2711 | SCM result; |
3c9a524f DH |
2712 | |
2713 | if (idx == len) | |
2714 | return SCM_BOOL_F; | |
2715 | ||
7351e207 MV |
2716 | if (idx+5 <= len && !strncmp (mem+idx, "inf.0", 5)) |
2717 | { | |
2718 | *p_idx = idx+5; | |
2719 | return scm_inf (); | |
2720 | } | |
2721 | ||
2722 | if (idx+4 < len && !strncmp (mem+idx, "nan.", 4)) | |
2723 | { | |
2724 | enum t_exactness x = EXACT; | |
2725 | ||
d8592269 MV |
2726 | /* Cobble up the fractional part. We might want to set the |
2727 | NaN's mantissa from it. */ | |
7351e207 MV |
2728 | idx += 4; |
2729 | mem2uinteger (mem, len, &idx, 10, &x); | |
2730 | *p_idx = idx; | |
2731 | return scm_nan (); | |
2732 | } | |
2733 | ||
3c9a524f DH |
2734 | if (mem[idx] == '.') |
2735 | { | |
2736 | if (radix != 10) | |
2737 | return SCM_BOOL_F; | |
2738 | else if (idx + 1 == len) | |
2739 | return SCM_BOOL_F; | |
71df73ac | 2740 | else if (!isdigit ((int) (unsigned char) mem[idx + 1])) |
3c9a524f DH |
2741 | return SCM_BOOL_F; |
2742 | else | |
d956fa6f | 2743 | result = mem2decimal_from_point (SCM_I_MAKINUM (0), mem, len, |
164d2481 | 2744 | p_idx, p_exactness); |
f872b822 | 2745 | } |
3c9a524f DH |
2746 | else |
2747 | { | |
2748 | enum t_exactness x = EXACT; | |
2749 | SCM uinteger; | |
3c9a524f DH |
2750 | |
2751 | uinteger = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2752 | if (scm_is_false (uinteger)) |
3c9a524f DH |
2753 | return SCM_BOOL_F; |
2754 | ||
2755 | if (idx == len) | |
2756 | result = uinteger; | |
2757 | else if (mem[idx] == '/') | |
f872b822 | 2758 | { |
3c9a524f DH |
2759 | SCM divisor; |
2760 | ||
2761 | idx++; | |
2762 | ||
2763 | divisor = mem2uinteger (mem, len, &idx, radix, &x); | |
73e4de09 | 2764 | if (scm_is_false (divisor)) |
3c9a524f DH |
2765 | return SCM_BOOL_F; |
2766 | ||
f92e85f7 | 2767 | /* both are int/big here, I assume */ |
cba42c93 | 2768 | result = scm_i_make_ratio (uinteger, divisor); |
f872b822 | 2769 | } |
3c9a524f DH |
2770 | else if (radix == 10) |
2771 | { | |
2772 | result = mem2decimal_from_point (uinteger, mem, len, &idx, &x); | |
73e4de09 | 2773 | if (scm_is_false (result)) |
3c9a524f DH |
2774 | return SCM_BOOL_F; |
2775 | } | |
2776 | else | |
2777 | result = uinteger; | |
2778 | ||
2779 | *p_idx = idx; | |
2780 | if (x == INEXACT) | |
2781 | *p_exactness = x; | |
f872b822 | 2782 | } |
164d2481 MV |
2783 | |
2784 | /* When returning an inexact zero, make sure it is represented as a | |
2785 | floating point value so that we can change its sign. | |
2786 | */ | |
bc36d050 | 2787 | if (scm_is_eq (result, SCM_I_MAKINUM(0)) && *p_exactness == INEXACT) |
55f26379 | 2788 | result = scm_from_double (0.0); |
164d2481 MV |
2789 | |
2790 | return result; | |
3c9a524f | 2791 | } |
0f2d19dd | 2792 | |
0f2d19dd | 2793 | |
3c9a524f | 2794 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2795 | |
3c9a524f DH |
2796 | static SCM |
2797 | mem2complex (const char* mem, size_t len, unsigned int idx, | |
2798 | unsigned int radix, enum t_exactness *p_exactness) | |
2799 | { | |
2800 | char c; | |
2801 | int sign = 0; | |
2802 | SCM ureal; | |
2803 | ||
2804 | if (idx == len) | |
2805 | return SCM_BOOL_F; | |
2806 | ||
2807 | c = mem[idx]; | |
2808 | if (c == '+') | |
2809 | { | |
2810 | idx++; | |
2811 | sign = 1; | |
2812 | } | |
2813 | else if (c == '-') | |
2814 | { | |
2815 | idx++; | |
2816 | sign = -1; | |
0f2d19dd | 2817 | } |
0f2d19dd | 2818 | |
3c9a524f DH |
2819 | if (idx == len) |
2820 | return SCM_BOOL_F; | |
2821 | ||
2822 | ureal = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2823 | if (scm_is_false (ureal)) |
f872b822 | 2824 | { |
3c9a524f DH |
2825 | /* input must be either +i or -i */ |
2826 | ||
2827 | if (sign == 0) | |
2828 | return SCM_BOOL_F; | |
2829 | ||
2830 | if (mem[idx] == 'i' || mem[idx] == 'I') | |
f872b822 | 2831 | { |
3c9a524f DH |
2832 | idx++; |
2833 | if (idx != len) | |
2834 | return SCM_BOOL_F; | |
2835 | ||
d956fa6f | 2836 | return scm_make_rectangular (SCM_I_MAKINUM (0), SCM_I_MAKINUM (sign)); |
f872b822 | 2837 | } |
3c9a524f DH |
2838 | else |
2839 | return SCM_BOOL_F; | |
0f2d19dd | 2840 | } |
3c9a524f DH |
2841 | else |
2842 | { | |
73e4de09 | 2843 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f | 2844 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 2845 | |
3c9a524f DH |
2846 | if (idx == len) |
2847 | return ureal; | |
2848 | ||
2849 | c = mem[idx]; | |
2850 | switch (c) | |
f872b822 | 2851 | { |
3c9a524f DH |
2852 | case 'i': case 'I': |
2853 | /* either +<ureal>i or -<ureal>i */ | |
2854 | ||
2855 | idx++; | |
2856 | if (sign == 0) | |
2857 | return SCM_BOOL_F; | |
2858 | if (idx != len) | |
2859 | return SCM_BOOL_F; | |
d956fa6f | 2860 | return scm_make_rectangular (SCM_I_MAKINUM (0), ureal); |
3c9a524f DH |
2861 | |
2862 | case '@': | |
2863 | /* polar input: <real>@<real>. */ | |
2864 | ||
2865 | idx++; | |
2866 | if (idx == len) | |
2867 | return SCM_BOOL_F; | |
2868 | else | |
f872b822 | 2869 | { |
3c9a524f DH |
2870 | int sign; |
2871 | SCM angle; | |
2872 | SCM result; | |
2873 | ||
2874 | c = mem[idx]; | |
2875 | if (c == '+') | |
2876 | { | |
2877 | idx++; | |
2878 | sign = 1; | |
2879 | } | |
2880 | else if (c == '-') | |
2881 | { | |
2882 | idx++; | |
2883 | sign = -1; | |
2884 | } | |
2885 | else | |
2886 | sign = 1; | |
2887 | ||
2888 | angle = mem2ureal (mem, len, &idx, radix, p_exactness); | |
73e4de09 | 2889 | if (scm_is_false (angle)) |
3c9a524f DH |
2890 | return SCM_BOOL_F; |
2891 | if (idx != len) | |
2892 | return SCM_BOOL_F; | |
2893 | ||
73e4de09 | 2894 | if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
3c9a524f DH |
2895 | angle = scm_difference (angle, SCM_UNDEFINED); |
2896 | ||
2897 | result = scm_make_polar (ureal, angle); | |
2898 | return result; | |
f872b822 | 2899 | } |
3c9a524f DH |
2900 | case '+': |
2901 | case '-': | |
2902 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 2903 | |
3c9a524f DH |
2904 | idx++; |
2905 | if (idx == len) | |
2906 | return SCM_BOOL_F; | |
2907 | else | |
2908 | { | |
2909 | int sign = (c == '+') ? 1 : -1; | |
2910 | SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness); | |
0f2d19dd | 2911 | |
73e4de09 | 2912 | if (scm_is_false (imag)) |
d956fa6f | 2913 | imag = SCM_I_MAKINUM (sign); |
73e4de09 | 2914 | else if (sign == -1 && scm_is_false (scm_nan_p (ureal))) |
1fe5e088 | 2915 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 2916 | |
3c9a524f DH |
2917 | if (idx == len) |
2918 | return SCM_BOOL_F; | |
2919 | if (mem[idx] != 'i' && mem[idx] != 'I') | |
2920 | return SCM_BOOL_F; | |
0f2d19dd | 2921 | |
3c9a524f DH |
2922 | idx++; |
2923 | if (idx != len) | |
2924 | return SCM_BOOL_F; | |
0f2d19dd | 2925 | |
1fe5e088 | 2926 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
2927 | } |
2928 | default: | |
2929 | return SCM_BOOL_F; | |
2930 | } | |
2931 | } | |
0f2d19dd | 2932 | } |
0f2d19dd JB |
2933 | |
2934 | ||
3c9a524f DH |
2935 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
2936 | ||
2937 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 2938 | |
0f2d19dd | 2939 | SCM |
3c9a524f | 2940 | scm_i_mem2number (const char* mem, size_t len, unsigned int default_radix) |
0f2d19dd | 2941 | { |
3c9a524f DH |
2942 | unsigned int idx = 0; |
2943 | unsigned int radix = NO_RADIX; | |
2944 | enum t_exactness forced_x = NO_EXACTNESS; | |
2945 | enum t_exactness implicit_x = EXACT; | |
2946 | SCM result; | |
2947 | ||
2948 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
2949 | while (idx + 2 < len && mem[idx] == '#') | |
2950 | { | |
2951 | switch (mem[idx + 1]) | |
2952 | { | |
2953 | case 'b': case 'B': | |
2954 | if (radix != NO_RADIX) | |
2955 | return SCM_BOOL_F; | |
2956 | radix = DUAL; | |
2957 | break; | |
2958 | case 'd': case 'D': | |
2959 | if (radix != NO_RADIX) | |
2960 | return SCM_BOOL_F; | |
2961 | radix = DEC; | |
2962 | break; | |
2963 | case 'i': case 'I': | |
2964 | if (forced_x != NO_EXACTNESS) | |
2965 | return SCM_BOOL_F; | |
2966 | forced_x = INEXACT; | |
2967 | break; | |
2968 | case 'e': case 'E': | |
2969 | if (forced_x != NO_EXACTNESS) | |
2970 | return SCM_BOOL_F; | |
2971 | forced_x = EXACT; | |
2972 | break; | |
2973 | case 'o': case 'O': | |
2974 | if (radix != NO_RADIX) | |
2975 | return SCM_BOOL_F; | |
2976 | radix = OCT; | |
2977 | break; | |
2978 | case 'x': case 'X': | |
2979 | if (radix != NO_RADIX) | |
2980 | return SCM_BOOL_F; | |
2981 | radix = HEX; | |
2982 | break; | |
2983 | default: | |
f872b822 | 2984 | return SCM_BOOL_F; |
3c9a524f DH |
2985 | } |
2986 | idx += 2; | |
2987 | } | |
2988 | ||
2989 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
2990 | if (radix == NO_RADIX) | |
2991 | result = mem2complex (mem, len, idx, default_radix, &implicit_x); | |
2992 | else | |
2993 | result = mem2complex (mem, len, idx, (unsigned int) radix, &implicit_x); | |
2994 | ||
73e4de09 | 2995 | if (scm_is_false (result)) |
3c9a524f | 2996 | return SCM_BOOL_F; |
f872b822 | 2997 | |
3c9a524f | 2998 | switch (forced_x) |
f872b822 | 2999 | { |
3c9a524f DH |
3000 | case EXACT: |
3001 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
3002 | return scm_inexact_to_exact (result); |
3003 | else | |
3004 | return result; | |
3005 | case INEXACT: | |
3006 | if (SCM_INEXACTP (result)) | |
3007 | return result; | |
3008 | else | |
3009 | return scm_exact_to_inexact (result); | |
3010 | case NO_EXACTNESS: | |
3011 | default: | |
3012 | if (implicit_x == INEXACT) | |
3013 | { | |
3014 | if (SCM_INEXACTP (result)) | |
3015 | return result; | |
3016 | else | |
3017 | return scm_exact_to_inexact (result); | |
3018 | } | |
3019 | else | |
3020 | return result; | |
f872b822 | 3021 | } |
0f2d19dd JB |
3022 | } |
3023 | ||
3024 | ||
a1ec6916 | 3025 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 3026 | (SCM string, SCM radix), |
1e6808ea | 3027 | "Return a number of the maximally precise representation\n" |
942e5b91 | 3028 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
3029 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
3030 | "is a default radix that may be overridden by an explicit radix\n" | |
3031 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
3032 | "supplied, then the default radix is 10. If string is not a\n" | |
3033 | "syntactically valid notation for a number, then\n" | |
3034 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 3035 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
3036 | { |
3037 | SCM answer; | |
5efd3c7d | 3038 | unsigned int base; |
a6d9e5ab | 3039 | SCM_VALIDATE_STRING (1, string); |
5efd3c7d MV |
3040 | |
3041 | if (SCM_UNBNDP (radix)) | |
3042 | base = 10; | |
3043 | else | |
3044 | base = scm_to_unsigned_integer (radix, 2, INT_MAX); | |
3045 | ||
cc95e00a MV |
3046 | answer = scm_i_mem2number (scm_i_string_chars (string), |
3047 | scm_i_string_length (string), | |
d8592269 | 3048 | base); |
8824ac88 MV |
3049 | scm_remember_upto_here_1 (string); |
3050 | return answer; | |
0f2d19dd | 3051 | } |
1bbd0b84 | 3052 | #undef FUNC_NAME |
3c9a524f DH |
3053 | |
3054 | ||
0f2d19dd JB |
3055 | /*** END strs->nums ***/ |
3056 | ||
5986c47d | 3057 | |
0f2d19dd | 3058 | SCM |
1bbd0b84 | 3059 | scm_bigequal (SCM x, SCM y) |
0f2d19dd | 3060 | { |
47ae1f0e | 3061 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
ca46fb90 | 3062 | scm_remember_upto_here_2 (x, y); |
73e4de09 | 3063 | return scm_from_bool (0 == result); |
0f2d19dd JB |
3064 | } |
3065 | ||
0f2d19dd | 3066 | SCM |
f3ae5d60 | 3067 | scm_real_equalp (SCM x, SCM y) |
0f2d19dd | 3068 | { |
73e4de09 | 3069 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0f2d19dd JB |
3070 | } |
3071 | ||
f3ae5d60 MD |
3072 | SCM |
3073 | scm_complex_equalp (SCM x, SCM y) | |
3074 | { | |
73e4de09 | 3075 | return scm_from_bool (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) |
f3ae5d60 MD |
3076 | && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); |
3077 | } | |
0f2d19dd | 3078 | |
f92e85f7 MV |
3079 | SCM |
3080 | scm_i_fraction_equalp (SCM x, SCM y) | |
3081 | { | |
3082 | scm_i_fraction_reduce (x); | |
3083 | scm_i_fraction_reduce (y); | |
73e4de09 | 3084 | if (scm_is_false (scm_equal_p (SCM_FRACTION_NUMERATOR (x), |
02164269 | 3085 | SCM_FRACTION_NUMERATOR (y))) |
73e4de09 | 3086 | || scm_is_false (scm_equal_p (SCM_FRACTION_DENOMINATOR (x), |
02164269 MV |
3087 | SCM_FRACTION_DENOMINATOR (y)))) |
3088 | return SCM_BOOL_F; | |
3089 | else | |
3090 | return SCM_BOOL_T; | |
f92e85f7 | 3091 | } |
0f2d19dd JB |
3092 | |
3093 | ||
8507ec80 MV |
3094 | SCM_DEFINE (scm_number_p, "number?", 1, 0, 0, |
3095 | (SCM x), | |
3096 | "Return @code{#t} if @var{x} is a number, @code{#f}\n" | |
3097 | "otherwise.") | |
3098 | #define FUNC_NAME s_scm_number_p | |
3099 | { | |
3100 | return scm_from_bool (SCM_NUMBERP (x)); | |
3101 | } | |
3102 | #undef FUNC_NAME | |
3103 | ||
3104 | SCM_DEFINE (scm_complex_p, "complex?", 1, 0, 0, | |
1bbd0b84 | 3105 | (SCM x), |
942e5b91 | 3106 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 3107 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
3108 | "values form subsets of the set of complex numbers, i. e. the\n" |
3109 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
3110 | "rational or integer number.") | |
8507ec80 | 3111 | #define FUNC_NAME s_scm_complex_p |
0f2d19dd | 3112 | { |
8507ec80 MV |
3113 | /* all numbers are complex. */ |
3114 | return scm_number_p (x); | |
0f2d19dd | 3115 | } |
1bbd0b84 | 3116 | #undef FUNC_NAME |
0f2d19dd | 3117 | |
f92e85f7 MV |
3118 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
3119 | (SCM x), | |
3120 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
3121 | "otherwise. Note that the set of integer values forms a subset of\n" | |
3122 | "the set of real numbers, i. e. the predicate will also be\n" | |
3123 | "fulfilled if @var{x} is an integer number.") | |
3124 | #define FUNC_NAME s_scm_real_p | |
3125 | { | |
3126 | /* we can't represent irrational numbers. */ | |
3127 | return scm_rational_p (x); | |
3128 | } | |
3129 | #undef FUNC_NAME | |
3130 | ||
3131 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 3132 | (SCM x), |
942e5b91 | 3133 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 3134 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 3135 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
3136 | "fulfilled if @var{x} is an integer number.") |
3137 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 3138 | { |
e11e83f3 | 3139 | if (SCM_I_INUMP (x)) |
0f2d19dd | 3140 | return SCM_BOOL_T; |
0aacf84e | 3141 | else if (SCM_IMP (x)) |
0f2d19dd | 3142 | return SCM_BOOL_F; |
0aacf84e | 3143 | else if (SCM_BIGP (x)) |
0f2d19dd | 3144 | return SCM_BOOL_T; |
f92e85f7 MV |
3145 | else if (SCM_FRACTIONP (x)) |
3146 | return SCM_BOOL_T; | |
3147 | else if (SCM_REALP (x)) | |
3148 | /* due to their limited precision, all floating point numbers are | |
3149 | rational as well. */ | |
3150 | return SCM_BOOL_T; | |
0aacf84e | 3151 | else |
bb628794 | 3152 | return SCM_BOOL_F; |
0f2d19dd | 3153 | } |
1bbd0b84 | 3154 | #undef FUNC_NAME |
0f2d19dd | 3155 | |
a1ec6916 | 3156 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 3157 | (SCM x), |
942e5b91 MG |
3158 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
3159 | "else.") | |
1bbd0b84 | 3160 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd JB |
3161 | { |
3162 | double r; | |
e11e83f3 | 3163 | if (SCM_I_INUMP (x)) |
f872b822 MD |
3164 | return SCM_BOOL_T; |
3165 | if (SCM_IMP (x)) | |
3166 | return SCM_BOOL_F; | |
f872b822 MD |
3167 | if (SCM_BIGP (x)) |
3168 | return SCM_BOOL_T; | |
3c9a524f | 3169 | if (!SCM_INEXACTP (x)) |
f872b822 | 3170 | return SCM_BOOL_F; |
3c9a524f | 3171 | if (SCM_COMPLEXP (x)) |
f872b822 | 3172 | return SCM_BOOL_F; |
5986c47d | 3173 | r = SCM_REAL_VALUE (x); |
1e35a229 | 3174 | /* +/-inf passes r==floor(r), making those #t */ |
f872b822 MD |
3175 | if (r == floor (r)) |
3176 | return SCM_BOOL_T; | |
0f2d19dd JB |
3177 | return SCM_BOOL_F; |
3178 | } | |
1bbd0b84 | 3179 | #undef FUNC_NAME |
0f2d19dd JB |
3180 | |
3181 | ||
a1ec6916 | 3182 | SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, |
1bbd0b84 | 3183 | (SCM x), |
942e5b91 MG |
3184 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" |
3185 | "else.") | |
1bbd0b84 | 3186 | #define FUNC_NAME s_scm_inexact_p |
0f2d19dd | 3187 | { |
eb927cb9 MV |
3188 | if (SCM_INEXACTP (x)) |
3189 | return SCM_BOOL_T; | |
3190 | if (SCM_NUMBERP (x)) | |
3191 | return SCM_BOOL_F; | |
3192 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 3193 | } |
1bbd0b84 | 3194 | #undef FUNC_NAME |
0f2d19dd JB |
3195 | |
3196 | ||
152f82bf | 3197 | SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p); |
942e5b91 | 3198 | /* "Return @code{#t} if all parameters are numerically equal." */ |
0f2d19dd | 3199 | SCM |
6e8d25a6 | 3200 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 3201 | { |
d8b95e27 | 3202 | again: |
e11e83f3 | 3203 | if (SCM_I_INUMP (x)) |
0aacf84e | 3204 | { |
e11e83f3 MV |
3205 | long xx = SCM_I_INUM (x); |
3206 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3207 | { |
e11e83f3 | 3208 | long yy = SCM_I_INUM (y); |
73e4de09 | 3209 | return scm_from_bool (xx == yy); |
0aacf84e MD |
3210 | } |
3211 | else if (SCM_BIGP (y)) | |
3212 | return SCM_BOOL_F; | |
3213 | else if (SCM_REALP (y)) | |
73e4de09 | 3214 | return scm_from_bool ((double) xx == SCM_REAL_VALUE (y)); |
0aacf84e | 3215 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3216 | return scm_from_bool (((double) xx == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3217 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 MV |
3218 | else if (SCM_FRACTIONP (y)) |
3219 | return SCM_BOOL_F; | |
0aacf84e MD |
3220 | else |
3221 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3222 | } |
0aacf84e MD |
3223 | else if (SCM_BIGP (x)) |
3224 | { | |
e11e83f3 | 3225 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3226 | return SCM_BOOL_F; |
3227 | else if (SCM_BIGP (y)) | |
3228 | { | |
3229 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3230 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3231 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3232 | } |
3233 | else if (SCM_REALP (y)) | |
3234 | { | |
3235 | int cmp; | |
3236 | if (xisnan (SCM_REAL_VALUE (y))) | |
3237 | return SCM_BOOL_F; | |
3238 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3239 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3240 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3241 | } |
3242 | else if (SCM_COMPLEXP (y)) | |
3243 | { | |
3244 | int cmp; | |
3245 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
3246 | return SCM_BOOL_F; | |
3247 | if (xisnan (SCM_COMPLEX_REAL (y))) | |
3248 | return SCM_BOOL_F; | |
3249 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
3250 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3251 | return scm_from_bool (0 == cmp); |
0aacf84e | 3252 | } |
f92e85f7 MV |
3253 | else if (SCM_FRACTIONP (y)) |
3254 | return SCM_BOOL_F; | |
0aacf84e MD |
3255 | else |
3256 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3257 | } |
0aacf84e MD |
3258 | else if (SCM_REALP (x)) |
3259 | { | |
e11e83f3 MV |
3260 | if (SCM_I_INUMP (y)) |
3261 | return scm_from_bool (SCM_REAL_VALUE (x) == (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3262 | else if (SCM_BIGP (y)) |
3263 | { | |
3264 | int cmp; | |
3265 | if (xisnan (SCM_REAL_VALUE (x))) | |
3266 | return SCM_BOOL_F; | |
3267 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3268 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3269 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3270 | } |
3271 | else if (SCM_REALP (y)) | |
73e4de09 | 3272 | return scm_from_bool (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0aacf84e | 3273 | else if (SCM_COMPLEXP (y)) |
73e4de09 | 3274 | return scm_from_bool ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3275 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3276 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3277 | { |
3278 | double xx = SCM_REAL_VALUE (x); | |
3279 | if (xisnan (xx)) | |
3280 | return SCM_BOOL_F; | |
3281 | if (xisinf (xx)) | |
73e4de09 | 3282 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3283 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3284 | goto again; | |
3285 | } | |
0aacf84e MD |
3286 | else |
3287 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3288 | } |
0aacf84e MD |
3289 | else if (SCM_COMPLEXP (x)) |
3290 | { | |
e11e83f3 MV |
3291 | if (SCM_I_INUMP (y)) |
3292 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == (double) SCM_I_INUM (y)) | |
0aacf84e MD |
3293 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3294 | else if (SCM_BIGP (y)) | |
3295 | { | |
3296 | int cmp; | |
3297 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
3298 | return SCM_BOOL_F; | |
3299 | if (xisnan (SCM_COMPLEX_REAL (x))) | |
3300 | return SCM_BOOL_F; | |
3301 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
3302 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3303 | return scm_from_bool (0 == cmp); |
0aacf84e MD |
3304 | } |
3305 | else if (SCM_REALP (y)) | |
73e4de09 | 3306 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) |
0aacf84e MD |
3307 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3308 | else if (SCM_COMPLEXP (y)) | |
73e4de09 | 3309 | return scm_from_bool ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) |
0aacf84e | 3310 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); |
f92e85f7 | 3311 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3312 | { |
3313 | double xx; | |
3314 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
3315 | return SCM_BOOL_F; | |
3316 | xx = SCM_COMPLEX_REAL (x); | |
3317 | if (xisnan (xx)) | |
3318 | return SCM_BOOL_F; | |
3319 | if (xisinf (xx)) | |
73e4de09 | 3320 | return scm_from_bool (xx < 0.0); |
d8b95e27 KR |
3321 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3322 | goto again; | |
3323 | } | |
f92e85f7 MV |
3324 | else |
3325 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
3326 | } | |
3327 | else if (SCM_FRACTIONP (x)) | |
3328 | { | |
e11e83f3 | 3329 | if (SCM_I_INUMP (y)) |
f92e85f7 MV |
3330 | return SCM_BOOL_F; |
3331 | else if (SCM_BIGP (y)) | |
3332 | return SCM_BOOL_F; | |
3333 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
3334 | { |
3335 | double yy = SCM_REAL_VALUE (y); | |
3336 | if (xisnan (yy)) | |
3337 | return SCM_BOOL_F; | |
3338 | if (xisinf (yy)) | |
73e4de09 | 3339 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3340 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3341 | goto again; | |
3342 | } | |
f92e85f7 | 3343 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
3344 | { |
3345 | double yy; | |
3346 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
3347 | return SCM_BOOL_F; | |
3348 | yy = SCM_COMPLEX_REAL (y); | |
3349 | if (xisnan (yy)) | |
3350 | return SCM_BOOL_F; | |
3351 | if (xisinf (yy)) | |
73e4de09 | 3352 | return scm_from_bool (0.0 < yy); |
d8b95e27 KR |
3353 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3354 | goto again; | |
3355 | } | |
f92e85f7 MV |
3356 | else if (SCM_FRACTIONP (y)) |
3357 | return scm_i_fraction_equalp (x, y); | |
0aacf84e MD |
3358 | else |
3359 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3360 | } |
0aacf84e | 3361 | else |
f4c627b3 | 3362 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p); |
0f2d19dd JB |
3363 | } |
3364 | ||
3365 | ||
a5f0b599 KR |
3366 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
3367 | done are good for inums, but for bignums an answer can almost always be | |
3368 | had by just examining a few high bits of the operands, as done by GMP in | |
3369 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
3370 | of the float exponent to take into account. */ | |
3371 | ||
152f82bf | 3372 | SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p); |
942e5b91 MG |
3373 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3374 | * "increasing." | |
3375 | */ | |
0f2d19dd | 3376 | SCM |
6e8d25a6 | 3377 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3378 | { |
a5f0b599 | 3379 | again: |
e11e83f3 | 3380 | if (SCM_I_INUMP (x)) |
0aacf84e | 3381 | { |
e11e83f3 MV |
3382 | long xx = SCM_I_INUM (x); |
3383 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3384 | { |
e11e83f3 | 3385 | long yy = SCM_I_INUM (y); |
73e4de09 | 3386 | return scm_from_bool (xx < yy); |
0aacf84e MD |
3387 | } |
3388 | else if (SCM_BIGP (y)) | |
3389 | { | |
3390 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3391 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3392 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3393 | } |
3394 | else if (SCM_REALP (y)) | |
73e4de09 | 3395 | return scm_from_bool ((double) xx < SCM_REAL_VALUE (y)); |
f92e85f7 | 3396 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3397 | { |
3398 | /* "x < a/b" becomes "x*b < a" */ | |
3399 | int_frac: | |
3400 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
3401 | y = SCM_FRACTION_NUMERATOR (y); | |
3402 | goto again; | |
3403 | } | |
0aacf84e MD |
3404 | else |
3405 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3406 | } |
0aacf84e MD |
3407 | else if (SCM_BIGP (x)) |
3408 | { | |
e11e83f3 | 3409 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3410 | { |
3411 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3412 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3413 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3414 | } |
3415 | else if (SCM_BIGP (y)) | |
3416 | { | |
3417 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3418 | scm_remember_upto_here_2 (x, y); | |
73e4de09 | 3419 | return scm_from_bool (cmp < 0); |
0aacf84e MD |
3420 | } |
3421 | else if (SCM_REALP (y)) | |
3422 | { | |
3423 | int cmp; | |
3424 | if (xisnan (SCM_REAL_VALUE (y))) | |
3425 | return SCM_BOOL_F; | |
3426 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3427 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3428 | return scm_from_bool (cmp < 0); |
0aacf84e | 3429 | } |
f92e85f7 | 3430 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 3431 | goto int_frac; |
0aacf84e MD |
3432 | else |
3433 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f4c627b3 | 3434 | } |
0aacf84e MD |
3435 | else if (SCM_REALP (x)) |
3436 | { | |
e11e83f3 MV |
3437 | if (SCM_I_INUMP (y)) |
3438 | return scm_from_bool (SCM_REAL_VALUE (x) < (double) SCM_I_INUM (y)); | |
0aacf84e MD |
3439 | else if (SCM_BIGP (y)) |
3440 | { | |
3441 | int cmp; | |
3442 | if (xisnan (SCM_REAL_VALUE (x))) | |
3443 | return SCM_BOOL_F; | |
3444 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3445 | scm_remember_upto_here_1 (y); | |
73e4de09 | 3446 | return scm_from_bool (cmp > 0); |
0aacf84e MD |
3447 | } |
3448 | else if (SCM_REALP (y)) | |
73e4de09 | 3449 | return scm_from_bool (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); |
f92e85f7 | 3450 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3451 | { |
3452 | double xx = SCM_REAL_VALUE (x); | |
3453 | if (xisnan (xx)) | |
3454 | return SCM_BOOL_F; | |
3455 | if (xisinf (xx)) | |
73e4de09 | 3456 | return scm_from_bool (xx < 0.0); |
a5f0b599 KR |
3457 | x = scm_inexact_to_exact (x); /* with x as frac or int */ |
3458 | goto again; | |
3459 | } | |
f92e85f7 MV |
3460 | else |
3461 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
3462 | } | |
3463 | else if (SCM_FRACTIONP (x)) | |
3464 | { | |
e11e83f3 | 3465 | if (SCM_I_INUMP (y) || SCM_BIGP (y)) |
a5f0b599 KR |
3466 | { |
3467 | /* "a/b < y" becomes "a < y*b" */ | |
3468 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
3469 | x = SCM_FRACTION_NUMERATOR (x); | |
3470 | goto again; | |
3471 | } | |
f92e85f7 | 3472 | else if (SCM_REALP (y)) |
a5f0b599 KR |
3473 | { |
3474 | double yy = SCM_REAL_VALUE (y); | |
3475 | if (xisnan (yy)) | |
3476 | return SCM_BOOL_F; | |
3477 | if (xisinf (yy)) | |
73e4de09 | 3478 | return scm_from_bool (0.0 < yy); |
a5f0b599 KR |
3479 | y = scm_inexact_to_exact (y); /* with y as frac or int */ |
3480 | goto again; | |
3481 | } | |
f92e85f7 | 3482 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3483 | { |
3484 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
3485 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
3486 | SCM_FRACTION_DENOMINATOR (y)); | |
3487 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
3488 | SCM_FRACTION_DENOMINATOR (x)); | |
3489 | x = new_x; | |
3490 | y = new_y; | |
3491 | goto again; | |
3492 | } | |
0aacf84e MD |
3493 | else |
3494 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3495 | } |
0aacf84e | 3496 | else |
f4c627b3 | 3497 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p); |
0f2d19dd JB |
3498 | } |
3499 | ||
3500 | ||
c76b1eaf | 3501 | SCM_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p); |
942e5b91 MG |
3502 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3503 | * "decreasing." | |
c76b1eaf | 3504 | */ |
1bbd0b84 | 3505 | #define FUNC_NAME s_scm_gr_p |
c76b1eaf MD |
3506 | SCM |
3507 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3508 | { |
c76b1eaf MD |
3509 | if (!SCM_NUMBERP (x)) |
3510 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME); | |
3511 | else if (!SCM_NUMBERP (y)) | |
3512 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME); | |
3513 | else | |
3514 | return scm_less_p (y, x); | |
0f2d19dd | 3515 | } |
1bbd0b84 | 3516 | #undef FUNC_NAME |
0f2d19dd JB |
3517 | |
3518 | ||
c76b1eaf | 3519 | SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p); |
942e5b91 | 3520 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3521 | * "non-decreasing." |
3522 | */ | |
1bbd0b84 | 3523 | #define FUNC_NAME s_scm_leq_p |
c76b1eaf MD |
3524 | SCM |
3525 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3526 | { |
c76b1eaf MD |
3527 | if (!SCM_NUMBERP (x)) |
3528 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3529 | else if (!SCM_NUMBERP (y)) | |
3530 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3531 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3532 | return SCM_BOOL_F; |
c76b1eaf | 3533 | else |
73e4de09 | 3534 | return scm_not (scm_less_p (y, x)); |
0f2d19dd | 3535 | } |
1bbd0b84 | 3536 | #undef FUNC_NAME |
0f2d19dd JB |
3537 | |
3538 | ||
c76b1eaf | 3539 | SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p); |
942e5b91 | 3540 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3541 | * "non-increasing." |
3542 | */ | |
1bbd0b84 | 3543 | #define FUNC_NAME s_scm_geq_p |
c76b1eaf MD |
3544 | SCM |
3545 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3546 | { |
c76b1eaf MD |
3547 | if (!SCM_NUMBERP (x)) |
3548 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3549 | else if (!SCM_NUMBERP (y)) | |
3550 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME); | |
73e4de09 | 3551 | else if (scm_is_true (scm_nan_p (x)) || scm_is_true (scm_nan_p (y))) |
fc194577 | 3552 | return SCM_BOOL_F; |
c76b1eaf | 3553 | else |
73e4de09 | 3554 | return scm_not (scm_less_p (x, y)); |
0f2d19dd | 3555 | } |
1bbd0b84 | 3556 | #undef FUNC_NAME |
0f2d19dd JB |
3557 | |
3558 | ||
152f82bf | 3559 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3560 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3561 | * "zero." | |
3562 | */ | |
0f2d19dd | 3563 | SCM |
6e8d25a6 | 3564 | scm_zero_p (SCM z) |
0f2d19dd | 3565 | { |
e11e83f3 | 3566 | if (SCM_I_INUMP (z)) |
bc36d050 | 3567 | return scm_from_bool (scm_is_eq (z, SCM_INUM0)); |
0aacf84e | 3568 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 3569 | return SCM_BOOL_F; |
0aacf84e | 3570 | else if (SCM_REALP (z)) |
73e4de09 | 3571 | return scm_from_bool (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 3572 | else if (SCM_COMPLEXP (z)) |
73e4de09 | 3573 | return scm_from_bool (SCM_COMPLEX_REAL (z) == 0.0 |
c2ff8ab0 | 3574 | && SCM_COMPLEX_IMAG (z) == 0.0); |
f92e85f7 MV |
3575 | else if (SCM_FRACTIONP (z)) |
3576 | return SCM_BOOL_F; | |
0aacf84e | 3577 | else |
c2ff8ab0 | 3578 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); |
0f2d19dd JB |
3579 | } |
3580 | ||
3581 | ||
152f82bf | 3582 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3583 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3584 | * "zero." | |
3585 | */ | |
0f2d19dd | 3586 | SCM |
6e8d25a6 | 3587 | scm_positive_p (SCM x) |
0f2d19dd | 3588 | { |
e11e83f3 MV |
3589 | if (SCM_I_INUMP (x)) |
3590 | return scm_from_bool (SCM_I_INUM (x) > 0); | |
0aacf84e MD |
3591 | else if (SCM_BIGP (x)) |
3592 | { | |
3593 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3594 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3595 | return scm_from_bool (sgn > 0); |
0aacf84e MD |
3596 | } |
3597 | else if (SCM_REALP (x)) | |
73e4de09 | 3598 | return scm_from_bool(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
3599 | else if (SCM_FRACTIONP (x)) |
3600 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3601 | else |
c2ff8ab0 | 3602 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); |
0f2d19dd JB |
3603 | } |
3604 | ||
3605 | ||
152f82bf | 3606 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3607 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3608 | * "zero." | |
3609 | */ | |
0f2d19dd | 3610 | SCM |
6e8d25a6 | 3611 | scm_negative_p (SCM x) |
0f2d19dd | 3612 | { |
e11e83f3 MV |
3613 | if (SCM_I_INUMP (x)) |
3614 | return scm_from_bool (SCM_I_INUM (x) < 0); | |
0aacf84e MD |
3615 | else if (SCM_BIGP (x)) |
3616 | { | |
3617 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3618 | scm_remember_upto_here_1 (x); | |
73e4de09 | 3619 | return scm_from_bool (sgn < 0); |
0aacf84e MD |
3620 | } |
3621 | else if (SCM_REALP (x)) | |
73e4de09 | 3622 | return scm_from_bool(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
3623 | else if (SCM_FRACTIONP (x)) |
3624 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3625 | else |
c2ff8ab0 | 3626 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); |
0f2d19dd JB |
3627 | } |
3628 | ||
3629 | ||
2a06f791 KR |
3630 | /* scm_min and scm_max return an inexact when either argument is inexact, as |
3631 | required by r5rs. On that basis, for exact/inexact combinations the | |
3632 | exact is converted to inexact to compare and possibly return. This is | |
3633 | unlike scm_less_p above which takes some trouble to preserve all bits in | |
3634 | its test, such trouble is not required for min and max. */ | |
3635 | ||
9de33deb | 3636 | SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max); |
942e5b91 MG |
3637 | /* "Return the maximum of all parameter values." |
3638 | */ | |
0f2d19dd | 3639 | SCM |
6e8d25a6 | 3640 | scm_max (SCM x, SCM y) |
0f2d19dd | 3641 | { |
0aacf84e MD |
3642 | if (SCM_UNBNDP (y)) |
3643 | { | |
3644 | if (SCM_UNBNDP (x)) | |
3645 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
e11e83f3 | 3646 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3647 | return x; |
3648 | else | |
3649 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3650 | } |
f4c627b3 | 3651 | |
e11e83f3 | 3652 | if (SCM_I_INUMP (x)) |
0aacf84e | 3653 | { |
e11e83f3 MV |
3654 | long xx = SCM_I_INUM (x); |
3655 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3656 | { |
e11e83f3 | 3657 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3658 | return (xx < yy) ? y : x; |
3659 | } | |
3660 | else if (SCM_BIGP (y)) | |
3661 | { | |
3662 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3663 | scm_remember_upto_here_1 (y); | |
3664 | return (sgn < 0) ? x : y; | |
3665 | } | |
3666 | else if (SCM_REALP (y)) | |
3667 | { | |
3668 | double z = xx; | |
3669 | /* if y==NaN then ">" is false and we return NaN */ | |
55f26379 | 3670 | return (z > SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3671 | } |
f92e85f7 MV |
3672 | else if (SCM_FRACTIONP (y)) |
3673 | { | |
e4bc5d6c | 3674 | use_less: |
73e4de09 | 3675 | return (scm_is_false (scm_less_p (x, y)) ? x : y); |
f92e85f7 | 3676 | } |
0aacf84e MD |
3677 | else |
3678 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3679 | } |
0aacf84e MD |
3680 | else if (SCM_BIGP (x)) |
3681 | { | |
e11e83f3 | 3682 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3683 | { |
3684 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3685 | scm_remember_upto_here_1 (x); | |
3686 | return (sgn < 0) ? y : x; | |
3687 | } | |
3688 | else if (SCM_BIGP (y)) | |
3689 | { | |
3690 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3691 | scm_remember_upto_here_2 (x, y); | |
3692 | return (cmp > 0) ? x : y; | |
3693 | } | |
3694 | else if (SCM_REALP (y)) | |
3695 | { | |
2a06f791 KR |
3696 | /* if y==NaN then xx>yy is false, so we return the NaN y */ |
3697 | double xx, yy; | |
3698 | big_real: | |
3699 | xx = scm_i_big2dbl (x); | |
3700 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3701 | return (xx > yy ? scm_from_double (xx) : y); |
0aacf84e | 3702 | } |
f92e85f7 MV |
3703 | else if (SCM_FRACTIONP (y)) |
3704 | { | |
e4bc5d6c | 3705 | goto use_less; |
f92e85f7 | 3706 | } |
0aacf84e MD |
3707 | else |
3708 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 3709 | } |
0aacf84e MD |
3710 | else if (SCM_REALP (x)) |
3711 | { | |
e11e83f3 | 3712 | if (SCM_I_INUMP (y)) |
0aacf84e | 3713 | { |
e11e83f3 | 3714 | double z = SCM_I_INUM (y); |
0aacf84e | 3715 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3716 | return (SCM_REAL_VALUE (x) < z) ? scm_from_double (z) : x; |
0aacf84e MD |
3717 | } |
3718 | else if (SCM_BIGP (y)) | |
3719 | { | |
b6f8f763 | 3720 | SCM_SWAP (x, y); |
2a06f791 | 3721 | goto big_real; |
0aacf84e MD |
3722 | } |
3723 | else if (SCM_REALP (y)) | |
3724 | { | |
3725 | /* if x==NaN then our explicit check means we return NaN | |
3726 | if y==NaN then ">" is false and we return NaN | |
3727 | calling isnan is unavoidable, since it's the only way to know | |
3728 | which of x or y causes any compares to be false */ | |
3729 | double xx = SCM_REAL_VALUE (x); | |
3730 | return (xisnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y; | |
3731 | } | |
f92e85f7 MV |
3732 | else if (SCM_FRACTIONP (y)) |
3733 | { | |
3734 | double yy = scm_i_fraction2double (y); | |
3735 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3736 | return (xx < yy) ? scm_from_double (yy) : x; |
f92e85f7 MV |
3737 | } |
3738 | else | |
3739 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3740 | } | |
3741 | else if (SCM_FRACTIONP (x)) | |
3742 | { | |
e11e83f3 | 3743 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3744 | { |
e4bc5d6c | 3745 | goto use_less; |
f92e85f7 MV |
3746 | } |
3747 | else if (SCM_BIGP (y)) | |
3748 | { | |
e4bc5d6c | 3749 | goto use_less; |
f92e85f7 MV |
3750 | } |
3751 | else if (SCM_REALP (y)) | |
3752 | { | |
3753 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3754 | return (xx < SCM_REAL_VALUE (y)) ? y : scm_from_double (xx); |
f92e85f7 MV |
3755 | } |
3756 | else if (SCM_FRACTIONP (y)) | |
3757 | { | |
e4bc5d6c | 3758 | goto use_less; |
f92e85f7 | 3759 | } |
0aacf84e MD |
3760 | else |
3761 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3762 | } |
0aacf84e | 3763 | else |
f4c627b3 | 3764 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
3765 | } |
3766 | ||
3767 | ||
9de33deb | 3768 | SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min); |
942e5b91 MG |
3769 | /* "Return the minium of all parameter values." |
3770 | */ | |
0f2d19dd | 3771 | SCM |
6e8d25a6 | 3772 | scm_min (SCM x, SCM y) |
0f2d19dd | 3773 | { |
0aacf84e MD |
3774 | if (SCM_UNBNDP (y)) |
3775 | { | |
3776 | if (SCM_UNBNDP (x)) | |
3777 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
e11e83f3 | 3778 | else if (SCM_I_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3779 | return x; |
3780 | else | |
3781 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 3782 | } |
f4c627b3 | 3783 | |
e11e83f3 | 3784 | if (SCM_I_INUMP (x)) |
0aacf84e | 3785 | { |
e11e83f3 MV |
3786 | long xx = SCM_I_INUM (x); |
3787 | if (SCM_I_INUMP (y)) | |
0aacf84e | 3788 | { |
e11e83f3 | 3789 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
3790 | return (xx < yy) ? x : y; |
3791 | } | |
3792 | else if (SCM_BIGP (y)) | |
3793 | { | |
3794 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3795 | scm_remember_upto_here_1 (y); | |
3796 | return (sgn < 0) ? y : x; | |
3797 | } | |
3798 | else if (SCM_REALP (y)) | |
3799 | { | |
3800 | double z = xx; | |
3801 | /* if y==NaN then "<" is false and we return NaN */ | |
55f26379 | 3802 | return (z < SCM_REAL_VALUE (y)) ? scm_from_double (z) : y; |
0aacf84e | 3803 | } |
f92e85f7 MV |
3804 | else if (SCM_FRACTIONP (y)) |
3805 | { | |
e4bc5d6c | 3806 | use_less: |
73e4de09 | 3807 | return (scm_is_false (scm_less_p (x, y)) ? y : x); |
f92e85f7 | 3808 | } |
0aacf84e MD |
3809 | else |
3810 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3811 | } |
0aacf84e MD |
3812 | else if (SCM_BIGP (x)) |
3813 | { | |
e11e83f3 | 3814 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3815 | { |
3816 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3817 | scm_remember_upto_here_1 (x); | |
3818 | return (sgn < 0) ? x : y; | |
3819 | } | |
3820 | else if (SCM_BIGP (y)) | |
3821 | { | |
3822 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3823 | scm_remember_upto_here_2 (x, y); | |
3824 | return (cmp > 0) ? y : x; | |
3825 | } | |
3826 | else if (SCM_REALP (y)) | |
3827 | { | |
2a06f791 KR |
3828 | /* if y==NaN then xx<yy is false, so we return the NaN y */ |
3829 | double xx, yy; | |
3830 | big_real: | |
3831 | xx = scm_i_big2dbl (x); | |
3832 | yy = SCM_REAL_VALUE (y); | |
55f26379 | 3833 | return (xx < yy ? scm_from_double (xx) : y); |
0aacf84e | 3834 | } |
f92e85f7 MV |
3835 | else if (SCM_FRACTIONP (y)) |
3836 | { | |
e4bc5d6c | 3837 | goto use_less; |
f92e85f7 | 3838 | } |
0aacf84e MD |
3839 | else |
3840 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 3841 | } |
0aacf84e MD |
3842 | else if (SCM_REALP (x)) |
3843 | { | |
e11e83f3 | 3844 | if (SCM_I_INUMP (y)) |
0aacf84e | 3845 | { |
e11e83f3 | 3846 | double z = SCM_I_INUM (y); |
0aacf84e | 3847 | /* if x==NaN then "<" is false and we return NaN */ |
55f26379 | 3848 | return (z < SCM_REAL_VALUE (x)) ? scm_from_double (z) : x; |
0aacf84e MD |
3849 | } |
3850 | else if (SCM_BIGP (y)) | |
3851 | { | |
b6f8f763 | 3852 | SCM_SWAP (x, y); |
2a06f791 | 3853 | goto big_real; |
0aacf84e MD |
3854 | } |
3855 | else if (SCM_REALP (y)) | |
3856 | { | |
3857 | /* if x==NaN then our explicit check means we return NaN | |
3858 | if y==NaN then "<" is false and we return NaN | |
3859 | calling isnan is unavoidable, since it's the only way to know | |
3860 | which of x or y causes any compares to be false */ | |
3861 | double xx = SCM_REAL_VALUE (x); | |
3862 | return (xisnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y; | |
3863 | } | |
f92e85f7 MV |
3864 | else if (SCM_FRACTIONP (y)) |
3865 | { | |
3866 | double yy = scm_i_fraction2double (y); | |
3867 | double xx = SCM_REAL_VALUE (x); | |
55f26379 | 3868 | return (yy < xx) ? scm_from_double (yy) : x; |
f92e85f7 | 3869 | } |
0aacf84e MD |
3870 | else |
3871 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3872 | } |
f92e85f7 MV |
3873 | else if (SCM_FRACTIONP (x)) |
3874 | { | |
e11e83f3 | 3875 | if (SCM_I_INUMP (y)) |
f92e85f7 | 3876 | { |
e4bc5d6c | 3877 | goto use_less; |
f92e85f7 MV |
3878 | } |
3879 | else if (SCM_BIGP (y)) | |
3880 | { | |
e4bc5d6c | 3881 | goto use_less; |
f92e85f7 MV |
3882 | } |
3883 | else if (SCM_REALP (y)) | |
3884 | { | |
3885 | double xx = scm_i_fraction2double (x); | |
55f26379 | 3886 | return (SCM_REAL_VALUE (y) < xx) ? y : scm_from_double (xx); |
f92e85f7 MV |
3887 | } |
3888 | else if (SCM_FRACTIONP (y)) | |
3889 | { | |
e4bc5d6c | 3890 | goto use_less; |
f92e85f7 MV |
3891 | } |
3892 | else | |
3893 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3894 | } | |
0aacf84e | 3895 | else |
f4c627b3 | 3896 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
3897 | } |
3898 | ||
3899 | ||
9de33deb | 3900 | SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum); |
942e5b91 MG |
3901 | /* "Return the sum of all parameter values. Return 0 if called without\n" |
3902 | * "any parameters." | |
3903 | */ | |
0f2d19dd | 3904 | SCM |
6e8d25a6 | 3905 | scm_sum (SCM x, SCM y) |
0f2d19dd | 3906 | { |
ca46fb90 RB |
3907 | if (SCM_UNBNDP (y)) |
3908 | { | |
3909 | if (SCM_NUMBERP (x)) return x; | |
3910 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 3911 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 3912 | } |
c209c88e | 3913 | |
e11e83f3 | 3914 | if (SCM_I_INUMP (x)) |
ca46fb90 | 3915 | { |
e11e83f3 | 3916 | if (SCM_I_INUMP (y)) |
ca46fb90 | 3917 | { |
e11e83f3 MV |
3918 | long xx = SCM_I_INUM (x); |
3919 | long yy = SCM_I_INUM (y); | |
ca46fb90 | 3920 | long int z = xx + yy; |
d956fa6f | 3921 | return SCM_FIXABLE (z) ? SCM_I_MAKINUM (z) : scm_i_long2big (z); |
ca46fb90 RB |
3922 | } |
3923 | else if (SCM_BIGP (y)) | |
3924 | { | |
3925 | SCM_SWAP (x, y); | |
3926 | goto add_big_inum; | |
3927 | } | |
3928 | else if (SCM_REALP (y)) | |
3929 | { | |
e11e83f3 | 3930 | long int xx = SCM_I_INUM (x); |
55f26379 | 3931 | return scm_from_double (xx + SCM_REAL_VALUE (y)); |
ca46fb90 RB |
3932 | } |
3933 | else if (SCM_COMPLEXP (y)) | |
3934 | { | |
e11e83f3 | 3935 | long int xx = SCM_I_INUM (x); |
8507ec80 | 3936 | return scm_c_make_rectangular (xx + SCM_COMPLEX_REAL (y), |
ca46fb90 RB |
3937 | SCM_COMPLEX_IMAG (y)); |
3938 | } | |
f92e85f7 | 3939 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 3940 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
3941 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
3942 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
3943 | else |
3944 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
3945 | } else if (SCM_BIGP (x)) |
3946 | { | |
e11e83f3 | 3947 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
3948 | { |
3949 | long int inum; | |
3950 | int bigsgn; | |
3951 | add_big_inum: | |
e11e83f3 | 3952 | inum = SCM_I_INUM (y); |
0aacf84e MD |
3953 | if (inum == 0) |
3954 | return x; | |
3955 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3956 | if (inum < 0) | |
3957 | { | |
3958 | SCM result = scm_i_mkbig (); | |
3959 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
3960 | scm_remember_upto_here_1 (x); | |
3961 | /* we know the result will have to be a bignum */ | |
3962 | if (bigsgn == -1) | |
3963 | return result; | |
3964 | return scm_i_normbig (result); | |
3965 | } | |
3966 | else | |
3967 | { | |
3968 | SCM result = scm_i_mkbig (); | |
3969 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
3970 | scm_remember_upto_here_1 (x); | |
3971 | /* we know the result will have to be a bignum */ | |
3972 | if (bigsgn == 1) | |
3973 | return result; | |
3974 | return scm_i_normbig (result); | |
3975 | } | |
3976 | } | |
3977 | else if (SCM_BIGP (y)) | |
3978 | { | |
3979 | SCM result = scm_i_mkbig (); | |
3980 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3981 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3982 | mpz_add (SCM_I_BIG_MPZ (result), | |
3983 | SCM_I_BIG_MPZ (x), | |
3984 | SCM_I_BIG_MPZ (y)); | |
3985 | scm_remember_upto_here_2 (x, y); | |
3986 | /* we know the result will have to be a bignum */ | |
3987 | if (sgn_x == sgn_y) | |
3988 | return result; | |
3989 | return scm_i_normbig (result); | |
3990 | } | |
3991 | else if (SCM_REALP (y)) | |
3992 | { | |
3993 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
3994 | scm_remember_upto_here_1 (x); | |
55f26379 | 3995 | return scm_from_double (result); |
0aacf84e MD |
3996 | } |
3997 | else if (SCM_COMPLEXP (y)) | |
3998 | { | |
3999 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4000 | + SCM_COMPLEX_REAL (y)); | |
4001 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4002 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4003 | } |
f92e85f7 | 4004 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4005 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), |
f92e85f7 MV |
4006 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), |
4007 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4008 | else |
4009 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 4010 | } |
0aacf84e MD |
4011 | else if (SCM_REALP (x)) |
4012 | { | |
e11e83f3 | 4013 | if (SCM_I_INUMP (y)) |
55f26379 | 4014 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_I_INUM (y)); |
0aacf84e MD |
4015 | else if (SCM_BIGP (y)) |
4016 | { | |
4017 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
4018 | scm_remember_upto_here_1 (y); | |
55f26379 | 4019 | return scm_from_double (result); |
0aacf84e MD |
4020 | } |
4021 | else if (SCM_REALP (y)) | |
55f26379 | 4022 | return scm_from_double (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); |
0aacf84e | 4023 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4024 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4025 | SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4026 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4027 | return scm_from_double (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); |
0aacf84e MD |
4028 | else |
4029 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 4030 | } |
0aacf84e MD |
4031 | else if (SCM_COMPLEXP (x)) |
4032 | { | |
e11e83f3 | 4033 | if (SCM_I_INUMP (y)) |
8507ec80 | 4034 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_I_INUM (y), |
0aacf84e MD |
4035 | SCM_COMPLEX_IMAG (x)); |
4036 | else if (SCM_BIGP (y)) | |
4037 | { | |
4038 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
4039 | + SCM_COMPLEX_REAL (x)); | |
4040 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4041 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4042 | } |
4043 | else if (SCM_REALP (y)) | |
8507ec80 | 4044 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), |
0aacf84e MD |
4045 | SCM_COMPLEX_IMAG (x)); |
4046 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4047 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), |
0aacf84e | 4048 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4049 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4050 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), |
f92e85f7 MV |
4051 | SCM_COMPLEX_IMAG (x)); |
4052 | else | |
4053 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
4054 | } | |
4055 | else if (SCM_FRACTIONP (x)) | |
4056 | { | |
e11e83f3 | 4057 | if (SCM_I_INUMP (y)) |
cba42c93 | 4058 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4059 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4060 | SCM_FRACTION_DENOMINATOR (x)); | |
4061 | else if (SCM_BIGP (y)) | |
cba42c93 | 4062 | return scm_i_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4063 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), |
4064 | SCM_FRACTION_DENOMINATOR (x)); | |
4065 | else if (SCM_REALP (y)) | |
55f26379 | 4066 | return scm_from_double (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); |
f92e85f7 | 4067 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4068 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), |
f92e85f7 MV |
4069 | SCM_COMPLEX_IMAG (y)); |
4070 | else if (SCM_FRACTIONP (y)) | |
4071 | /* a/b + c/d = (ad + bc) / bd */ | |
cba42c93 | 4072 | return scm_i_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4073 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4074 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4075 | else |
4076 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 4077 | } |
0aacf84e | 4078 | else |
98cb6e75 | 4079 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
4080 | } |
4081 | ||
4082 | ||
9de33deb | 4083 | SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference); |
609c3d30 MG |
4084 | /* If called with one argument @var{z1}, -@var{z1} returned. Otherwise |
4085 | * the sum of all but the first argument are subtracted from the first | |
4086 | * argument. */ | |
c05e97b7 | 4087 | #define FUNC_NAME s_difference |
0f2d19dd | 4088 | SCM |
6e8d25a6 | 4089 | scm_difference (SCM x, SCM y) |
0f2d19dd | 4090 | { |
ca46fb90 RB |
4091 | if (SCM_UNBNDP (y)) |
4092 | { | |
4093 | if (SCM_UNBNDP (x)) | |
4094 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
4095 | else | |
e11e83f3 | 4096 | if (SCM_I_INUMP (x)) |
ca46fb90 | 4097 | { |
e11e83f3 | 4098 | long xx = -SCM_I_INUM (x); |
ca46fb90 | 4099 | if (SCM_FIXABLE (xx)) |
d956fa6f | 4100 | return SCM_I_MAKINUM (xx); |
ca46fb90 RB |
4101 | else |
4102 | return scm_i_long2big (xx); | |
4103 | } | |
4104 | else if (SCM_BIGP (x)) | |
a9ad4847 KR |
4105 | /* Must scm_i_normbig here because -SCM_MOST_NEGATIVE_FIXNUM is a |
4106 | bignum, but negating that gives a fixnum. */ | |
ca46fb90 RB |
4107 | return scm_i_normbig (scm_i_clonebig (x, 0)); |
4108 | else if (SCM_REALP (x)) | |
55f26379 | 4109 | return scm_from_double (-SCM_REAL_VALUE (x)); |
ca46fb90 | 4110 | else if (SCM_COMPLEXP (x)) |
8507ec80 | 4111 | return scm_c_make_rectangular (-SCM_COMPLEX_REAL (x), |
ca46fb90 | 4112 | -SCM_COMPLEX_IMAG (x)); |
f92e85f7 | 4113 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4114 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), |
f92e85f7 | 4115 | SCM_FRACTION_DENOMINATOR (x)); |
ca46fb90 RB |
4116 | else |
4117 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 4118 | } |
ca46fb90 | 4119 | |
e11e83f3 | 4120 | if (SCM_I_INUMP (x)) |
0aacf84e | 4121 | { |
e11e83f3 | 4122 | if (SCM_I_INUMP (y)) |
0aacf84e | 4123 | { |
e11e83f3 MV |
4124 | long int xx = SCM_I_INUM (x); |
4125 | long int yy = SCM_I_INUM (y); | |
0aacf84e MD |
4126 | long int z = xx - yy; |
4127 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4128 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4129 | else |
4130 | return scm_i_long2big (z); | |
4131 | } | |
4132 | else if (SCM_BIGP (y)) | |
4133 | { | |
4134 | /* inum-x - big-y */ | |
e11e83f3 | 4135 | long xx = SCM_I_INUM (x); |
ca46fb90 | 4136 | |
0aacf84e MD |
4137 | if (xx == 0) |
4138 | return scm_i_clonebig (y, 0); | |
4139 | else | |
4140 | { | |
4141 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4142 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4143 | |
0aacf84e MD |
4144 | if (xx >= 0) |
4145 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
4146 | else | |
4147 | { | |
4148 | /* x - y == -(y + -x) */ | |
4149 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
4150 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4151 | } | |
4152 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 4153 | |
0aacf84e MD |
4154 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
4155 | /* we know the result will have to be a bignum */ | |
4156 | return result; | |
4157 | else | |
4158 | return scm_i_normbig (result); | |
4159 | } | |
4160 | } | |
4161 | else if (SCM_REALP (y)) | |
4162 | { | |
e11e83f3 | 4163 | long int xx = SCM_I_INUM (x); |
55f26379 | 4164 | return scm_from_double (xx - SCM_REAL_VALUE (y)); |
0aacf84e MD |
4165 | } |
4166 | else if (SCM_COMPLEXP (y)) | |
4167 | { | |
e11e83f3 | 4168 | long int xx = SCM_I_INUM (x); |
8507ec80 | 4169 | return scm_c_make_rectangular (xx - SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4170 | - SCM_COMPLEX_IMAG (y)); |
4171 | } | |
f92e85f7 MV |
4172 | else if (SCM_FRACTIONP (y)) |
4173 | /* a - b/c = (ac - b) / c */ | |
cba42c93 | 4174 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4175 | SCM_FRACTION_NUMERATOR (y)), |
4176 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4177 | else |
4178 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 4179 | } |
0aacf84e MD |
4180 | else if (SCM_BIGP (x)) |
4181 | { | |
e11e83f3 | 4182 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4183 | { |
4184 | /* big-x - inum-y */ | |
e11e83f3 | 4185 | long yy = SCM_I_INUM (y); |
0aacf84e | 4186 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); |
ca46fb90 | 4187 | |
0aacf84e MD |
4188 | scm_remember_upto_here_1 (x); |
4189 | if (sgn_x == 0) | |
c71b0706 MV |
4190 | return (SCM_FIXABLE (-yy) ? |
4191 | SCM_I_MAKINUM (-yy) : scm_from_long (-yy)); | |
0aacf84e MD |
4192 | else |
4193 | { | |
4194 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 4195 | |
708f22c6 KR |
4196 | if (yy >= 0) |
4197 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
4198 | else | |
4199 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 4200 | scm_remember_upto_here_1 (x); |
ca46fb90 | 4201 | |
0aacf84e MD |
4202 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
4203 | /* we know the result will have to be a bignum */ | |
4204 | return result; | |
4205 | else | |
4206 | return scm_i_normbig (result); | |
4207 | } | |
4208 | } | |
4209 | else if (SCM_BIGP (y)) | |
4210 | { | |
4211 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
4212 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
4213 | SCM result = scm_i_mkbig (); | |
4214 | mpz_sub (SCM_I_BIG_MPZ (result), | |
4215 | SCM_I_BIG_MPZ (x), | |
4216 | SCM_I_BIG_MPZ (y)); | |
4217 | scm_remember_upto_here_2 (x, y); | |
4218 | /* we know the result will have to be a bignum */ | |
4219 | if ((sgn_x == 1) && (sgn_y == -1)) | |
4220 | return result; | |
4221 | if ((sgn_x == -1) && (sgn_y == 1)) | |
4222 | return result; | |
4223 | return scm_i_normbig (result); | |
4224 | } | |
4225 | else if (SCM_REALP (y)) | |
4226 | { | |
4227 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
4228 | scm_remember_upto_here_1 (x); | |
55f26379 | 4229 | return scm_from_double (result); |
0aacf84e MD |
4230 | } |
4231 | else if (SCM_COMPLEXP (y)) | |
4232 | { | |
4233 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4234 | - SCM_COMPLEX_REAL (y)); | |
4235 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4236 | return scm_c_make_rectangular (real_part, - SCM_COMPLEX_IMAG (y)); |
0aacf84e | 4237 | } |
f92e85f7 | 4238 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4239 | return scm_i_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4240 | SCM_FRACTION_NUMERATOR (y)), |
4241 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 4242 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 4243 | } |
0aacf84e MD |
4244 | else if (SCM_REALP (x)) |
4245 | { | |
e11e83f3 | 4246 | if (SCM_I_INUMP (y)) |
55f26379 | 4247 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_I_INUM (y)); |
0aacf84e MD |
4248 | else if (SCM_BIGP (y)) |
4249 | { | |
4250 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4251 | scm_remember_upto_here_1 (x); | |
55f26379 | 4252 | return scm_from_double (result); |
0aacf84e MD |
4253 | } |
4254 | else if (SCM_REALP (y)) | |
55f26379 | 4255 | return scm_from_double (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); |
0aacf84e | 4256 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4257 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4258 | -SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4259 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4260 | return scm_from_double (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); |
0aacf84e MD |
4261 | else |
4262 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4263 | } |
0aacf84e MD |
4264 | else if (SCM_COMPLEXP (x)) |
4265 | { | |
e11e83f3 | 4266 | if (SCM_I_INUMP (y)) |
8507ec80 | 4267 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_I_INUM (y), |
0aacf84e MD |
4268 | SCM_COMPLEX_IMAG (x)); |
4269 | else if (SCM_BIGP (y)) | |
4270 | { | |
4271 | double real_part = (SCM_COMPLEX_REAL (x) | |
4272 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
4273 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4274 | return scm_c_make_rectangular (real_part, SCM_COMPLEX_IMAG (y)); |
0aacf84e MD |
4275 | } |
4276 | else if (SCM_REALP (y)) | |
8507ec80 | 4277 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), |
0aacf84e MD |
4278 | SCM_COMPLEX_IMAG (x)); |
4279 | else if (SCM_COMPLEXP (y)) | |
8507ec80 | 4280 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), |
0aacf84e | 4281 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4282 | else if (SCM_FRACTIONP (y)) |
8507ec80 | 4283 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), |
f92e85f7 MV |
4284 | SCM_COMPLEX_IMAG (x)); |
4285 | else | |
4286 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
4287 | } | |
4288 | else if (SCM_FRACTIONP (x)) | |
4289 | { | |
e11e83f3 | 4290 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4291 | /* a/b - c = (a - cb) / b */ |
cba42c93 | 4292 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4293 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4294 | SCM_FRACTION_DENOMINATOR (x)); | |
4295 | else if (SCM_BIGP (y)) | |
cba42c93 | 4296 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4297 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), |
4298 | SCM_FRACTION_DENOMINATOR (x)); | |
4299 | else if (SCM_REALP (y)) | |
55f26379 | 4300 | return scm_from_double (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); |
f92e85f7 | 4301 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4302 | return scm_c_make_rectangular (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4303 | -SCM_COMPLEX_IMAG (y)); |
4304 | else if (SCM_FRACTIONP (y)) | |
4305 | /* a/b - c/d = (ad - bc) / bd */ | |
cba42c93 | 4306 | return scm_i_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4307 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), |
4308 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4309 | else |
4310 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4311 | } |
0aacf84e | 4312 | else |
98cb6e75 | 4313 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 4314 | } |
c05e97b7 | 4315 | #undef FUNC_NAME |
0f2d19dd | 4316 | |
ca46fb90 | 4317 | |
9de33deb | 4318 | SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product); |
942e5b91 MG |
4319 | /* "Return the product of all arguments. If called without arguments,\n" |
4320 | * "1 is returned." | |
4321 | */ | |
0f2d19dd | 4322 | SCM |
6e8d25a6 | 4323 | scm_product (SCM x, SCM y) |
0f2d19dd | 4324 | { |
0aacf84e MD |
4325 | if (SCM_UNBNDP (y)) |
4326 | { | |
4327 | if (SCM_UNBNDP (x)) | |
d956fa6f | 4328 | return SCM_I_MAKINUM (1L); |
0aacf84e MD |
4329 | else if (SCM_NUMBERP (x)) |
4330 | return x; | |
4331 | else | |
4332 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 4333 | } |
ca46fb90 | 4334 | |
e11e83f3 | 4335 | if (SCM_I_INUMP (x)) |
0aacf84e MD |
4336 | { |
4337 | long xx; | |
f4c627b3 | 4338 | |
0aacf84e | 4339 | intbig: |
e11e83f3 | 4340 | xx = SCM_I_INUM (x); |
f4c627b3 | 4341 | |
0aacf84e MD |
4342 | switch (xx) |
4343 | { | |
ca46fb90 RB |
4344 | case 0: return x; break; |
4345 | case 1: return y; break; | |
0aacf84e | 4346 | } |
f4c627b3 | 4347 | |
e11e83f3 | 4348 | if (SCM_I_INUMP (y)) |
0aacf84e | 4349 | { |
e11e83f3 | 4350 | long yy = SCM_I_INUM (y); |
0aacf84e | 4351 | long kk = xx * yy; |
d956fa6f | 4352 | SCM k = SCM_I_MAKINUM (kk); |
e11e83f3 | 4353 | if ((kk == SCM_I_INUM (k)) && (kk / xx == yy)) |
0aacf84e MD |
4354 | return k; |
4355 | else | |
4356 | { | |
4357 | SCM result = scm_i_long2big (xx); | |
4358 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); | |
4359 | return scm_i_normbig (result); | |
4360 | } | |
4361 | } | |
4362 | else if (SCM_BIGP (y)) | |
4363 | { | |
4364 | SCM result = scm_i_mkbig (); | |
4365 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
4366 | scm_remember_upto_here_1 (y); | |
4367 | return result; | |
4368 | } | |
4369 | else if (SCM_REALP (y)) | |
55f26379 | 4370 | return scm_from_double (xx * SCM_REAL_VALUE (y)); |
0aacf84e | 4371 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4372 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
0aacf84e | 4373 | xx * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4374 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4375 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4376 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4377 | else |
4378 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4379 | } |
0aacf84e MD |
4380 | else if (SCM_BIGP (x)) |
4381 | { | |
e11e83f3 | 4382 | if (SCM_I_INUMP (y)) |
0aacf84e MD |
4383 | { |
4384 | SCM_SWAP (x, y); | |
4385 | goto intbig; | |
4386 | } | |
4387 | else if (SCM_BIGP (y)) | |
4388 | { | |
4389 | SCM result = scm_i_mkbig (); | |
4390 | mpz_mul (SCM_I_BIG_MPZ (result), | |
4391 | SCM_I_BIG_MPZ (x), | |
4392 | SCM_I_BIG_MPZ (y)); | |
4393 | scm_remember_upto_here_2 (x, y); | |
4394 | return result; | |
4395 | } | |
4396 | else if (SCM_REALP (y)) | |
4397 | { | |
4398 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
4399 | scm_remember_upto_here_1 (x); | |
55f26379 | 4400 | return scm_from_double (result); |
0aacf84e MD |
4401 | } |
4402 | else if (SCM_COMPLEXP (y)) | |
4403 | { | |
4404 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4405 | scm_remember_upto_here_1 (x); | |
8507ec80 | 4406 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (y), |
0aacf84e MD |
4407 | z * SCM_COMPLEX_IMAG (y)); |
4408 | } | |
f92e85f7 | 4409 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4410 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), |
f92e85f7 | 4411 | SCM_FRACTION_DENOMINATOR (y)); |
0aacf84e MD |
4412 | else |
4413 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4414 | } |
0aacf84e MD |
4415 | else if (SCM_REALP (x)) |
4416 | { | |
e11e83f3 | 4417 | if (SCM_I_INUMP (y)) |
55f26379 | 4418 | return scm_from_double (SCM_I_INUM (y) * SCM_REAL_VALUE (x)); |
0aacf84e MD |
4419 | else if (SCM_BIGP (y)) |
4420 | { | |
4421 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
4422 | scm_remember_upto_here_1 (y); | |
55f26379 | 4423 | return scm_from_double (result); |
0aacf84e MD |
4424 | } |
4425 | else if (SCM_REALP (y)) | |
55f26379 | 4426 | return scm_from_double (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); |
0aacf84e | 4427 | else if (SCM_COMPLEXP (y)) |
8507ec80 | 4428 | return scm_c_make_rectangular (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), |
0aacf84e | 4429 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); |
f92e85f7 | 4430 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4431 | return scm_from_double (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); |
0aacf84e MD |
4432 | else |
4433 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4434 | } |
0aacf84e MD |
4435 | else if (SCM_COMPLEXP (x)) |
4436 | { | |
e11e83f3 | 4437 | if (SCM_I_INUMP (y)) |
8507ec80 | 4438 | return scm_c_make_rectangular (SCM_I_INUM (y) * SCM_COMPLEX_REAL (x), |
e11e83f3 | 4439 | SCM_I_INUM (y) * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4440 | else if (SCM_BIGP (y)) |
4441 | { | |
4442 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4443 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4444 | return scm_c_make_rectangular (z * SCM_COMPLEX_REAL (x), |
76506335 | 4445 | z * SCM_COMPLEX_IMAG (x)); |
0aacf84e MD |
4446 | } |
4447 | else if (SCM_REALP (y)) | |
8507ec80 | 4448 | return scm_c_make_rectangular (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), |
0aacf84e MD |
4449 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); |
4450 | else if (SCM_COMPLEXP (y)) | |
4451 | { | |
8507ec80 | 4452 | return scm_c_make_rectangular (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) |
0aacf84e MD |
4453 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), |
4454 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
4455 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
4456 | } | |
f92e85f7 MV |
4457 | else if (SCM_FRACTIONP (y)) |
4458 | { | |
4459 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4460 | return scm_c_make_rectangular (yy * SCM_COMPLEX_REAL (x), |
f92e85f7 MV |
4461 | yy * SCM_COMPLEX_IMAG (x)); |
4462 | } | |
4463 | else | |
4464 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
4465 | } | |
4466 | else if (SCM_FRACTIONP (x)) | |
4467 | { | |
e11e83f3 | 4468 | if (SCM_I_INUMP (y)) |
cba42c93 | 4469 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4470 | SCM_FRACTION_DENOMINATOR (x)); |
4471 | else if (SCM_BIGP (y)) | |
cba42c93 | 4472 | return scm_i_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), |
f92e85f7 MV |
4473 | SCM_FRACTION_DENOMINATOR (x)); |
4474 | else if (SCM_REALP (y)) | |
55f26379 | 4475 | return scm_from_double (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); |
f92e85f7 MV |
4476 | else if (SCM_COMPLEXP (y)) |
4477 | { | |
4478 | double xx = scm_i_fraction2double (x); | |
8507ec80 | 4479 | return scm_c_make_rectangular (xx * SCM_COMPLEX_REAL (y), |
f92e85f7 MV |
4480 | xx * SCM_COMPLEX_IMAG (y)); |
4481 | } | |
4482 | else if (SCM_FRACTIONP (y)) | |
4483 | /* a/b * c/d = ac / bd */ | |
cba42c93 | 4484 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4485 | SCM_FRACTION_NUMERATOR (y)), |
4486 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
4487 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4488 | else |
4489 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4490 | } |
0aacf84e | 4491 | else |
f4c627b3 | 4492 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
4493 | } |
4494 | ||
7351e207 MV |
4495 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
4496 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
4497 | #define ALLOW_DIVIDE_BY_ZERO | |
4498 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
4499 | #endif | |
0f2d19dd | 4500 | |
ba74ef4e MV |
4501 | /* The code below for complex division is adapted from the GNU |
4502 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
4503 | this copyright: */ | |
4504 | ||
4505 | /**************************************************************** | |
4506 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
4507 | ||
4508 | Permission to use, copy, modify, and distribute this software | |
4509 | and its documentation for any purpose and without fee is hereby | |
4510 | granted, provided that the above copyright notice appear in all | |
4511 | copies and that both that the copyright notice and this | |
4512 | permission notice and warranty disclaimer appear in supporting | |
4513 | documentation, and that the names of AT&T Bell Laboratories or | |
4514 | Bellcore or any of their entities not be used in advertising or | |
4515 | publicity pertaining to distribution of the software without | |
4516 | specific, written prior permission. | |
4517 | ||
4518 | AT&T and Bellcore disclaim all warranties with regard to this | |
4519 | software, including all implied warranties of merchantability | |
4520 | and fitness. In no event shall AT&T or Bellcore be liable for | |
4521 | any special, indirect or consequential damages or any damages | |
4522 | whatsoever resulting from loss of use, data or profits, whether | |
4523 | in an action of contract, negligence or other tortious action, | |
4524 | arising out of or in connection with the use or performance of | |
4525 | this software. | |
4526 | ****************************************************************/ | |
4527 | ||
9de33deb | 4528 | SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide); |
609c3d30 MG |
4529 | /* Divide the first argument by the product of the remaining |
4530 | arguments. If called with one argument @var{z1}, 1/@var{z1} is | |
4531 | returned. */ | |
c05e97b7 | 4532 | #define FUNC_NAME s_divide |
f92e85f7 MV |
4533 | static SCM |
4534 | scm_i_divide (SCM x, SCM y, int inexact) | |
0f2d19dd | 4535 | { |
f8de44c1 DH |
4536 | double a; |
4537 | ||
0aacf84e MD |
4538 | if (SCM_UNBNDP (y)) |
4539 | { | |
4540 | if (SCM_UNBNDP (x)) | |
4541 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
e11e83f3 | 4542 | else if (SCM_I_INUMP (x)) |
0aacf84e | 4543 | { |
e11e83f3 | 4544 | long xx = SCM_I_INUM (x); |
0aacf84e MD |
4545 | if (xx == 1 || xx == -1) |
4546 | return x; | |
7351e207 | 4547 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4548 | else if (xx == 0) |
4549 | scm_num_overflow (s_divide); | |
7351e207 | 4550 | #endif |
0aacf84e | 4551 | else |
f92e85f7 MV |
4552 | { |
4553 | if (inexact) | |
55f26379 | 4554 | return scm_from_double (1.0 / (double) xx); |
cba42c93 | 4555 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4556 | } |
0aacf84e MD |
4557 | } |
4558 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
4559 | { |
4560 | if (inexact) | |
55f26379 | 4561 | return scm_from_double (1.0 / scm_i_big2dbl (x)); |
cba42c93 | 4562 | else return scm_i_make_ratio (SCM_I_MAKINUM(1), x); |
f92e85f7 | 4563 | } |
0aacf84e MD |
4564 | else if (SCM_REALP (x)) |
4565 | { | |
4566 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 4567 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4568 | if (xx == 0.0) |
4569 | scm_num_overflow (s_divide); | |
4570 | else | |
7351e207 | 4571 | #endif |
55f26379 | 4572 | return scm_from_double (1.0 / xx); |
0aacf84e MD |
4573 | } |
4574 | else if (SCM_COMPLEXP (x)) | |
4575 | { | |
4576 | double r = SCM_COMPLEX_REAL (x); | |
4577 | double i = SCM_COMPLEX_IMAG (x); | |
4578 | if (r <= i) | |
4579 | { | |
4580 | double t = r / i; | |
4581 | double d = i * (1.0 + t * t); | |
8507ec80 | 4582 | return scm_c_make_rectangular (t / d, -1.0 / d); |
0aacf84e MD |
4583 | } |
4584 | else | |
4585 | { | |
4586 | double t = i / r; | |
4587 | double d = r * (1.0 + t * t); | |
8507ec80 | 4588 | return scm_c_make_rectangular (1.0 / d, -t / d); |
0aacf84e MD |
4589 | } |
4590 | } | |
f92e85f7 | 4591 | else if (SCM_FRACTIONP (x)) |
cba42c93 | 4592 | return scm_i_make_ratio (SCM_FRACTION_DENOMINATOR (x), |
f92e85f7 | 4593 | SCM_FRACTION_NUMERATOR (x)); |
0aacf84e MD |
4594 | else |
4595 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 4596 | } |
f8de44c1 | 4597 | |
e11e83f3 | 4598 | if (SCM_I_INUMP (x)) |
0aacf84e | 4599 | { |
e11e83f3 MV |
4600 | long xx = SCM_I_INUM (x); |
4601 | if (SCM_I_INUMP (y)) | |
0aacf84e | 4602 | { |
e11e83f3 | 4603 | long yy = SCM_I_INUM (y); |
0aacf84e MD |
4604 | if (yy == 0) |
4605 | { | |
7351e207 | 4606 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4607 | scm_num_overflow (s_divide); |
7351e207 | 4608 | #else |
55f26379 | 4609 | return scm_from_double ((double) xx / (double) yy); |
7351e207 | 4610 | #endif |
0aacf84e MD |
4611 | } |
4612 | else if (xx % yy != 0) | |
f92e85f7 MV |
4613 | { |
4614 | if (inexact) | |
55f26379 | 4615 | return scm_from_double ((double) xx / (double) yy); |
cba42c93 | 4616 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4617 | } |
0aacf84e MD |
4618 | else |
4619 | { | |
4620 | long z = xx / yy; | |
4621 | if (SCM_FIXABLE (z)) | |
d956fa6f | 4622 | return SCM_I_MAKINUM (z); |
0aacf84e MD |
4623 | else |
4624 | return scm_i_long2big (z); | |
4625 | } | |
f872b822 | 4626 | } |
0aacf84e | 4627 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
4628 | { |
4629 | if (inexact) | |
55f26379 | 4630 | return scm_from_double ((double) xx / scm_i_big2dbl (y)); |
cba42c93 | 4631 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4632 | } |
0aacf84e MD |
4633 | else if (SCM_REALP (y)) |
4634 | { | |
4635 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4636 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4637 | if (yy == 0.0) |
4638 | scm_num_overflow (s_divide); | |
4639 | else | |
7351e207 | 4640 | #endif |
55f26379 | 4641 | return scm_from_double ((double) xx / yy); |
ba74ef4e | 4642 | } |
0aacf84e MD |
4643 | else if (SCM_COMPLEXP (y)) |
4644 | { | |
4645 | a = xx; | |
4646 | complex_div: /* y _must_ be a complex number */ | |
4647 | { | |
4648 | double r = SCM_COMPLEX_REAL (y); | |
4649 | double i = SCM_COMPLEX_IMAG (y); | |
4650 | if (r <= i) | |
4651 | { | |
4652 | double t = r / i; | |
4653 | double d = i * (1.0 + t * t); | |
8507ec80 | 4654 | return scm_c_make_rectangular ((a * t) / d, -a / d); |
0aacf84e MD |
4655 | } |
4656 | else | |
4657 | { | |
4658 | double t = i / r; | |
4659 | double d = r * (1.0 + t * t); | |
8507ec80 | 4660 | return scm_c_make_rectangular (a / d, -(a * t) / d); |
0aacf84e MD |
4661 | } |
4662 | } | |
4663 | } | |
f92e85f7 MV |
4664 | else if (SCM_FRACTIONP (y)) |
4665 | /* a / b/c = ac / b */ | |
cba42c93 | 4666 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4667 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4668 | else |
4669 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4670 | } |
0aacf84e MD |
4671 | else if (SCM_BIGP (x)) |
4672 | { | |
e11e83f3 | 4673 | if (SCM_I_INUMP (y)) |
0aacf84e | 4674 | { |
e11e83f3 | 4675 | long int yy = SCM_I_INUM (y); |
0aacf84e MD |
4676 | if (yy == 0) |
4677 | { | |
7351e207 | 4678 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4679 | scm_num_overflow (s_divide); |
7351e207 | 4680 | #else |
0aacf84e MD |
4681 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4682 | scm_remember_upto_here_1 (x); | |
4683 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 4684 | #endif |
0aacf84e MD |
4685 | } |
4686 | else if (yy == 1) | |
4687 | return x; | |
4688 | else | |
4689 | { | |
4690 | /* FIXME: HMM, what are the relative performance issues here? | |
4691 | We need to test. Is it faster on average to test | |
4692 | divisible_p, then perform whichever operation, or is it | |
4693 | faster to perform the integer div opportunistically and | |
4694 | switch to real if there's a remainder? For now we take the | |
4695 | middle ground: test, then if divisible, use the faster div | |
4696 | func. */ | |
4697 | ||
4698 | long abs_yy = yy < 0 ? -yy : yy; | |
4699 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); | |
4700 | ||
4701 | if (divisible_p) | |
4702 | { | |
4703 | SCM result = scm_i_mkbig (); | |
4704 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
4705 | scm_remember_upto_here_1 (x); | |
4706 | if (yy < 0) | |
4707 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4708 | return scm_i_normbig (result); | |
4709 | } | |
4710 | else | |
f92e85f7 MV |
4711 | { |
4712 | if (inexact) | |
55f26379 | 4713 | return scm_from_double (scm_i_big2dbl (x) / (double) yy); |
cba42c93 | 4714 | else return scm_i_make_ratio (x, y); |
f92e85f7 | 4715 | } |
0aacf84e MD |
4716 | } |
4717 | } | |
4718 | else if (SCM_BIGP (y)) | |
4719 | { | |
4720 | int y_is_zero = (mpz_sgn (SCM_I_BIG_MPZ (y)) == 0); | |
4721 | if (y_is_zero) | |
4722 | { | |
ca46fb90 | 4723 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4724 | scm_num_overflow (s_divide); |
f872b822 | 4725 | #else |
0aacf84e MD |
4726 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4727 | scm_remember_upto_here_1 (x); | |
4728 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
f872b822 | 4729 | #endif |
0aacf84e MD |
4730 | } |
4731 | else | |
4732 | { | |
4733 | /* big_x / big_y */ | |
4734 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), | |
4735 | SCM_I_BIG_MPZ (y)); | |
4736 | if (divisible_p) | |
4737 | { | |
4738 | SCM result = scm_i_mkbig (); | |
4739 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
4740 | SCM_I_BIG_MPZ (x), | |
4741 | SCM_I_BIG_MPZ (y)); | |
4742 | scm_remember_upto_here_2 (x, y); | |
4743 | return scm_i_normbig (result); | |
4744 | } | |
4745 | else | |
4746 | { | |
f92e85f7 MV |
4747 | if (inexact) |
4748 | { | |
4749 | double dbx = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4750 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4751 | scm_remember_upto_here_2 (x, y); | |
55f26379 | 4752 | return scm_from_double (dbx / dby); |
f92e85f7 | 4753 | } |
cba42c93 | 4754 | else return scm_i_make_ratio (x, y); |
0aacf84e MD |
4755 | } |
4756 | } | |
4757 | } | |
4758 | else if (SCM_REALP (y)) | |
4759 | { | |
4760 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4761 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4762 | if (yy == 0.0) |
4763 | scm_num_overflow (s_divide); | |
4764 | else | |
7351e207 | 4765 | #endif |
55f26379 | 4766 | return scm_from_double (scm_i_big2dbl (x) / yy); |
0aacf84e MD |
4767 | } |
4768 | else if (SCM_COMPLEXP (y)) | |
4769 | { | |
4770 | a = scm_i_big2dbl (x); | |
4771 | goto complex_div; | |
4772 | } | |
f92e85f7 | 4773 | else if (SCM_FRACTIONP (y)) |
cba42c93 | 4774 | return scm_i_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 | 4775 | SCM_FRACTION_NUMERATOR (y)); |
0aacf84e MD |
4776 | else |
4777 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4778 | } |
0aacf84e MD |
4779 | else if (SCM_REALP (x)) |
4780 | { | |
4781 | double rx = SCM_REAL_VALUE (x); | |
e11e83f3 | 4782 | if (SCM_I_INUMP (y)) |
0aacf84e | 4783 | { |
e11e83f3 | 4784 | long int yy = SCM_I_INUM (y); |
7351e207 | 4785 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4786 | if (yy == 0) |
4787 | scm_num_overflow (s_divide); | |
4788 | else | |
7351e207 | 4789 | #endif |
55f26379 | 4790 | return scm_from_double (rx / (double) yy); |
0aacf84e MD |
4791 | } |
4792 | else if (SCM_BIGP (y)) | |
4793 | { | |
4794 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4795 | scm_remember_upto_here_1 (y); | |
55f26379 | 4796 | return scm_from_double (rx / dby); |
0aacf84e MD |
4797 | } |
4798 | else if (SCM_REALP (y)) | |
4799 | { | |
4800 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4801 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4802 | if (yy == 0.0) |
4803 | scm_num_overflow (s_divide); | |
4804 | else | |
7351e207 | 4805 | #endif |
55f26379 | 4806 | return scm_from_double (rx / yy); |
0aacf84e MD |
4807 | } |
4808 | else if (SCM_COMPLEXP (y)) | |
4809 | { | |
4810 | a = rx; | |
4811 | goto complex_div; | |
4812 | } | |
f92e85f7 | 4813 | else if (SCM_FRACTIONP (y)) |
55f26379 | 4814 | return scm_from_double (rx / scm_i_fraction2double (y)); |
0aacf84e MD |
4815 | else |
4816 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4817 | } |
0aacf84e MD |
4818 | else if (SCM_COMPLEXP (x)) |
4819 | { | |
4820 | double rx = SCM_COMPLEX_REAL (x); | |
4821 | double ix = SCM_COMPLEX_IMAG (x); | |
e11e83f3 | 4822 | if (SCM_I_INUMP (y)) |
0aacf84e | 4823 | { |
e11e83f3 | 4824 | long int yy = SCM_I_INUM (y); |
7351e207 | 4825 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4826 | if (yy == 0) |
4827 | scm_num_overflow (s_divide); | |
4828 | else | |
7351e207 | 4829 | #endif |
0aacf84e MD |
4830 | { |
4831 | double d = yy; | |
8507ec80 | 4832 | return scm_c_make_rectangular (rx / d, ix / d); |
0aacf84e MD |
4833 | } |
4834 | } | |
4835 | else if (SCM_BIGP (y)) | |
4836 | { | |
4837 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4838 | scm_remember_upto_here_1 (y); | |
8507ec80 | 4839 | return scm_c_make_rectangular (rx / dby, ix / dby); |
0aacf84e MD |
4840 | } |
4841 | else if (SCM_REALP (y)) | |
4842 | { | |
4843 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4844 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4845 | if (yy == 0.0) |
4846 | scm_num_overflow (s_divide); | |
4847 | else | |
7351e207 | 4848 | #endif |
8507ec80 | 4849 | return scm_c_make_rectangular (rx / yy, ix / yy); |
0aacf84e MD |
4850 | } |
4851 | else if (SCM_COMPLEXP (y)) | |
4852 | { | |
4853 | double ry = SCM_COMPLEX_REAL (y); | |
4854 | double iy = SCM_COMPLEX_IMAG (y); | |
4855 | if (ry <= iy) | |
4856 | { | |
4857 | double t = ry / iy; | |
4858 | double d = iy * (1.0 + t * t); | |
8507ec80 | 4859 | return scm_c_make_rectangular ((rx * t + ix) / d, (ix * t - rx) / d); |
0aacf84e MD |
4860 | } |
4861 | else | |
4862 | { | |
4863 | double t = iy / ry; | |
4864 | double d = ry * (1.0 + t * t); | |
8507ec80 | 4865 | return scm_c_make_rectangular ((rx + ix * t) / d, (ix - rx * t) / d); |
0aacf84e MD |
4866 | } |
4867 | } | |
f92e85f7 MV |
4868 | else if (SCM_FRACTIONP (y)) |
4869 | { | |
4870 | double yy = scm_i_fraction2double (y); | |
8507ec80 | 4871 | return scm_c_make_rectangular (rx / yy, ix / yy); |
f92e85f7 | 4872 | } |
0aacf84e MD |
4873 | else |
4874 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4875 | } |
f92e85f7 MV |
4876 | else if (SCM_FRACTIONP (x)) |
4877 | { | |
e11e83f3 | 4878 | if (SCM_I_INUMP (y)) |
f92e85f7 | 4879 | { |
e11e83f3 | 4880 | long int yy = SCM_I_INUM (y); |
f92e85f7 MV |
4881 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
4882 | if (yy == 0) | |
4883 | scm_num_overflow (s_divide); | |
4884 | else | |
4885 | #endif | |
cba42c93 | 4886 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4887 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4888 | } | |
4889 | else if (SCM_BIGP (y)) | |
4890 | { | |
cba42c93 | 4891 | return scm_i_make_ratio (SCM_FRACTION_NUMERATOR (x), |
f92e85f7 MV |
4892 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); |
4893 | } | |
4894 | else if (SCM_REALP (y)) | |
4895 | { | |
4896 | double yy = SCM_REAL_VALUE (y); | |
4897 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
4898 | if (yy == 0.0) | |
4899 | scm_num_overflow (s_divide); | |
4900 | else | |
4901 | #endif | |
55f26379 | 4902 | return scm_from_double (scm_i_fraction2double (x) / yy); |
f92e85f7 MV |
4903 | } |
4904 | else if (SCM_COMPLEXP (y)) | |
4905 | { | |
4906 | a = scm_i_fraction2double (x); | |
4907 | goto complex_div; | |
4908 | } | |
4909 | else if (SCM_FRACTIONP (y)) | |
cba42c93 | 4910 | return scm_i_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), |
f92e85f7 MV |
4911 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); |
4912 | else | |
4913 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
4914 | } | |
0aacf84e | 4915 | else |
f8de44c1 | 4916 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 4917 | } |
f92e85f7 MV |
4918 | |
4919 | SCM | |
4920 | scm_divide (SCM x, SCM y) | |
4921 | { | |
4922 | return scm_i_divide (x, y, 0); | |
4923 | } | |
4924 | ||
4925 | static SCM scm_divide2real (SCM x, SCM y) | |
4926 | { | |
4927 | return scm_i_divide (x, y, 1); | |
4928 | } | |
c05e97b7 | 4929 | #undef FUNC_NAME |
0f2d19dd | 4930 | |
fa605590 | 4931 | |
0f2d19dd | 4932 | double |
6e8d25a6 | 4933 | scm_asinh (double x) |
0f2d19dd | 4934 | { |
fa605590 KR |
4935 | #if HAVE_ASINH |
4936 | return asinh (x); | |
4937 | #else | |
4938 | #define asinh scm_asinh | |
f872b822 | 4939 | return log (x + sqrt (x * x + 1)); |
fa605590 | 4940 | #endif |
0f2d19dd | 4941 | } |
fa605590 KR |
4942 | SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_dsubr, (SCM (*)()) asinh, g_asinh); |
4943 | /* "Return the inverse hyperbolic sine of @var{x}." | |
4944 | */ | |
0f2d19dd JB |
4945 | |
4946 | ||
0f2d19dd | 4947 | double |
6e8d25a6 | 4948 | scm_acosh (double x) |
0f2d19dd | 4949 | { |
fa605590 KR |
4950 | #if HAVE_ACOSH |
4951 | return acosh (x); | |
4952 | #else | |
4953 | #define acosh scm_acosh | |
f872b822 | 4954 | return log (x + sqrt (x * x - 1)); |
fa605590 | 4955 | #endif |
0f2d19dd | 4956 | } |
fa605590 KR |
4957 | SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_dsubr, (SCM (*)()) acosh, g_acosh); |
4958 | /* "Return the inverse hyperbolic cosine of @var{x}." | |
4959 | */ | |
0f2d19dd JB |
4960 | |
4961 | ||
0f2d19dd | 4962 | double |
6e8d25a6 | 4963 | scm_atanh (double x) |
0f2d19dd | 4964 | { |
fa605590 KR |
4965 | #if HAVE_ATANH |
4966 | return atanh (x); | |
4967 | #else | |
4968 | #define atanh scm_atanh | |
f872b822 | 4969 | return 0.5 * log ((1 + x) / (1 - x)); |
fa605590 | 4970 | #endif |
0f2d19dd | 4971 | } |
fa605590 KR |
4972 | SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_dsubr, (SCM (*)()) atanh, g_atanh); |
4973 | /* "Return the inverse hyperbolic tangent of @var{x}." | |
4974 | */ | |
0f2d19dd JB |
4975 | |
4976 | ||
0f2d19dd | 4977 | double |
3101f40f | 4978 | scm_c_truncate (double x) |
0f2d19dd | 4979 | { |
fa605590 KR |
4980 | #if HAVE_TRUNC |
4981 | return trunc (x); | |
4982 | #else | |
f872b822 MD |
4983 | if (x < 0.0) |
4984 | return -floor (-x); | |
4985 | return floor (x); | |
fa605590 | 4986 | #endif |
0f2d19dd | 4987 | } |
0f2d19dd | 4988 | |
3101f40f MV |
4989 | /* scm_c_round is done using floor(x+0.5) to round to nearest and with |
4990 | half-way case (ie. when x is an integer plus 0.5) going upwards. | |
4991 | Then half-way cases are identified and adjusted down if the | |
4992 | round-upwards didn't give the desired even integer. | |
6187f48b KR |
4993 | |
4994 | "plus_half == result" identifies a half-way case. If plus_half, which is | |
4995 | x + 0.5, is an integer then x must be an integer plus 0.5. | |
4996 | ||
4997 | An odd "result" value is identified with result/2 != floor(result/2). | |
4998 | This is done with plus_half, since that value is ready for use sooner in | |
4999 | a pipelined cpu, and we're already requiring plus_half == result. | |
5000 | ||
5001 | Note however that we need to be careful when x is big and already an | |
5002 | integer. In that case "x+0.5" may round to an adjacent integer, causing | |
5003 | us to return such a value, incorrectly. For instance if the hardware is | |
5004 | in the usual default nearest-even rounding, then for x = 0x1FFFFFFFFFFFFF | |
5005 | (ie. 53 one bits) we will have x+0.5 = 0x20000000000000 and that value | |
5006 | returned. Or if the hardware is in round-upwards mode, then other bigger | |
5007 | values like say x == 2^128 will see x+0.5 rounding up to the next higher | |
5008 | representable value, 2^128+2^76 (or whatever), again incorrect. | |
5009 | ||
5010 | These bad roundings of x+0.5 are avoided by testing at the start whether | |
5011 | x is already an integer. If it is then clearly that's the desired result | |
5012 | already. And if it's not then the exponent must be small enough to allow | |
5013 | an 0.5 to be represented, and hence added without a bad rounding. */ | |
5014 | ||
0f2d19dd | 5015 | double |
3101f40f | 5016 | scm_c_round (double x) |
0f2d19dd | 5017 | { |
6187f48b KR |
5018 | double plus_half, result; |
5019 | ||
5020 | if (x == floor (x)) | |
5021 | return x; | |
5022 | ||
5023 | plus_half = x + 0.5; | |
5024 | result = floor (plus_half); | |
3101f40f | 5025 | /* Adjust so that the rounding is towards even. */ |
0aacf84e MD |
5026 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
5027 | ? result - 1 | |
5028 | : result); | |
0f2d19dd JB |
5029 | } |
5030 | ||
f92e85f7 MV |
5031 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
5032 | (SCM x), | |
5033 | "Round the number @var{x} towards zero.") | |
5034 | #define FUNC_NAME s_scm_truncate_number | |
5035 | { | |
73e4de09 | 5036 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5037 | return scm_floor (x); |
5038 | else | |
5039 | return scm_ceiling (x); | |
5040 | } | |
5041 | #undef FUNC_NAME | |
5042 | ||
5043 | static SCM exactly_one_half; | |
5044 | ||
5045 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, | |
5046 | (SCM x), | |
5047 | "Round the number @var{x} towards the nearest integer. " | |
5048 | "When it is exactly halfway between two integers, " | |
5049 | "round towards the even one.") | |
5050 | #define FUNC_NAME s_scm_round_number | |
5051 | { | |
e11e83f3 | 5052 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
bae30667 KR |
5053 | return x; |
5054 | else if (SCM_REALP (x)) | |
3101f40f | 5055 | return scm_from_double (scm_c_round (SCM_REAL_VALUE (x))); |
f92e85f7 | 5056 | else |
bae30667 KR |
5057 | { |
5058 | /* OPTIMIZE-ME: Fraction case could be done more efficiently by a | |
5059 | single quotient+remainder division then examining to see which way | |
5060 | the rounding should go. */ | |
5061 | SCM plus_half = scm_sum (x, exactly_one_half); | |
5062 | SCM result = scm_floor (plus_half); | |
3101f40f | 5063 | /* Adjust so that the rounding is towards even. */ |
73e4de09 MV |
5064 | if (scm_is_true (scm_num_eq_p (plus_half, result)) |
5065 | && scm_is_true (scm_odd_p (result))) | |
d956fa6f | 5066 | return scm_difference (result, SCM_I_MAKINUM (1)); |
bae30667 KR |
5067 | else |
5068 | return result; | |
5069 | } | |
f92e85f7 MV |
5070 | } |
5071 | #undef FUNC_NAME | |
5072 | ||
5073 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
5074 | (SCM x), | |
5075 | "Round the number @var{x} towards minus infinity.") | |
5076 | #define FUNC_NAME s_scm_floor | |
5077 | { | |
e11e83f3 | 5078 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5079 | return x; |
5080 | else if (SCM_REALP (x)) | |
55f26379 | 5081 | return scm_from_double (floor (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5082 | else if (SCM_FRACTIONP (x)) |
5083 | { | |
5084 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5085 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5086 | if (scm_is_false (scm_negative_p (x))) |
f92e85f7 MV |
5087 | { |
5088 | /* For positive x, rounding towards zero is correct. */ | |
5089 | return q; | |
5090 | } | |
5091 | else | |
5092 | { | |
5093 | /* For negative x, we need to return q-1 unless x is an | |
5094 | integer. But fractions are never integer, per our | |
5095 | assumptions. */ | |
d956fa6f | 5096 | return scm_difference (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5097 | } |
5098 | } | |
5099 | else | |
5100 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
5101 | } | |
5102 | #undef FUNC_NAME | |
5103 | ||
5104 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
5105 | (SCM x), | |
5106 | "Round the number @var{x} towards infinity.") | |
5107 | #define FUNC_NAME s_scm_ceiling | |
5108 | { | |
e11e83f3 | 5109 | if (SCM_I_INUMP (x) || SCM_BIGP (x)) |
f92e85f7 MV |
5110 | return x; |
5111 | else if (SCM_REALP (x)) | |
55f26379 | 5112 | return scm_from_double (ceil (SCM_REAL_VALUE (x))); |
f92e85f7 MV |
5113 | else if (SCM_FRACTIONP (x)) |
5114 | { | |
5115 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
5116 | SCM_FRACTION_DENOMINATOR (x)); | |
73e4de09 | 5117 | if (scm_is_false (scm_positive_p (x))) |
f92e85f7 MV |
5118 | { |
5119 | /* For negative x, rounding towards zero is correct. */ | |
5120 | return q; | |
5121 | } | |
5122 | else | |
5123 | { | |
5124 | /* For positive x, we need to return q+1 unless x is an | |
5125 | integer. But fractions are never integer, per our | |
5126 | assumptions. */ | |
d956fa6f | 5127 | return scm_sum (q, SCM_I_MAKINUM (1)); |
f92e85f7 MV |
5128 | } |
5129 | } | |
5130 | else | |
5131 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
5132 | } | |
5133 | #undef FUNC_NAME | |
0f2d19dd | 5134 | |
14b18ed6 | 5135 | SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_dsubr, (SCM (*)()) sqrt, g_i_sqrt); |
942e5b91 MG |
5136 | /* "Return the square root of the real number @var{x}." |
5137 | */ | |
14b18ed6 | 5138 | SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_dsubr, (SCM (*)()) fabs, g_i_abs); |
942e5b91 MG |
5139 | /* "Return the absolute value of the real number @var{x}." |
5140 | */ | |
14b18ed6 | 5141 | SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_dsubr, (SCM (*)()) exp, g_i_exp); |
942e5b91 MG |
5142 | /* "Return the @var{x}th power of e." |
5143 | */ | |
14b18ed6 | 5144 | SCM_GPROC1 (s_i_log, "$log", scm_tc7_dsubr, (SCM (*)()) log, g_i_log); |
b3fcac34 | 5145 | /* "Return the natural logarithm of the real number @var{x}." |
942e5b91 | 5146 | */ |
14b18ed6 | 5147 | SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_dsubr, (SCM (*)()) sin, g_i_sin); |
942e5b91 MG |
5148 | /* "Return the sine of the real number @var{x}." |
5149 | */ | |
14b18ed6 | 5150 | SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_dsubr, (SCM (*)()) cos, g_i_cos); |
942e5b91 MG |
5151 | /* "Return the cosine of the real number @var{x}." |
5152 | */ | |
14b18ed6 | 5153 | SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_dsubr, (SCM (*)()) tan, g_i_tan); |
942e5b91 MG |
5154 | /* "Return the tangent of the real number @var{x}." |
5155 | */ | |
14b18ed6 | 5156 | SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_dsubr, (SCM (*)()) asin, g_i_asin); |
942e5b91 MG |
5157 | /* "Return the arc sine of the real number @var{x}." |
5158 | */ | |
14b18ed6 | 5159 | SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_dsubr, (SCM (*)()) acos, g_i_acos); |
942e5b91 MG |
5160 | /* "Return the arc cosine of the real number @var{x}." |
5161 | */ | |
14b18ed6 | 5162 | SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_dsubr, (SCM (*)()) atan, g_i_atan); |
942e5b91 MG |
5163 | /* "Return the arc tangent of the real number @var{x}." |
5164 | */ | |
14b18ed6 | 5165 | SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_dsubr, (SCM (*)()) sinh, g_i_sinh); |
942e5b91 MG |
5166 | /* "Return the hyperbolic sine of the real number @var{x}." |
5167 | */ | |
14b18ed6 | 5168 | SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_dsubr, (SCM (*)()) cosh, g_i_cosh); |
942e5b91 MG |
5169 | /* "Return the hyperbolic cosine of the real number @var{x}." |
5170 | */ | |
14b18ed6 | 5171 | SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_dsubr, (SCM (*)()) tanh, g_i_tanh); |
942e5b91 MG |
5172 | /* "Return the hyperbolic tangent of the real number @var{x}." |
5173 | */ | |
f872b822 MD |
5174 | |
5175 | struct dpair | |
5176 | { | |
5177 | double x, y; | |
5178 | }; | |
5179 | ||
27c37006 NJ |
5180 | static void scm_two_doubles (SCM x, |
5181 | SCM y, | |
3eeba8d4 JB |
5182 | const char *sstring, |
5183 | struct dpair * xy); | |
f872b822 MD |
5184 | |
5185 | static void | |
27c37006 NJ |
5186 | scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy) |
5187 | { | |
e11e83f3 MV |
5188 | if (SCM_I_INUMP (x)) |
5189 | xy->x = SCM_I_INUM (x); | |
0aacf84e | 5190 | else if (SCM_BIGP (x)) |
1be6b49c | 5191 | xy->x = scm_i_big2dbl (x); |
0aacf84e | 5192 | else if (SCM_REALP (x)) |
27c37006 | 5193 | xy->x = SCM_REAL_VALUE (x); |
f92e85f7 MV |
5194 | else if (SCM_FRACTIONP (x)) |
5195 | xy->x = scm_i_fraction2double (x); | |
0aacf84e | 5196 | else |
27c37006 | 5197 | scm_wrong_type_arg (sstring, SCM_ARG1, x); |
98cb6e75 | 5198 | |
e11e83f3 MV |
5199 | if (SCM_I_INUMP (y)) |
5200 | xy->y = SCM_I_INUM (y); | |
0aacf84e | 5201 | else if (SCM_BIGP (y)) |
1be6b49c | 5202 | xy->y = scm_i_big2dbl (y); |
0aacf84e | 5203 | else if (SCM_REALP (y)) |
27c37006 | 5204 | xy->y = SCM_REAL_VALUE (y); |
f92e85f7 MV |
5205 | else if (SCM_FRACTIONP (y)) |
5206 | xy->y = scm_i_fraction2double (y); | |
0aacf84e | 5207 | else |
27c37006 | 5208 | scm_wrong_type_arg (sstring, SCM_ARG2, y); |
0f2d19dd JB |
5209 | } |
5210 | ||
5211 | ||
a1ec6916 | 5212 | SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0, |
27c37006 NJ |
5213 | (SCM x, SCM y), |
5214 | "Return @var{x} raised to the power of @var{y}. This\n" | |
0137a31b | 5215 | "procedure does not accept complex arguments.") |
1bbd0b84 | 5216 | #define FUNC_NAME s_scm_sys_expt |
0f2d19dd JB |
5217 | { |
5218 | struct dpair xy; | |
27c37006 | 5219 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5220 | return scm_from_double (pow (xy.x, xy.y)); |
0f2d19dd | 5221 | } |
1bbd0b84 | 5222 | #undef FUNC_NAME |
0f2d19dd JB |
5223 | |
5224 | ||
a1ec6916 | 5225 | SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0, |
27c37006 NJ |
5226 | (SCM x, SCM y), |
5227 | "Return the arc tangent of the two arguments @var{x} and\n" | |
5228 | "@var{y}. This is similar to calculating the arc tangent of\n" | |
5229 | "@var{x} / @var{y}, except that the signs of both arguments\n" | |
0137a31b MG |
5230 | "are used to determine the quadrant of the result. This\n" |
5231 | "procedure does not accept complex arguments.") | |
1bbd0b84 | 5232 | #define FUNC_NAME s_scm_sys_atan2 |
0f2d19dd JB |
5233 | { |
5234 | struct dpair xy; | |
27c37006 | 5235 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
55f26379 | 5236 | return scm_from_double (atan2 (xy.x, xy.y)); |
0f2d19dd | 5237 | } |
1bbd0b84 | 5238 | #undef FUNC_NAME |
0f2d19dd | 5239 | |
8507ec80 MV |
5240 | SCM |
5241 | scm_c_make_rectangular (double re, double im) | |
5242 | { | |
5243 | if (im == 0.0) | |
5244 | return scm_from_double (re); | |
5245 | else | |
5246 | { | |
5247 | SCM z; | |
5248 | SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (sizeof (scm_t_complex), | |
5249 | "complex")); | |
5250 | SCM_COMPLEX_REAL (z) = re; | |
5251 | SCM_COMPLEX_IMAG (z) = im; | |
5252 | return z; | |
5253 | } | |
5254 | } | |
0f2d19dd | 5255 | |
a1ec6916 | 5256 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
bb628794 | 5257 | (SCM real, SCM imaginary), |
942e5b91 MG |
5258 | "Return a complex number constructed of the given @var{real} and\n" |
5259 | "@var{imaginary} parts.") | |
1bbd0b84 | 5260 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd JB |
5261 | { |
5262 | struct dpair xy; | |
bb628794 | 5263 | scm_two_doubles (real, imaginary, FUNC_NAME, &xy); |
8507ec80 | 5264 | return scm_c_make_rectangular (xy.x, xy.y); |
0f2d19dd | 5265 | } |
1bbd0b84 | 5266 | #undef FUNC_NAME |
0f2d19dd | 5267 | |
8507ec80 MV |
5268 | SCM |
5269 | scm_c_make_polar (double mag, double ang) | |
5270 | { | |
5271 | double s, c; | |
5272 | #if HAVE_SINCOS | |
5273 | sincos (ang, &s, &c); | |
5274 | #else | |
5275 | s = sin (ang); | |
5276 | c = cos (ang); | |
5277 | #endif | |
5278 | return scm_c_make_rectangular (mag * c, mag * s); | |
5279 | } | |
0f2d19dd | 5280 | |
a1ec6916 | 5281 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 5282 | (SCM x, SCM y), |
942e5b91 | 5283 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 5284 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd JB |
5285 | { |
5286 | struct dpair xy; | |
27c37006 | 5287 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
8507ec80 | 5288 | return scm_c_make_polar (xy.x, xy.y); |
0f2d19dd | 5289 | } |
1bbd0b84 | 5290 | #undef FUNC_NAME |
0f2d19dd JB |
5291 | |
5292 | ||
152f82bf | 5293 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
5294 | /* "Return the real part of the number @var{z}." |
5295 | */ | |
0f2d19dd | 5296 | SCM |
6e8d25a6 | 5297 | scm_real_part (SCM z) |
0f2d19dd | 5298 | { |
e11e83f3 | 5299 | if (SCM_I_INUMP (z)) |
c2ff8ab0 | 5300 | return z; |
0aacf84e | 5301 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5302 | return z; |
0aacf84e | 5303 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5304 | return z; |
0aacf84e | 5305 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5306 | return scm_from_double (SCM_COMPLEX_REAL (z)); |
f92e85f7 | 5307 | else if (SCM_FRACTIONP (z)) |
2fa2d879 | 5308 | return z; |
0aacf84e | 5309 | else |
c2ff8ab0 | 5310 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); |
0f2d19dd JB |
5311 | } |
5312 | ||
5313 | ||
152f82bf | 5314 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
5315 | /* "Return the imaginary part of the number @var{z}." |
5316 | */ | |
0f2d19dd | 5317 | SCM |
6e8d25a6 | 5318 | scm_imag_part (SCM z) |
0f2d19dd | 5319 | { |
e11e83f3 | 5320 | if (SCM_I_INUMP (z)) |
f872b822 | 5321 | return SCM_INUM0; |
0aacf84e | 5322 | else if (SCM_BIGP (z)) |
f872b822 | 5323 | return SCM_INUM0; |
0aacf84e | 5324 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5325 | return scm_flo0; |
0aacf84e | 5326 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5327 | return scm_from_double (SCM_COMPLEX_IMAG (z)); |
f92e85f7 MV |
5328 | else if (SCM_FRACTIONP (z)) |
5329 | return SCM_INUM0; | |
0aacf84e | 5330 | else |
c2ff8ab0 | 5331 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); |
0f2d19dd JB |
5332 | } |
5333 | ||
f92e85f7 MV |
5334 | SCM_GPROC (s_numerator, "numerator", 1, 0, 0, scm_numerator, g_numerator); |
5335 | /* "Return the numerator of the number @var{z}." | |
5336 | */ | |
5337 | SCM | |
5338 | scm_numerator (SCM z) | |
5339 | { | |
e11e83f3 | 5340 | if (SCM_I_INUMP (z)) |
f92e85f7 MV |
5341 | return z; |
5342 | else if (SCM_BIGP (z)) | |
5343 | return z; | |
5344 | else if (SCM_FRACTIONP (z)) | |
5345 | { | |
5346 | scm_i_fraction_reduce (z); | |
5347 | return SCM_FRACTION_NUMERATOR (z); | |
5348 | } | |
5349 | else if (SCM_REALP (z)) | |
5350 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
5351 | else | |
5352 | SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator); | |
5353 | } | |
5354 | ||
5355 | ||
5356 | SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator); | |
5357 | /* "Return the denominator of the number @var{z}." | |
5358 | */ | |
5359 | SCM | |
5360 | scm_denominator (SCM z) | |
5361 | { | |
e11e83f3 | 5362 | if (SCM_I_INUMP (z)) |
d956fa6f | 5363 | return SCM_I_MAKINUM (1); |
f92e85f7 | 5364 | else if (SCM_BIGP (z)) |
d956fa6f | 5365 | return SCM_I_MAKINUM (1); |
f92e85f7 MV |
5366 | else if (SCM_FRACTIONP (z)) |
5367 | { | |
5368 | scm_i_fraction_reduce (z); | |
5369 | return SCM_FRACTION_DENOMINATOR (z); | |
5370 | } | |
5371 | else if (SCM_REALP (z)) | |
5372 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
5373 | else | |
5374 | SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator); | |
5375 | } | |
0f2d19dd | 5376 | |
9de33deb | 5377 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
5378 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
5379 | * "@code{abs} for real arguments, but also allows complex numbers." | |
5380 | */ | |
0f2d19dd | 5381 | SCM |
6e8d25a6 | 5382 | scm_magnitude (SCM z) |
0f2d19dd | 5383 | { |
e11e83f3 | 5384 | if (SCM_I_INUMP (z)) |
0aacf84e | 5385 | { |
e11e83f3 | 5386 | long int zz = SCM_I_INUM (z); |
0aacf84e MD |
5387 | if (zz >= 0) |
5388 | return z; | |
5389 | else if (SCM_POSFIXABLE (-zz)) | |
d956fa6f | 5390 | return SCM_I_MAKINUM (-zz); |
0aacf84e MD |
5391 | else |
5392 | return scm_i_long2big (-zz); | |
5986c47d | 5393 | } |
0aacf84e MD |
5394 | else if (SCM_BIGP (z)) |
5395 | { | |
5396 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5397 | scm_remember_upto_here_1 (z); | |
5398 | if (sgn < 0) | |
5399 | return scm_i_clonebig (z, 0); | |
5400 | else | |
5401 | return z; | |
5986c47d | 5402 | } |
0aacf84e | 5403 | else if (SCM_REALP (z)) |
55f26379 | 5404 | return scm_from_double (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 5405 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5406 | return scm_from_double (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
5407 | else if (SCM_FRACTIONP (z)) |
5408 | { | |
73e4de09 | 5409 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5410 | return z; |
cba42c93 | 5411 | return scm_i_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), |
f92e85f7 MV |
5412 | SCM_FRACTION_DENOMINATOR (z)); |
5413 | } | |
0aacf84e | 5414 | else |
c2ff8ab0 | 5415 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); |
0f2d19dd JB |
5416 | } |
5417 | ||
5418 | ||
9de33deb | 5419 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
5420 | /* "Return the angle of the complex number @var{z}." |
5421 | */ | |
0f2d19dd | 5422 | SCM |
6e8d25a6 | 5423 | scm_angle (SCM z) |
0f2d19dd | 5424 | { |
c8ae173e | 5425 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
55f26379 | 5426 | scm_flo0 to save allocating a new flonum with scm_from_double each time. |
c8ae173e KR |
5427 | But if atan2 follows the floating point rounding mode, then the value |
5428 | is not a constant. Maybe it'd be close enough though. */ | |
e11e83f3 | 5429 | if (SCM_I_INUMP (z)) |
0aacf84e | 5430 | { |
e11e83f3 | 5431 | if (SCM_I_INUM (z) >= 0) |
c8ae173e | 5432 | return scm_flo0; |
0aacf84e | 5433 | else |
55f26379 | 5434 | return scm_from_double (atan2 (0.0, -1.0)); |
f872b822 | 5435 | } |
0aacf84e MD |
5436 | else if (SCM_BIGP (z)) |
5437 | { | |
5438 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5439 | scm_remember_upto_here_1 (z); | |
5440 | if (sgn < 0) | |
55f26379 | 5441 | return scm_from_double (atan2 (0.0, -1.0)); |
0aacf84e | 5442 | else |
c8ae173e | 5443 | return scm_flo0; |
0f2d19dd | 5444 | } |
0aacf84e | 5445 | else if (SCM_REALP (z)) |
c8ae173e KR |
5446 | { |
5447 | if (SCM_REAL_VALUE (z) >= 0) | |
5448 | return scm_flo0; | |
5449 | else | |
55f26379 | 5450 | return scm_from_double (atan2 (0.0, -1.0)); |
c8ae173e | 5451 | } |
0aacf84e | 5452 | else if (SCM_COMPLEXP (z)) |
55f26379 | 5453 | return scm_from_double (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
5454 | else if (SCM_FRACTIONP (z)) |
5455 | { | |
73e4de09 | 5456 | if (scm_is_false (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) |
f92e85f7 | 5457 | return scm_flo0; |
55f26379 | 5458 | else return scm_from_double (atan2 (0.0, -1.0)); |
f92e85f7 | 5459 | } |
0aacf84e | 5460 | else |
f4c627b3 | 5461 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); |
0f2d19dd JB |
5462 | } |
5463 | ||
5464 | ||
3c9a524f DH |
5465 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
5466 | /* Convert the number @var{x} to its inexact representation.\n" | |
5467 | */ | |
5468 | SCM | |
5469 | scm_exact_to_inexact (SCM z) | |
5470 | { | |
e11e83f3 | 5471 | if (SCM_I_INUMP (z)) |
55f26379 | 5472 | return scm_from_double ((double) SCM_I_INUM (z)); |
3c9a524f | 5473 | else if (SCM_BIGP (z)) |
55f26379 | 5474 | return scm_from_double (scm_i_big2dbl (z)); |
f92e85f7 | 5475 | else if (SCM_FRACTIONP (z)) |
55f26379 | 5476 | return scm_from_double (scm_i_fraction2double (z)); |
3c9a524f DH |
5477 | else if (SCM_INEXACTP (z)) |
5478 | return z; | |
5479 | else | |
5480 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
5481 | } | |
5482 | ||
5483 | ||
a1ec6916 | 5484 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 5485 | (SCM z), |
1e6808ea | 5486 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 5487 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 5488 | { |
e11e83f3 | 5489 | if (SCM_I_INUMP (z)) |
f872b822 | 5490 | return z; |
0aacf84e | 5491 | else if (SCM_BIGP (z)) |
f872b822 | 5492 | return z; |
0aacf84e MD |
5493 | else if (SCM_REALP (z)) |
5494 | { | |
f92e85f7 MV |
5495 | if (xisinf (SCM_REAL_VALUE (z)) || xisnan (SCM_REAL_VALUE (z))) |
5496 | SCM_OUT_OF_RANGE (1, z); | |
2be24db4 | 5497 | else |
f92e85f7 MV |
5498 | { |
5499 | mpq_t frac; | |
5500 | SCM q; | |
5501 | ||
5502 | mpq_init (frac); | |
5503 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
cba42c93 | 5504 | q = scm_i_make_ratio (scm_i_mpz2num (mpq_numref (frac)), |
f92e85f7 MV |
5505 | scm_i_mpz2num (mpq_denref (frac))); |
5506 | ||
cba42c93 | 5507 | /* When scm_i_make_ratio throws, we leak the memory allocated |
f92e85f7 MV |
5508 | for frac... |
5509 | */ | |
5510 | mpq_clear (frac); | |
5511 | return q; | |
5512 | } | |
c2ff8ab0 | 5513 | } |
f92e85f7 MV |
5514 | else if (SCM_FRACTIONP (z)) |
5515 | return z; | |
0aacf84e | 5516 | else |
c2ff8ab0 | 5517 | SCM_WRONG_TYPE_ARG (1, z); |
0f2d19dd | 5518 | } |
1bbd0b84 | 5519 | #undef FUNC_NAME |
0f2d19dd | 5520 | |
f92e85f7 MV |
5521 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
5522 | (SCM x, SCM err), | |
5523 | "Return an exact number that is within @var{err} of @var{x}.") | |
5524 | #define FUNC_NAME s_scm_rationalize | |
5525 | { | |
e11e83f3 | 5526 | if (SCM_I_INUMP (x)) |
f92e85f7 MV |
5527 | return x; |
5528 | else if (SCM_BIGP (x)) | |
5529 | return x; | |
5530 | else if ((SCM_REALP (x)) || SCM_FRACTIONP (x)) | |
5531 | { | |
5532 | /* Use continued fractions to find closest ratio. All | |
5533 | arithmetic is done with exact numbers. | |
5534 | */ | |
5535 | ||
5536 | SCM ex = scm_inexact_to_exact (x); | |
5537 | SCM int_part = scm_floor (ex); | |
d956fa6f MV |
5538 | SCM tt = SCM_I_MAKINUM (1); |
5539 | SCM a1 = SCM_I_MAKINUM (0), a2 = SCM_I_MAKINUM (1), a = SCM_I_MAKINUM (0); | |
5540 | SCM b1 = SCM_I_MAKINUM (1), b2 = SCM_I_MAKINUM (0), b = SCM_I_MAKINUM (0); | |
f92e85f7 MV |
5541 | SCM rx; |
5542 | int i = 0; | |
5543 | ||
73e4de09 | 5544 | if (scm_is_true (scm_num_eq_p (ex, int_part))) |
f92e85f7 MV |
5545 | return ex; |
5546 | ||
5547 | ex = scm_difference (ex, int_part); /* x = x-int_part */ | |
5548 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
5549 | ||
5550 | /* We stop after a million iterations just to be absolutely sure | |
5551 | that we don't go into an infinite loop. The process normally | |
5552 | converges after less than a dozen iterations. | |
5553 | */ | |
5554 | ||
5555 | err = scm_abs (err); | |
5556 | while (++i < 1000000) | |
5557 | { | |
5558 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
5559 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
73e4de09 MV |
5560 | if (scm_is_false (scm_zero_p (b)) && /* b != 0 */ |
5561 | scm_is_false | |
f92e85f7 MV |
5562 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), |
5563 | err))) /* abs(x-a/b) <= err */ | |
02164269 MV |
5564 | { |
5565 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
73e4de09 MV |
5566 | if (scm_is_false (scm_exact_p (x)) |
5567 | || scm_is_false (scm_exact_p (err))) | |
02164269 MV |
5568 | return scm_exact_to_inexact (res); |
5569 | else | |
5570 | return res; | |
5571 | } | |
f92e85f7 MV |
5572 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
5573 | SCM_UNDEFINED); | |
5574 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
5575 | a2 = a1; | |
5576 | b2 = b1; | |
5577 | a1 = a; | |
5578 | b1 = b; | |
5579 | } | |
5580 | scm_num_overflow (s_scm_rationalize); | |
5581 | } | |
5582 | else | |
5583 | SCM_WRONG_TYPE_ARG (1, x); | |
5584 | } | |
5585 | #undef FUNC_NAME | |
5586 | ||
73e4de09 MV |
5587 | /* conversion functions */ |
5588 | ||
5589 | int | |
5590 | scm_is_integer (SCM val) | |
5591 | { | |
5592 | return scm_is_true (scm_integer_p (val)); | |
5593 | } | |
5594 | ||
5595 | int | |
5596 | scm_is_signed_integer (SCM val, scm_t_intmax min, scm_t_intmax max) | |
5597 | { | |
e11e83f3 | 5598 | if (SCM_I_INUMP (val)) |
73e4de09 | 5599 | { |
e11e83f3 | 5600 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5601 | return n >= min && n <= max; |
5602 | } | |
5603 | else if (SCM_BIGP (val)) | |
5604 | { | |
5605 | if (min >= SCM_MOST_NEGATIVE_FIXNUM && max <= SCM_MOST_POSITIVE_FIXNUM) | |
5606 | return 0; | |
5607 | else if (min >= LONG_MIN && max <= LONG_MAX) | |
d956fa6f MV |
5608 | { |
5609 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (val))) | |
5610 | { | |
5611 | long n = mpz_get_si (SCM_I_BIG_MPZ (val)); | |
5612 | return n >= min && n <= max; | |
5613 | } | |
5614 | else | |
5615 | return 0; | |
5616 | } | |
73e4de09 MV |
5617 | else |
5618 | { | |
d956fa6f MV |
5619 | scm_t_intmax n; |
5620 | size_t count; | |
73e4de09 | 5621 | |
d956fa6f MV |
5622 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5623 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
5624 | return 0; | |
5625 | ||
5626 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5627 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5628 | |
d956fa6f | 5629 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) >= 0) |
73e4de09 | 5630 | { |
d956fa6f MV |
5631 | if (n < 0) |
5632 | return 0; | |
73e4de09 | 5633 | } |
73e4de09 MV |
5634 | else |
5635 | { | |
d956fa6f MV |
5636 | n = -n; |
5637 | if (n >= 0) | |
5638 | return 0; | |
73e4de09 | 5639 | } |
d956fa6f MV |
5640 | |
5641 | return n >= min && n <= max; | |
73e4de09 MV |
5642 | } |
5643 | } | |
73e4de09 MV |
5644 | else |
5645 | return 0; | |
5646 | } | |
5647 | ||
5648 | int | |
5649 | scm_is_unsigned_integer (SCM val, scm_t_uintmax min, scm_t_uintmax max) | |
5650 | { | |
e11e83f3 | 5651 | if (SCM_I_INUMP (val)) |
73e4de09 | 5652 | { |
e11e83f3 | 5653 | scm_t_signed_bits n = SCM_I_INUM (val); |
73e4de09 MV |
5654 | return n >= 0 && ((scm_t_uintmax)n) >= min && ((scm_t_uintmax)n) <= max; |
5655 | } | |
5656 | else if (SCM_BIGP (val)) | |
5657 | { | |
5658 | if (max <= SCM_MOST_POSITIVE_FIXNUM) | |
5659 | return 0; | |
5660 | else if (max <= ULONG_MAX) | |
d956fa6f MV |
5661 | { |
5662 | if (mpz_fits_ulong_p (SCM_I_BIG_MPZ (val))) | |
5663 | { | |
5664 | unsigned long n = mpz_get_ui (SCM_I_BIG_MPZ (val)); | |
5665 | return n >= min && n <= max; | |
5666 | } | |
5667 | else | |
5668 | return 0; | |
5669 | } | |
73e4de09 MV |
5670 | else |
5671 | { | |
d956fa6f MV |
5672 | scm_t_uintmax n; |
5673 | size_t count; | |
73e4de09 | 5674 | |
d956fa6f MV |
5675 | if (mpz_sgn (SCM_I_BIG_MPZ (val)) < 0) |
5676 | return 0; | |
73e4de09 | 5677 | |
d956fa6f MV |
5678 | if (mpz_sizeinbase (SCM_I_BIG_MPZ (val), 2) |
5679 | > CHAR_BIT*sizeof (scm_t_uintmax)) | |
73e4de09 | 5680 | return 0; |
d956fa6f MV |
5681 | |
5682 | mpz_export (&n, &count, 1, sizeof (scm_t_uintmax), 0, 0, | |
5683 | SCM_I_BIG_MPZ (val)); | |
73e4de09 | 5684 | |
d956fa6f | 5685 | return n >= min && n <= max; |
73e4de09 MV |
5686 | } |
5687 | } | |
73e4de09 MV |
5688 | else |
5689 | return 0; | |
5690 | } | |
5691 | ||
1713d319 MV |
5692 | static void |
5693 | scm_i_range_error (SCM bad_val, SCM min, SCM max) | |
5694 | { | |
5695 | scm_error (scm_out_of_range_key, | |
5696 | NULL, | |
5697 | "Value out of range ~S to ~S: ~S", | |
5698 | scm_list_3 (min, max, bad_val), | |
5699 | scm_list_1 (bad_val)); | |
5700 | } | |
5701 | ||
bfd7932e MV |
5702 | #define TYPE scm_t_intmax |
5703 | #define TYPE_MIN min | |
5704 | #define TYPE_MAX max | |
5705 | #define SIZEOF_TYPE 0 | |
5706 | #define SCM_TO_TYPE_PROTO(arg) scm_to_signed_integer (arg, scm_t_intmax min, scm_t_intmax max) | |
5707 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_signed_integer (arg) | |
5708 | #include "libguile/conv-integer.i.c" | |
5709 | ||
5710 | #define TYPE scm_t_uintmax | |
5711 | #define TYPE_MIN min | |
5712 | #define TYPE_MAX max | |
5713 | #define SIZEOF_TYPE 0 | |
5714 | #define SCM_TO_TYPE_PROTO(arg) scm_to_unsigned_integer (arg, scm_t_uintmax min, scm_t_uintmax max) | |
5715 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_unsigned_integer (arg) | |
5716 | #include "libguile/conv-uinteger.i.c" | |
5717 | ||
5718 | #define TYPE scm_t_int8 | |
5719 | #define TYPE_MIN SCM_T_INT8_MIN | |
5720 | #define TYPE_MAX SCM_T_INT8_MAX | |
5721 | #define SIZEOF_TYPE 1 | |
5722 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int8 (arg) | |
5723 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int8 (arg) | |
5724 | #include "libguile/conv-integer.i.c" | |
5725 | ||
5726 | #define TYPE scm_t_uint8 | |
5727 | #define TYPE_MIN 0 | |
5728 | #define TYPE_MAX SCM_T_UINT8_MAX | |
5729 | #define SIZEOF_TYPE 1 | |
5730 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint8 (arg) | |
5731 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint8 (arg) | |
5732 | #include "libguile/conv-uinteger.i.c" | |
5733 | ||
5734 | #define TYPE scm_t_int16 | |
5735 | #define TYPE_MIN SCM_T_INT16_MIN | |
5736 | #define TYPE_MAX SCM_T_INT16_MAX | |
5737 | #define SIZEOF_TYPE 2 | |
5738 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int16 (arg) | |
5739 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int16 (arg) | |
5740 | #include "libguile/conv-integer.i.c" | |
5741 | ||
5742 | #define TYPE scm_t_uint16 | |
5743 | #define TYPE_MIN 0 | |
5744 | #define TYPE_MAX SCM_T_UINT16_MAX | |
5745 | #define SIZEOF_TYPE 2 | |
5746 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint16 (arg) | |
5747 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint16 (arg) | |
5748 | #include "libguile/conv-uinteger.i.c" | |
5749 | ||
5750 | #define TYPE scm_t_int32 | |
5751 | #define TYPE_MIN SCM_T_INT32_MIN | |
5752 | #define TYPE_MAX SCM_T_INT32_MAX | |
5753 | #define SIZEOF_TYPE 4 | |
5754 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int32 (arg) | |
5755 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int32 (arg) | |
5756 | #include "libguile/conv-integer.i.c" | |
5757 | ||
5758 | #define TYPE scm_t_uint32 | |
5759 | #define TYPE_MIN 0 | |
5760 | #define TYPE_MAX SCM_T_UINT32_MAX | |
5761 | #define SIZEOF_TYPE 4 | |
5762 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint32 (arg) | |
5763 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint32 (arg) | |
5764 | #include "libguile/conv-uinteger.i.c" | |
5765 | ||
5766 | #if SCM_HAVE_T_INT64 | |
5767 | ||
5768 | #define TYPE scm_t_int64 | |
5769 | #define TYPE_MIN SCM_T_INT64_MIN | |
5770 | #define TYPE_MAX SCM_T_INT64_MAX | |
5771 | #define SIZEOF_TYPE 8 | |
5772 | #define SCM_TO_TYPE_PROTO(arg) scm_to_int64 (arg) | |
5773 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_int64 (arg) | |
5774 | #include "libguile/conv-integer.i.c" | |
5775 | ||
5776 | #define TYPE scm_t_uint64 | |
5777 | #define TYPE_MIN 0 | |
5778 | #define TYPE_MAX SCM_T_UINT64_MAX | |
5779 | #define SIZEOF_TYPE 8 | |
5780 | #define SCM_TO_TYPE_PROTO(arg) scm_to_uint64 (arg) | |
5781 | #define SCM_FROM_TYPE_PROTO(arg) scm_from_uint64 (arg) | |
5782 | #include "libguile/conv-uinteger.i.c" | |
73e4de09 | 5783 | |
bfd7932e | 5784 | #endif |
73e4de09 | 5785 | |
cd036260 MV |
5786 | void |
5787 | scm_to_mpz (SCM val, mpz_t rop) | |
5788 | { | |
5789 | if (SCM_I_INUMP (val)) | |
5790 | mpz_set_si (rop, SCM_I_INUM (val)); | |
5791 | else if (SCM_BIGP (val)) | |
5792 | mpz_set (rop, SCM_I_BIG_MPZ (val)); | |
5793 | else | |
5794 | scm_wrong_type_arg_msg (NULL, 0, val, "exact integer"); | |
5795 | } | |
5796 | ||
5797 | SCM | |
5798 | scm_from_mpz (mpz_t val) | |
5799 | { | |
5800 | return scm_i_mpz2num (val); | |
5801 | } | |
5802 | ||
73e4de09 MV |
5803 | int |
5804 | scm_is_real (SCM val) | |
5805 | { | |
5806 | return scm_is_true (scm_real_p (val)); | |
5807 | } | |
5808 | ||
55f26379 MV |
5809 | int |
5810 | scm_is_rational (SCM val) | |
5811 | { | |
5812 | return scm_is_true (scm_rational_p (val)); | |
5813 | } | |
5814 | ||
73e4de09 MV |
5815 | double |
5816 | scm_to_double (SCM val) | |
5817 | { | |
55f26379 MV |
5818 | if (SCM_I_INUMP (val)) |
5819 | return SCM_I_INUM (val); | |
5820 | else if (SCM_BIGP (val)) | |
5821 | return scm_i_big2dbl (val); | |
5822 | else if (SCM_FRACTIONP (val)) | |
5823 | return scm_i_fraction2double (val); | |
5824 | else if (SCM_REALP (val)) | |
5825 | return SCM_REAL_VALUE (val); | |
5826 | else | |
7a1aba42 | 5827 | scm_wrong_type_arg_msg (NULL, 0, val, "real number"); |
73e4de09 MV |
5828 | } |
5829 | ||
5830 | SCM | |
5831 | scm_from_double (double val) | |
5832 | { | |
55f26379 MV |
5833 | SCM z = scm_double_cell (scm_tc16_real, 0, 0, 0); |
5834 | SCM_REAL_VALUE (z) = val; | |
5835 | return z; | |
73e4de09 MV |
5836 | } |
5837 | ||
55f26379 MV |
5838 | #if SCM_ENABLE_DISCOURAGED == 1 |
5839 | ||
5840 | float | |
5841 | scm_num2float (SCM num, unsigned long int pos, const char *s_caller) | |
5842 | { | |
5843 | if (SCM_BIGP (num)) | |
5844 | { | |
5845 | float res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5846 | if (!xisinf (res)) | |
5847 | return res; | |
5848 | else | |
5849 | scm_out_of_range (NULL, num); | |
5850 | } | |
5851 | else | |
5852 | return scm_to_double (num); | |
5853 | } | |
5854 | ||
5855 | double | |
5856 | scm_num2double (SCM num, unsigned long int pos, const char *s_caller) | |
5857 | { | |
5858 | if (SCM_BIGP (num)) | |
5859 | { | |
5860 | double res = mpz_get_d (SCM_I_BIG_MPZ (num)); | |
5861 | if (!xisinf (res)) | |
5862 | return res; | |
5863 | else | |
5864 | scm_out_of_range (NULL, num); | |
5865 | } | |
5866 | else | |
5867 | return scm_to_double (num); | |
5868 | } | |
5869 | ||
5870 | #endif | |
5871 | ||
8507ec80 MV |
5872 | int |
5873 | scm_is_complex (SCM val) | |
5874 | { | |
5875 | return scm_is_true (scm_complex_p (val)); | |
5876 | } | |
5877 | ||
5878 | double | |
5879 | scm_c_real_part (SCM z) | |
5880 | { | |
5881 | if (SCM_COMPLEXP (z)) | |
5882 | return SCM_COMPLEX_REAL (z); | |
5883 | else | |
5884 | { | |
5885 | /* Use the scm_real_part to get proper error checking and | |
5886 | dispatching. | |
5887 | */ | |
5888 | return scm_to_double (scm_real_part (z)); | |
5889 | } | |
5890 | } | |
5891 | ||
5892 | double | |
5893 | scm_c_imag_part (SCM z) | |
5894 | { | |
5895 | if (SCM_COMPLEXP (z)) | |
5896 | return SCM_COMPLEX_IMAG (z); | |
5897 | else | |
5898 | { | |
5899 | /* Use the scm_imag_part to get proper error checking and | |
5900 | dispatching. The result will almost always be 0.0, but not | |
5901 | always. | |
5902 | */ | |
5903 | return scm_to_double (scm_imag_part (z)); | |
5904 | } | |
5905 | } | |
5906 | ||
5907 | double | |
5908 | scm_c_magnitude (SCM z) | |
5909 | { | |
5910 | return scm_to_double (scm_magnitude (z)); | |
5911 | } | |
5912 | ||
5913 | double | |
5914 | scm_c_angle (SCM z) | |
5915 | { | |
5916 | return scm_to_double (scm_angle (z)); | |
5917 | } | |
5918 | ||
5919 | int | |
5920 | scm_is_number (SCM z) | |
5921 | { | |
5922 | return scm_is_true (scm_number_p (z)); | |
5923 | } | |
5924 | ||
0f2d19dd JB |
5925 | void |
5926 | scm_init_numbers () | |
0f2d19dd | 5927 | { |
0b799eea MV |
5928 | int i; |
5929 | ||
713a4259 KR |
5930 | mpz_init_set_si (z_negative_one, -1); |
5931 | ||
a261c0e9 DH |
5932 | /* It may be possible to tune the performance of some algorithms by using |
5933 | * the following constants to avoid the creation of bignums. Please, before | |
5934 | * using these values, remember the two rules of program optimization: | |
5935 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe | 5936 | scm_c_define ("most-positive-fixnum", |
d956fa6f | 5937 | SCM_I_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); |
86d31dfe | 5938 | scm_c_define ("most-negative-fixnum", |
d956fa6f | 5939 | SCM_I_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); |
a261c0e9 | 5940 | |
f3ae5d60 MD |
5941 | scm_add_feature ("complex"); |
5942 | scm_add_feature ("inexact"); | |
55f26379 | 5943 | scm_flo0 = scm_from_double (0.0); |
0b799eea MV |
5944 | |
5945 | /* determine floating point precision */ | |
55f26379 | 5946 | for (i=2; i <= SCM_MAX_DBL_RADIX; ++i) |
0b799eea MV |
5947 | { |
5948 | init_dblprec(&scm_dblprec[i-2],i); | |
5949 | init_fx_radix(fx_per_radix[i-2],i); | |
5950 | } | |
f872b822 | 5951 | #ifdef DBL_DIG |
0b799eea MV |
5952 | /* hard code precision for base 10 if the preprocessor tells us to... */ |
5953 | scm_dblprec[10-2] = (DBL_DIG > 20) ? 20 : DBL_DIG; | |
5954 | #endif | |
1be6b49c | 5955 | |
d956fa6f MV |
5956 | exactly_one_half = scm_permanent_object (scm_divide (SCM_I_MAKINUM (1), |
5957 | SCM_I_MAKINUM (2))); | |
a0599745 | 5958 | #include "libguile/numbers.x" |
0f2d19dd | 5959 | } |
89e00824 ML |
5960 | |
5961 | /* | |
5962 | Local Variables: | |
5963 | c-file-style: "gnu" | |
5964 | End: | |
5965 | */ |