Commit | Line | Data |
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238ebcef | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002,2003,2004 Free Software Foundation, Inc. |
ba74ef4e MV |
2 | * |
3 | * Portions Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories | |
4 | * and Bellcore. See scm_divide. | |
5 | * | |
f81e080b | 6 | * |
73be1d9e MV |
7 | * This library is free software; you can redistribute it and/or |
8 | * modify it under the terms of the GNU Lesser General Public | |
9 | * License as published by the Free Software Foundation; either | |
10 | * version 2.1 of the License, or (at your option) any later version. | |
0f2d19dd | 11 | * |
73be1d9e MV |
12 | * This library is distributed in the hope that it will be useful, |
13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
15 | * Lesser General Public License for more details. | |
0f2d19dd | 16 | * |
73be1d9e MV |
17 | * You should have received a copy of the GNU Lesser General Public |
18 | * License along with this library; if not, write to the Free Software | |
19 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA | |
20 | */ | |
1bbd0b84 | 21 | |
0f2d19dd | 22 | \f |
ca46fb90 RB |
23 | /* General assumptions: |
24 | * All objects satisfying SCM_COMPLEXP() have a non-zero complex component. | |
25 | * All objects satisfying SCM_BIGP() are too large to fit in a fixnum. | |
26 | * If an object satisfies integer?, it's either an inum, a bignum, or a real. | |
27 | * If floor (r) == r, r is an int, and mpz_set_d will DTRT. | |
f92e85f7 | 28 | * All objects satisfying SCM_FRACTIONP are never an integer. |
ca46fb90 RB |
29 | */ |
30 | ||
31 | /* TODO: | |
32 | ||
33 | - see if special casing bignums and reals in integer-exponent when | |
34 | possible (to use mpz_pow and mpf_pow_ui) is faster. | |
35 | ||
36 | - look in to better short-circuiting of common cases in | |
37 | integer-expt and elsewhere. | |
38 | ||
39 | - see if direct mpz operations can help in ash and elsewhere. | |
40 | ||
41 | */ | |
0f2d19dd | 42 | |
fa605590 KR |
43 | /* tell glibc (2.3) to give prototype for C99 trunc() */ |
44 | #define _GNU_SOURCE | |
45 | ||
ee33d62a RB |
46 | #if HAVE_CONFIG_H |
47 | # include <config.h> | |
48 | #endif | |
49 | ||
0f2d19dd | 50 | #include <math.h> |
3c9a524f | 51 | #include <ctype.h> |
fc194577 | 52 | #include <string.h> |
ca46fb90 | 53 | #include <gmp.h> |
f92e85f7 | 54 | |
a0599745 | 55 | #include "libguile/_scm.h" |
a0599745 MD |
56 | #include "libguile/feature.h" |
57 | #include "libguile/ports.h" | |
58 | #include "libguile/root.h" | |
59 | #include "libguile/smob.h" | |
60 | #include "libguile/strings.h" | |
a0599745 MD |
61 | |
62 | #include "libguile/validate.h" | |
63 | #include "libguile/numbers.h" | |
1be6b49c | 64 | #include "libguile/deprecation.h" |
f4c627b3 | 65 | |
f92e85f7 MV |
66 | #include "libguile/eq.h" |
67 | ||
0f2d19dd | 68 | \f |
f4c627b3 | 69 | |
ca46fb90 RB |
70 | /* |
71 | Wonder if this might be faster for some of our code? A switch on | |
72 | the numtag would jump directly to the right case, and the | |
73 | SCM_I_NUMTAG code might be faster than repeated SCM_FOOP tests... | |
74 | ||
75 | #define SCM_I_NUMTAG_NOTNUM 0 | |
76 | #define SCM_I_NUMTAG_INUM 1 | |
77 | #define SCM_I_NUMTAG_BIG scm_tc16_big | |
78 | #define SCM_I_NUMTAG_REAL scm_tc16_real | |
79 | #define SCM_I_NUMTAG_COMPLEX scm_tc16_complex | |
80 | #define SCM_I_NUMTAG(x) \ | |
81 | (SCM_INUMP(x) ? SCM_I_NUMTAG_INUM \ | |
82 | : (SCM_IMP(x) ? SCM_I_NUMTAG_NOTNUM \ | |
534c55a9 | 83 | : (((0xfcff & SCM_CELL_TYPE (x)) == scm_tc7_number) ? SCM_TYP16(x) \ |
ca46fb90 RB |
84 | : SCM_I_NUMTAG_NOTNUM))) |
85 | */ | |
f92e85f7 | 86 | /* the macro above will not work as is with fractions */ |
f4c627b3 DH |
87 | |
88 | ||
34d19ef6 | 89 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 | 90 | |
56e55ac7 | 91 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
92 | * printed or scm_string representation of an inexact number. |
93 | */ | |
56e55ac7 | 94 | #define FLOBUFLEN (10+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 95 | |
7351e207 MV |
96 | #if defined (SCO) |
97 | #if ! defined (HAVE_ISNAN) | |
98 | #define HAVE_ISNAN | |
99 | static int | |
100 | isnan (double x) | |
101 | { | |
102 | return (IsNANorINF (x) && NaN (x) && ! IsINF (x)) ? 1 : 0; | |
103 | } | |
0f2d19dd | 104 | #endif |
7351e207 MV |
105 | #if ! defined (HAVE_ISINF) |
106 | #define HAVE_ISINF | |
107 | static int | |
108 | isinf (double x) | |
109 | { | |
110 | return (IsNANorINF (x) && IsINF (x)) ? 1 : 0; | |
111 | } | |
0f2d19dd | 112 | |
7351e207 | 113 | #endif |
e6f3ef58 MD |
114 | #endif |
115 | ||
b127c712 KR |
116 | |
117 | /* mpz_cmp_d only recognises infinities in gmp 4.2 and up. | |
118 | For prior versions use an explicit check here. */ | |
119 | #if __GNU_MP_VERSION < 4 \ | |
120 | || (__GNU_MP_VERSION == 4 && __GNU_MP_VERSION_MINOR < 2) | |
121 | #define xmpz_cmp_d(z, d) \ | |
122 | (xisinf (d) ? (d < 0.0 ? 1 : -1) : mpz_cmp_d (z, d)) | |
123 | #else | |
124 | #define xmpz_cmp_d(z, d) mpz_cmp_d (z, d) | |
125 | #endif | |
126 | ||
f92e85f7 MV |
127 | static int |
128 | xisinf (double x) | |
129 | { | |
130 | #if defined (HAVE_ISINF) | |
131 | return isinf (x); | |
132 | #elif defined (HAVE_FINITE) && defined (HAVE_ISNAN) | |
133 | return (! (finite (x) || isnan (x))); | |
134 | #else | |
135 | return 0; | |
136 | #endif | |
137 | } | |
138 | ||
139 | static int | |
140 | xisnan (double x) | |
141 | { | |
142 | #if defined (HAVE_ISNAN) | |
143 | return isnan (x); | |
144 | #else | |
145 | return 0; | |
146 | #endif | |
147 | } | |
148 | ||
0f2d19dd JB |
149 | \f |
150 | ||
ac0c002c | 151 | static SCM abs_most_negative_fixnum; |
713a4259 | 152 | static mpz_t z_negative_one; |
ac0c002c DH |
153 | |
154 | \f | |
155 | ||
570b6821 | 156 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
157 | scm_i_mkbig () |
158 | { | |
159 | /* Return a newly created bignum. */ | |
160 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
161 | mpz_init (SCM_I_BIG_MPZ (z)); | |
162 | return z; | |
163 | } | |
164 | ||
570b6821 | 165 | SCM_C_INLINE_KEYWORD static SCM |
ca46fb90 RB |
166 | scm_i_clonebig (SCM src_big, int same_sign_p) |
167 | { | |
168 | /* Copy src_big's value, negate it if same_sign_p is false, and return. */ | |
169 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
170 | mpz_init_set (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (src_big)); | |
0aacf84e MD |
171 | if (!same_sign_p) |
172 | mpz_neg (SCM_I_BIG_MPZ (z), SCM_I_BIG_MPZ (z)); | |
ca46fb90 RB |
173 | return z; |
174 | } | |
175 | ||
570b6821 | 176 | SCM_C_INLINE_KEYWORD int |
ca46fb90 RB |
177 | scm_i_bigcmp (SCM x, SCM y) |
178 | { | |
179 | /* Return neg if x < y, pos if x > y, and 0 if x == y */ | |
180 | /* presume we already know x and y are bignums */ | |
181 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
182 | scm_remember_upto_here_2 (x, y); | |
183 | return result; | |
184 | } | |
185 | ||
570b6821 | 186 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
187 | scm_i_dbl2big (double d) |
188 | { | |
189 | /* results are only defined if d is an integer */ | |
190 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
191 | mpz_init_set_d (SCM_I_BIG_MPZ (z), d); | |
192 | return z; | |
193 | } | |
194 | ||
f92e85f7 MV |
195 | /* Convert a integer in double representation to a SCM number. */ |
196 | ||
197 | SCM_C_INLINE_KEYWORD SCM | |
198 | scm_i_dbl2num (double u) | |
199 | { | |
200 | /* SCM_MOST_POSITIVE_FIXNUM+1 and SCM_MOST_NEGATIVE_FIXNUM are both | |
201 | powers of 2, so there's no rounding when making "double" values | |
202 | from them. If plain SCM_MOST_POSITIVE_FIXNUM was used it could | |
203 | get rounded on a 64-bit machine, hence the "+1". | |
204 | ||
205 | The use of floor() to force to an integer value ensures we get a | |
206 | "numerically closest" value without depending on how a | |
207 | double->long cast or how mpz_set_d will round. For reference, | |
208 | double->long probably follows the hardware rounding mode, | |
209 | mpz_set_d truncates towards zero. */ | |
210 | ||
211 | /* XXX - what happens when SCM_MOST_POSITIVE_FIXNUM etc is not | |
212 | representable as a double? */ | |
213 | ||
214 | if (u < (double) (SCM_MOST_POSITIVE_FIXNUM+1) | |
215 | && u >= (double) SCM_MOST_NEGATIVE_FIXNUM) | |
216 | return SCM_MAKINUM ((long) u); | |
217 | else | |
218 | return scm_i_dbl2big (u); | |
219 | } | |
220 | ||
089c9a59 KR |
221 | /* scm_i_big2dbl() rounds to the closest representable double, in accordance |
222 | with R5RS exact->inexact. | |
223 | ||
224 | The approach is to use mpz_get_d to pick out the high DBL_MANT_DIG bits | |
225 | (ie. it truncates towards zero), then adjust to get the closest double by | |
226 | examining the next lower bit and adding 1 if necessary. | |
227 | ||
228 | Note that bignums exactly half way between representable doubles are | |
229 | rounded to the next higher absolute value (ie. away from zero). This | |
230 | seems like an adequate interpretation of R5RS "numerically closest", and | |
231 | it's easier and faster than a full "nearest-even" style. | |
232 | ||
233 | The bit test is done on the absolute value of the mpz_t, which means we | |
234 | must use mpz_getlimbn. mpz_tstbit is not right, it treats negatives as | |
235 | twos complement. | |
236 | ||
237 | Prior to GMP 4.2, the rounding done by mpz_get_d was unspecified. It | |
238 | happened to follow the hardware rounding mode, but on the absolute value | |
239 | of its operand. This is not what we want, so we put the high | |
240 | DBL_MANT_DIG bits into a temporary. This extra init/clear is a slowdown, | |
241 | but doesn't matter too much since it's only for older GMP. */ | |
242 | ||
243 | double | |
ca46fb90 RB |
244 | scm_i_big2dbl (SCM b) |
245 | { | |
089c9a59 KR |
246 | double result; |
247 | size_t bits; | |
248 | ||
249 | bits = mpz_sizeinbase (SCM_I_BIG_MPZ (b), 2); | |
250 | ||
251 | #if __GNU_MP_VERSION < 4 \ | |
252 | || (__GNU_MP_VERSION == 4 && __GNU_MP_VERSION_MINOR < 2) | |
253 | { | |
254 | /* GMP prior to 4.2, force truncate towards zero */ | |
255 | mpz_t tmp; | |
256 | if (bits > DBL_MANT_DIG) | |
257 | { | |
258 | size_t shift = bits - DBL_MANT_DIG; | |
259 | mpz_init2 (tmp, DBL_MANT_DIG); | |
260 | mpz_tdiv_q_2exp (tmp, SCM_I_BIG_MPZ (b), shift); | |
261 | result = ldexp (mpz_get_d (tmp), shift); | |
262 | mpz_clear (tmp); | |
263 | } | |
264 | else | |
265 | { | |
266 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
267 | } | |
268 | } | |
269 | #else | |
270 | /* GMP 4.2 and up */ | |
271 | result = mpz_get_d (SCM_I_BIG_MPZ (b)); | |
272 | #endif | |
273 | ||
274 | if (bits > DBL_MANT_DIG) | |
275 | { | |
276 | unsigned long pos = bits - DBL_MANT_DIG - 1; | |
277 | /* test bit number "pos" in absolute value */ | |
278 | if (mpz_getlimbn (SCM_I_BIG_MPZ (b), pos / GMP_NUMB_BITS) | |
279 | & ((mp_limb_t) 1 << (pos % GMP_NUMB_BITS))) | |
280 | { | |
281 | result += ldexp ((double) mpz_sgn (SCM_I_BIG_MPZ (b)), pos + 1); | |
282 | } | |
283 | } | |
284 | ||
ca46fb90 RB |
285 | scm_remember_upto_here_1 (b); |
286 | return result; | |
287 | } | |
288 | ||
570b6821 | 289 | SCM_C_INLINE_KEYWORD SCM |
ca46fb90 RB |
290 | scm_i_normbig (SCM b) |
291 | { | |
292 | /* convert a big back to a fixnum if it'll fit */ | |
293 | /* presume b is a bignum */ | |
294 | if (mpz_fits_slong_p (SCM_I_BIG_MPZ (b))) | |
295 | { | |
296 | long val = mpz_get_si (SCM_I_BIG_MPZ (b)); | |
297 | if (SCM_FIXABLE (val)) | |
298 | b = SCM_MAKINUM (val); | |
299 | } | |
300 | return b; | |
301 | } | |
f872b822 | 302 | |
f92e85f7 MV |
303 | static SCM_C_INLINE_KEYWORD SCM |
304 | scm_i_mpz2num (mpz_t b) | |
305 | { | |
306 | /* convert a mpz number to a SCM number. */ | |
307 | if (mpz_fits_slong_p (b)) | |
308 | { | |
309 | long val = mpz_get_si (b); | |
310 | if (SCM_FIXABLE (val)) | |
311 | return SCM_MAKINUM (val); | |
312 | } | |
313 | ||
314 | { | |
315 | SCM z = scm_double_cell (scm_tc16_big, 0, 0, 0); | |
316 | mpz_init_set (SCM_I_BIG_MPZ (z), b); | |
317 | return z; | |
318 | } | |
319 | } | |
320 | ||
321 | /* this is needed when we want scm_divide to make a float, not a ratio, even if passed two ints */ | |
322 | static SCM scm_divide2real (SCM x, SCM y); | |
323 | ||
324 | SCM | |
325 | scm_make_ratio (SCM numerator, SCM denominator) | |
c60e130c | 326 | #define FUNC_NAME "make-ratio" |
f92e85f7 | 327 | { |
c60e130c MV |
328 | /* First make sure the arguments are proper. |
329 | */ | |
f92e85f7 MV |
330 | if (SCM_INUMP (denominator)) |
331 | { | |
332 | if (SCM_EQ_P (denominator, SCM_INUM0)) | |
333 | scm_num_overflow ("make-ratio"); | |
334 | if (SCM_EQ_P (denominator, SCM_MAKINUM(1))) | |
335 | return numerator; | |
336 | } | |
337 | else | |
338 | { | |
339 | if (!(SCM_BIGP(denominator))) | |
340 | SCM_WRONG_TYPE_ARG (2, denominator); | |
341 | } | |
c60e130c MV |
342 | if (!SCM_INUMP (numerator) && !SCM_BIGP (numerator)) |
343 | SCM_WRONG_TYPE_ARG (1, numerator); | |
344 | ||
345 | /* Then flip signs so that the denominator is positive. | |
346 | */ | |
347 | if (SCM_NFALSEP (scm_negative_p (denominator))) | |
348 | { | |
349 | numerator = scm_difference (numerator, SCM_UNDEFINED); | |
350 | denominator = scm_difference (denominator, SCM_UNDEFINED); | |
351 | } | |
352 | ||
353 | /* Now consider for each of the four fixnum/bignum combinations | |
354 | whether the rational number is really an integer. | |
355 | */ | |
f92e85f7 MV |
356 | if (SCM_INUMP (numerator)) |
357 | { | |
dd5130ca | 358 | long x = SCM_INUM (numerator); |
f92e85f7 MV |
359 | if (SCM_EQ_P (numerator, SCM_INUM0)) |
360 | return SCM_INUM0; | |
361 | if (SCM_INUMP (denominator)) | |
362 | { | |
dd5130ca | 363 | long y; |
f92e85f7 MV |
364 | y = SCM_INUM (denominator); |
365 | if (x == y) | |
366 | return SCM_MAKINUM(1); | |
367 | if ((x % y) == 0) | |
368 | return SCM_MAKINUM (x / y); | |
f92e85f7 | 369 | } |
dd5130ca KR |
370 | else |
371 | { | |
372 | /* When x == SCM_MOST_NEGATIVE_FIXNUM we could have the negative | |
373 | of that value for the denominator, as a bignum. */ | |
374 | long abs_x = (x >= 0 ? x : -x); | |
375 | if (mpz_cmpabs_ui (SCM_I_BIG_MPZ (denominator), abs_x) == 0) | |
376 | return SCM_MAKINUM(-1); | |
377 | } | |
f92e85f7 | 378 | } |
c60e130c | 379 | else if (SCM_BIGP (numerator)) |
f92e85f7 | 380 | { |
c60e130c MV |
381 | if (SCM_INUMP (denominator)) |
382 | { | |
383 | long yy = SCM_INUM (denominator); | |
384 | if (mpz_divisible_ui_p (SCM_I_BIG_MPZ (numerator), yy)) | |
385 | return scm_divide (numerator, denominator); | |
386 | } | |
387 | else | |
f92e85f7 | 388 | { |
c60e130c MV |
389 | if (SCM_EQ_P (numerator, denominator)) |
390 | return SCM_MAKINUM(1); | |
391 | if (mpz_divisible_p (SCM_I_BIG_MPZ (numerator), | |
392 | SCM_I_BIG_MPZ (denominator))) | |
393 | return scm_divide(numerator, denominator); | |
f92e85f7 | 394 | } |
f92e85f7 | 395 | } |
c60e130c MV |
396 | |
397 | /* No, it's a proper fraction. | |
398 | */ | |
399 | return scm_double_cell (scm_tc16_fraction, | |
400 | SCM_UNPACK (numerator), | |
401 | SCM_UNPACK (denominator), 0); | |
f92e85f7 | 402 | } |
c60e130c | 403 | #undef FUNC_NAME |
f92e85f7 MV |
404 | |
405 | static void scm_i_fraction_reduce (SCM z) | |
406 | { | |
407 | if (!(SCM_FRACTION_REDUCED (z))) | |
408 | { | |
409 | SCM divisor; | |
410 | divisor = scm_gcd (SCM_FRACTION_NUMERATOR (z), SCM_FRACTION_DENOMINATOR (z)); | |
411 | if (!(SCM_EQ_P (divisor, SCM_MAKINUM(1)))) | |
412 | { | |
413 | /* is this safe? */ | |
414 | SCM_FRACTION_SET_NUMERATOR (z, scm_divide (SCM_FRACTION_NUMERATOR (z), divisor)); | |
415 | SCM_FRACTION_SET_DENOMINATOR (z, scm_divide (SCM_FRACTION_DENOMINATOR (z), divisor)); | |
416 | } | |
417 | SCM_FRACTION_REDUCED_SET (z); | |
418 | } | |
419 | } | |
420 | ||
421 | double | |
422 | scm_i_fraction2double (SCM z) | |
423 | { | |
424 | return scm_num2dbl (scm_divide2real (SCM_FRACTION_NUMERATOR (z), | |
425 | SCM_FRACTION_DENOMINATOR (z)), | |
426 | "fraction2real"); | |
427 | } | |
428 | ||
a1ec6916 | 429 | SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0, |
1bbd0b84 | 430 | (SCM x), |
942e5b91 MG |
431 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
432 | "otherwise.") | |
1bbd0b84 | 433 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 434 | { |
0aacf84e MD |
435 | if (SCM_INUMP (x)) |
436 | return SCM_BOOL_T; | |
437 | if (SCM_BIGP (x)) | |
438 | return SCM_BOOL_T; | |
f92e85f7 MV |
439 | if (SCM_FRACTIONP (x)) |
440 | return SCM_BOOL_T; | |
eb927cb9 MV |
441 | if (SCM_NUMBERP (x)) |
442 | return SCM_BOOL_F; | |
443 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 444 | } |
1bbd0b84 | 445 | #undef FUNC_NAME |
0f2d19dd | 446 | |
4219f20d | 447 | |
a1ec6916 | 448 | SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 449 | (SCM n), |
942e5b91 MG |
450 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
451 | "otherwise.") | |
1bbd0b84 | 452 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 453 | { |
0aacf84e MD |
454 | if (SCM_INUMP (n)) |
455 | { | |
456 | long val = SCM_INUM (n); | |
457 | return SCM_BOOL ((val & 1L) != 0); | |
458 | } | |
459 | else if (SCM_BIGP (n)) | |
460 | { | |
461 | int odd_p = mpz_odd_p (SCM_I_BIG_MPZ (n)); | |
462 | scm_remember_upto_here_1 (n); | |
463 | return SCM_BOOL (odd_p); | |
464 | } | |
465 | else if (!SCM_FALSEP (scm_inf_p (n))) | |
7351e207 | 466 | return SCM_BOOL_T; |
f92e85f7 MV |
467 | else if (SCM_REALP (n)) |
468 | { | |
469 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
470 | if (rem == 1.0) | |
471 | return SCM_BOOL_T; | |
472 | else if (rem == 0.0) | |
473 | return SCM_BOOL_F; | |
474 | else | |
475 | SCM_WRONG_TYPE_ARG (1, n); | |
476 | } | |
0aacf84e | 477 | else |
a1a33b0f | 478 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 479 | } |
1bbd0b84 | 480 | #undef FUNC_NAME |
0f2d19dd | 481 | |
4219f20d | 482 | |
a1ec6916 | 483 | SCM_DEFINE (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 484 | (SCM n), |
942e5b91 MG |
485 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
486 | "otherwise.") | |
1bbd0b84 | 487 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 488 | { |
0aacf84e MD |
489 | if (SCM_INUMP (n)) |
490 | { | |
491 | long val = SCM_INUM (n); | |
492 | return SCM_BOOL ((val & 1L) == 0); | |
493 | } | |
494 | else if (SCM_BIGP (n)) | |
495 | { | |
496 | int even_p = mpz_even_p (SCM_I_BIG_MPZ (n)); | |
497 | scm_remember_upto_here_1 (n); | |
498 | return SCM_BOOL (even_p); | |
499 | } | |
500 | else if (!SCM_FALSEP (scm_inf_p (n))) | |
7351e207 | 501 | return SCM_BOOL_T; |
f92e85f7 MV |
502 | else if (SCM_REALP (n)) |
503 | { | |
504 | double rem = fabs (fmod (SCM_REAL_VALUE(n), 2.0)); | |
505 | if (rem == 1.0) | |
506 | return SCM_BOOL_F; | |
507 | else if (rem == 0.0) | |
508 | return SCM_BOOL_T; | |
509 | else | |
510 | SCM_WRONG_TYPE_ARG (1, n); | |
511 | } | |
0aacf84e | 512 | else |
a1a33b0f | 513 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 514 | } |
1bbd0b84 | 515 | #undef FUNC_NAME |
0f2d19dd | 516 | |
7351e207 MV |
517 | SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0, |
518 | (SCM n), | |
519 | "Return @code{#t} if @var{n} is infinite, @code{#f}\n" | |
520 | "otherwise.") | |
521 | #define FUNC_NAME s_scm_inf_p | |
522 | { | |
0aacf84e | 523 | if (SCM_REALP (n)) |
7351e207 | 524 | return SCM_BOOL (xisinf (SCM_REAL_VALUE (n))); |
0aacf84e | 525 | else if (SCM_COMPLEXP (n)) |
7351e207 MV |
526 | return SCM_BOOL (xisinf (SCM_COMPLEX_REAL (n)) |
527 | || xisinf (SCM_COMPLEX_IMAG (n))); | |
0aacf84e | 528 | else |
7351e207 | 529 | return SCM_BOOL_F; |
7351e207 MV |
530 | } |
531 | #undef FUNC_NAME | |
532 | ||
533 | SCM_DEFINE (scm_nan_p, "nan?", 1, 0, 0, | |
534 | (SCM n), | |
535 | "Return @code{#t} if @var{n} is a NaN, @code{#f}\n" | |
536 | "otherwise.") | |
537 | #define FUNC_NAME s_scm_nan_p | |
538 | { | |
0aacf84e | 539 | if (SCM_REALP (n)) |
7351e207 | 540 | return SCM_BOOL (xisnan (SCM_REAL_VALUE (n))); |
0aacf84e | 541 | else if (SCM_COMPLEXP (n)) |
7351e207 MV |
542 | return SCM_BOOL (xisnan (SCM_COMPLEX_REAL (n)) |
543 | || xisnan (SCM_COMPLEX_IMAG (n))); | |
0aacf84e | 544 | else |
7351e207 | 545 | return SCM_BOOL_F; |
7351e207 MV |
546 | } |
547 | #undef FUNC_NAME | |
548 | ||
549 | /* Guile's idea of infinity. */ | |
550 | static double guile_Inf; | |
551 | ||
552 | /* Guile's idea of not a number. */ | |
553 | static double guile_NaN; | |
554 | ||
555 | static void | |
556 | guile_ieee_init (void) | |
557 | { | |
558 | #if defined (HAVE_ISINF) || defined (HAVE_FINITE) | |
559 | ||
560 | /* Some version of gcc on some old version of Linux used to crash when | |
561 | trying to make Inf and NaN. */ | |
562 | ||
563 | #if defined (SCO) | |
564 | double tmp = 1.0; | |
565 | guile_Inf = 1.0 / (tmp - tmp); | |
566 | #elif defined (__alpha__) && ! defined (linux) | |
567 | extern unsigned int DINFINITY[2]; | |
568 | guile_Inf = (*(X_CAST(double *, DINFINITY))); | |
569 | #else | |
570 | double tmp = 1e+10; | |
571 | guile_Inf = tmp; | |
572 | for (;;) | |
573 | { | |
574 | guile_Inf *= 1e+10; | |
575 | if (guile_Inf == tmp) | |
576 | break; | |
577 | tmp = guile_Inf; | |
578 | } | |
579 | #endif | |
580 | ||
581 | #endif | |
582 | ||
583 | #if defined (HAVE_ISNAN) | |
584 | ||
585 | #if defined (__alpha__) && ! defined (linux) | |
586 | extern unsigned int DQNAN[2]; | |
587 | guile_NaN = (*(X_CAST(double *, DQNAN))); | |
588 | #else | |
589 | guile_NaN = guile_Inf / guile_Inf; | |
590 | #endif | |
591 | ||
592 | #endif | |
593 | } | |
594 | ||
595 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
596 | (void), | |
597 | "Return Inf.") | |
598 | #define FUNC_NAME s_scm_inf | |
599 | { | |
600 | static int initialized = 0; | |
601 | if (! initialized) | |
602 | { | |
603 | guile_ieee_init (); | |
604 | initialized = 1; | |
605 | } | |
606 | return scm_make_real (guile_Inf); | |
607 | } | |
608 | #undef FUNC_NAME | |
609 | ||
610 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
611 | (void), | |
612 | "Return NaN.") | |
613 | #define FUNC_NAME s_scm_nan | |
614 | { | |
615 | static int initialized = 0; | |
0aacf84e | 616 | if (!initialized) |
7351e207 MV |
617 | { |
618 | guile_ieee_init (); | |
619 | initialized = 1; | |
620 | } | |
621 | return scm_make_real (guile_NaN); | |
622 | } | |
623 | #undef FUNC_NAME | |
624 | ||
4219f20d | 625 | |
a48d60b1 MD |
626 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
627 | (SCM x), | |
628 | "Return the absolute value of @var{x}.") | |
629 | #define FUNC_NAME | |
0f2d19dd | 630 | { |
0aacf84e MD |
631 | if (SCM_INUMP (x)) |
632 | { | |
633 | long int xx = SCM_INUM (x); | |
634 | if (xx >= 0) | |
635 | return x; | |
636 | else if (SCM_POSFIXABLE (-xx)) | |
637 | return SCM_MAKINUM (-xx); | |
638 | else | |
639 | return scm_i_long2big (-xx); | |
4219f20d | 640 | } |
0aacf84e MD |
641 | else if (SCM_BIGP (x)) |
642 | { | |
643 | const int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
644 | if (sgn < 0) | |
645 | return scm_i_clonebig (x, 0); | |
646 | else | |
647 | return x; | |
4219f20d | 648 | } |
0aacf84e | 649 | else if (SCM_REALP (x)) |
ae38324d KR |
650 | { |
651 | /* note that if x is a NaN then xx<0 is false so we return x unchanged */ | |
652 | double xx = SCM_REAL_VALUE (x); | |
653 | if (xx < 0.0) | |
654 | return scm_make_real (-xx); | |
655 | else | |
656 | return x; | |
657 | } | |
f92e85f7 MV |
658 | else if (SCM_FRACTIONP (x)) |
659 | { | |
660 | if (SCM_FALSEP (scm_negative_p (SCM_FRACTION_NUMERATOR (x)))) | |
661 | return x; | |
662 | return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), | |
663 | SCM_FRACTION_DENOMINATOR (x)); | |
664 | } | |
0aacf84e | 665 | else |
a48d60b1 | 666 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
0f2d19dd | 667 | } |
a48d60b1 | 668 | #undef FUNC_NAME |
0f2d19dd | 669 | |
4219f20d | 670 | |
9de33deb | 671 | SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); |
942e5b91 MG |
672 | /* "Return the quotient of the numbers @var{x} and @var{y}." |
673 | */ | |
0f2d19dd | 674 | SCM |
6e8d25a6 | 675 | scm_quotient (SCM x, SCM y) |
0f2d19dd | 676 | { |
0aacf84e MD |
677 | if (SCM_INUMP (x)) |
678 | { | |
679 | long xx = SCM_INUM (x); | |
680 | if (SCM_INUMP (y)) | |
681 | { | |
682 | long yy = SCM_INUM (y); | |
683 | if (yy == 0) | |
684 | scm_num_overflow (s_quotient); | |
685 | else | |
686 | { | |
687 | long z = xx / yy; | |
688 | if (SCM_FIXABLE (z)) | |
689 | return SCM_MAKINUM (z); | |
690 | else | |
691 | return scm_i_long2big (z); | |
692 | } | |
828865c3 | 693 | } |
0aacf84e | 694 | else if (SCM_BIGP (y)) |
ac0c002c | 695 | { |
0aacf84e MD |
696 | if ((SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
697 | && (scm_i_bigcmp (abs_most_negative_fixnum, y) == 0)) | |
698 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
699 | return SCM_MAKINUM (-1); | |
700 | else | |
701 | return SCM_MAKINUM (0); | |
ac0c002c DH |
702 | } |
703 | else | |
0aacf84e | 704 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); |
828865c3 | 705 | } |
0aacf84e MD |
706 | else if (SCM_BIGP (x)) |
707 | { | |
708 | if (SCM_INUMP (y)) | |
709 | { | |
710 | long yy = SCM_INUM (y); | |
711 | if (yy == 0) | |
712 | scm_num_overflow (s_quotient); | |
713 | else if (yy == 1) | |
714 | return x; | |
715 | else | |
716 | { | |
717 | SCM result = scm_i_mkbig (); | |
718 | if (yy < 0) | |
719 | { | |
720 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), | |
721 | SCM_I_BIG_MPZ (x), | |
722 | - yy); | |
723 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
724 | } | |
725 | else | |
726 | mpz_tdiv_q_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
727 | scm_remember_upto_here_1 (x); | |
728 | return scm_i_normbig (result); | |
729 | } | |
730 | } | |
731 | else if (SCM_BIGP (y)) | |
732 | { | |
733 | SCM result = scm_i_mkbig (); | |
734 | mpz_tdiv_q (SCM_I_BIG_MPZ (result), | |
735 | SCM_I_BIG_MPZ (x), | |
736 | SCM_I_BIG_MPZ (y)); | |
737 | scm_remember_upto_here_2 (x, y); | |
738 | return scm_i_normbig (result); | |
739 | } | |
740 | else | |
741 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); | |
f872b822 | 742 | } |
0aacf84e | 743 | else |
89a7e495 | 744 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient); |
0f2d19dd JB |
745 | } |
746 | ||
9de33deb | 747 | SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); |
942e5b91 MG |
748 | /* "Return the remainder of the numbers @var{x} and @var{y}.\n" |
749 | * "@lisp\n" | |
750 | * "(remainder 13 4) @result{} 1\n" | |
751 | * "(remainder -13 4) @result{} -1\n" | |
752 | * "@end lisp" | |
753 | */ | |
0f2d19dd | 754 | SCM |
6e8d25a6 | 755 | scm_remainder (SCM x, SCM y) |
0f2d19dd | 756 | { |
0aacf84e MD |
757 | if (SCM_INUMP (x)) |
758 | { | |
759 | if (SCM_INUMP (y)) | |
760 | { | |
761 | long yy = SCM_INUM (y); | |
762 | if (yy == 0) | |
763 | scm_num_overflow (s_remainder); | |
764 | else | |
765 | { | |
766 | long z = SCM_INUM (x) % yy; | |
767 | return SCM_MAKINUM (z); | |
768 | } | |
769 | } | |
770 | else if (SCM_BIGP (y)) | |
ac0c002c | 771 | { |
0aacf84e MD |
772 | if ((SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM) |
773 | && (scm_i_bigcmp (abs_most_negative_fixnum, y) == 0)) | |
774 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
775 | return SCM_MAKINUM (0); | |
776 | else | |
777 | return x; | |
ac0c002c DH |
778 | } |
779 | else | |
0aacf84e | 780 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); |
89a7e495 | 781 | } |
0aacf84e MD |
782 | else if (SCM_BIGP (x)) |
783 | { | |
784 | if (SCM_INUMP (y)) | |
785 | { | |
786 | long yy = SCM_INUM (y); | |
787 | if (yy == 0) | |
788 | scm_num_overflow (s_remainder); | |
789 | else | |
790 | { | |
791 | SCM result = scm_i_mkbig (); | |
792 | if (yy < 0) | |
793 | yy = - yy; | |
794 | mpz_tdiv_r_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ(x), yy); | |
795 | scm_remember_upto_here_1 (x); | |
796 | return scm_i_normbig (result); | |
797 | } | |
798 | } | |
799 | else if (SCM_BIGP (y)) | |
800 | { | |
801 | SCM result = scm_i_mkbig (); | |
802 | mpz_tdiv_r (SCM_I_BIG_MPZ (result), | |
803 | SCM_I_BIG_MPZ (x), | |
804 | SCM_I_BIG_MPZ (y)); | |
805 | scm_remember_upto_here_2 (x, y); | |
806 | return scm_i_normbig (result); | |
807 | } | |
808 | else | |
809 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); | |
f872b822 | 810 | } |
0aacf84e | 811 | else |
89a7e495 | 812 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder); |
0f2d19dd JB |
813 | } |
814 | ||
89a7e495 | 815 | |
9de33deb | 816 | SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); |
942e5b91 MG |
817 | /* "Return the modulo of the numbers @var{x} and @var{y}.\n" |
818 | * "@lisp\n" | |
819 | * "(modulo 13 4) @result{} 1\n" | |
820 | * "(modulo -13 4) @result{} 3\n" | |
821 | * "@end lisp" | |
822 | */ | |
0f2d19dd | 823 | SCM |
6e8d25a6 | 824 | scm_modulo (SCM x, SCM y) |
0f2d19dd | 825 | { |
0aacf84e MD |
826 | if (SCM_INUMP (x)) |
827 | { | |
828 | long xx = SCM_INUM (x); | |
829 | if (SCM_INUMP (y)) | |
830 | { | |
831 | long yy = SCM_INUM (y); | |
832 | if (yy == 0) | |
833 | scm_num_overflow (s_modulo); | |
834 | else | |
835 | { | |
836 | /* FIXME: I think this may be a bug on some arches -- results | |
837 | of % with negative second arg are undefined... */ | |
838 | long z = xx % yy; | |
839 | long result; | |
840 | ||
841 | if (yy < 0) | |
842 | { | |
843 | if (z > 0) | |
844 | result = z + yy; | |
845 | else | |
846 | result = z; | |
847 | } | |
848 | else | |
849 | { | |
850 | if (z < 0) | |
851 | result = z + yy; | |
852 | else | |
853 | result = z; | |
854 | } | |
855 | return SCM_MAKINUM (result); | |
856 | } | |
857 | } | |
858 | else if (SCM_BIGP (y)) | |
859 | { | |
860 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
861 | ||
862 | if (sgn_y == 0) | |
863 | scm_num_overflow (s_modulo); | |
864 | else | |
865 | { | |
866 | mpz_t z_x; | |
867 | SCM result; | |
868 | ||
869 | if (sgn_y < 0) | |
870 | { | |
871 | SCM pos_y = scm_i_clonebig (y, 0); | |
872 | /* do this after the last scm_op */ | |
873 | mpz_init_set_si (z_x, xx); | |
874 | result = pos_y; /* re-use this bignum */ | |
875 | mpz_mod (SCM_I_BIG_MPZ (result), | |
876 | z_x, | |
877 | SCM_I_BIG_MPZ (pos_y)); | |
878 | scm_remember_upto_here_1 (pos_y); | |
879 | } | |
880 | else | |
881 | { | |
882 | result = scm_i_mkbig (); | |
883 | /* do this after the last scm_op */ | |
884 | mpz_init_set_si (z_x, xx); | |
885 | mpz_mod (SCM_I_BIG_MPZ (result), | |
886 | z_x, | |
887 | SCM_I_BIG_MPZ (y)); | |
888 | scm_remember_upto_here_1 (y); | |
889 | } | |
ca46fb90 | 890 | |
0aacf84e MD |
891 | if ((sgn_y < 0) && mpz_sgn (SCM_I_BIG_MPZ (result)) != 0) |
892 | mpz_add (SCM_I_BIG_MPZ (result), | |
893 | SCM_I_BIG_MPZ (y), | |
894 | SCM_I_BIG_MPZ (result)); | |
895 | scm_remember_upto_here_1 (y); | |
896 | /* and do this before the next one */ | |
897 | mpz_clear (z_x); | |
898 | return scm_i_normbig (result); | |
899 | } | |
900 | } | |
901 | else | |
902 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
f872b822 | 903 | } |
0aacf84e MD |
904 | else if (SCM_BIGP (x)) |
905 | { | |
906 | if (SCM_INUMP (y)) | |
907 | { | |
908 | long yy = SCM_INUM (y); | |
909 | if (yy == 0) | |
910 | scm_num_overflow (s_modulo); | |
911 | else | |
912 | { | |
913 | SCM result = scm_i_mkbig (); | |
914 | mpz_mod_ui (SCM_I_BIG_MPZ (result), | |
915 | SCM_I_BIG_MPZ (x), | |
916 | (yy < 0) ? - yy : yy); | |
917 | scm_remember_upto_here_1 (x); | |
918 | if ((yy < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
919 | mpz_sub_ui (SCM_I_BIG_MPZ (result), | |
920 | SCM_I_BIG_MPZ (result), | |
921 | - yy); | |
922 | return scm_i_normbig (result); | |
923 | } | |
924 | } | |
925 | else if (SCM_BIGP (y)) | |
926 | { | |
927 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
928 | if (sgn_y == 0) | |
929 | scm_num_overflow (s_modulo); | |
930 | else | |
931 | { | |
932 | SCM result = scm_i_mkbig (); | |
933 | int y_sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
934 | SCM pos_y = scm_i_clonebig (y, y_sgn >= 0); | |
935 | mpz_mod (SCM_I_BIG_MPZ (result), | |
936 | SCM_I_BIG_MPZ (x), | |
937 | SCM_I_BIG_MPZ (pos_y)); | |
ca46fb90 | 938 | |
0aacf84e MD |
939 | scm_remember_upto_here_1 (x); |
940 | if ((y_sgn < 0) && (mpz_sgn (SCM_I_BIG_MPZ (result)) != 0)) | |
941 | mpz_add (SCM_I_BIG_MPZ (result), | |
942 | SCM_I_BIG_MPZ (y), | |
943 | SCM_I_BIG_MPZ (result)); | |
944 | scm_remember_upto_here_2 (y, pos_y); | |
945 | return scm_i_normbig (result); | |
946 | } | |
947 | } | |
948 | else | |
949 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
828865c3 | 950 | } |
0aacf84e | 951 | else |
09fb7599 | 952 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); |
0f2d19dd JB |
953 | } |
954 | ||
9de33deb | 955 | SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd); |
942e5b91 MG |
956 | /* "Return the greatest common divisor of all arguments.\n" |
957 | * "If called without arguments, 0 is returned." | |
958 | */ | |
0f2d19dd | 959 | SCM |
6e8d25a6 | 960 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 961 | { |
ca46fb90 | 962 | if (SCM_UNBNDP (y)) |
0aacf84e | 963 | return SCM_UNBNDP (x) ? SCM_INUM0 : x; |
ca46fb90 RB |
964 | |
965 | if (SCM_INUMP (x)) | |
966 | { | |
967 | if (SCM_INUMP (y)) | |
968 | { | |
969 | long xx = SCM_INUM (x); | |
970 | long yy = SCM_INUM (y); | |
971 | long u = xx < 0 ? -xx : xx; | |
972 | long v = yy < 0 ? -yy : yy; | |
973 | long result; | |
0aacf84e MD |
974 | if (xx == 0) |
975 | result = v; | |
976 | else if (yy == 0) | |
977 | result = u; | |
978 | else | |
979 | { | |
980 | long k = 1; | |
981 | long t; | |
982 | /* Determine a common factor 2^k */ | |
983 | while (!(1 & (u | v))) | |
984 | { | |
985 | k <<= 1; | |
986 | u >>= 1; | |
987 | v >>= 1; | |
988 | } | |
989 | /* Now, any factor 2^n can be eliminated */ | |
990 | if (u & 1) | |
991 | t = -v; | |
992 | else | |
993 | { | |
994 | t = u; | |
995 | b3: | |
996 | t = SCM_SRS (t, 1); | |
997 | } | |
998 | if (!(1 & t)) | |
999 | goto b3; | |
1000 | if (t > 0) | |
1001 | u = t; | |
1002 | else | |
1003 | v = -t; | |
1004 | t = u - v; | |
1005 | if (t != 0) | |
1006 | goto b3; | |
1007 | result = u * k; | |
1008 | } | |
1009 | return (SCM_POSFIXABLE (result) | |
1010 | ? SCM_MAKINUM (result) | |
1011 | : scm_i_long2big (result)); | |
ca46fb90 RB |
1012 | } |
1013 | else if (SCM_BIGP (y)) | |
1014 | { | |
1015 | SCM result = scm_i_mkbig (); | |
1016 | SCM mx = scm_i_mkbig (); | |
0aacf84e | 1017 | mpz_set_si (SCM_I_BIG_MPZ (mx), SCM_INUM (x)); |
ca46fb90 | 1018 | scm_remember_upto_here_1 (x); |
0aacf84e MD |
1019 | mpz_gcd (SCM_I_BIG_MPZ (result), |
1020 | SCM_I_BIG_MPZ (mx), | |
1021 | SCM_I_BIG_MPZ (y)); | |
1022 | scm_remember_upto_here_2 (mx, y); | |
ca46fb90 RB |
1023 | return scm_i_normbig (result); |
1024 | } | |
1025 | else | |
1026 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 1027 | } |
ca46fb90 RB |
1028 | else if (SCM_BIGP (x)) |
1029 | { | |
1030 | if (SCM_INUMP (y)) | |
1031 | { | |
1032 | unsigned long result; | |
1033 | long yy = SCM_INUM (y); | |
8c5b0afc KR |
1034 | if (yy == 0) |
1035 | return scm_abs (x); | |
0aacf84e MD |
1036 | if (yy < 0) |
1037 | yy = -yy; | |
ca46fb90 RB |
1038 | result = mpz_gcd_ui (NULL, SCM_I_BIG_MPZ (x), yy); |
1039 | scm_remember_upto_here_1 (x); | |
0aacf84e MD |
1040 | return (SCM_POSFIXABLE (result) |
1041 | ? SCM_MAKINUM (result) | |
1042 | : scm_ulong2num (result)); | |
ca46fb90 RB |
1043 | } |
1044 | else if (SCM_BIGP (y)) | |
1045 | { | |
1046 | SCM result = scm_i_mkbig (); | |
0aacf84e MD |
1047 | mpz_gcd (SCM_I_BIG_MPZ (result), |
1048 | SCM_I_BIG_MPZ (x), | |
1049 | SCM_I_BIG_MPZ (y)); | |
1050 | scm_remember_upto_here_2 (x, y); | |
ca46fb90 RB |
1051 | return scm_i_normbig (result); |
1052 | } | |
1053 | else | |
1054 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
09fb7599 | 1055 | } |
ca46fb90 | 1056 | else |
09fb7599 | 1057 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); |
0f2d19dd JB |
1058 | } |
1059 | ||
9de33deb | 1060 | SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm); |
942e5b91 MG |
1061 | /* "Return the least common multiple of the arguments.\n" |
1062 | * "If called without arguments, 1 is returned." | |
1063 | */ | |
0f2d19dd | 1064 | SCM |
6e8d25a6 | 1065 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 1066 | { |
ca46fb90 RB |
1067 | if (SCM_UNBNDP (n2)) |
1068 | { | |
1069 | if (SCM_UNBNDP (n1)) | |
1070 | return SCM_MAKINUM (1L); | |
09fb7599 DH |
1071 | n2 = SCM_MAKINUM (1L); |
1072 | } | |
09fb7599 | 1073 | |
09fb7599 | 1074 | SCM_GASSERT2 (SCM_INUMP (n1) || SCM_BIGP (n1), |
ca46fb90 | 1075 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
09fb7599 | 1076 | SCM_GASSERT2 (SCM_INUMP (n2) || SCM_BIGP (n2), |
ca46fb90 | 1077 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
09fb7599 | 1078 | |
ca46fb90 RB |
1079 | if (SCM_INUMP (n1)) |
1080 | { | |
1081 | if (SCM_INUMP (n2)) | |
1082 | { | |
1083 | SCM d = scm_gcd (n1, n2); | |
1084 | if (SCM_EQ_P (d, SCM_INUM0)) | |
1085 | return d; | |
1086 | else | |
1087 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
1088 | } | |
1089 | else | |
1090 | { | |
1091 | /* inum n1, big n2 */ | |
1092 | inumbig: | |
1093 | { | |
1094 | SCM result = scm_i_mkbig (); | |
1095 | long nn1 = SCM_INUM (n1); | |
1096 | if (nn1 == 0) return SCM_INUM0; | |
1097 | if (nn1 < 0) nn1 = - nn1; | |
1098 | mpz_lcm_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n2), nn1); | |
1099 | scm_remember_upto_here_1 (n2); | |
1100 | return result; | |
1101 | } | |
1102 | } | |
1103 | } | |
1104 | else | |
1105 | { | |
1106 | /* big n1 */ | |
1107 | if (SCM_INUMP (n2)) | |
1108 | { | |
1109 | SCM_SWAP (n1, n2); | |
1110 | goto inumbig; | |
1111 | } | |
1112 | else | |
1113 | { | |
1114 | SCM result = scm_i_mkbig (); | |
1115 | mpz_lcm(SCM_I_BIG_MPZ (result), | |
1116 | SCM_I_BIG_MPZ (n1), | |
1117 | SCM_I_BIG_MPZ (n2)); | |
1118 | scm_remember_upto_here_2(n1, n2); | |
1119 | /* shouldn't need to normalize b/c lcm of 2 bigs should be big */ | |
1120 | return result; | |
1121 | } | |
f872b822 | 1122 | } |
0f2d19dd JB |
1123 | } |
1124 | ||
0f2d19dd | 1125 | #ifndef scm_long2num |
c1bfcf60 GB |
1126 | #define SCM_LOGOP_RETURN(x) scm_ulong2num(x) |
1127 | #else | |
1128 | #define SCM_LOGOP_RETURN(x) SCM_MAKINUM(x) | |
1129 | #endif | |
1130 | ||
8a525303 GB |
1131 | /* Emulating 2's complement bignums with sign magnitude arithmetic: |
1132 | ||
1133 | Logand: | |
1134 | X Y Result Method: | |
1135 | (len) | |
1136 | + + + x (map digit:logand X Y) | |
1137 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
1138 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
1139 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
1140 | ||
1141 | Logior: | |
1142 | X Y Result Method: | |
1143 | ||
1144 | + + + (map digit:logior X Y) | |
1145 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
1146 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
1147 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
1148 | ||
1149 | Logxor: | |
1150 | X Y Result Method: | |
1151 | ||
1152 | + + + (map digit:logxor X Y) | |
1153 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
1154 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
1155 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
1156 | ||
1157 | Logtest: | |
1158 | X Y Result | |
1159 | ||
1160 | + + (any digit:logand X Y) | |
1161 | + - (any digit:logand X (lognot (+ -1 Y))) | |
1162 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
1163 | - - #t | |
1164 | ||
1165 | */ | |
1166 | ||
c3ee7520 | 1167 | SCM_DEFINE1 (scm_logand, "logand", scm_tc7_asubr, |
1bbd0b84 | 1168 | (SCM n1, SCM n2), |
3c3db128 GH |
1169 | "Return the bitwise AND of the integer arguments.\n\n" |
1170 | "@lisp\n" | |
1171 | "(logand) @result{} -1\n" | |
1172 | "(logand 7) @result{} 7\n" | |
535f2a51 | 1173 | "(logand #b111 #b011 #b001) @result{} 1\n" |
3c3db128 | 1174 | "@end lisp") |
1bbd0b84 | 1175 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 1176 | { |
9a00c9fc DH |
1177 | long int nn1; |
1178 | ||
0aacf84e MD |
1179 | if (SCM_UNBNDP (n2)) |
1180 | { | |
1181 | if (SCM_UNBNDP (n1)) | |
1182 | return SCM_MAKINUM (-1); | |
1183 | else if (!SCM_NUMBERP (n1)) | |
1184 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1185 | else if (SCM_NUMBERP (n1)) | |
1186 | return n1; | |
1187 | else | |
1188 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1189 | } |
09fb7599 | 1190 | |
0aacf84e MD |
1191 | if (SCM_INUMP (n1)) |
1192 | { | |
9a00c9fc | 1193 | nn1 = SCM_INUM (n1); |
0aacf84e MD |
1194 | if (SCM_INUMP (n2)) |
1195 | { | |
1196 | long nn2 = SCM_INUM (n2); | |
1197 | return SCM_MAKINUM (nn1 & nn2); | |
1198 | } | |
1199 | else if SCM_BIGP (n2) | |
1200 | { | |
1201 | intbig: | |
1202 | if (n1 == 0) | |
1203 | return SCM_INUM0; | |
1204 | { | |
1205 | SCM result_z = scm_i_mkbig (); | |
1206 | mpz_t nn1_z; | |
1207 | mpz_init_set_si (nn1_z, nn1); | |
1208 | mpz_and (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1209 | scm_remember_upto_here_1 (n2); | |
1210 | mpz_clear (nn1_z); | |
1211 | return scm_i_normbig (result_z); | |
1212 | } | |
1213 | } | |
1214 | else | |
1215 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1216 | } | |
1217 | else if (SCM_BIGP (n1)) | |
1218 | { | |
1219 | if (SCM_INUMP (n2)) | |
1220 | { | |
1221 | SCM_SWAP (n1, n2); | |
1222 | nn1 = SCM_INUM (n1); | |
1223 | goto intbig; | |
1224 | } | |
1225 | else if (SCM_BIGP (n2)) | |
1226 | { | |
1227 | SCM result_z = scm_i_mkbig (); | |
1228 | mpz_and (SCM_I_BIG_MPZ (result_z), | |
1229 | SCM_I_BIG_MPZ (n1), | |
1230 | SCM_I_BIG_MPZ (n2)); | |
1231 | scm_remember_upto_here_2 (n1, n2); | |
1232 | return scm_i_normbig (result_z); | |
1233 | } | |
1234 | else | |
1235 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1236 | } |
0aacf84e | 1237 | else |
09fb7599 | 1238 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1239 | } |
1bbd0b84 | 1240 | #undef FUNC_NAME |
0f2d19dd | 1241 | |
09fb7599 | 1242 | |
c3ee7520 | 1243 | SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr, |
1bbd0b84 | 1244 | (SCM n1, SCM n2), |
3c3db128 GH |
1245 | "Return the bitwise OR of the integer arguments.\n\n" |
1246 | "@lisp\n" | |
1247 | "(logior) @result{} 0\n" | |
1248 | "(logior 7) @result{} 7\n" | |
1249 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1e6808ea | 1250 | "@end lisp") |
1bbd0b84 | 1251 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 1252 | { |
9a00c9fc DH |
1253 | long int nn1; |
1254 | ||
0aacf84e MD |
1255 | if (SCM_UNBNDP (n2)) |
1256 | { | |
1257 | if (SCM_UNBNDP (n1)) | |
1258 | return SCM_INUM0; | |
1259 | else if (SCM_NUMBERP (n1)) | |
1260 | return n1; | |
1261 | else | |
1262 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1263 | } |
09fb7599 | 1264 | |
0aacf84e MD |
1265 | if (SCM_INUMP (n1)) |
1266 | { | |
9a00c9fc | 1267 | nn1 = SCM_INUM (n1); |
0aacf84e MD |
1268 | if (SCM_INUMP (n2)) |
1269 | { | |
1270 | long nn2 = SCM_INUM (n2); | |
1271 | return SCM_MAKINUM (nn1 | nn2); | |
1272 | } | |
1273 | else if (SCM_BIGP (n2)) | |
1274 | { | |
1275 | intbig: | |
1276 | if (nn1 == 0) | |
1277 | return n2; | |
1278 | { | |
1279 | SCM result_z = scm_i_mkbig (); | |
1280 | mpz_t nn1_z; | |
1281 | mpz_init_set_si (nn1_z, nn1); | |
1282 | mpz_ior (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1283 | scm_remember_upto_here_1 (n2); | |
1284 | mpz_clear (nn1_z); | |
1285 | return result_z; | |
1286 | } | |
1287 | } | |
1288 | else | |
1289 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1290 | } | |
1291 | else if (SCM_BIGP (n1)) | |
1292 | { | |
1293 | if (SCM_INUMP (n2)) | |
1294 | { | |
1295 | SCM_SWAP (n1, n2); | |
1296 | nn1 = SCM_INUM (n1); | |
1297 | goto intbig; | |
1298 | } | |
1299 | else if (SCM_BIGP (n2)) | |
1300 | { | |
1301 | SCM result_z = scm_i_mkbig (); | |
1302 | mpz_ior (SCM_I_BIG_MPZ (result_z), | |
1303 | SCM_I_BIG_MPZ (n1), | |
1304 | SCM_I_BIG_MPZ (n2)); | |
1305 | scm_remember_upto_here_2 (n1, n2); | |
1306 | return result_z; | |
1307 | } | |
1308 | else | |
1309 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1310 | } |
0aacf84e | 1311 | else |
09fb7599 | 1312 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1313 | } |
1bbd0b84 | 1314 | #undef FUNC_NAME |
0f2d19dd | 1315 | |
09fb7599 | 1316 | |
c3ee7520 | 1317 | SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr, |
1bbd0b84 | 1318 | (SCM n1, SCM n2), |
3c3db128 GH |
1319 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1320 | "set in the result if it is set in an odd number of arguments.\n" | |
1321 | "@lisp\n" | |
1322 | "(logxor) @result{} 0\n" | |
1323 | "(logxor 7) @result{} 7\n" | |
1324 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1325 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1326 | "@end lisp") |
1bbd0b84 | 1327 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1328 | { |
9a00c9fc DH |
1329 | long int nn1; |
1330 | ||
0aacf84e MD |
1331 | if (SCM_UNBNDP (n2)) |
1332 | { | |
1333 | if (SCM_UNBNDP (n1)) | |
1334 | return SCM_INUM0; | |
1335 | else if (SCM_NUMBERP (n1)) | |
1336 | return n1; | |
1337 | else | |
1338 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1339 | } |
09fb7599 | 1340 | |
0aacf84e MD |
1341 | if (SCM_INUMP (n1)) |
1342 | { | |
9a00c9fc | 1343 | nn1 = SCM_INUM (n1); |
0aacf84e MD |
1344 | if (SCM_INUMP (n2)) |
1345 | { | |
1346 | long nn2 = SCM_INUM (n2); | |
1347 | return SCM_MAKINUM (nn1 ^ nn2); | |
1348 | } | |
1349 | else if (SCM_BIGP (n2)) | |
1350 | { | |
1351 | intbig: | |
1352 | { | |
1353 | SCM result_z = scm_i_mkbig (); | |
1354 | mpz_t nn1_z; | |
1355 | mpz_init_set_si (nn1_z, nn1); | |
1356 | mpz_xor (SCM_I_BIG_MPZ (result_z), nn1_z, SCM_I_BIG_MPZ (n2)); | |
1357 | scm_remember_upto_here_1 (n2); | |
1358 | mpz_clear (nn1_z); | |
1359 | return scm_i_normbig (result_z); | |
1360 | } | |
1361 | } | |
1362 | else | |
1363 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1364 | } | |
1365 | else if (SCM_BIGP (n1)) | |
1366 | { | |
1367 | if (SCM_INUMP (n2)) | |
1368 | { | |
1369 | SCM_SWAP (n1, n2); | |
1370 | nn1 = SCM_INUM (n1); | |
1371 | goto intbig; | |
1372 | } | |
1373 | else if (SCM_BIGP (n2)) | |
1374 | { | |
1375 | SCM result_z = scm_i_mkbig (); | |
1376 | mpz_xor (SCM_I_BIG_MPZ (result_z), | |
1377 | SCM_I_BIG_MPZ (n1), | |
1378 | SCM_I_BIG_MPZ (n2)); | |
1379 | scm_remember_upto_here_2 (n1, n2); | |
1380 | return scm_i_normbig (result_z); | |
1381 | } | |
1382 | else | |
1383 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
09fb7599 | 1384 | } |
0aacf84e | 1385 | else |
09fb7599 | 1386 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); |
0f2d19dd | 1387 | } |
1bbd0b84 | 1388 | #undef FUNC_NAME |
0f2d19dd | 1389 | |
09fb7599 | 1390 | |
a1ec6916 | 1391 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea MG |
1392 | (SCM j, SCM k), |
1393 | "@lisp\n" | |
b380b885 MD |
1394 | "(logtest j k) @equiv{} (not (zero? (logand j k)))\n\n" |
1395 | "(logtest #b0100 #b1011) @result{} #f\n" | |
1396 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1397 | "@end lisp") |
1bbd0b84 | 1398 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1399 | { |
1e6808ea | 1400 | long int nj; |
9a00c9fc | 1401 | |
0aacf84e MD |
1402 | if (SCM_INUMP (j)) |
1403 | { | |
1e6808ea | 1404 | nj = SCM_INUM (j); |
0aacf84e MD |
1405 | if (SCM_INUMP (k)) |
1406 | { | |
1407 | long nk = SCM_INUM (k); | |
1408 | return SCM_BOOL (nj & nk); | |
1409 | } | |
1410 | else if (SCM_BIGP (k)) | |
1411 | { | |
1412 | intbig: | |
1413 | if (nj == 0) | |
1414 | return SCM_BOOL_F; | |
1415 | { | |
1416 | SCM result; | |
1417 | mpz_t nj_z; | |
1418 | mpz_init_set_si (nj_z, nj); | |
1419 | mpz_and (nj_z, nj_z, SCM_I_BIG_MPZ (k)); | |
1420 | scm_remember_upto_here_1 (k); | |
1421 | result = SCM_BOOL (mpz_sgn (nj_z) != 0); | |
1422 | mpz_clear (nj_z); | |
1423 | return result; | |
1424 | } | |
1425 | } | |
1426 | else | |
1427 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1428 | } | |
1429 | else if (SCM_BIGP (j)) | |
1430 | { | |
1431 | if (SCM_INUMP (k)) | |
1432 | { | |
1433 | SCM_SWAP (j, k); | |
1434 | nj = SCM_INUM (j); | |
1435 | goto intbig; | |
1436 | } | |
1437 | else if (SCM_BIGP (k)) | |
1438 | { | |
1439 | SCM result; | |
1440 | mpz_t result_z; | |
1441 | mpz_init (result_z); | |
1442 | mpz_and (result_z, | |
1443 | SCM_I_BIG_MPZ (j), | |
1444 | SCM_I_BIG_MPZ (k)); | |
1445 | scm_remember_upto_here_2 (j, k); | |
1446 | result = SCM_BOOL (mpz_sgn (result_z) != 0); | |
1447 | mpz_clear (result_z); | |
1448 | return result; | |
1449 | } | |
1450 | else | |
1451 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); | |
1452 | } | |
1453 | else | |
1454 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); | |
0f2d19dd | 1455 | } |
1bbd0b84 | 1456 | #undef FUNC_NAME |
0f2d19dd | 1457 | |
c1bfcf60 | 1458 | |
a1ec6916 | 1459 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1460 | (SCM index, SCM j), |
1e6808ea | 1461 | "@lisp\n" |
b380b885 MD |
1462 | "(logbit? index j) @equiv{} (logtest (integer-expt 2 index) j)\n\n" |
1463 | "(logbit? 0 #b1101) @result{} #t\n" | |
1464 | "(logbit? 1 #b1101) @result{} #f\n" | |
1465 | "(logbit? 2 #b1101) @result{} #t\n" | |
1466 | "(logbit? 3 #b1101) @result{} #t\n" | |
1467 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1468 | "@end lisp") |
1bbd0b84 | 1469 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1470 | { |
78166ad5 DH |
1471 | unsigned long int iindex; |
1472 | ||
1473 | SCM_VALIDATE_INUM_MIN (SCM_ARG1, index, 0); | |
1474 | iindex = (unsigned long int) SCM_INUM (index); | |
1475 | ||
0aacf84e | 1476 | if (SCM_INUMP (j)) |
78166ad5 | 1477 | return SCM_BOOL ((1L << iindex) & SCM_INUM (j)); |
0aacf84e MD |
1478 | else if (SCM_BIGP (j)) |
1479 | { | |
1480 | int val = mpz_tstbit (SCM_I_BIG_MPZ (j), iindex); | |
1481 | scm_remember_upto_here_1 (j); | |
1482 | return SCM_BOOL (val); | |
1483 | } | |
1484 | else | |
78166ad5 | 1485 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); |
0f2d19dd | 1486 | } |
1bbd0b84 | 1487 | #undef FUNC_NAME |
0f2d19dd | 1488 | |
78166ad5 | 1489 | |
a1ec6916 | 1490 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1491 | (SCM n), |
4d814788 | 1492 | "Return the integer which is the ones-complement of the integer\n" |
1e6808ea MG |
1493 | "argument.\n" |
1494 | "\n" | |
b380b885 MD |
1495 | "@lisp\n" |
1496 | "(number->string (lognot #b10000000) 2)\n" | |
1497 | " @result{} \"-10000001\"\n" | |
1498 | "(number->string (lognot #b0) 2)\n" | |
1499 | " @result{} \"-1\"\n" | |
1e6808ea | 1500 | "@end lisp") |
1bbd0b84 | 1501 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1502 | { |
f9811f9f KR |
1503 | if (SCM_INUMP (n)) { |
1504 | /* No overflow here, just need to toggle all the bits making up the inum. | |
1505 | Enhancement: No need to strip the tag and add it back, could just xor | |
1506 | a block of 1 bits, if that worked with the various debug versions of | |
1507 | the SCM typedef. */ | |
1508 | return SCM_MAKINUM (~ SCM_INUM (n)); | |
1509 | ||
1510 | } else if (SCM_BIGP (n)) { | |
1511 | SCM result = scm_i_mkbig (); | |
1512 | mpz_com (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (n)); | |
1513 | scm_remember_upto_here_1 (n); | |
1514 | return result; | |
1515 | ||
1516 | } else { | |
1517 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1518 | } | |
0f2d19dd | 1519 | } |
1bbd0b84 | 1520 | #undef FUNC_NAME |
0f2d19dd | 1521 | |
a1ec6916 | 1522 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1523 | (SCM n, SCM k), |
1e6808ea MG |
1524 | "Return @var{n} raised to the non-negative integer exponent\n" |
1525 | "@var{k}.\n" | |
1526 | "\n" | |
b380b885 MD |
1527 | "@lisp\n" |
1528 | "(integer-expt 2 5)\n" | |
1529 | " @result{} 32\n" | |
1530 | "(integer-expt -3 3)\n" | |
1531 | " @result{} -27\n" | |
1532 | "@end lisp") | |
1bbd0b84 | 1533 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1534 | { |
1c35cb19 RB |
1535 | long i2 = 0; |
1536 | SCM z_i2 = SCM_BOOL_F; | |
1537 | int i2_is_big = 0; | |
f872b822 | 1538 | SCM acc = SCM_MAKINUM (1L); |
ca46fb90 | 1539 | |
d57ed702 | 1540 | /* 0^0 == 1 according to R5RS */ |
4260a7fc | 1541 | if (SCM_EQ_P (n, SCM_INUM0) || SCM_EQ_P (n, acc)) |
7b3381f4 | 1542 | return SCM_FALSEP (scm_zero_p(k)) ? n : acc; |
4260a7fc DH |
1543 | else if (SCM_EQ_P (n, SCM_MAKINUM (-1L))) |
1544 | return SCM_FALSEP (scm_even_p (k)) ? n : acc; | |
ca46fb90 | 1545 | |
ca46fb90 RB |
1546 | if (SCM_INUMP (k)) |
1547 | i2 = SCM_INUM (k); | |
1548 | else if (SCM_BIGP (k)) | |
1549 | { | |
1550 | z_i2 = scm_i_clonebig (k, 1); | |
ca46fb90 RB |
1551 | scm_remember_upto_here_1 (k); |
1552 | i2_is_big = 1; | |
1553 | } | |
1554 | else if (SCM_REALP (k)) | |
2830fd91 MD |
1555 | { |
1556 | double r = SCM_REAL_VALUE (k); | |
ca46fb90 RB |
1557 | if (floor (r) != r) |
1558 | SCM_WRONG_TYPE_ARG (2, k); | |
1559 | if ((r > SCM_MOST_POSITIVE_FIXNUM) || (r < SCM_MOST_NEGATIVE_FIXNUM)) | |
1560 | { | |
1561 | z_i2 = scm_i_mkbig (); | |
753ac1e7 | 1562 | mpz_set_d (SCM_I_BIG_MPZ (z_i2), r); |
ca46fb90 RB |
1563 | i2_is_big = 1; |
1564 | } | |
1565 | else | |
1566 | { | |
1567 | i2 = r; | |
1568 | } | |
2830fd91 MD |
1569 | } |
1570 | else | |
ca46fb90 RB |
1571 | SCM_WRONG_TYPE_ARG (2, k); |
1572 | ||
1573 | if (i2_is_big) | |
f872b822 | 1574 | { |
ca46fb90 RB |
1575 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == -1) |
1576 | { | |
1577 | mpz_neg (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2)); | |
1578 | n = scm_divide (n, SCM_UNDEFINED); | |
1579 | } | |
1580 | while (1) | |
1581 | { | |
1582 | if (mpz_sgn(SCM_I_BIG_MPZ (z_i2)) == 0) | |
1583 | { | |
ca46fb90 RB |
1584 | return acc; |
1585 | } | |
1586 | if (mpz_cmp_ui(SCM_I_BIG_MPZ (z_i2), 1) == 0) | |
1587 | { | |
ca46fb90 RB |
1588 | return scm_product (acc, n); |
1589 | } | |
1590 | if (mpz_tstbit(SCM_I_BIG_MPZ (z_i2), 0)) | |
1591 | acc = scm_product (acc, n); | |
1592 | n = scm_product (n, n); | |
1593 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ (z_i2), SCM_I_BIG_MPZ (z_i2), 1); | |
1594 | } | |
f872b822 | 1595 | } |
ca46fb90 | 1596 | else |
f872b822 | 1597 | { |
ca46fb90 RB |
1598 | if (i2 < 0) |
1599 | { | |
1600 | i2 = -i2; | |
1601 | n = scm_divide (n, SCM_UNDEFINED); | |
1602 | } | |
1603 | while (1) | |
1604 | { | |
1605 | if (0 == i2) | |
1606 | return acc; | |
1607 | if (1 == i2) | |
1608 | return scm_product (acc, n); | |
1609 | if (i2 & 1) | |
1610 | acc = scm_product (acc, n); | |
1611 | n = scm_product (n, n); | |
1612 | i2 >>= 1; | |
1613 | } | |
f872b822 | 1614 | } |
0f2d19dd | 1615 | } |
1bbd0b84 | 1616 | #undef FUNC_NAME |
0f2d19dd | 1617 | |
a1ec6916 | 1618 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1619 | (SCM n, SCM cnt), |
32f19569 KR |
1620 | "Return @var{n} shifted left by @var{cnt} bits, or shifted right\n" |
1621 | "if @var{cnt} is negative. This is an ``arithmetic'' shift.\n" | |
1e6808ea | 1622 | "\n" |
32f19569 KR |
1623 | "This is effectively a multiplication by 2^@var{cnt}}, and when\n" |
1624 | "@var{cnt} is negative it's a division, rounded towards negative\n" | |
1625 | "infinity. (Note that this is not the same rounding as\n" | |
1626 | "@code{quotient} does.)\n" | |
1627 | "\n" | |
1628 | "With @var{n} viewed as an infinite precision twos complement,\n" | |
1629 | "@code{ash} means a left shift introducing zero bits, or a right\n" | |
1630 | "shift dropping bits.\n" | |
1e6808ea | 1631 | "\n" |
b380b885 | 1632 | "@lisp\n" |
1e6808ea MG |
1633 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1634 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
32f19569 KR |
1635 | "\n" |
1636 | ";; -23 is bits ...11101001, -6 is bits ...111010\n" | |
1637 | "(ash -23 -2) @result{} -6\n" | |
a3c8b9fc | 1638 | "@end lisp") |
1bbd0b84 | 1639 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1640 | { |
3ab9f56e DH |
1641 | long bits_to_shift; |
1642 | ||
3ab9f56e DH |
1643 | SCM_VALIDATE_INUM (2, cnt); |
1644 | ||
1645 | bits_to_shift = SCM_INUM (cnt); | |
ca46fb90 RB |
1646 | |
1647 | if (bits_to_shift < 0) | |
1648 | { | |
1649 | /* Shift right by abs(cnt) bits. This is realized as a division | |
1650 | by div:=2^abs(cnt). However, to guarantee the floor | |
1651 | rounding, negative values require some special treatment. | |
1652 | */ | |
1653 | SCM div = scm_integer_expt (SCM_MAKINUM (2), | |
1654 | SCM_MAKINUM (-bits_to_shift)); | |
f92e85f7 MV |
1655 | |
1656 | /* scm_quotient assumes its arguments are integers, but it's legal to (ash 1/2 -1) */ | |
ca46fb90 RB |
1657 | if (SCM_FALSEP (scm_negative_p (n))) |
1658 | return scm_quotient (n, div); | |
1659 | else | |
1660 | return scm_sum (SCM_MAKINUM (-1L), | |
1661 | scm_quotient (scm_sum (SCM_MAKINUM (1L), n), div)); | |
1662 | } | |
1663 | else | |
3ab9f56e | 1664 | /* Shift left is done by multiplication with 2^CNT */ |
f872b822 | 1665 | return scm_product (n, scm_integer_expt (SCM_MAKINUM (2), cnt)); |
0f2d19dd | 1666 | } |
1bbd0b84 | 1667 | #undef FUNC_NAME |
0f2d19dd | 1668 | |
3c9f20f8 | 1669 | |
7f848242 KR |
1670 | #define MIN(x,y) ((x) < (y) ? (x) : (y)) |
1671 | ||
a1ec6916 | 1672 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 1673 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
1674 | "Return the integer composed of the @var{start} (inclusive)\n" |
1675 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
1676 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
1677 | "\n" | |
b380b885 MD |
1678 | "@lisp\n" |
1679 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
1680 | " @result{} \"1010\"\n" | |
1681 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
1682 | " @result{} \"10110\"\n" | |
1683 | "@end lisp") | |
1bbd0b84 | 1684 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 1685 | { |
7f848242 | 1686 | unsigned long int istart, iend, bits; |
34d19ef6 | 1687 | SCM_VALIDATE_INUM_MIN_COPY (2, start,0, istart); |
c1bfcf60 GB |
1688 | SCM_VALIDATE_INUM_MIN_COPY (3, end, 0, iend); |
1689 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); | |
78166ad5 | 1690 | |
7f848242 KR |
1691 | /* how many bits to keep */ |
1692 | bits = iend - istart; | |
1693 | ||
0aacf84e MD |
1694 | if (SCM_INUMP (n)) |
1695 | { | |
1696 | long int in = SCM_INUM (n); | |
7f848242 KR |
1697 | |
1698 | /* When istart>=SCM_I_FIXNUM_BIT we can just limit the shift to | |
1699 | SCM_I_FIXNUM_BIT-1 to get either 0 or -1 per the sign of "in". | |
1700 | FIXME: This shift relies on signed right shifts being arithmetic, | |
1701 | which is not guaranteed by C99. */ | |
1702 | in >>= MIN (istart, SCM_I_FIXNUM_BIT-1); | |
ac0c002c | 1703 | |
0aacf84e MD |
1704 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
1705 | { | |
1706 | /* Since we emulate two's complement encoded numbers, this | |
1707 | * special case requires us to produce a result that has | |
7f848242 | 1708 | * more bits than can be stored in a fixnum. |
0aacf84e | 1709 | */ |
7f848242 KR |
1710 | SCM result = scm_i_long2big (in); |
1711 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), | |
1712 | bits); | |
1713 | return result; | |
0aacf84e | 1714 | } |
ac0c002c | 1715 | |
7f848242 KR |
1716 | /* mask down to requisite bits */ |
1717 | bits = MIN (bits, SCM_I_FIXNUM_BIT); | |
1718 | return SCM_MAKINUM (in & ((1L << bits) - 1)); | |
0aacf84e MD |
1719 | } |
1720 | else if (SCM_BIGP (n)) | |
ac0c002c | 1721 | { |
7f848242 KR |
1722 | SCM result; |
1723 | if (bits == 1) | |
1724 | { | |
1725 | result = SCM_MAKINUM (mpz_tstbit (SCM_I_BIG_MPZ (n), istart)); | |
1726 | } | |
1727 | else | |
1728 | { | |
1729 | /* ENHANCE-ME: It'd be nice not to allocate a new bignum when | |
1730 | bits<SCM_I_FIXNUM_BIT. Would want some help from GMP to get | |
1731 | such bits into a ulong. */ | |
1732 | result = scm_i_mkbig (); | |
1733 | mpz_fdiv_q_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(n), istart); | |
1734 | mpz_fdiv_r_2exp (SCM_I_BIG_MPZ(result), SCM_I_BIG_MPZ(result), bits); | |
1735 | result = scm_i_normbig (result); | |
1736 | } | |
1737 | scm_remember_upto_here_1 (n); | |
1738 | return result; | |
ac0c002c | 1739 | } |
0aacf84e | 1740 | else |
78166ad5 | 1741 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
0f2d19dd | 1742 | } |
1bbd0b84 | 1743 | #undef FUNC_NAME |
0f2d19dd | 1744 | |
7f848242 | 1745 | |
e4755e5c JB |
1746 | static const char scm_logtab[] = { |
1747 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
1748 | }; | |
1cc91f1b | 1749 | |
a1ec6916 | 1750 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 1751 | (SCM n), |
1e6808ea MG |
1752 | "Return the number of bits in integer @var{n}. If integer is\n" |
1753 | "positive, the 1-bits in its binary representation are counted.\n" | |
1754 | "If negative, the 0-bits in its two's-complement binary\n" | |
1755 | "representation are counted. If 0, 0 is returned.\n" | |
1756 | "\n" | |
b380b885 MD |
1757 | "@lisp\n" |
1758 | "(logcount #b10101010)\n" | |
ca46fb90 RB |
1759 | " @result{} 4\n" |
1760 | "(logcount 0)\n" | |
1761 | " @result{} 0\n" | |
1762 | "(logcount -2)\n" | |
1763 | " @result{} 1\n" | |
1764 | "@end lisp") | |
1765 | #define FUNC_NAME s_scm_logcount | |
1766 | { | |
1767 | if (SCM_INUMP (n)) | |
f872b822 | 1768 | { |
ca46fb90 RB |
1769 | unsigned long int c = 0; |
1770 | long int nn = SCM_INUM (n); | |
1771 | if (nn < 0) | |
1772 | nn = -1 - nn; | |
1773 | while (nn) | |
1774 | { | |
1775 | c += scm_logtab[15 & nn]; | |
1776 | nn >>= 4; | |
1777 | } | |
1778 | return SCM_MAKINUM (c); | |
f872b822 | 1779 | } |
ca46fb90 | 1780 | else if (SCM_BIGP (n)) |
f872b822 | 1781 | { |
ca46fb90 | 1782 | unsigned long count; |
713a4259 KR |
1783 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) >= 0) |
1784 | count = mpz_popcount (SCM_I_BIG_MPZ (n)); | |
ca46fb90 | 1785 | else |
713a4259 KR |
1786 | count = mpz_hamdist (SCM_I_BIG_MPZ (n), z_negative_one); |
1787 | scm_remember_upto_here_1 (n); | |
ca46fb90 | 1788 | return SCM_MAKINUM (count); |
f872b822 | 1789 | } |
ca46fb90 RB |
1790 | else |
1791 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
0f2d19dd | 1792 | } |
ca46fb90 | 1793 | #undef FUNC_NAME |
0f2d19dd JB |
1794 | |
1795 | ||
ca46fb90 RB |
1796 | static const char scm_ilentab[] = { |
1797 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
1798 | }; | |
1799 | ||
0f2d19dd | 1800 | |
ca46fb90 RB |
1801 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
1802 | (SCM n), | |
1803 | "Return the number of bits necessary to represent @var{n}.\n" | |
1804 | "\n" | |
1805 | "@lisp\n" | |
1806 | "(integer-length #b10101010)\n" | |
1807 | " @result{} 8\n" | |
1808 | "(integer-length 0)\n" | |
1809 | " @result{} 0\n" | |
1810 | "(integer-length #b1111)\n" | |
1811 | " @result{} 4\n" | |
1812 | "@end lisp") | |
1813 | #define FUNC_NAME s_scm_integer_length | |
1814 | { | |
0aacf84e MD |
1815 | if (SCM_INUMP (n)) |
1816 | { | |
1817 | unsigned long int c = 0; | |
1818 | unsigned int l = 4; | |
1819 | long int nn = SCM_INUM (n); | |
1820 | if (nn < 0) | |
1821 | nn = -1 - nn; | |
1822 | while (nn) | |
1823 | { | |
1824 | c += 4; | |
1825 | l = scm_ilentab [15 & nn]; | |
1826 | nn >>= 4; | |
1827 | } | |
1828 | return SCM_MAKINUM (c - 4 + l); | |
1829 | } | |
1830 | else if (SCM_BIGP (n)) | |
1831 | { | |
1832 | /* mpz_sizeinbase looks at the absolute value of negatives, whereas we | |
1833 | want a ones-complement. If n is ...111100..00 then mpz_sizeinbase is | |
1834 | 1 too big, so check for that and adjust. */ | |
1835 | size_t size = mpz_sizeinbase (SCM_I_BIG_MPZ (n), 2); | |
1836 | if (mpz_sgn (SCM_I_BIG_MPZ (n)) < 0 | |
1837 | && mpz_scan0 (SCM_I_BIG_MPZ (n), /* no 0 bits above the lowest 1 */ | |
1838 | mpz_scan1 (SCM_I_BIG_MPZ (n), 0)) == ULONG_MAX) | |
1839 | size--; | |
1840 | scm_remember_upto_here_1 (n); | |
1841 | return SCM_MAKINUM (size); | |
1842 | } | |
1843 | else | |
ca46fb90 | 1844 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); |
ca46fb90 RB |
1845 | } |
1846 | #undef FUNC_NAME | |
0f2d19dd JB |
1847 | |
1848 | /*** NUMBERS -> STRINGS ***/ | |
0f2d19dd | 1849 | int scm_dblprec; |
e4755e5c | 1850 | static const double fx[] = |
f872b822 MD |
1851 | { 0.0, 5e-1, 5e-2, 5e-3, 5e-4, 5e-5, |
1852 | 5e-6, 5e-7, 5e-8, 5e-9, 5e-10, | |
1853 | 5e-11, 5e-12, 5e-13, 5e-14, 5e-15, | |
1854 | 5e-16, 5e-17, 5e-18, 5e-19, 5e-20}; | |
0f2d19dd | 1855 | |
1be6b49c | 1856 | static size_t |
1bbd0b84 | 1857 | idbl2str (double f, char *a) |
0f2d19dd JB |
1858 | { |
1859 | int efmt, dpt, d, i, wp = scm_dblprec; | |
1be6b49c | 1860 | size_t ch = 0; |
0f2d19dd JB |
1861 | int exp = 0; |
1862 | ||
f872b822 | 1863 | if (f == 0.0) |
abb7e44d MV |
1864 | { |
1865 | #ifdef HAVE_COPYSIGN | |
1866 | double sgn = copysign (1.0, f); | |
1867 | ||
1868 | if (sgn < 0.0) | |
1869 | a[ch++] = '-'; | |
1870 | #endif | |
1871 | ||
1872 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ | |
1873 | } | |
7351e207 MV |
1874 | |
1875 | if (xisinf (f)) | |
1876 | { | |
1877 | if (f < 0) | |
1878 | strcpy (a, "-inf.0"); | |
1879 | else | |
1880 | strcpy (a, "+inf.0"); | |
1881 | return ch+6; | |
1882 | } | |
1883 | else if (xisnan (f)) | |
1884 | { | |
1885 | strcpy (a, "+nan.0"); | |
1886 | return ch+6; | |
1887 | } | |
1888 | ||
f872b822 MD |
1889 | if (f < 0.0) |
1890 | { | |
1891 | f = -f; | |
1892 | a[ch++] = '-'; | |
1893 | } | |
7351e207 | 1894 | |
f872b822 MD |
1895 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
1896 | make-uniform-vector, from causing infinite loops. */ | |
1897 | while (f < 1.0) | |
1898 | { | |
1899 | f *= 10.0; | |
1900 | if (exp-- < DBL_MIN_10_EXP) | |
7351e207 MV |
1901 | { |
1902 | a[ch++] = '#'; | |
1903 | a[ch++] = '.'; | |
1904 | a[ch++] = '#'; | |
1905 | return ch; | |
1906 | } | |
f872b822 MD |
1907 | } |
1908 | while (f > 10.0) | |
1909 | { | |
1910 | f *= 0.10; | |
1911 | if (exp++ > DBL_MAX_10_EXP) | |
7351e207 MV |
1912 | { |
1913 | a[ch++] = '#'; | |
1914 | a[ch++] = '.'; | |
1915 | a[ch++] = '#'; | |
1916 | return ch; | |
1917 | } | |
f872b822 MD |
1918 | } |
1919 | #else | |
1920 | while (f < 1.0) | |
1921 | { | |
1922 | f *= 10.0; | |
1923 | exp--; | |
1924 | } | |
1925 | while (f > 10.0) | |
1926 | { | |
1927 | f /= 10.0; | |
1928 | exp++; | |
1929 | } | |
1930 | #endif | |
1931 | if (f + fx[wp] >= 10.0) | |
1932 | { | |
1933 | f = 1.0; | |
1934 | exp++; | |
1935 | } | |
0f2d19dd | 1936 | zero: |
f872b822 MD |
1937 | #ifdef ENGNOT |
1938 | dpt = (exp + 9999) % 3; | |
0f2d19dd JB |
1939 | exp -= dpt++; |
1940 | efmt = 1; | |
f872b822 MD |
1941 | #else |
1942 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 1943 | if (!efmt) |
cda139a7 MD |
1944 | { |
1945 | if (exp < 0) | |
1946 | { | |
1947 | a[ch++] = '0'; | |
1948 | a[ch++] = '.'; | |
1949 | dpt = exp; | |
f872b822 MD |
1950 | while (++dpt) |
1951 | a[ch++] = '0'; | |
cda139a7 MD |
1952 | } |
1953 | else | |
f872b822 | 1954 | dpt = exp + 1; |
cda139a7 | 1955 | } |
0f2d19dd JB |
1956 | else |
1957 | dpt = 1; | |
f872b822 MD |
1958 | #endif |
1959 | ||
1960 | do | |
1961 | { | |
1962 | d = f; | |
1963 | f -= d; | |
1964 | a[ch++] = d + '0'; | |
1965 | if (f < fx[wp]) | |
1966 | break; | |
1967 | if (f + fx[wp] >= 1.0) | |
1968 | { | |
1969 | a[ch - 1]++; | |
1970 | break; | |
1971 | } | |
1972 | f *= 10.0; | |
1973 | if (!(--dpt)) | |
1974 | a[ch++] = '.'; | |
0f2d19dd | 1975 | } |
f872b822 | 1976 | while (wp--); |
0f2d19dd JB |
1977 | |
1978 | if (dpt > 0) | |
cda139a7 | 1979 | { |
f872b822 | 1980 | #ifndef ENGNOT |
cda139a7 MD |
1981 | if ((dpt > 4) && (exp > 6)) |
1982 | { | |
f872b822 | 1983 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 1984 | for (i = ch++; i > d; i--) |
f872b822 | 1985 | a[i] = a[i - 1]; |
cda139a7 MD |
1986 | a[d] = '.'; |
1987 | efmt = 1; | |
1988 | } | |
1989 | else | |
f872b822 | 1990 | #endif |
cda139a7 | 1991 | { |
f872b822 MD |
1992 | while (--dpt) |
1993 | a[ch++] = '0'; | |
cda139a7 MD |
1994 | a[ch++] = '.'; |
1995 | } | |
1996 | } | |
f872b822 MD |
1997 | if (a[ch - 1] == '.') |
1998 | a[ch++] = '0'; /* trailing zero */ | |
1999 | if (efmt && exp) | |
2000 | { | |
2001 | a[ch++] = 'e'; | |
2002 | if (exp < 0) | |
2003 | { | |
2004 | exp = -exp; | |
2005 | a[ch++] = '-'; | |
2006 | } | |
2007 | for (i = 10; i <= exp; i *= 10); | |
2008 | for (i /= 10; i; i /= 10) | |
2009 | { | |
2010 | a[ch++] = exp / i + '0'; | |
2011 | exp %= i; | |
2012 | } | |
0f2d19dd | 2013 | } |
0f2d19dd JB |
2014 | return ch; |
2015 | } | |
2016 | ||
1cc91f1b | 2017 | |
1be6b49c | 2018 | static size_t |
1bbd0b84 | 2019 | iflo2str (SCM flt, char *str) |
0f2d19dd | 2020 | { |
1be6b49c | 2021 | size_t i; |
3c9a524f | 2022 | if (SCM_REALP (flt)) |
f3ae5d60 | 2023 | i = idbl2str (SCM_REAL_VALUE (flt), str); |
0f2d19dd | 2024 | else |
f872b822 | 2025 | { |
f3ae5d60 MD |
2026 | i = idbl2str (SCM_COMPLEX_REAL (flt), str); |
2027 | if (SCM_COMPLEX_IMAG (flt) != 0.0) | |
2028 | { | |
7351e207 MV |
2029 | double imag = SCM_COMPLEX_IMAG (flt); |
2030 | /* Don't output a '+' for negative numbers or for Inf and | |
2031 | NaN. They will provide their own sign. */ | |
2032 | if (0 <= imag && !xisinf (imag) && !xisnan (imag)) | |
f3ae5d60 | 2033 | str[i++] = '+'; |
7351e207 | 2034 | i += idbl2str (imag, &str[i]); |
f3ae5d60 MD |
2035 | str[i++] = 'i'; |
2036 | } | |
f872b822 | 2037 | } |
0f2d19dd JB |
2038 | return i; |
2039 | } | |
0f2d19dd | 2040 | |
5c11cc9d | 2041 | /* convert a long to a string (unterminated). returns the number of |
1bbd0b84 GB |
2042 | characters in the result. |
2043 | rad is output base | |
2044 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2045 | size_t |
1bbd0b84 | 2046 | scm_iint2str (long num, int rad, char *p) |
0f2d19dd | 2047 | { |
1be6b49c ML |
2048 | size_t j = 1; |
2049 | size_t i; | |
5c11cc9d GH |
2050 | unsigned long n = (num < 0) ? -num : num; |
2051 | ||
f872b822 | 2052 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2053 | j++; |
2054 | ||
2055 | i = j; | |
2056 | if (num < 0) | |
f872b822 | 2057 | { |
f872b822 | 2058 | *p++ = '-'; |
5c11cc9d GH |
2059 | j++; |
2060 | n = -num; | |
f872b822 | 2061 | } |
5c11cc9d GH |
2062 | else |
2063 | n = num; | |
f872b822 MD |
2064 | while (i--) |
2065 | { | |
5c11cc9d GH |
2066 | int d = n % rad; |
2067 | ||
f872b822 MD |
2068 | n /= rad; |
2069 | p[i] = d + ((d < 10) ? '0' : 'a' - 10); | |
2070 | } | |
0f2d19dd JB |
2071 | return j; |
2072 | } | |
2073 | ||
a1ec6916 | 2074 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2075 | (SCM n, SCM radix), |
2076 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2077 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2078 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2079 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2080 | { |
1bbd0b84 | 2081 | int base; |
98cb6e75 | 2082 | |
0aacf84e | 2083 | if (SCM_UNBNDP (radix)) |
98cb6e75 | 2084 | base = 10; |
0aacf84e MD |
2085 | else |
2086 | { | |
2087 | SCM_VALIDATE_INUM (2, radix); | |
2088 | base = SCM_INUM (radix); | |
2089 | /* FIXME: ask if range limit was OK, and if so, document */ | |
2090 | SCM_ASSERT_RANGE (2, radix, (base >= 2) && (base <= 36)); | |
2091 | } | |
98cb6e75 | 2092 | |
0aacf84e MD |
2093 | if (SCM_INUMP (n)) |
2094 | { | |
2095 | char num_buf [SCM_INTBUFLEN]; | |
2096 | size_t length = scm_iint2str (SCM_INUM (n), base, num_buf); | |
2097 | return scm_mem2string (num_buf, length); | |
2098 | } | |
2099 | else if (SCM_BIGP (n)) | |
2100 | { | |
2101 | char *str = mpz_get_str (NULL, base, SCM_I_BIG_MPZ (n)); | |
2102 | scm_remember_upto_here_1 (n); | |
2103 | return scm_take0str (str); | |
2104 | } | |
f92e85f7 MV |
2105 | else if (SCM_FRACTIONP (n)) |
2106 | { | |
2107 | scm_i_fraction_reduce (n); | |
2108 | return scm_string_append (scm_list_3 (scm_number_to_string (SCM_FRACTION_NUMERATOR (n), radix), | |
2109 | scm_mem2string ("/", 1), | |
2110 | scm_number_to_string (SCM_FRACTION_DENOMINATOR (n), radix))); | |
2111 | } | |
0aacf84e MD |
2112 | else if (SCM_INEXACTP (n)) |
2113 | { | |
2114 | char num_buf [FLOBUFLEN]; | |
2115 | return scm_mem2string (num_buf, iflo2str (n, num_buf)); | |
2116 | } | |
2117 | else | |
bb628794 | 2118 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd | 2119 | } |
1bbd0b84 | 2120 | #undef FUNC_NAME |
0f2d19dd JB |
2121 | |
2122 | ||
ca46fb90 RB |
2123 | /* These print routines used to be stubbed here so that scm_repl.c |
2124 | wouldn't need SCM_BIGDIG conditionals (pre GMP) */ | |
1cc91f1b | 2125 | |
0f2d19dd | 2126 | int |
e81d98ec | 2127 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2128 | { |
56e55ac7 | 2129 | char num_buf[FLOBUFLEN]; |
f872b822 | 2130 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port); |
0f2d19dd JB |
2131 | return !0; |
2132 | } | |
2133 | ||
f3ae5d60 | 2134 | int |
e81d98ec | 2135 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f92e85f7 | 2136 | |
f3ae5d60 | 2137 | { |
56e55ac7 | 2138 | char num_buf[FLOBUFLEN]; |
f3ae5d60 MD |
2139 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port); |
2140 | return !0; | |
2141 | } | |
1cc91f1b | 2142 | |
f92e85f7 MV |
2143 | int |
2144 | scm_i_print_fraction (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) | |
2145 | { | |
2146 | SCM str; | |
2147 | scm_i_fraction_reduce (sexp); | |
2148 | str = scm_number_to_string (sexp, SCM_UNDEFINED); | |
2149 | scm_lfwrite (SCM_STRING_CHARS (str), SCM_STRING_LENGTH (str), port); | |
2150 | scm_remember_upto_here_1 (str); | |
2151 | return !0; | |
2152 | } | |
2153 | ||
0f2d19dd | 2154 | int |
e81d98ec | 2155 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2156 | { |
ca46fb90 RB |
2157 | char *str = mpz_get_str (NULL, 10, SCM_I_BIG_MPZ (exp)); |
2158 | scm_remember_upto_here_1 (exp); | |
2159 | scm_lfwrite (str, (size_t) strlen (str), port); | |
2160 | free (str); | |
0f2d19dd JB |
2161 | return !0; |
2162 | } | |
2163 | /*** END nums->strs ***/ | |
2164 | ||
3c9a524f | 2165 | |
0f2d19dd | 2166 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2167 | |
3c9a524f DH |
2168 | /* The following functions implement the conversion from strings to numbers. |
2169 | * The implementation somehow follows the grammar for numbers as it is given | |
2170 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2171 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2172 | * points should be noted about the implementation: | |
2173 | * * Each function keeps a local index variable 'idx' that points at the | |
2174 | * current position within the parsed string. The global index is only | |
2175 | * updated if the function could parse the corresponding syntactic unit | |
2176 | * successfully. | |
2177 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2178 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2179 | * global exactness information is only updated after each part has been | |
2180 | * successfully parsed. | |
2181 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2182 | * Only if these fixnums would overflow, the result variables are updated | |
2183 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2184 | * the temporary variables holding the fixnums are cleared, and the process | |
2185 | * starts over again. If for example fixnums were able to store five decimal | |
2186 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2187 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2188 | * only every five digits two bignum operations were performed. | |
2189 | */ | |
2190 | ||
2191 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2192 | ||
2193 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2194 | ||
2195 | /* In non ASCII-style encodings the following macro might not work. */ | |
2196 | #define XDIGIT2UINT(d) (isdigit (d) ? (d) - '0' : tolower (d) - 'a' + 10) | |
2197 | ||
2a8fecee | 2198 | static SCM |
3c9a524f DH |
2199 | mem2uinteger (const char* mem, size_t len, unsigned int *p_idx, |
2200 | unsigned int radix, enum t_exactness *p_exactness) | |
2a8fecee | 2201 | { |
3c9a524f DH |
2202 | unsigned int idx = *p_idx; |
2203 | unsigned int hash_seen = 0; | |
2204 | scm_t_bits shift = 1; | |
2205 | scm_t_bits add = 0; | |
2206 | unsigned int digit_value; | |
2207 | SCM result; | |
2208 | char c; | |
2209 | ||
2210 | if (idx == len) | |
2211 | return SCM_BOOL_F; | |
2a8fecee | 2212 | |
3c9a524f DH |
2213 | c = mem[idx]; |
2214 | if (!isxdigit (c)) | |
2215 | return SCM_BOOL_F; | |
2216 | digit_value = XDIGIT2UINT (c); | |
2217 | if (digit_value >= radix) | |
2218 | return SCM_BOOL_F; | |
2219 | ||
2220 | idx++; | |
2221 | result = SCM_MAKINUM (digit_value); | |
2222 | while (idx != len) | |
f872b822 | 2223 | { |
3c9a524f DH |
2224 | char c = mem[idx]; |
2225 | if (isxdigit (c)) | |
f872b822 | 2226 | { |
3c9a524f | 2227 | if (hash_seen) |
1fe5e088 | 2228 | break; |
3c9a524f DH |
2229 | digit_value = XDIGIT2UINT (c); |
2230 | if (digit_value >= radix) | |
1fe5e088 | 2231 | break; |
f872b822 | 2232 | } |
3c9a524f DH |
2233 | else if (c == '#') |
2234 | { | |
2235 | hash_seen = 1; | |
2236 | digit_value = 0; | |
2237 | } | |
2238 | else | |
2239 | break; | |
2240 | ||
2241 | idx++; | |
2242 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2243 | { | |
2244 | result = scm_product (result, SCM_MAKINUM (shift)); | |
2245 | if (add > 0) | |
2246 | result = scm_sum (result, SCM_MAKINUM (add)); | |
2247 | ||
2248 | shift = radix; | |
2249 | add = digit_value; | |
2250 | } | |
2251 | else | |
2252 | { | |
2253 | shift = shift * radix; | |
2254 | add = add * radix + digit_value; | |
2255 | } | |
2256 | }; | |
2257 | ||
2258 | if (shift > 1) | |
2259 | result = scm_product (result, SCM_MAKINUM (shift)); | |
2260 | if (add > 0) | |
2261 | result = scm_sum (result, SCM_MAKINUM (add)); | |
2262 | ||
2263 | *p_idx = idx; | |
2264 | if (hash_seen) | |
2265 | *p_exactness = INEXACT; | |
2266 | ||
2267 | return result; | |
2a8fecee JB |
2268 | } |
2269 | ||
2270 | ||
3c9a524f DH |
2271 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2272 | * covers the parts of the rules that start at a potential point. The value | |
2273 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2274 | * in variable result. The content of *p_exactness indicates, whether a hash |
2275 | * has already been seen in the digits before the point. | |
3c9a524f | 2276 | */ |
1cc91f1b | 2277 | |
3c9a524f DH |
2278 | /* In non ASCII-style encodings the following macro might not work. */ |
2279 | #define DIGIT2UINT(d) ((d) - '0') | |
2280 | ||
2281 | static SCM | |
79d34f68 | 2282 | mem2decimal_from_point (SCM result, const char* mem, size_t len, |
3c9a524f | 2283 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2284 | { |
3c9a524f DH |
2285 | unsigned int idx = *p_idx; |
2286 | enum t_exactness x = *p_exactness; | |
3c9a524f DH |
2287 | |
2288 | if (idx == len) | |
79d34f68 | 2289 | return result; |
3c9a524f DH |
2290 | |
2291 | if (mem[idx] == '.') | |
2292 | { | |
2293 | scm_t_bits shift = 1; | |
2294 | scm_t_bits add = 0; | |
2295 | unsigned int digit_value; | |
79d34f68 | 2296 | SCM big_shift = SCM_MAKINUM (1); |
3c9a524f DH |
2297 | |
2298 | idx++; | |
2299 | while (idx != len) | |
2300 | { | |
2301 | char c = mem[idx]; | |
2302 | if (isdigit (c)) | |
2303 | { | |
2304 | if (x == INEXACT) | |
2305 | return SCM_BOOL_F; | |
2306 | else | |
2307 | digit_value = DIGIT2UINT (c); | |
2308 | } | |
2309 | else if (c == '#') | |
2310 | { | |
2311 | x = INEXACT; | |
2312 | digit_value = 0; | |
2313 | } | |
2314 | else | |
2315 | break; | |
2316 | ||
2317 | idx++; | |
2318 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2319 | { | |
2320 | big_shift = scm_product (big_shift, SCM_MAKINUM (shift)); | |
79d34f68 | 2321 | result = scm_product (result, SCM_MAKINUM (shift)); |
3c9a524f | 2322 | if (add > 0) |
79d34f68 | 2323 | result = scm_sum (result, SCM_MAKINUM (add)); |
3c9a524f DH |
2324 | |
2325 | shift = 10; | |
2326 | add = digit_value; | |
2327 | } | |
2328 | else | |
2329 | { | |
2330 | shift = shift * 10; | |
2331 | add = add * 10 + digit_value; | |
2332 | } | |
2333 | }; | |
2334 | ||
2335 | if (add > 0) | |
2336 | { | |
2337 | big_shift = scm_product (big_shift, SCM_MAKINUM (shift)); | |
79d34f68 DH |
2338 | result = scm_product (result, SCM_MAKINUM (shift)); |
2339 | result = scm_sum (result, SCM_MAKINUM (add)); | |
3c9a524f DH |
2340 | } |
2341 | ||
d8592269 | 2342 | result = scm_divide (result, big_shift); |
79d34f68 | 2343 | |
3c9a524f DH |
2344 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2345 | x = INEXACT; | |
f872b822 | 2346 | } |
3c9a524f | 2347 | |
3c9a524f | 2348 | if (idx != len) |
f872b822 | 2349 | { |
3c9a524f DH |
2350 | int sign = 1; |
2351 | unsigned int start; | |
2352 | char c; | |
2353 | int exponent; | |
2354 | SCM e; | |
2355 | ||
2356 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2357 | ||
2358 | switch (mem[idx]) | |
f872b822 | 2359 | { |
3c9a524f DH |
2360 | case 'd': case 'D': |
2361 | case 'e': case 'E': | |
2362 | case 'f': case 'F': | |
2363 | case 'l': case 'L': | |
2364 | case 's': case 'S': | |
2365 | idx++; | |
2366 | start = idx; | |
2367 | c = mem[idx]; | |
2368 | if (c == '-') | |
2369 | { | |
2370 | idx++; | |
2371 | sign = -1; | |
2372 | c = mem[idx]; | |
2373 | } | |
2374 | else if (c == '+') | |
2375 | { | |
2376 | idx++; | |
2377 | sign = 1; | |
2378 | c = mem[idx]; | |
2379 | } | |
2380 | else | |
2381 | sign = 1; | |
2382 | ||
2383 | if (!isdigit (c)) | |
2384 | return SCM_BOOL_F; | |
2385 | ||
2386 | idx++; | |
2387 | exponent = DIGIT2UINT (c); | |
2388 | while (idx != len) | |
f872b822 | 2389 | { |
3c9a524f DH |
2390 | char c = mem[idx]; |
2391 | if (isdigit (c)) | |
2392 | { | |
2393 | idx++; | |
2394 | if (exponent <= SCM_MAXEXP) | |
2395 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2396 | } | |
2397 | else | |
2398 | break; | |
f872b822 | 2399 | } |
3c9a524f DH |
2400 | |
2401 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2402 | { |
3c9a524f DH |
2403 | size_t exp_len = idx - start; |
2404 | SCM exp_string = scm_mem2string (&mem[start], exp_len); | |
2405 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); | |
2406 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2407 | } |
3c9a524f DH |
2408 | |
2409 | e = scm_integer_expt (SCM_MAKINUM (10), SCM_MAKINUM (exponent)); | |
2410 | if (sign == 1) | |
2411 | result = scm_product (result, e); | |
2412 | else | |
f92e85f7 | 2413 | result = scm_divide2real (result, e); |
3c9a524f DH |
2414 | |
2415 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2416 | x = INEXACT; | |
2417 | ||
f872b822 | 2418 | break; |
3c9a524f | 2419 | |
f872b822 | 2420 | default: |
3c9a524f | 2421 | break; |
f872b822 | 2422 | } |
0f2d19dd | 2423 | } |
3c9a524f DH |
2424 | |
2425 | *p_idx = idx; | |
2426 | if (x == INEXACT) | |
2427 | *p_exactness = x; | |
2428 | ||
2429 | return result; | |
0f2d19dd | 2430 | } |
0f2d19dd | 2431 | |
3c9a524f DH |
2432 | |
2433 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2434 | ||
2435 | static SCM | |
2436 | mem2ureal (const char* mem, size_t len, unsigned int *p_idx, | |
2437 | unsigned int radix, enum t_exactness *p_exactness) | |
0f2d19dd | 2438 | { |
3c9a524f | 2439 | unsigned int idx = *p_idx; |
164d2481 | 2440 | SCM result; |
3c9a524f DH |
2441 | |
2442 | if (idx == len) | |
2443 | return SCM_BOOL_F; | |
2444 | ||
7351e207 MV |
2445 | if (idx+5 <= len && !strncmp (mem+idx, "inf.0", 5)) |
2446 | { | |
2447 | *p_idx = idx+5; | |
2448 | return scm_inf (); | |
2449 | } | |
2450 | ||
2451 | if (idx+4 < len && !strncmp (mem+idx, "nan.", 4)) | |
2452 | { | |
2453 | enum t_exactness x = EXACT; | |
2454 | ||
d8592269 MV |
2455 | /* Cobble up the fractional part. We might want to set the |
2456 | NaN's mantissa from it. */ | |
7351e207 MV |
2457 | idx += 4; |
2458 | mem2uinteger (mem, len, &idx, 10, &x); | |
2459 | *p_idx = idx; | |
2460 | return scm_nan (); | |
2461 | } | |
2462 | ||
3c9a524f DH |
2463 | if (mem[idx] == '.') |
2464 | { | |
2465 | if (radix != 10) | |
2466 | return SCM_BOOL_F; | |
2467 | else if (idx + 1 == len) | |
2468 | return SCM_BOOL_F; | |
2469 | else if (!isdigit (mem[idx + 1])) | |
2470 | return SCM_BOOL_F; | |
2471 | else | |
164d2481 MV |
2472 | result = mem2decimal_from_point (SCM_MAKINUM (0), mem, len, |
2473 | p_idx, p_exactness); | |
f872b822 | 2474 | } |
3c9a524f DH |
2475 | else |
2476 | { | |
2477 | enum t_exactness x = EXACT; | |
2478 | SCM uinteger; | |
3c9a524f DH |
2479 | |
2480 | uinteger = mem2uinteger (mem, len, &idx, radix, &x); | |
2481 | if (SCM_FALSEP (uinteger)) | |
2482 | return SCM_BOOL_F; | |
2483 | ||
2484 | if (idx == len) | |
2485 | result = uinteger; | |
2486 | else if (mem[idx] == '/') | |
f872b822 | 2487 | { |
3c9a524f DH |
2488 | SCM divisor; |
2489 | ||
2490 | idx++; | |
2491 | ||
2492 | divisor = mem2uinteger (mem, len, &idx, radix, &x); | |
2493 | if (SCM_FALSEP (divisor)) | |
2494 | return SCM_BOOL_F; | |
2495 | ||
f92e85f7 MV |
2496 | /* both are int/big here, I assume */ |
2497 | result = scm_make_ratio (uinteger, divisor); | |
f872b822 | 2498 | } |
3c9a524f DH |
2499 | else if (radix == 10) |
2500 | { | |
2501 | result = mem2decimal_from_point (uinteger, mem, len, &idx, &x); | |
2502 | if (SCM_FALSEP (result)) | |
2503 | return SCM_BOOL_F; | |
2504 | } | |
2505 | else | |
2506 | result = uinteger; | |
2507 | ||
2508 | *p_idx = idx; | |
2509 | if (x == INEXACT) | |
2510 | *p_exactness = x; | |
f872b822 | 2511 | } |
164d2481 MV |
2512 | |
2513 | /* When returning an inexact zero, make sure it is represented as a | |
2514 | floating point value so that we can change its sign. | |
2515 | */ | |
2516 | if (SCM_EQ_P (result, SCM_MAKINUM(0)) && *p_exactness == INEXACT) | |
2517 | result = scm_make_real (0.0); | |
2518 | ||
2519 | return result; | |
3c9a524f | 2520 | } |
0f2d19dd | 2521 | |
0f2d19dd | 2522 | |
3c9a524f | 2523 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2524 | |
3c9a524f DH |
2525 | static SCM |
2526 | mem2complex (const char* mem, size_t len, unsigned int idx, | |
2527 | unsigned int radix, enum t_exactness *p_exactness) | |
2528 | { | |
2529 | char c; | |
2530 | int sign = 0; | |
2531 | SCM ureal; | |
2532 | ||
2533 | if (idx == len) | |
2534 | return SCM_BOOL_F; | |
2535 | ||
2536 | c = mem[idx]; | |
2537 | if (c == '+') | |
2538 | { | |
2539 | idx++; | |
2540 | sign = 1; | |
2541 | } | |
2542 | else if (c == '-') | |
2543 | { | |
2544 | idx++; | |
2545 | sign = -1; | |
0f2d19dd | 2546 | } |
0f2d19dd | 2547 | |
3c9a524f DH |
2548 | if (idx == len) |
2549 | return SCM_BOOL_F; | |
2550 | ||
2551 | ureal = mem2ureal (mem, len, &idx, radix, p_exactness); | |
2552 | if (SCM_FALSEP (ureal)) | |
f872b822 | 2553 | { |
3c9a524f DH |
2554 | /* input must be either +i or -i */ |
2555 | ||
2556 | if (sign == 0) | |
2557 | return SCM_BOOL_F; | |
2558 | ||
2559 | if (mem[idx] == 'i' || mem[idx] == 'I') | |
f872b822 | 2560 | { |
3c9a524f DH |
2561 | idx++; |
2562 | if (idx != len) | |
2563 | return SCM_BOOL_F; | |
2564 | ||
2565 | return scm_make_rectangular (SCM_MAKINUM (0), SCM_MAKINUM (sign)); | |
f872b822 | 2566 | } |
3c9a524f DH |
2567 | else |
2568 | return SCM_BOOL_F; | |
0f2d19dd | 2569 | } |
3c9a524f DH |
2570 | else |
2571 | { | |
fc194577 | 2572 | if (sign == -1 && SCM_FALSEP (scm_nan_p (ureal))) |
3c9a524f | 2573 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 2574 | |
3c9a524f DH |
2575 | if (idx == len) |
2576 | return ureal; | |
2577 | ||
2578 | c = mem[idx]; | |
2579 | switch (c) | |
f872b822 | 2580 | { |
3c9a524f DH |
2581 | case 'i': case 'I': |
2582 | /* either +<ureal>i or -<ureal>i */ | |
2583 | ||
2584 | idx++; | |
2585 | if (sign == 0) | |
2586 | return SCM_BOOL_F; | |
2587 | if (idx != len) | |
2588 | return SCM_BOOL_F; | |
2589 | return scm_make_rectangular (SCM_MAKINUM (0), ureal); | |
2590 | ||
2591 | case '@': | |
2592 | /* polar input: <real>@<real>. */ | |
2593 | ||
2594 | idx++; | |
2595 | if (idx == len) | |
2596 | return SCM_BOOL_F; | |
2597 | else | |
f872b822 | 2598 | { |
3c9a524f DH |
2599 | int sign; |
2600 | SCM angle; | |
2601 | SCM result; | |
2602 | ||
2603 | c = mem[idx]; | |
2604 | if (c == '+') | |
2605 | { | |
2606 | idx++; | |
2607 | sign = 1; | |
2608 | } | |
2609 | else if (c == '-') | |
2610 | { | |
2611 | idx++; | |
2612 | sign = -1; | |
2613 | } | |
2614 | else | |
2615 | sign = 1; | |
2616 | ||
2617 | angle = mem2ureal (mem, len, &idx, radix, p_exactness); | |
2618 | if (SCM_FALSEP (angle)) | |
2619 | return SCM_BOOL_F; | |
2620 | if (idx != len) | |
2621 | return SCM_BOOL_F; | |
2622 | ||
fc194577 | 2623 | if (sign == -1 && SCM_FALSEP (scm_nan_p (ureal))) |
3c9a524f DH |
2624 | angle = scm_difference (angle, SCM_UNDEFINED); |
2625 | ||
2626 | result = scm_make_polar (ureal, angle); | |
2627 | return result; | |
f872b822 | 2628 | } |
3c9a524f DH |
2629 | case '+': |
2630 | case '-': | |
2631 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 2632 | |
3c9a524f DH |
2633 | idx++; |
2634 | if (idx == len) | |
2635 | return SCM_BOOL_F; | |
2636 | else | |
2637 | { | |
2638 | int sign = (c == '+') ? 1 : -1; | |
2639 | SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness); | |
0f2d19dd | 2640 | |
3c9a524f DH |
2641 | if (SCM_FALSEP (imag)) |
2642 | imag = SCM_MAKINUM (sign); | |
fc194577 | 2643 | else if (sign == -1 && SCM_FALSEP (scm_nan_p (ureal))) |
1fe5e088 | 2644 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 2645 | |
3c9a524f DH |
2646 | if (idx == len) |
2647 | return SCM_BOOL_F; | |
2648 | if (mem[idx] != 'i' && mem[idx] != 'I') | |
2649 | return SCM_BOOL_F; | |
0f2d19dd | 2650 | |
3c9a524f DH |
2651 | idx++; |
2652 | if (idx != len) | |
2653 | return SCM_BOOL_F; | |
0f2d19dd | 2654 | |
1fe5e088 | 2655 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
2656 | } |
2657 | default: | |
2658 | return SCM_BOOL_F; | |
2659 | } | |
2660 | } | |
0f2d19dd | 2661 | } |
0f2d19dd JB |
2662 | |
2663 | ||
3c9a524f DH |
2664 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
2665 | ||
2666 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 2667 | |
0f2d19dd | 2668 | SCM |
3c9a524f | 2669 | scm_i_mem2number (const char* mem, size_t len, unsigned int default_radix) |
0f2d19dd | 2670 | { |
3c9a524f DH |
2671 | unsigned int idx = 0; |
2672 | unsigned int radix = NO_RADIX; | |
2673 | enum t_exactness forced_x = NO_EXACTNESS; | |
2674 | enum t_exactness implicit_x = EXACT; | |
2675 | SCM result; | |
2676 | ||
2677 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
2678 | while (idx + 2 < len && mem[idx] == '#') | |
2679 | { | |
2680 | switch (mem[idx + 1]) | |
2681 | { | |
2682 | case 'b': case 'B': | |
2683 | if (radix != NO_RADIX) | |
2684 | return SCM_BOOL_F; | |
2685 | radix = DUAL; | |
2686 | break; | |
2687 | case 'd': case 'D': | |
2688 | if (radix != NO_RADIX) | |
2689 | return SCM_BOOL_F; | |
2690 | radix = DEC; | |
2691 | break; | |
2692 | case 'i': case 'I': | |
2693 | if (forced_x != NO_EXACTNESS) | |
2694 | return SCM_BOOL_F; | |
2695 | forced_x = INEXACT; | |
2696 | break; | |
2697 | case 'e': case 'E': | |
2698 | if (forced_x != NO_EXACTNESS) | |
2699 | return SCM_BOOL_F; | |
2700 | forced_x = EXACT; | |
2701 | break; | |
2702 | case 'o': case 'O': | |
2703 | if (radix != NO_RADIX) | |
2704 | return SCM_BOOL_F; | |
2705 | radix = OCT; | |
2706 | break; | |
2707 | case 'x': case 'X': | |
2708 | if (radix != NO_RADIX) | |
2709 | return SCM_BOOL_F; | |
2710 | radix = HEX; | |
2711 | break; | |
2712 | default: | |
f872b822 | 2713 | return SCM_BOOL_F; |
3c9a524f DH |
2714 | } |
2715 | idx += 2; | |
2716 | } | |
2717 | ||
2718 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
2719 | if (radix == NO_RADIX) | |
2720 | result = mem2complex (mem, len, idx, default_radix, &implicit_x); | |
2721 | else | |
2722 | result = mem2complex (mem, len, idx, (unsigned int) radix, &implicit_x); | |
2723 | ||
2724 | if (SCM_FALSEP (result)) | |
2725 | return SCM_BOOL_F; | |
f872b822 | 2726 | |
3c9a524f | 2727 | switch (forced_x) |
f872b822 | 2728 | { |
3c9a524f DH |
2729 | case EXACT: |
2730 | if (SCM_INEXACTP (result)) | |
3c9a524f DH |
2731 | return scm_inexact_to_exact (result); |
2732 | else | |
2733 | return result; | |
2734 | case INEXACT: | |
2735 | if (SCM_INEXACTP (result)) | |
2736 | return result; | |
2737 | else | |
2738 | return scm_exact_to_inexact (result); | |
2739 | case NO_EXACTNESS: | |
2740 | default: | |
2741 | if (implicit_x == INEXACT) | |
2742 | { | |
2743 | if (SCM_INEXACTP (result)) | |
2744 | return result; | |
2745 | else | |
2746 | return scm_exact_to_inexact (result); | |
2747 | } | |
2748 | else | |
2749 | return result; | |
f872b822 | 2750 | } |
0f2d19dd JB |
2751 | } |
2752 | ||
2753 | ||
a1ec6916 | 2754 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 2755 | (SCM string, SCM radix), |
1e6808ea | 2756 | "Return a number of the maximally precise representation\n" |
942e5b91 | 2757 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
2758 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
2759 | "is a default radix that may be overridden by an explicit radix\n" | |
2760 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
2761 | "supplied, then the default radix is 10. If string is not a\n" | |
2762 | "syntactically valid notation for a number, then\n" | |
2763 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 2764 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
2765 | { |
2766 | SCM answer; | |
1bbd0b84 | 2767 | int base; |
a6d9e5ab | 2768 | SCM_VALIDATE_STRING (1, string); |
34d19ef6 | 2769 | SCM_VALIDATE_INUM_MIN_DEF_COPY (2, radix,2,10, base); |
3c9a524f | 2770 | answer = scm_i_mem2number (SCM_STRING_CHARS (string), |
d8592269 MV |
2771 | SCM_STRING_LENGTH (string), |
2772 | base); | |
bb628794 | 2773 | return scm_return_first (answer, string); |
0f2d19dd | 2774 | } |
1bbd0b84 | 2775 | #undef FUNC_NAME |
3c9a524f DH |
2776 | |
2777 | ||
0f2d19dd JB |
2778 | /*** END strs->nums ***/ |
2779 | ||
5986c47d | 2780 | |
0f2d19dd | 2781 | SCM |
f3ae5d60 | 2782 | scm_make_real (double x) |
0f2d19dd | 2783 | { |
3553e1d1 GH |
2784 | SCM z = scm_double_cell (scm_tc16_real, 0, 0, 0); |
2785 | ||
3a9809df | 2786 | SCM_REAL_VALUE (z) = x; |
0f2d19dd JB |
2787 | return z; |
2788 | } | |
0f2d19dd | 2789 | |
5986c47d | 2790 | |
f3ae5d60 MD |
2791 | SCM |
2792 | scm_make_complex (double x, double y) | |
2793 | { | |
0aacf84e | 2794 | if (y == 0.0) |
3a9809df | 2795 | return scm_make_real (x); |
0aacf84e MD |
2796 | else |
2797 | { | |
2798 | SCM z; | |
29c4382a | 2799 | SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (sizeof (scm_t_complex), |
0aacf84e MD |
2800 | "complex")); |
2801 | SCM_COMPLEX_REAL (z) = x; | |
2802 | SCM_COMPLEX_IMAG (z) = y; | |
2803 | return z; | |
2804 | } | |
f3ae5d60 | 2805 | } |
1cc91f1b | 2806 | |
5986c47d | 2807 | |
0f2d19dd | 2808 | SCM |
1bbd0b84 | 2809 | scm_bigequal (SCM x, SCM y) |
0f2d19dd | 2810 | { |
47ae1f0e | 2811 | int result = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); |
ca46fb90 RB |
2812 | scm_remember_upto_here_2 (x, y); |
2813 | return SCM_BOOL (0 == result); | |
0f2d19dd JB |
2814 | } |
2815 | ||
0f2d19dd | 2816 | SCM |
f3ae5d60 | 2817 | scm_real_equalp (SCM x, SCM y) |
0f2d19dd | 2818 | { |
f3ae5d60 | 2819 | return SCM_BOOL (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0f2d19dd JB |
2820 | } |
2821 | ||
f3ae5d60 MD |
2822 | SCM |
2823 | scm_complex_equalp (SCM x, SCM y) | |
2824 | { | |
2825 | return SCM_BOOL (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) | |
2826 | && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); | |
2827 | } | |
0f2d19dd | 2828 | |
f92e85f7 MV |
2829 | SCM |
2830 | scm_i_fraction_equalp (SCM x, SCM y) | |
2831 | { | |
2832 | scm_i_fraction_reduce (x); | |
2833 | scm_i_fraction_reduce (y); | |
02164269 MV |
2834 | if (SCM_FALSEP (scm_equal_p (SCM_FRACTION_NUMERATOR (x), |
2835 | SCM_FRACTION_NUMERATOR (y))) | |
2836 | || SCM_FALSEP (scm_equal_p (SCM_FRACTION_DENOMINATOR (x), | |
2837 | SCM_FRACTION_DENOMINATOR (y)))) | |
2838 | return SCM_BOOL_F; | |
2839 | else | |
2840 | return SCM_BOOL_T; | |
f92e85f7 | 2841 | } |
0f2d19dd JB |
2842 | |
2843 | ||
1bbd0b84 | 2844 | SCM_REGISTER_PROC (s_number_p, "number?", 1, 0, 0, scm_number_p); |
942e5b91 MG |
2845 | /* "Return @code{#t} if @var{x} is a number, @code{#f}\n" |
2846 | * "else. Note that the sets of complex, real, rational and\n" | |
2847 | * "integer values form subsets of the set of numbers, i. e. the\n" | |
2848 | * "predicate will be fulfilled for any number." | |
2849 | */ | |
a1ec6916 | 2850 | SCM_DEFINE (scm_number_p, "complex?", 1, 0, 0, |
1bbd0b84 | 2851 | (SCM x), |
942e5b91 | 2852 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 2853 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
2854 | "values form subsets of the set of complex numbers, i. e. the\n" |
2855 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
2856 | "rational or integer number.") | |
1bbd0b84 | 2857 | #define FUNC_NAME s_scm_number_p |
0f2d19dd | 2858 | { |
bb628794 | 2859 | return SCM_BOOL (SCM_NUMBERP (x)); |
0f2d19dd | 2860 | } |
1bbd0b84 | 2861 | #undef FUNC_NAME |
0f2d19dd JB |
2862 | |
2863 | ||
f92e85f7 MV |
2864 | SCM_DEFINE (scm_real_p, "real?", 1, 0, 0, |
2865 | (SCM x), | |
2866 | "Return @code{#t} if @var{x} is a real number, @code{#f}\n" | |
2867 | "otherwise. Note that the set of integer values forms a subset of\n" | |
2868 | "the set of real numbers, i. e. the predicate will also be\n" | |
2869 | "fulfilled if @var{x} is an integer number.") | |
2870 | #define FUNC_NAME s_scm_real_p | |
2871 | { | |
2872 | /* we can't represent irrational numbers. */ | |
2873 | return scm_rational_p (x); | |
2874 | } | |
2875 | #undef FUNC_NAME | |
2876 | ||
2877 | SCM_DEFINE (scm_rational_p, "rational?", 1, 0, 0, | |
1bbd0b84 | 2878 | (SCM x), |
942e5b91 | 2879 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 2880 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 | 2881 | "the set of rational numbers, i. e. the predicate will also be\n" |
f92e85f7 MV |
2882 | "fulfilled if @var{x} is an integer number.") |
2883 | #define FUNC_NAME s_scm_rational_p | |
0f2d19dd | 2884 | { |
0aacf84e | 2885 | if (SCM_INUMP (x)) |
0f2d19dd | 2886 | return SCM_BOOL_T; |
0aacf84e | 2887 | else if (SCM_IMP (x)) |
0f2d19dd | 2888 | return SCM_BOOL_F; |
0aacf84e | 2889 | else if (SCM_BIGP (x)) |
0f2d19dd | 2890 | return SCM_BOOL_T; |
f92e85f7 MV |
2891 | else if (SCM_FRACTIONP (x)) |
2892 | return SCM_BOOL_T; | |
2893 | else if (SCM_REALP (x)) | |
2894 | /* due to their limited precision, all floating point numbers are | |
2895 | rational as well. */ | |
2896 | return SCM_BOOL_T; | |
0aacf84e | 2897 | else |
bb628794 | 2898 | return SCM_BOOL_F; |
0f2d19dd | 2899 | } |
1bbd0b84 | 2900 | #undef FUNC_NAME |
0f2d19dd JB |
2901 | |
2902 | ||
a1ec6916 | 2903 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 2904 | (SCM x), |
942e5b91 MG |
2905 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
2906 | "else.") | |
1bbd0b84 | 2907 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd JB |
2908 | { |
2909 | double r; | |
f872b822 MD |
2910 | if (SCM_INUMP (x)) |
2911 | return SCM_BOOL_T; | |
2912 | if (SCM_IMP (x)) | |
2913 | return SCM_BOOL_F; | |
f872b822 MD |
2914 | if (SCM_BIGP (x)) |
2915 | return SCM_BOOL_T; | |
3c9a524f | 2916 | if (!SCM_INEXACTP (x)) |
f872b822 | 2917 | return SCM_BOOL_F; |
3c9a524f | 2918 | if (SCM_COMPLEXP (x)) |
f872b822 | 2919 | return SCM_BOOL_F; |
5986c47d | 2920 | r = SCM_REAL_VALUE (x); |
f872b822 MD |
2921 | if (r == floor (r)) |
2922 | return SCM_BOOL_T; | |
0f2d19dd JB |
2923 | return SCM_BOOL_F; |
2924 | } | |
1bbd0b84 | 2925 | #undef FUNC_NAME |
0f2d19dd JB |
2926 | |
2927 | ||
a1ec6916 | 2928 | SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, |
1bbd0b84 | 2929 | (SCM x), |
942e5b91 MG |
2930 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" |
2931 | "else.") | |
1bbd0b84 | 2932 | #define FUNC_NAME s_scm_inexact_p |
0f2d19dd | 2933 | { |
eb927cb9 MV |
2934 | if (SCM_INEXACTP (x)) |
2935 | return SCM_BOOL_T; | |
2936 | if (SCM_NUMBERP (x)) | |
2937 | return SCM_BOOL_F; | |
2938 | SCM_WRONG_TYPE_ARG (1, x); | |
0f2d19dd | 2939 | } |
1bbd0b84 | 2940 | #undef FUNC_NAME |
0f2d19dd JB |
2941 | |
2942 | ||
152f82bf | 2943 | SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p); |
942e5b91 | 2944 | /* "Return @code{#t} if all parameters are numerically equal." */ |
0f2d19dd | 2945 | SCM |
6e8d25a6 | 2946 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 2947 | { |
d8b95e27 | 2948 | again: |
0aacf84e MD |
2949 | if (SCM_INUMP (x)) |
2950 | { | |
2951 | long xx = SCM_INUM (x); | |
2952 | if (SCM_INUMP (y)) | |
2953 | { | |
2954 | long yy = SCM_INUM (y); | |
2955 | return SCM_BOOL (xx == yy); | |
2956 | } | |
2957 | else if (SCM_BIGP (y)) | |
2958 | return SCM_BOOL_F; | |
2959 | else if (SCM_REALP (y)) | |
2960 | return SCM_BOOL ((double) xx == SCM_REAL_VALUE (y)); | |
2961 | else if (SCM_COMPLEXP (y)) | |
2962 | return SCM_BOOL (((double) xx == SCM_COMPLEX_REAL (y)) | |
2963 | && (0.0 == SCM_COMPLEX_IMAG (y))); | |
f92e85f7 MV |
2964 | else if (SCM_FRACTIONP (y)) |
2965 | return SCM_BOOL_F; | |
0aacf84e MD |
2966 | else |
2967 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 2968 | } |
0aacf84e MD |
2969 | else if (SCM_BIGP (x)) |
2970 | { | |
2971 | if (SCM_INUMP (y)) | |
2972 | return SCM_BOOL_F; | |
2973 | else if (SCM_BIGP (y)) | |
2974 | { | |
2975 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
2976 | scm_remember_upto_here_2 (x, y); | |
2977 | return SCM_BOOL (0 == cmp); | |
2978 | } | |
2979 | else if (SCM_REALP (y)) | |
2980 | { | |
2981 | int cmp; | |
2982 | if (xisnan (SCM_REAL_VALUE (y))) | |
2983 | return SCM_BOOL_F; | |
2984 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
2985 | scm_remember_upto_here_1 (x); | |
2986 | return SCM_BOOL (0 == cmp); | |
2987 | } | |
2988 | else if (SCM_COMPLEXP (y)) | |
2989 | { | |
2990 | int cmp; | |
2991 | if (0.0 != SCM_COMPLEX_IMAG (y)) | |
2992 | return SCM_BOOL_F; | |
2993 | if (xisnan (SCM_COMPLEX_REAL (y))) | |
2994 | return SCM_BOOL_F; | |
2995 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_COMPLEX_REAL (y)); | |
2996 | scm_remember_upto_here_1 (x); | |
2997 | return SCM_BOOL (0 == cmp); | |
2998 | } | |
f92e85f7 MV |
2999 | else if (SCM_FRACTIONP (y)) |
3000 | return SCM_BOOL_F; | |
0aacf84e MD |
3001 | else |
3002 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3003 | } |
0aacf84e MD |
3004 | else if (SCM_REALP (x)) |
3005 | { | |
3006 | if (SCM_INUMP (y)) | |
3007 | return SCM_BOOL (SCM_REAL_VALUE (x) == (double) SCM_INUM (y)); | |
3008 | else if (SCM_BIGP (y)) | |
3009 | { | |
3010 | int cmp; | |
3011 | if (xisnan (SCM_REAL_VALUE (x))) | |
3012 | return SCM_BOOL_F; | |
3013 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3014 | scm_remember_upto_here_1 (y); | |
3015 | return SCM_BOOL (0 == cmp); | |
3016 | } | |
3017 | else if (SCM_REALP (y)) | |
3018 | return SCM_BOOL (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); | |
3019 | else if (SCM_COMPLEXP (y)) | |
3020 | return SCM_BOOL ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) | |
3021 | && (0.0 == SCM_COMPLEX_IMAG (y))); | |
f92e85f7 | 3022 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3023 | { |
3024 | double xx = SCM_REAL_VALUE (x); | |
3025 | if (xisnan (xx)) | |
3026 | return SCM_BOOL_F; | |
3027 | if (xisinf (xx)) | |
3028 | return SCM_BOOL (xx < 0.0); | |
3029 | x = scm_inexact_to_exact (x); /* with x as frac or int */ | |
3030 | goto again; | |
3031 | } | |
0aacf84e MD |
3032 | else |
3033 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3034 | } |
0aacf84e MD |
3035 | else if (SCM_COMPLEXP (x)) |
3036 | { | |
3037 | if (SCM_INUMP (y)) | |
3038 | return SCM_BOOL ((SCM_COMPLEX_REAL (x) == (double) SCM_INUM (y)) | |
3039 | && (SCM_COMPLEX_IMAG (x) == 0.0)); | |
3040 | else if (SCM_BIGP (y)) | |
3041 | { | |
3042 | int cmp; | |
3043 | if (0.0 != SCM_COMPLEX_IMAG (x)) | |
3044 | return SCM_BOOL_F; | |
3045 | if (xisnan (SCM_COMPLEX_REAL (x))) | |
3046 | return SCM_BOOL_F; | |
3047 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_COMPLEX_REAL (x)); | |
3048 | scm_remember_upto_here_1 (y); | |
3049 | return SCM_BOOL (0 == cmp); | |
3050 | } | |
3051 | else if (SCM_REALP (y)) | |
3052 | return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) | |
3053 | && (SCM_COMPLEX_IMAG (x) == 0.0)); | |
3054 | else if (SCM_COMPLEXP (y)) | |
3055 | return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) | |
3056 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); | |
f92e85f7 | 3057 | else if (SCM_FRACTIONP (y)) |
d8b95e27 KR |
3058 | { |
3059 | double xx; | |
3060 | if (SCM_COMPLEX_IMAG (x) != 0.0) | |
3061 | return SCM_BOOL_F; | |
3062 | xx = SCM_COMPLEX_REAL (x); | |
3063 | if (xisnan (xx)) | |
3064 | return SCM_BOOL_F; | |
3065 | if (xisinf (xx)) | |
3066 | return SCM_BOOL (xx < 0.0); | |
3067 | x = scm_inexact_to_exact (x); /* with x as frac or int */ | |
3068 | goto again; | |
3069 | } | |
f92e85f7 MV |
3070 | else |
3071 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
3072 | } | |
3073 | else if (SCM_FRACTIONP (x)) | |
3074 | { | |
3075 | if (SCM_INUMP (y)) | |
3076 | return SCM_BOOL_F; | |
3077 | else if (SCM_BIGP (y)) | |
3078 | return SCM_BOOL_F; | |
3079 | else if (SCM_REALP (y)) | |
d8b95e27 KR |
3080 | { |
3081 | double yy = SCM_REAL_VALUE (y); | |
3082 | if (xisnan (yy)) | |
3083 | return SCM_BOOL_F; | |
3084 | if (xisinf (yy)) | |
3085 | return SCM_BOOL (0.0 < yy); | |
3086 | y = scm_inexact_to_exact (y); /* with y as frac or int */ | |
3087 | goto again; | |
3088 | } | |
f92e85f7 | 3089 | else if (SCM_COMPLEXP (y)) |
d8b95e27 KR |
3090 | { |
3091 | double yy; | |
3092 | if (SCM_COMPLEX_IMAG (y) != 0.0) | |
3093 | return SCM_BOOL_F; | |
3094 | yy = SCM_COMPLEX_REAL (y); | |
3095 | if (xisnan (yy)) | |
3096 | return SCM_BOOL_F; | |
3097 | if (xisinf (yy)) | |
3098 | return SCM_BOOL (0.0 < yy); | |
3099 | y = scm_inexact_to_exact (y); /* with y as frac or int */ | |
3100 | goto again; | |
3101 | } | |
f92e85f7 MV |
3102 | else if (SCM_FRACTIONP (y)) |
3103 | return scm_i_fraction_equalp (x, y); | |
0aacf84e MD |
3104 | else |
3105 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f4c627b3 | 3106 | } |
0aacf84e | 3107 | else |
f4c627b3 | 3108 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p); |
0f2d19dd JB |
3109 | } |
3110 | ||
3111 | ||
a5f0b599 KR |
3112 | /* OPTIMIZE-ME: For int/frac and frac/frac compares, the multiplications |
3113 | done are good for inums, but for bignums an answer can almost always be | |
3114 | had by just examining a few high bits of the operands, as done by GMP in | |
3115 | mpq_cmp. flonum/frac compares likewise, but with the slight complication | |
3116 | of the float exponent to take into account. */ | |
3117 | ||
152f82bf | 3118 | SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p); |
942e5b91 MG |
3119 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3120 | * "increasing." | |
3121 | */ | |
0f2d19dd | 3122 | SCM |
6e8d25a6 | 3123 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3124 | { |
a5f0b599 | 3125 | again: |
0aacf84e MD |
3126 | if (SCM_INUMP (x)) |
3127 | { | |
3128 | long xx = SCM_INUM (x); | |
3129 | if (SCM_INUMP (y)) | |
3130 | { | |
3131 | long yy = SCM_INUM (y); | |
3132 | return SCM_BOOL (xx < yy); | |
3133 | } | |
3134 | else if (SCM_BIGP (y)) | |
3135 | { | |
3136 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3137 | scm_remember_upto_here_1 (y); | |
3138 | return SCM_BOOL (sgn > 0); | |
3139 | } | |
3140 | else if (SCM_REALP (y)) | |
3141 | return SCM_BOOL ((double) xx < SCM_REAL_VALUE (y)); | |
f92e85f7 | 3142 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3143 | { |
3144 | /* "x < a/b" becomes "x*b < a" */ | |
3145 | int_frac: | |
3146 | x = scm_product (x, SCM_FRACTION_DENOMINATOR (y)); | |
3147 | y = SCM_FRACTION_NUMERATOR (y); | |
3148 | goto again; | |
3149 | } | |
0aacf84e MD |
3150 | else |
3151 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3152 | } |
0aacf84e MD |
3153 | else if (SCM_BIGP (x)) |
3154 | { | |
3155 | if (SCM_INUMP (y)) | |
3156 | { | |
3157 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3158 | scm_remember_upto_here_1 (x); | |
3159 | return SCM_BOOL (sgn < 0); | |
3160 | } | |
3161 | else if (SCM_BIGP (y)) | |
3162 | { | |
3163 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3164 | scm_remember_upto_here_2 (x, y); | |
3165 | return SCM_BOOL (cmp < 0); | |
3166 | } | |
3167 | else if (SCM_REALP (y)) | |
3168 | { | |
3169 | int cmp; | |
3170 | if (xisnan (SCM_REAL_VALUE (y))) | |
3171 | return SCM_BOOL_F; | |
3172 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), SCM_REAL_VALUE (y)); | |
3173 | scm_remember_upto_here_1 (x); | |
3174 | return SCM_BOOL (cmp < 0); | |
3175 | } | |
f92e85f7 | 3176 | else if (SCM_FRACTIONP (y)) |
a5f0b599 | 3177 | goto int_frac; |
0aacf84e MD |
3178 | else |
3179 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f4c627b3 | 3180 | } |
0aacf84e MD |
3181 | else if (SCM_REALP (x)) |
3182 | { | |
3183 | if (SCM_INUMP (y)) | |
3184 | return SCM_BOOL (SCM_REAL_VALUE (x) < (double) SCM_INUM (y)); | |
3185 | else if (SCM_BIGP (y)) | |
3186 | { | |
3187 | int cmp; | |
3188 | if (xisnan (SCM_REAL_VALUE (x))) | |
3189 | return SCM_BOOL_F; | |
3190 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), SCM_REAL_VALUE (x)); | |
3191 | scm_remember_upto_here_1 (y); | |
3192 | return SCM_BOOL (cmp > 0); | |
3193 | } | |
3194 | else if (SCM_REALP (y)) | |
3195 | return SCM_BOOL (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); | |
f92e85f7 | 3196 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3197 | { |
3198 | double xx = SCM_REAL_VALUE (x); | |
3199 | if (xisnan (xx)) | |
3200 | return SCM_BOOL_F; | |
3201 | if (xisinf (xx)) | |
3202 | return SCM_BOOL (xx < 0.0); | |
3203 | x = scm_inexact_to_exact (x); /* with x as frac or int */ | |
3204 | goto again; | |
3205 | } | |
f92e85f7 MV |
3206 | else |
3207 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
3208 | } | |
3209 | else if (SCM_FRACTIONP (x)) | |
3210 | { | |
a5f0b599 KR |
3211 | if (SCM_INUMP (y) || SCM_BIGP (y)) |
3212 | { | |
3213 | /* "a/b < y" becomes "a < y*b" */ | |
3214 | y = scm_product (y, SCM_FRACTION_DENOMINATOR (x)); | |
3215 | x = SCM_FRACTION_NUMERATOR (x); | |
3216 | goto again; | |
3217 | } | |
f92e85f7 | 3218 | else if (SCM_REALP (y)) |
a5f0b599 KR |
3219 | { |
3220 | double yy = SCM_REAL_VALUE (y); | |
3221 | if (xisnan (yy)) | |
3222 | return SCM_BOOL_F; | |
3223 | if (xisinf (yy)) | |
3224 | return SCM_BOOL (0.0 < yy); | |
3225 | y = scm_inexact_to_exact (y); /* with y as frac or int */ | |
3226 | goto again; | |
3227 | } | |
f92e85f7 | 3228 | else if (SCM_FRACTIONP (y)) |
a5f0b599 KR |
3229 | { |
3230 | /* "a/b < c/d" becomes "a*d < c*b" */ | |
3231 | SCM new_x = scm_product (SCM_FRACTION_NUMERATOR (x), | |
3232 | SCM_FRACTION_DENOMINATOR (y)); | |
3233 | SCM new_y = scm_product (SCM_FRACTION_NUMERATOR (y), | |
3234 | SCM_FRACTION_DENOMINATOR (x)); | |
3235 | x = new_x; | |
3236 | y = new_y; | |
3237 | goto again; | |
3238 | } | |
0aacf84e MD |
3239 | else |
3240 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3241 | } |
0aacf84e | 3242 | else |
f4c627b3 | 3243 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p); |
0f2d19dd JB |
3244 | } |
3245 | ||
3246 | ||
c76b1eaf | 3247 | SCM_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p); |
942e5b91 MG |
3248 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3249 | * "decreasing." | |
c76b1eaf | 3250 | */ |
1bbd0b84 | 3251 | #define FUNC_NAME s_scm_gr_p |
c76b1eaf MD |
3252 | SCM |
3253 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3254 | { |
c76b1eaf MD |
3255 | if (!SCM_NUMBERP (x)) |
3256 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME); | |
3257 | else if (!SCM_NUMBERP (y)) | |
3258 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME); | |
3259 | else | |
3260 | return scm_less_p (y, x); | |
0f2d19dd | 3261 | } |
1bbd0b84 | 3262 | #undef FUNC_NAME |
0f2d19dd JB |
3263 | |
3264 | ||
c76b1eaf | 3265 | SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p); |
942e5b91 | 3266 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3267 | * "non-decreasing." |
3268 | */ | |
1bbd0b84 | 3269 | #define FUNC_NAME s_scm_leq_p |
c76b1eaf MD |
3270 | SCM |
3271 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3272 | { |
c76b1eaf MD |
3273 | if (!SCM_NUMBERP (x)) |
3274 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3275 | else if (!SCM_NUMBERP (y)) | |
3276 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME); | |
fc194577 MV |
3277 | else if (SCM_NFALSEP (scm_nan_p (x)) || SCM_NFALSEP (scm_nan_p (y))) |
3278 | return SCM_BOOL_F; | |
c76b1eaf MD |
3279 | else |
3280 | return SCM_BOOL_NOT (scm_less_p (y, x)); | |
0f2d19dd | 3281 | } |
1bbd0b84 | 3282 | #undef FUNC_NAME |
0f2d19dd JB |
3283 | |
3284 | ||
c76b1eaf | 3285 | SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p); |
942e5b91 | 3286 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3287 | * "non-increasing." |
3288 | */ | |
1bbd0b84 | 3289 | #define FUNC_NAME s_scm_geq_p |
c76b1eaf MD |
3290 | SCM |
3291 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3292 | { |
c76b1eaf MD |
3293 | if (!SCM_NUMBERP (x)) |
3294 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3295 | else if (!SCM_NUMBERP (y)) | |
3296 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME); | |
fc194577 MV |
3297 | else if (SCM_NFALSEP (scm_nan_p (x)) || SCM_NFALSEP (scm_nan_p (y))) |
3298 | return SCM_BOOL_F; | |
c76b1eaf | 3299 | else |
fc194577 | 3300 | return SCM_BOOL_NOT (scm_less_p (x, y)); |
0f2d19dd | 3301 | } |
1bbd0b84 | 3302 | #undef FUNC_NAME |
0f2d19dd JB |
3303 | |
3304 | ||
152f82bf | 3305 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3306 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3307 | * "zero." | |
3308 | */ | |
0f2d19dd | 3309 | SCM |
6e8d25a6 | 3310 | scm_zero_p (SCM z) |
0f2d19dd | 3311 | { |
0aacf84e | 3312 | if (SCM_INUMP (z)) |
c2ff8ab0 | 3313 | return SCM_BOOL (SCM_EQ_P (z, SCM_INUM0)); |
0aacf84e | 3314 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 3315 | return SCM_BOOL_F; |
0aacf84e | 3316 | else if (SCM_REALP (z)) |
c2ff8ab0 | 3317 | return SCM_BOOL (SCM_REAL_VALUE (z) == 0.0); |
0aacf84e | 3318 | else if (SCM_COMPLEXP (z)) |
c2ff8ab0 DH |
3319 | return SCM_BOOL (SCM_COMPLEX_REAL (z) == 0.0 |
3320 | && SCM_COMPLEX_IMAG (z) == 0.0); | |
f92e85f7 MV |
3321 | else if (SCM_FRACTIONP (z)) |
3322 | return SCM_BOOL_F; | |
0aacf84e | 3323 | else |
c2ff8ab0 | 3324 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); |
0f2d19dd JB |
3325 | } |
3326 | ||
3327 | ||
152f82bf | 3328 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3329 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3330 | * "zero." | |
3331 | */ | |
0f2d19dd | 3332 | SCM |
6e8d25a6 | 3333 | scm_positive_p (SCM x) |
0f2d19dd | 3334 | { |
0aacf84e | 3335 | if (SCM_INUMP (x)) |
c2ff8ab0 | 3336 | return SCM_BOOL (SCM_INUM (x) > 0); |
0aacf84e MD |
3337 | else if (SCM_BIGP (x)) |
3338 | { | |
3339 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3340 | scm_remember_upto_here_1 (x); | |
3341 | return SCM_BOOL (sgn > 0); | |
3342 | } | |
3343 | else if (SCM_REALP (x)) | |
c2ff8ab0 | 3344 | return SCM_BOOL(SCM_REAL_VALUE (x) > 0.0); |
f92e85f7 MV |
3345 | else if (SCM_FRACTIONP (x)) |
3346 | return scm_positive_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3347 | else |
c2ff8ab0 | 3348 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); |
0f2d19dd JB |
3349 | } |
3350 | ||
3351 | ||
152f82bf | 3352 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3353 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3354 | * "zero." | |
3355 | */ | |
0f2d19dd | 3356 | SCM |
6e8d25a6 | 3357 | scm_negative_p (SCM x) |
0f2d19dd | 3358 | { |
0aacf84e | 3359 | if (SCM_INUMP (x)) |
c2ff8ab0 | 3360 | return SCM_BOOL (SCM_INUM (x) < 0); |
0aacf84e MD |
3361 | else if (SCM_BIGP (x)) |
3362 | { | |
3363 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3364 | scm_remember_upto_here_1 (x); | |
3365 | return SCM_BOOL (sgn < 0); | |
3366 | } | |
3367 | else if (SCM_REALP (x)) | |
c2ff8ab0 | 3368 | return SCM_BOOL(SCM_REAL_VALUE (x) < 0.0); |
f92e85f7 MV |
3369 | else if (SCM_FRACTIONP (x)) |
3370 | return scm_negative_p (SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e | 3371 | else |
c2ff8ab0 | 3372 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); |
0f2d19dd JB |
3373 | } |
3374 | ||
3375 | ||
9de33deb | 3376 | SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max); |
942e5b91 MG |
3377 | /* "Return the maximum of all parameter values." |
3378 | */ | |
0f2d19dd | 3379 | SCM |
6e8d25a6 | 3380 | scm_max (SCM x, SCM y) |
0f2d19dd | 3381 | { |
0aacf84e MD |
3382 | if (SCM_UNBNDP (y)) |
3383 | { | |
3384 | if (SCM_UNBNDP (x)) | |
3385 | SCM_WTA_DISPATCH_0 (g_max, s_max); | |
dab4e67a | 3386 | else if (SCM_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3387 | return x; |
3388 | else | |
3389 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3390 | } |
f4c627b3 | 3391 | |
0aacf84e MD |
3392 | if (SCM_INUMP (x)) |
3393 | { | |
3394 | long xx = SCM_INUM (x); | |
3395 | if (SCM_INUMP (y)) | |
3396 | { | |
3397 | long yy = SCM_INUM (y); | |
3398 | return (xx < yy) ? y : x; | |
3399 | } | |
3400 | else if (SCM_BIGP (y)) | |
3401 | { | |
3402 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3403 | scm_remember_upto_here_1 (y); | |
3404 | return (sgn < 0) ? x : y; | |
3405 | } | |
3406 | else if (SCM_REALP (y)) | |
3407 | { | |
3408 | double z = xx; | |
3409 | /* if y==NaN then ">" is false and we return NaN */ | |
3410 | return (z > SCM_REAL_VALUE (y)) ? scm_make_real (z) : y; | |
3411 | } | |
f92e85f7 MV |
3412 | else if (SCM_FRACTIONP (y)) |
3413 | { | |
3414 | double z = xx; | |
3415 | return (z > scm_i_fraction2double (y)) ? x : y; | |
3416 | } | |
0aacf84e MD |
3417 | else |
3418 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3419 | } |
0aacf84e MD |
3420 | else if (SCM_BIGP (x)) |
3421 | { | |
3422 | if (SCM_INUMP (y)) | |
3423 | { | |
3424 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3425 | scm_remember_upto_here_1 (x); | |
3426 | return (sgn < 0) ? y : x; | |
3427 | } | |
3428 | else if (SCM_BIGP (y)) | |
3429 | { | |
3430 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3431 | scm_remember_upto_here_2 (x, y); | |
3432 | return (cmp > 0) ? x : y; | |
3433 | } | |
3434 | else if (SCM_REALP (y)) | |
3435 | { | |
3436 | double yy = SCM_REAL_VALUE (y); | |
3437 | int cmp; | |
3438 | if (xisnan (yy)) | |
3439 | return y; | |
3440 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), yy); | |
3441 | scm_remember_upto_here_1 (x); | |
3442 | return (cmp > 0) ? x : y; | |
3443 | } | |
f92e85f7 MV |
3444 | else if (SCM_FRACTIONP (y)) |
3445 | { | |
3446 | double yy = scm_i_fraction2double (y); | |
3447 | int cmp; | |
3448 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), yy); | |
3449 | scm_remember_upto_here_1 (x); | |
3450 | return (cmp > 0) ? x : y; | |
3451 | } | |
0aacf84e MD |
3452 | else |
3453 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f4c627b3 | 3454 | } |
0aacf84e MD |
3455 | else if (SCM_REALP (x)) |
3456 | { | |
3457 | if (SCM_INUMP (y)) | |
3458 | { | |
3459 | double z = SCM_INUM (y); | |
3460 | /* if x==NaN then "<" is false and we return NaN */ | |
3461 | return (SCM_REAL_VALUE (x) < z) ? scm_make_real (z) : x; | |
3462 | } | |
3463 | else if (SCM_BIGP (y)) | |
3464 | { | |
3465 | double xx = SCM_REAL_VALUE (x); | |
3466 | int cmp; | |
3467 | if (xisnan (xx)) | |
3468 | return x; | |
3469 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), xx); | |
3470 | scm_remember_upto_here_1 (y); | |
3471 | return (cmp < 0) ? x : y; | |
3472 | } | |
3473 | else if (SCM_REALP (y)) | |
3474 | { | |
3475 | /* if x==NaN then our explicit check means we return NaN | |
3476 | if y==NaN then ">" is false and we return NaN | |
3477 | calling isnan is unavoidable, since it's the only way to know | |
3478 | which of x or y causes any compares to be false */ | |
3479 | double xx = SCM_REAL_VALUE (x); | |
3480 | return (xisnan (xx) || xx > SCM_REAL_VALUE (y)) ? x : y; | |
3481 | } | |
f92e85f7 MV |
3482 | else if (SCM_FRACTIONP (y)) |
3483 | { | |
3484 | double yy = scm_i_fraction2double (y); | |
3485 | double xx = SCM_REAL_VALUE (x); | |
3486 | return (xx < yy) ? scm_make_real (yy) : x; | |
3487 | } | |
3488 | else | |
3489 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3490 | } | |
3491 | else if (SCM_FRACTIONP (x)) | |
3492 | { | |
3493 | if (SCM_INUMP (y)) | |
3494 | { | |
3495 | double z = SCM_INUM (y); | |
3496 | return (scm_i_fraction2double (x) < z) ? y : x; | |
3497 | } | |
3498 | else if (SCM_BIGP (y)) | |
3499 | { | |
3500 | double xx = scm_i_fraction2double (x); | |
3501 | int cmp; | |
3502 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), xx); | |
3503 | scm_remember_upto_here_1 (y); | |
3504 | return (cmp < 0) ? x : y; | |
3505 | } | |
3506 | else if (SCM_REALP (y)) | |
3507 | { | |
3508 | double xx = scm_i_fraction2double (x); | |
3509 | return (xx < SCM_REAL_VALUE (y)) ? y : scm_make_real (xx); | |
3510 | } | |
3511 | else if (SCM_FRACTIONP (y)) | |
3512 | { | |
3513 | double yy = scm_i_fraction2double (y); | |
3514 | double xx = scm_i_fraction2double (x); | |
3515 | return (xx < yy) ? y : x; | |
3516 | } | |
0aacf84e MD |
3517 | else |
3518 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3519 | } |
0aacf84e | 3520 | else |
f4c627b3 | 3521 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); |
0f2d19dd JB |
3522 | } |
3523 | ||
3524 | ||
9de33deb | 3525 | SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min); |
942e5b91 MG |
3526 | /* "Return the minium of all parameter values." |
3527 | */ | |
0f2d19dd | 3528 | SCM |
6e8d25a6 | 3529 | scm_min (SCM x, SCM y) |
0f2d19dd | 3530 | { |
0aacf84e MD |
3531 | if (SCM_UNBNDP (y)) |
3532 | { | |
3533 | if (SCM_UNBNDP (x)) | |
3534 | SCM_WTA_DISPATCH_0 (g_min, s_min); | |
dab4e67a | 3535 | else if (SCM_INUMP(x) || SCM_BIGP(x) || SCM_REALP(x) || SCM_FRACTIONP(x)) |
0aacf84e MD |
3536 | return x; |
3537 | else | |
3538 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 3539 | } |
f4c627b3 | 3540 | |
0aacf84e MD |
3541 | if (SCM_INUMP (x)) |
3542 | { | |
3543 | long xx = SCM_INUM (x); | |
3544 | if (SCM_INUMP (y)) | |
3545 | { | |
3546 | long yy = SCM_INUM (y); | |
3547 | return (xx < yy) ? x : y; | |
3548 | } | |
3549 | else if (SCM_BIGP (y)) | |
3550 | { | |
3551 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3552 | scm_remember_upto_here_1 (y); | |
3553 | return (sgn < 0) ? y : x; | |
3554 | } | |
3555 | else if (SCM_REALP (y)) | |
3556 | { | |
3557 | double z = xx; | |
3558 | /* if y==NaN then "<" is false and we return NaN */ | |
3559 | return (z < SCM_REAL_VALUE (y)) ? scm_make_real (z) : y; | |
3560 | } | |
f92e85f7 MV |
3561 | else if (SCM_FRACTIONP (y)) |
3562 | { | |
3563 | double z = xx; | |
3564 | return (z < scm_i_fraction2double (y)) ? x : y; | |
3565 | } | |
0aacf84e MD |
3566 | else |
3567 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3568 | } |
0aacf84e MD |
3569 | else if (SCM_BIGP (x)) |
3570 | { | |
3571 | if (SCM_INUMP (y)) | |
3572 | { | |
3573 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3574 | scm_remember_upto_here_1 (x); | |
3575 | return (sgn < 0) ? x : y; | |
3576 | } | |
3577 | else if (SCM_BIGP (y)) | |
3578 | { | |
3579 | int cmp = mpz_cmp (SCM_I_BIG_MPZ (x), SCM_I_BIG_MPZ (y)); | |
3580 | scm_remember_upto_here_2 (x, y); | |
3581 | return (cmp > 0) ? y : x; | |
3582 | } | |
3583 | else if (SCM_REALP (y)) | |
3584 | { | |
3585 | double yy = SCM_REAL_VALUE (y); | |
3586 | int cmp; | |
3587 | if (xisnan (yy)) | |
3588 | return y; | |
3589 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), yy); | |
3590 | scm_remember_upto_here_1 (x); | |
3591 | return (cmp > 0) ? y : x; | |
3592 | } | |
f92e85f7 MV |
3593 | else if (SCM_FRACTIONP (y)) |
3594 | { | |
3595 | double yy = scm_i_fraction2double (y); | |
3596 | int cmp; | |
3597 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (x), yy); | |
3598 | scm_remember_upto_here_1 (x); | |
3599 | return (cmp > 0) ? y : x; | |
3600 | } | |
0aacf84e MD |
3601 | else |
3602 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f4c627b3 | 3603 | } |
0aacf84e MD |
3604 | else if (SCM_REALP (x)) |
3605 | { | |
3606 | if (SCM_INUMP (y)) | |
3607 | { | |
3608 | double z = SCM_INUM (y); | |
3609 | /* if x==NaN then "<" is false and we return NaN */ | |
3610 | return (z < SCM_REAL_VALUE (x)) ? scm_make_real (z) : x; | |
3611 | } | |
3612 | else if (SCM_BIGP (y)) | |
3613 | { | |
3614 | double xx = SCM_REAL_VALUE (x); | |
3615 | int cmp; | |
3616 | if (xisnan (xx)) | |
3617 | return x; | |
3618 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), xx); | |
3619 | scm_remember_upto_here_1 (y); | |
3620 | return (cmp < 0) ? y : x; | |
3621 | } | |
3622 | else if (SCM_REALP (y)) | |
3623 | { | |
3624 | /* if x==NaN then our explicit check means we return NaN | |
3625 | if y==NaN then "<" is false and we return NaN | |
3626 | calling isnan is unavoidable, since it's the only way to know | |
3627 | which of x or y causes any compares to be false */ | |
3628 | double xx = SCM_REAL_VALUE (x); | |
3629 | return (xisnan (xx) || xx < SCM_REAL_VALUE (y)) ? x : y; | |
3630 | } | |
f92e85f7 MV |
3631 | else if (SCM_FRACTIONP (y)) |
3632 | { | |
3633 | double yy = scm_i_fraction2double (y); | |
3634 | double xx = SCM_REAL_VALUE (x); | |
3635 | return (yy < xx) ? scm_make_real (yy) : x; | |
3636 | } | |
0aacf84e MD |
3637 | else |
3638 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3639 | } |
f92e85f7 MV |
3640 | else if (SCM_FRACTIONP (x)) |
3641 | { | |
3642 | if (SCM_INUMP (y)) | |
3643 | { | |
3644 | double z = SCM_INUM (y); | |
3645 | return (scm_i_fraction2double (x) < z) ? x : y; | |
3646 | } | |
3647 | else if (SCM_BIGP (y)) | |
3648 | { | |
3649 | double xx = scm_i_fraction2double (x); | |
3650 | int cmp; | |
3651 | cmp = xmpz_cmp_d (SCM_I_BIG_MPZ (y), xx); | |
3652 | scm_remember_upto_here_1 (y); | |
3653 | return (cmp < 0) ? y : x; | |
3654 | } | |
3655 | else if (SCM_REALP (y)) | |
3656 | { | |
3657 | double xx = scm_i_fraction2double (x); | |
3658 | return (SCM_REAL_VALUE (y) < xx) ? y : scm_make_real (xx); | |
3659 | } | |
3660 | else if (SCM_FRACTIONP (y)) | |
3661 | { | |
3662 | double yy = scm_i_fraction2double (y); | |
3663 | double xx = scm_i_fraction2double (x); | |
3664 | return (xx < yy) ? x : y; | |
3665 | } | |
3666 | else | |
3667 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3668 | } | |
0aacf84e | 3669 | else |
f4c627b3 | 3670 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); |
0f2d19dd JB |
3671 | } |
3672 | ||
3673 | ||
9de33deb | 3674 | SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum); |
942e5b91 MG |
3675 | /* "Return the sum of all parameter values. Return 0 if called without\n" |
3676 | * "any parameters." | |
3677 | */ | |
0f2d19dd | 3678 | SCM |
6e8d25a6 | 3679 | scm_sum (SCM x, SCM y) |
0f2d19dd | 3680 | { |
ca46fb90 RB |
3681 | if (SCM_UNBNDP (y)) |
3682 | { | |
3683 | if (SCM_NUMBERP (x)) return x; | |
3684 | if (SCM_UNBNDP (x)) return SCM_INUM0; | |
98cb6e75 | 3685 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); |
f872b822 | 3686 | } |
c209c88e | 3687 | |
ca46fb90 RB |
3688 | if (SCM_INUMP (x)) |
3689 | { | |
3690 | if (SCM_INUMP (y)) | |
3691 | { | |
3692 | long xx = SCM_INUM (x); | |
3693 | long yy = SCM_INUM (y); | |
3694 | long int z = xx + yy; | |
3695 | return SCM_FIXABLE (z) ? SCM_MAKINUM (z) : scm_i_long2big (z); | |
3696 | } | |
3697 | else if (SCM_BIGP (y)) | |
3698 | { | |
3699 | SCM_SWAP (x, y); | |
3700 | goto add_big_inum; | |
3701 | } | |
3702 | else if (SCM_REALP (y)) | |
3703 | { | |
3704 | long int xx = SCM_INUM (x); | |
3705 | return scm_make_real (xx + SCM_REAL_VALUE (y)); | |
3706 | } | |
3707 | else if (SCM_COMPLEXP (y)) | |
3708 | { | |
3709 | long int xx = SCM_INUM (x); | |
3710 | return scm_make_complex (xx + SCM_COMPLEX_REAL (y), | |
3711 | SCM_COMPLEX_IMAG (y)); | |
3712 | } | |
f92e85f7 MV |
3713 | else if (SCM_FRACTIONP (y)) |
3714 | return scm_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), | |
3715 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), | |
3716 | SCM_FRACTION_DENOMINATOR (y)); | |
ca46fb90 RB |
3717 | else |
3718 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0aacf84e MD |
3719 | } else if (SCM_BIGP (x)) |
3720 | { | |
3721 | if (SCM_INUMP (y)) | |
3722 | { | |
3723 | long int inum; | |
3724 | int bigsgn; | |
3725 | add_big_inum: | |
3726 | inum = SCM_INUM (y); | |
3727 | if (inum == 0) | |
3728 | return x; | |
3729 | bigsgn = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3730 | if (inum < 0) | |
3731 | { | |
3732 | SCM result = scm_i_mkbig (); | |
3733 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), - inum); | |
3734 | scm_remember_upto_here_1 (x); | |
3735 | /* we know the result will have to be a bignum */ | |
3736 | if (bigsgn == -1) | |
3737 | return result; | |
3738 | return scm_i_normbig (result); | |
3739 | } | |
3740 | else | |
3741 | { | |
3742 | SCM result = scm_i_mkbig (); | |
3743 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), inum); | |
3744 | scm_remember_upto_here_1 (x); | |
3745 | /* we know the result will have to be a bignum */ | |
3746 | if (bigsgn == 1) | |
3747 | return result; | |
3748 | return scm_i_normbig (result); | |
3749 | } | |
3750 | } | |
3751 | else if (SCM_BIGP (y)) | |
3752 | { | |
3753 | SCM result = scm_i_mkbig (); | |
3754 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3755 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3756 | mpz_add (SCM_I_BIG_MPZ (result), | |
3757 | SCM_I_BIG_MPZ (x), | |
3758 | SCM_I_BIG_MPZ (y)); | |
3759 | scm_remember_upto_here_2 (x, y); | |
3760 | /* we know the result will have to be a bignum */ | |
3761 | if (sgn_x == sgn_y) | |
3762 | return result; | |
3763 | return scm_i_normbig (result); | |
3764 | } | |
3765 | else if (SCM_REALP (y)) | |
3766 | { | |
3767 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) + SCM_REAL_VALUE (y); | |
3768 | scm_remember_upto_here_1 (x); | |
3769 | return scm_make_real (result); | |
3770 | } | |
3771 | else if (SCM_COMPLEXP (y)) | |
3772 | { | |
3773 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
3774 | + SCM_COMPLEX_REAL (y)); | |
3775 | scm_remember_upto_here_1 (x); | |
3776 | return scm_make_complex (real_part, SCM_COMPLEX_IMAG (y)); | |
3777 | } | |
f92e85f7 MV |
3778 | else if (SCM_FRACTIONP (y)) |
3779 | return scm_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (y), | |
3780 | scm_product (x, SCM_FRACTION_DENOMINATOR (y))), | |
3781 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
3782 | else |
3783 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
0f2d19dd | 3784 | } |
0aacf84e MD |
3785 | else if (SCM_REALP (x)) |
3786 | { | |
3787 | if (SCM_INUMP (y)) | |
3788 | return scm_make_real (SCM_REAL_VALUE (x) + SCM_INUM (y)); | |
3789 | else if (SCM_BIGP (y)) | |
3790 | { | |
3791 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) + SCM_REAL_VALUE (x); | |
3792 | scm_remember_upto_here_1 (y); | |
3793 | return scm_make_real (result); | |
3794 | } | |
3795 | else if (SCM_REALP (y)) | |
3796 | return scm_make_real (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); | |
3797 | else if (SCM_COMPLEXP (y)) | |
3798 | return scm_make_complex (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), | |
3799 | SCM_COMPLEX_IMAG (y)); | |
f92e85f7 MV |
3800 | else if (SCM_FRACTIONP (y)) |
3801 | return scm_make_real (SCM_REAL_VALUE (x) + scm_i_fraction2double (y)); | |
0aacf84e MD |
3802 | else |
3803 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 3804 | } |
0aacf84e MD |
3805 | else if (SCM_COMPLEXP (x)) |
3806 | { | |
3807 | if (SCM_INUMP (y)) | |
3808 | return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_INUM (y), | |
3809 | SCM_COMPLEX_IMAG (x)); | |
3810 | else if (SCM_BIGP (y)) | |
3811 | { | |
3812 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (y)) | |
3813 | + SCM_COMPLEX_REAL (x)); | |
3814 | scm_remember_upto_here_1 (y); | |
3815 | return scm_make_complex (real_part, SCM_COMPLEX_IMAG (x)); | |
3816 | } | |
3817 | else if (SCM_REALP (y)) | |
3818 | return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), | |
3819 | SCM_COMPLEX_IMAG (x)); | |
3820 | else if (SCM_COMPLEXP (y)) | |
3821 | return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), | |
3822 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); | |
f92e85f7 MV |
3823 | else if (SCM_FRACTIONP (y)) |
3824 | return scm_make_complex (SCM_COMPLEX_REAL (x) + scm_i_fraction2double (y), | |
3825 | SCM_COMPLEX_IMAG (x)); | |
3826 | else | |
3827 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
3828 | } | |
3829 | else if (SCM_FRACTIONP (x)) | |
3830 | { | |
3831 | if (SCM_INUMP (y)) | |
3832 | return scm_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), | |
3833 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), | |
3834 | SCM_FRACTION_DENOMINATOR (x)); | |
3835 | else if (SCM_BIGP (y)) | |
3836 | return scm_make_ratio (scm_sum (SCM_FRACTION_NUMERATOR (x), | |
3837 | scm_product (y, SCM_FRACTION_DENOMINATOR (x))), | |
3838 | SCM_FRACTION_DENOMINATOR (x)); | |
3839 | else if (SCM_REALP (y)) | |
3840 | return scm_make_real (SCM_REAL_VALUE (y) + scm_i_fraction2double (x)); | |
3841 | else if (SCM_COMPLEXP (y)) | |
3842 | return scm_make_complex (SCM_COMPLEX_REAL (y) + scm_i_fraction2double (x), | |
3843 | SCM_COMPLEX_IMAG (y)); | |
3844 | else if (SCM_FRACTIONP (y)) | |
3845 | /* a/b + c/d = (ad + bc) / bd */ | |
3846 | return scm_make_ratio (scm_sum (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), | |
3847 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), | |
3848 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
3849 | else |
3850 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
98cb6e75 | 3851 | } |
0aacf84e | 3852 | else |
98cb6e75 | 3853 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); |
0f2d19dd JB |
3854 | } |
3855 | ||
3856 | ||
9de33deb | 3857 | SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference); |
609c3d30 MG |
3858 | /* If called with one argument @var{z1}, -@var{z1} returned. Otherwise |
3859 | * the sum of all but the first argument are subtracted from the first | |
3860 | * argument. */ | |
c05e97b7 | 3861 | #define FUNC_NAME s_difference |
0f2d19dd | 3862 | SCM |
6e8d25a6 | 3863 | scm_difference (SCM x, SCM y) |
0f2d19dd | 3864 | { |
ca46fb90 RB |
3865 | if (SCM_UNBNDP (y)) |
3866 | { | |
3867 | if (SCM_UNBNDP (x)) | |
3868 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
3869 | else | |
3870 | if (SCM_INUMP (x)) | |
3871 | { | |
3872 | long xx = -SCM_INUM (x); | |
3873 | if (SCM_FIXABLE (xx)) | |
3874 | return SCM_MAKINUM (xx); | |
3875 | else | |
3876 | return scm_i_long2big (xx); | |
3877 | } | |
3878 | else if (SCM_BIGP (x)) | |
3879 | /* FIXME: do we really need to normalize here? */ | |
3880 | return scm_i_normbig (scm_i_clonebig (x, 0)); | |
3881 | else if (SCM_REALP (x)) | |
3882 | return scm_make_real (-SCM_REAL_VALUE (x)); | |
3883 | else if (SCM_COMPLEXP (x)) | |
3884 | return scm_make_complex (-SCM_COMPLEX_REAL (x), | |
3885 | -SCM_COMPLEX_IMAG (x)); | |
f92e85f7 MV |
3886 | else if (SCM_FRACTIONP (x)) |
3887 | return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), SCM_UNDEFINED), | |
3888 | SCM_FRACTION_DENOMINATOR (x)); | |
ca46fb90 RB |
3889 | else |
3890 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 3891 | } |
ca46fb90 | 3892 | |
0aacf84e MD |
3893 | if (SCM_INUMP (x)) |
3894 | { | |
3895 | if (SCM_INUMP (y)) | |
3896 | { | |
3897 | long int xx = SCM_INUM (x); | |
3898 | long int yy = SCM_INUM (y); | |
3899 | long int z = xx - yy; | |
3900 | if (SCM_FIXABLE (z)) | |
3901 | return SCM_MAKINUM (z); | |
3902 | else | |
3903 | return scm_i_long2big (z); | |
3904 | } | |
3905 | else if (SCM_BIGP (y)) | |
3906 | { | |
3907 | /* inum-x - big-y */ | |
3908 | long xx = SCM_INUM (x); | |
ca46fb90 | 3909 | |
0aacf84e MD |
3910 | if (xx == 0) |
3911 | return scm_i_clonebig (y, 0); | |
3912 | else | |
3913 | { | |
3914 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3915 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 3916 | |
0aacf84e MD |
3917 | if (xx >= 0) |
3918 | mpz_ui_sub (SCM_I_BIG_MPZ (result), xx, SCM_I_BIG_MPZ (y)); | |
3919 | else | |
3920 | { | |
3921 | /* x - y == -(y + -x) */ | |
3922 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), -xx); | |
3923 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
3924 | } | |
3925 | scm_remember_upto_here_1 (y); | |
ca46fb90 | 3926 | |
0aacf84e MD |
3927 | if ((xx < 0 && (sgn_y > 0)) || ((xx > 0) && sgn_y < 0)) |
3928 | /* we know the result will have to be a bignum */ | |
3929 | return result; | |
3930 | else | |
3931 | return scm_i_normbig (result); | |
3932 | } | |
3933 | } | |
3934 | else if (SCM_REALP (y)) | |
3935 | { | |
3936 | long int xx = SCM_INUM (x); | |
3937 | return scm_make_real (xx - SCM_REAL_VALUE (y)); | |
3938 | } | |
3939 | else if (SCM_COMPLEXP (y)) | |
3940 | { | |
3941 | long int xx = SCM_INUM (x); | |
3942 | return scm_make_complex (xx - SCM_COMPLEX_REAL (y), | |
3943 | - SCM_COMPLEX_IMAG (y)); | |
3944 | } | |
f92e85f7 MV |
3945 | else if (SCM_FRACTIONP (y)) |
3946 | /* a - b/c = (ac - b) / c */ | |
3947 | return scm_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), | |
3948 | SCM_FRACTION_NUMERATOR (y)), | |
3949 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
3950 | else |
3951 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 3952 | } |
0aacf84e MD |
3953 | else if (SCM_BIGP (x)) |
3954 | { | |
3955 | if (SCM_INUMP (y)) | |
3956 | { | |
3957 | /* big-x - inum-y */ | |
3958 | long yy = SCM_INUM (y); | |
3959 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
ca46fb90 | 3960 | |
0aacf84e MD |
3961 | scm_remember_upto_here_1 (x); |
3962 | if (sgn_x == 0) | |
3963 | return SCM_FIXABLE (-yy) ? SCM_MAKINUM (-yy) : scm_long2num (-yy); | |
3964 | else | |
3965 | { | |
3966 | SCM result = scm_i_mkbig (); | |
ca46fb90 | 3967 | |
708f22c6 KR |
3968 | if (yy >= 0) |
3969 | mpz_sub_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), yy); | |
3970 | else | |
3971 | mpz_add_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), -yy); | |
0aacf84e | 3972 | scm_remember_upto_here_1 (x); |
ca46fb90 | 3973 | |
0aacf84e MD |
3974 | if ((sgn_x < 0 && (yy > 0)) || ((sgn_x > 0) && yy < 0)) |
3975 | /* we know the result will have to be a bignum */ | |
3976 | return result; | |
3977 | else | |
3978 | return scm_i_normbig (result); | |
3979 | } | |
3980 | } | |
3981 | else if (SCM_BIGP (y)) | |
3982 | { | |
3983 | int sgn_x = mpz_sgn (SCM_I_BIG_MPZ (x)); | |
3984 | int sgn_y = mpz_sgn (SCM_I_BIG_MPZ (y)); | |
3985 | SCM result = scm_i_mkbig (); | |
3986 | mpz_sub (SCM_I_BIG_MPZ (result), | |
3987 | SCM_I_BIG_MPZ (x), | |
3988 | SCM_I_BIG_MPZ (y)); | |
3989 | scm_remember_upto_here_2 (x, y); | |
3990 | /* we know the result will have to be a bignum */ | |
3991 | if ((sgn_x == 1) && (sgn_y == -1)) | |
3992 | return result; | |
3993 | if ((sgn_x == -1) && (sgn_y == 1)) | |
3994 | return result; | |
3995 | return scm_i_normbig (result); | |
3996 | } | |
3997 | else if (SCM_REALP (y)) | |
3998 | { | |
3999 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) - SCM_REAL_VALUE (y); | |
4000 | scm_remember_upto_here_1 (x); | |
4001 | return scm_make_real (result); | |
4002 | } | |
4003 | else if (SCM_COMPLEXP (y)) | |
4004 | { | |
4005 | double real_part = (mpz_get_d (SCM_I_BIG_MPZ (x)) | |
4006 | - SCM_COMPLEX_REAL (y)); | |
4007 | scm_remember_upto_here_1 (x); | |
4008 | return scm_make_complex (real_part, - SCM_COMPLEX_IMAG (y)); | |
4009 | } | |
f92e85f7 MV |
4010 | else if (SCM_FRACTIONP (y)) |
4011 | return scm_make_ratio (scm_difference (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), | |
4012 | SCM_FRACTION_NUMERATOR (y)), | |
4013 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e | 4014 | else SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); |
ca46fb90 | 4015 | } |
0aacf84e MD |
4016 | else if (SCM_REALP (x)) |
4017 | { | |
4018 | if (SCM_INUMP (y)) | |
4019 | return scm_make_real (SCM_REAL_VALUE (x) - SCM_INUM (y)); | |
4020 | else if (SCM_BIGP (y)) | |
4021 | { | |
4022 | double result = SCM_REAL_VALUE (x) - mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4023 | scm_remember_upto_here_1 (x); | |
4024 | return scm_make_real (result); | |
4025 | } | |
4026 | else if (SCM_REALP (y)) | |
4027 | return scm_make_real (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); | |
4028 | else if (SCM_COMPLEXP (y)) | |
4029 | return scm_make_complex (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), | |
4030 | -SCM_COMPLEX_IMAG (y)); | |
f92e85f7 MV |
4031 | else if (SCM_FRACTIONP (y)) |
4032 | return scm_make_real (SCM_REAL_VALUE (x) - scm_i_fraction2double (y)); | |
0aacf84e MD |
4033 | else |
4034 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4035 | } |
0aacf84e MD |
4036 | else if (SCM_COMPLEXP (x)) |
4037 | { | |
4038 | if (SCM_INUMP (y)) | |
4039 | return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_INUM (y), | |
4040 | SCM_COMPLEX_IMAG (x)); | |
4041 | else if (SCM_BIGP (y)) | |
4042 | { | |
4043 | double real_part = (SCM_COMPLEX_REAL (x) | |
4044 | - mpz_get_d (SCM_I_BIG_MPZ (y))); | |
4045 | scm_remember_upto_here_1 (x); | |
4046 | return scm_make_complex (real_part, SCM_COMPLEX_IMAG (y)); | |
4047 | } | |
4048 | else if (SCM_REALP (y)) | |
4049 | return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), | |
4050 | SCM_COMPLEX_IMAG (x)); | |
4051 | else if (SCM_COMPLEXP (y)) | |
4052 | return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), | |
4053 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); | |
f92e85f7 MV |
4054 | else if (SCM_FRACTIONP (y)) |
4055 | return scm_make_complex (SCM_COMPLEX_REAL (x) - scm_i_fraction2double (y), | |
4056 | SCM_COMPLEX_IMAG (x)); | |
4057 | else | |
4058 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
4059 | } | |
4060 | else if (SCM_FRACTIONP (x)) | |
4061 | { | |
4062 | if (SCM_INUMP (y)) | |
4063 | /* a/b - c = (a - cb) / b */ | |
4064 | return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), | |
4065 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), | |
4066 | SCM_FRACTION_DENOMINATOR (x)); | |
4067 | else if (SCM_BIGP (y)) | |
4068 | return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (x), | |
4069 | scm_product(y, SCM_FRACTION_DENOMINATOR (x))), | |
4070 | SCM_FRACTION_DENOMINATOR (x)); | |
4071 | else if (SCM_REALP (y)) | |
4072 | return scm_make_real (scm_i_fraction2double (x) - SCM_REAL_VALUE (y)); | |
4073 | else if (SCM_COMPLEXP (y)) | |
4074 | return scm_make_complex (scm_i_fraction2double (x) - SCM_COMPLEX_REAL (y), | |
4075 | -SCM_COMPLEX_IMAG (y)); | |
4076 | else if (SCM_FRACTIONP (y)) | |
4077 | /* a/b - c/d = (ad - bc) / bd */ | |
4078 | return scm_make_ratio (scm_difference (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), | |
4079 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))), | |
4080 | scm_product (SCM_FRACTION_DENOMINATOR (x), SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4081 | else |
4082 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
98cb6e75 | 4083 | } |
0aacf84e | 4084 | else |
98cb6e75 | 4085 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); |
0f2d19dd | 4086 | } |
c05e97b7 | 4087 | #undef FUNC_NAME |
0f2d19dd | 4088 | |
ca46fb90 | 4089 | |
9de33deb | 4090 | SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product); |
942e5b91 MG |
4091 | /* "Return the product of all arguments. If called without arguments,\n" |
4092 | * "1 is returned." | |
4093 | */ | |
0f2d19dd | 4094 | SCM |
6e8d25a6 | 4095 | scm_product (SCM x, SCM y) |
0f2d19dd | 4096 | { |
0aacf84e MD |
4097 | if (SCM_UNBNDP (y)) |
4098 | { | |
4099 | if (SCM_UNBNDP (x)) | |
4100 | return SCM_MAKINUM (1L); | |
4101 | else if (SCM_NUMBERP (x)) | |
4102 | return x; | |
4103 | else | |
4104 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 4105 | } |
ca46fb90 | 4106 | |
0aacf84e MD |
4107 | if (SCM_INUMP (x)) |
4108 | { | |
4109 | long xx; | |
f4c627b3 | 4110 | |
0aacf84e MD |
4111 | intbig: |
4112 | xx = SCM_INUM (x); | |
f4c627b3 | 4113 | |
0aacf84e MD |
4114 | switch (xx) |
4115 | { | |
ca46fb90 RB |
4116 | case 0: return x; break; |
4117 | case 1: return y; break; | |
0aacf84e | 4118 | } |
f4c627b3 | 4119 | |
0aacf84e MD |
4120 | if (SCM_INUMP (y)) |
4121 | { | |
4122 | long yy = SCM_INUM (y); | |
4123 | long kk = xx * yy; | |
4124 | SCM k = SCM_MAKINUM (kk); | |
4125 | if ((kk == SCM_INUM (k)) && (kk / xx == yy)) | |
4126 | return k; | |
4127 | else | |
4128 | { | |
4129 | SCM result = scm_i_long2big (xx); | |
4130 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result), yy); | |
4131 | return scm_i_normbig (result); | |
4132 | } | |
4133 | } | |
4134 | else if (SCM_BIGP (y)) | |
4135 | { | |
4136 | SCM result = scm_i_mkbig (); | |
4137 | mpz_mul_si (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (y), xx); | |
4138 | scm_remember_upto_here_1 (y); | |
4139 | return result; | |
4140 | } | |
4141 | else if (SCM_REALP (y)) | |
4142 | return scm_make_real (xx * SCM_REAL_VALUE (y)); | |
4143 | else if (SCM_COMPLEXP (y)) | |
4144 | return scm_make_complex (xx * SCM_COMPLEX_REAL (y), | |
4145 | xx * SCM_COMPLEX_IMAG (y)); | |
f92e85f7 MV |
4146 | else if (SCM_FRACTIONP (y)) |
4147 | return scm_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), | |
4148 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4149 | else |
4150 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4151 | } |
0aacf84e MD |
4152 | else if (SCM_BIGP (x)) |
4153 | { | |
4154 | if (SCM_INUMP (y)) | |
4155 | { | |
4156 | SCM_SWAP (x, y); | |
4157 | goto intbig; | |
4158 | } | |
4159 | else if (SCM_BIGP (y)) | |
4160 | { | |
4161 | SCM result = scm_i_mkbig (); | |
4162 | mpz_mul (SCM_I_BIG_MPZ (result), | |
4163 | SCM_I_BIG_MPZ (x), | |
4164 | SCM_I_BIG_MPZ (y)); | |
4165 | scm_remember_upto_here_2 (x, y); | |
4166 | return result; | |
4167 | } | |
4168 | else if (SCM_REALP (y)) | |
4169 | { | |
4170 | double result = mpz_get_d (SCM_I_BIG_MPZ (x)) * SCM_REAL_VALUE (y); | |
4171 | scm_remember_upto_here_1 (x); | |
4172 | return scm_make_real (result); | |
4173 | } | |
4174 | else if (SCM_COMPLEXP (y)) | |
4175 | { | |
4176 | double z = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4177 | scm_remember_upto_here_1 (x); | |
4178 | return scm_make_complex (z * SCM_COMPLEX_REAL (y), | |
4179 | z * SCM_COMPLEX_IMAG (y)); | |
4180 | } | |
f92e85f7 MV |
4181 | else if (SCM_FRACTIONP (y)) |
4182 | return scm_make_ratio (scm_product (x, SCM_FRACTION_NUMERATOR (y)), | |
4183 | SCM_FRACTION_DENOMINATOR (y)); | |
0aacf84e MD |
4184 | else |
4185 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4186 | } |
0aacf84e MD |
4187 | else if (SCM_REALP (x)) |
4188 | { | |
4189 | if (SCM_INUMP (y)) | |
4190 | return scm_make_real (SCM_INUM (y) * SCM_REAL_VALUE (x)); | |
4191 | else if (SCM_BIGP (y)) | |
4192 | { | |
4193 | double result = mpz_get_d (SCM_I_BIG_MPZ (y)) * SCM_REAL_VALUE (x); | |
4194 | scm_remember_upto_here_1 (y); | |
4195 | return scm_make_real (result); | |
4196 | } | |
4197 | else if (SCM_REALP (y)) | |
4198 | return scm_make_real (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); | |
4199 | else if (SCM_COMPLEXP (y)) | |
4200 | return scm_make_complex (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), | |
4201 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); | |
f92e85f7 MV |
4202 | else if (SCM_FRACTIONP (y)) |
4203 | return scm_make_real (SCM_REAL_VALUE (x) * scm_i_fraction2double (y)); | |
0aacf84e MD |
4204 | else |
4205 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4206 | } |
0aacf84e MD |
4207 | else if (SCM_COMPLEXP (x)) |
4208 | { | |
4209 | if (SCM_INUMP (y)) | |
4210 | return scm_make_complex (SCM_INUM (y) * SCM_COMPLEX_REAL (x), | |
4211 | SCM_INUM (y) * SCM_COMPLEX_IMAG (x)); | |
4212 | else if (SCM_BIGP (y)) | |
4213 | { | |
4214 | double z = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4215 | scm_remember_upto_here_1 (y); | |
76506335 KR |
4216 | return scm_make_complex (z * SCM_COMPLEX_REAL (x), |
4217 | z * SCM_COMPLEX_IMAG (x)); | |
0aacf84e MD |
4218 | } |
4219 | else if (SCM_REALP (y)) | |
4220 | return scm_make_complex (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), | |
4221 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); | |
4222 | else if (SCM_COMPLEXP (y)) | |
4223 | { | |
4224 | return scm_make_complex (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) | |
4225 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), | |
4226 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
4227 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
4228 | } | |
f92e85f7 MV |
4229 | else if (SCM_FRACTIONP (y)) |
4230 | { | |
4231 | double yy = scm_i_fraction2double (y); | |
4232 | return scm_make_complex (yy * SCM_COMPLEX_REAL (x), | |
4233 | yy * SCM_COMPLEX_IMAG (x)); | |
4234 | } | |
4235 | else | |
4236 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
4237 | } | |
4238 | else if (SCM_FRACTIONP (x)) | |
4239 | { | |
4240 | if (SCM_INUMP (y)) | |
4241 | return scm_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), | |
4242 | SCM_FRACTION_DENOMINATOR (x)); | |
4243 | else if (SCM_BIGP (y)) | |
4244 | return scm_make_ratio (scm_product (y, SCM_FRACTION_NUMERATOR (x)), | |
4245 | SCM_FRACTION_DENOMINATOR (x)); | |
4246 | else if (SCM_REALP (y)) | |
4247 | return scm_make_real (scm_i_fraction2double (x) * SCM_REAL_VALUE (y)); | |
4248 | else if (SCM_COMPLEXP (y)) | |
4249 | { | |
4250 | double xx = scm_i_fraction2double (x); | |
4251 | return scm_make_complex (xx * SCM_COMPLEX_REAL (y), | |
4252 | xx * SCM_COMPLEX_IMAG (y)); | |
4253 | } | |
4254 | else if (SCM_FRACTIONP (y)) | |
4255 | /* a/b * c/d = ac / bd */ | |
4256 | return scm_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), | |
4257 | SCM_FRACTION_NUMERATOR (y)), | |
4258 | scm_product (SCM_FRACTION_DENOMINATOR (x), | |
4259 | SCM_FRACTION_DENOMINATOR (y))); | |
0aacf84e MD |
4260 | else |
4261 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
f4c627b3 | 4262 | } |
0aacf84e | 4263 | else |
f4c627b3 | 4264 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); |
0f2d19dd JB |
4265 | } |
4266 | ||
0f2d19dd | 4267 | double |
6e8d25a6 | 4268 | scm_num2dbl (SCM a, const char *why) |
f4c627b3 | 4269 | #define FUNC_NAME why |
0f2d19dd | 4270 | { |
0aacf84e | 4271 | if (SCM_INUMP (a)) |
0f2d19dd | 4272 | return (double) SCM_INUM (a); |
0aacf84e MD |
4273 | else if (SCM_BIGP (a)) |
4274 | { | |
4275 | double result = mpz_get_d (SCM_I_BIG_MPZ (a)); | |
4276 | scm_remember_upto_here_1 (a); | |
4277 | return result; | |
4278 | } | |
4279 | else if (SCM_REALP (a)) | |
f4c627b3 | 4280 | return (SCM_REAL_VALUE (a)); |
f92e85f7 MV |
4281 | else if (SCM_FRACTIONP (a)) |
4282 | return scm_i_fraction2double (a); | |
0aacf84e | 4283 | else |
f4c627b3 | 4284 | SCM_WRONG_TYPE_ARG (SCM_ARGn, a); |
0f2d19dd | 4285 | } |
f4c627b3 | 4286 | #undef FUNC_NAME |
0f2d19dd | 4287 | |
7351e207 MV |
4288 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
4289 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
4290 | #define ALLOW_DIVIDE_BY_ZERO | |
4291 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
4292 | #endif | |
0f2d19dd | 4293 | |
ba74ef4e MV |
4294 | /* The code below for complex division is adapted from the GNU |
4295 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
4296 | this copyright: */ | |
4297 | ||
4298 | /**************************************************************** | |
4299 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
4300 | ||
4301 | Permission to use, copy, modify, and distribute this software | |
4302 | and its documentation for any purpose and without fee is hereby | |
4303 | granted, provided that the above copyright notice appear in all | |
4304 | copies and that both that the copyright notice and this | |
4305 | permission notice and warranty disclaimer appear in supporting | |
4306 | documentation, and that the names of AT&T Bell Laboratories or | |
4307 | Bellcore or any of their entities not be used in advertising or | |
4308 | publicity pertaining to distribution of the software without | |
4309 | specific, written prior permission. | |
4310 | ||
4311 | AT&T and Bellcore disclaim all warranties with regard to this | |
4312 | software, including all implied warranties of merchantability | |
4313 | and fitness. In no event shall AT&T or Bellcore be liable for | |
4314 | any special, indirect or consequential damages or any damages | |
4315 | whatsoever resulting from loss of use, data or profits, whether | |
4316 | in an action of contract, negligence or other tortious action, | |
4317 | arising out of or in connection with the use or performance of | |
4318 | this software. | |
4319 | ****************************************************************/ | |
4320 | ||
9de33deb | 4321 | SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide); |
609c3d30 MG |
4322 | /* Divide the first argument by the product of the remaining |
4323 | arguments. If called with one argument @var{z1}, 1/@var{z1} is | |
4324 | returned. */ | |
c05e97b7 | 4325 | #define FUNC_NAME s_divide |
f92e85f7 MV |
4326 | static SCM |
4327 | scm_i_divide (SCM x, SCM y, int inexact) | |
0f2d19dd | 4328 | { |
f8de44c1 DH |
4329 | double a; |
4330 | ||
0aacf84e MD |
4331 | if (SCM_UNBNDP (y)) |
4332 | { | |
4333 | if (SCM_UNBNDP (x)) | |
4334 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); | |
4335 | else if (SCM_INUMP (x)) | |
4336 | { | |
4337 | long xx = SCM_INUM (x); | |
4338 | if (xx == 1 || xx == -1) | |
4339 | return x; | |
7351e207 | 4340 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4341 | else if (xx == 0) |
4342 | scm_num_overflow (s_divide); | |
7351e207 | 4343 | #endif |
0aacf84e | 4344 | else |
f92e85f7 MV |
4345 | { |
4346 | if (inexact) | |
4347 | return scm_make_real (1.0 / (double) xx); | |
4348 | else return scm_make_ratio (SCM_MAKINUM(1), x); | |
4349 | } | |
0aacf84e MD |
4350 | } |
4351 | else if (SCM_BIGP (x)) | |
f92e85f7 MV |
4352 | { |
4353 | if (inexact) | |
4354 | return scm_make_real (1.0 / scm_i_big2dbl (x)); | |
4355 | else return scm_make_ratio (SCM_MAKINUM(1), x); | |
4356 | } | |
0aacf84e MD |
4357 | else if (SCM_REALP (x)) |
4358 | { | |
4359 | double xx = SCM_REAL_VALUE (x); | |
7351e207 | 4360 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4361 | if (xx == 0.0) |
4362 | scm_num_overflow (s_divide); | |
4363 | else | |
7351e207 | 4364 | #endif |
0aacf84e MD |
4365 | return scm_make_real (1.0 / xx); |
4366 | } | |
4367 | else if (SCM_COMPLEXP (x)) | |
4368 | { | |
4369 | double r = SCM_COMPLEX_REAL (x); | |
4370 | double i = SCM_COMPLEX_IMAG (x); | |
4371 | if (r <= i) | |
4372 | { | |
4373 | double t = r / i; | |
4374 | double d = i * (1.0 + t * t); | |
4375 | return scm_make_complex (t / d, -1.0 / d); | |
4376 | } | |
4377 | else | |
4378 | { | |
4379 | double t = i / r; | |
4380 | double d = r * (1.0 + t * t); | |
4381 | return scm_make_complex (1.0 / d, -t / d); | |
4382 | } | |
4383 | } | |
f92e85f7 MV |
4384 | else if (SCM_FRACTIONP (x)) |
4385 | return scm_make_ratio (SCM_FRACTION_DENOMINATOR (x), | |
4386 | SCM_FRACTION_NUMERATOR (x)); | |
0aacf84e MD |
4387 | else |
4388 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
f8de44c1 | 4389 | } |
f8de44c1 | 4390 | |
0aacf84e MD |
4391 | if (SCM_INUMP (x)) |
4392 | { | |
4393 | long xx = SCM_INUM (x); | |
4394 | if (SCM_INUMP (y)) | |
4395 | { | |
4396 | long yy = SCM_INUM (y); | |
4397 | if (yy == 0) | |
4398 | { | |
7351e207 | 4399 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4400 | scm_num_overflow (s_divide); |
7351e207 | 4401 | #else |
0aacf84e | 4402 | return scm_make_real ((double) xx / (double) yy); |
7351e207 | 4403 | #endif |
0aacf84e MD |
4404 | } |
4405 | else if (xx % yy != 0) | |
f92e85f7 MV |
4406 | { |
4407 | if (inexact) | |
4408 | return scm_make_real ((double) xx / (double) yy); | |
4409 | else return scm_make_ratio (x, y); | |
4410 | } | |
0aacf84e MD |
4411 | else |
4412 | { | |
4413 | long z = xx / yy; | |
4414 | if (SCM_FIXABLE (z)) | |
4415 | return SCM_MAKINUM (z); | |
4416 | else | |
4417 | return scm_i_long2big (z); | |
4418 | } | |
f872b822 | 4419 | } |
0aacf84e | 4420 | else if (SCM_BIGP (y)) |
f92e85f7 MV |
4421 | { |
4422 | if (inexact) | |
4423 | return scm_make_real ((double) xx / scm_i_big2dbl (y)); | |
4424 | else return scm_make_ratio (x, y); | |
4425 | } | |
0aacf84e MD |
4426 | else if (SCM_REALP (y)) |
4427 | { | |
4428 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4429 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4430 | if (yy == 0.0) |
4431 | scm_num_overflow (s_divide); | |
4432 | else | |
7351e207 | 4433 | #endif |
0aacf84e | 4434 | return scm_make_real ((double) xx / yy); |
ba74ef4e | 4435 | } |
0aacf84e MD |
4436 | else if (SCM_COMPLEXP (y)) |
4437 | { | |
4438 | a = xx; | |
4439 | complex_div: /* y _must_ be a complex number */ | |
4440 | { | |
4441 | double r = SCM_COMPLEX_REAL (y); | |
4442 | double i = SCM_COMPLEX_IMAG (y); | |
4443 | if (r <= i) | |
4444 | { | |
4445 | double t = r / i; | |
4446 | double d = i * (1.0 + t * t); | |
4447 | return scm_make_complex ((a * t) / d, -a / d); | |
4448 | } | |
4449 | else | |
4450 | { | |
4451 | double t = i / r; | |
4452 | double d = r * (1.0 + t * t); | |
4453 | return scm_make_complex (a / d, -(a * t) / d); | |
4454 | } | |
4455 | } | |
4456 | } | |
f92e85f7 MV |
4457 | else if (SCM_FRACTIONP (y)) |
4458 | /* a / b/c = ac / b */ | |
4459 | return scm_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), | |
4460 | SCM_FRACTION_NUMERATOR (y)); | |
0aacf84e MD |
4461 | else |
4462 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4463 | } |
0aacf84e MD |
4464 | else if (SCM_BIGP (x)) |
4465 | { | |
4466 | if (SCM_INUMP (y)) | |
4467 | { | |
4468 | long int yy = SCM_INUM (y); | |
4469 | if (yy == 0) | |
4470 | { | |
7351e207 | 4471 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4472 | scm_num_overflow (s_divide); |
7351e207 | 4473 | #else |
0aacf84e MD |
4474 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4475 | scm_remember_upto_here_1 (x); | |
4476 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
7351e207 | 4477 | #endif |
0aacf84e MD |
4478 | } |
4479 | else if (yy == 1) | |
4480 | return x; | |
4481 | else | |
4482 | { | |
4483 | /* FIXME: HMM, what are the relative performance issues here? | |
4484 | We need to test. Is it faster on average to test | |
4485 | divisible_p, then perform whichever operation, or is it | |
4486 | faster to perform the integer div opportunistically and | |
4487 | switch to real if there's a remainder? For now we take the | |
4488 | middle ground: test, then if divisible, use the faster div | |
4489 | func. */ | |
4490 | ||
4491 | long abs_yy = yy < 0 ? -yy : yy; | |
4492 | int divisible_p = mpz_divisible_ui_p (SCM_I_BIG_MPZ (x), abs_yy); | |
4493 | ||
4494 | if (divisible_p) | |
4495 | { | |
4496 | SCM result = scm_i_mkbig (); | |
4497 | mpz_divexact_ui (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (x), abs_yy); | |
4498 | scm_remember_upto_here_1 (x); | |
4499 | if (yy < 0) | |
4500 | mpz_neg (SCM_I_BIG_MPZ (result), SCM_I_BIG_MPZ (result)); | |
4501 | return scm_i_normbig (result); | |
4502 | } | |
4503 | else | |
f92e85f7 MV |
4504 | { |
4505 | if (inexact) | |
4506 | return scm_make_real (scm_i_big2dbl (x) / (double) yy); | |
4507 | else return scm_make_ratio (x, y); | |
4508 | } | |
0aacf84e MD |
4509 | } |
4510 | } | |
4511 | else if (SCM_BIGP (y)) | |
4512 | { | |
4513 | int y_is_zero = (mpz_sgn (SCM_I_BIG_MPZ (y)) == 0); | |
4514 | if (y_is_zero) | |
4515 | { | |
ca46fb90 | 4516 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e | 4517 | scm_num_overflow (s_divide); |
f872b822 | 4518 | #else |
0aacf84e MD |
4519 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (x)); |
4520 | scm_remember_upto_here_1 (x); | |
4521 | return (sgn == 0) ? scm_nan () : scm_inf (); | |
f872b822 | 4522 | #endif |
0aacf84e MD |
4523 | } |
4524 | else | |
4525 | { | |
4526 | /* big_x / big_y */ | |
4527 | int divisible_p = mpz_divisible_p (SCM_I_BIG_MPZ (x), | |
4528 | SCM_I_BIG_MPZ (y)); | |
4529 | if (divisible_p) | |
4530 | { | |
4531 | SCM result = scm_i_mkbig (); | |
4532 | mpz_divexact (SCM_I_BIG_MPZ (result), | |
4533 | SCM_I_BIG_MPZ (x), | |
4534 | SCM_I_BIG_MPZ (y)); | |
4535 | scm_remember_upto_here_2 (x, y); | |
4536 | return scm_i_normbig (result); | |
4537 | } | |
4538 | else | |
4539 | { | |
f92e85f7 MV |
4540 | if (inexact) |
4541 | { | |
4542 | double dbx = mpz_get_d (SCM_I_BIG_MPZ (x)); | |
4543 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4544 | scm_remember_upto_here_2 (x, y); | |
4545 | return scm_make_real (dbx / dby); | |
4546 | } | |
4547 | else return scm_make_ratio (x, y); | |
0aacf84e MD |
4548 | } |
4549 | } | |
4550 | } | |
4551 | else if (SCM_REALP (y)) | |
4552 | { | |
4553 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4554 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4555 | if (yy == 0.0) |
4556 | scm_num_overflow (s_divide); | |
4557 | else | |
7351e207 | 4558 | #endif |
0aacf84e MD |
4559 | return scm_make_real (scm_i_big2dbl (x) / yy); |
4560 | } | |
4561 | else if (SCM_COMPLEXP (y)) | |
4562 | { | |
4563 | a = scm_i_big2dbl (x); | |
4564 | goto complex_div; | |
4565 | } | |
f92e85f7 MV |
4566 | else if (SCM_FRACTIONP (y)) |
4567 | return scm_make_ratio (scm_product (x, SCM_FRACTION_DENOMINATOR (y)), | |
4568 | SCM_FRACTION_NUMERATOR (y)); | |
0aacf84e MD |
4569 | else |
4570 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4571 | } |
0aacf84e MD |
4572 | else if (SCM_REALP (x)) |
4573 | { | |
4574 | double rx = SCM_REAL_VALUE (x); | |
4575 | if (SCM_INUMP (y)) | |
4576 | { | |
4577 | long int yy = SCM_INUM (y); | |
7351e207 | 4578 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4579 | if (yy == 0) |
4580 | scm_num_overflow (s_divide); | |
4581 | else | |
7351e207 | 4582 | #endif |
0aacf84e MD |
4583 | return scm_make_real (rx / (double) yy); |
4584 | } | |
4585 | else if (SCM_BIGP (y)) | |
4586 | { | |
4587 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4588 | scm_remember_upto_here_1 (y); | |
4589 | return scm_make_real (rx / dby); | |
4590 | } | |
4591 | else if (SCM_REALP (y)) | |
4592 | { | |
4593 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4594 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4595 | if (yy == 0.0) |
4596 | scm_num_overflow (s_divide); | |
4597 | else | |
7351e207 | 4598 | #endif |
0aacf84e MD |
4599 | return scm_make_real (rx / yy); |
4600 | } | |
4601 | else if (SCM_COMPLEXP (y)) | |
4602 | { | |
4603 | a = rx; | |
4604 | goto complex_div; | |
4605 | } | |
f92e85f7 MV |
4606 | else if (SCM_FRACTIONP (y)) |
4607 | return scm_make_real (rx / scm_i_fraction2double (y)); | |
0aacf84e MD |
4608 | else |
4609 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4610 | } |
0aacf84e MD |
4611 | else if (SCM_COMPLEXP (x)) |
4612 | { | |
4613 | double rx = SCM_COMPLEX_REAL (x); | |
4614 | double ix = SCM_COMPLEX_IMAG (x); | |
4615 | if (SCM_INUMP (y)) | |
4616 | { | |
4617 | long int yy = SCM_INUM (y); | |
7351e207 | 4618 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
0aacf84e MD |
4619 | if (yy == 0) |
4620 | scm_num_overflow (s_divide); | |
4621 | else | |
7351e207 | 4622 | #endif |
0aacf84e MD |
4623 | { |
4624 | double d = yy; | |
4625 | return scm_make_complex (rx / d, ix / d); | |
4626 | } | |
4627 | } | |
4628 | else if (SCM_BIGP (y)) | |
4629 | { | |
4630 | double dby = mpz_get_d (SCM_I_BIG_MPZ (y)); | |
4631 | scm_remember_upto_here_1 (y); | |
4632 | return scm_make_complex (rx / dby, ix / dby); | |
4633 | } | |
4634 | else if (SCM_REALP (y)) | |
4635 | { | |
4636 | double yy = SCM_REAL_VALUE (y); | |
7351e207 | 4637 | #ifndef ALLOW_DIVIDE_BY_ZERO |
0aacf84e MD |
4638 | if (yy == 0.0) |
4639 | scm_num_overflow (s_divide); | |
4640 | else | |
7351e207 | 4641 | #endif |
0aacf84e MD |
4642 | return scm_make_complex (rx / yy, ix / yy); |
4643 | } | |
4644 | else if (SCM_COMPLEXP (y)) | |
4645 | { | |
4646 | double ry = SCM_COMPLEX_REAL (y); | |
4647 | double iy = SCM_COMPLEX_IMAG (y); | |
4648 | if (ry <= iy) | |
4649 | { | |
4650 | double t = ry / iy; | |
4651 | double d = iy * (1.0 + t * t); | |
4652 | return scm_make_complex ((rx * t + ix) / d, (ix * t - rx) / d); | |
4653 | } | |
4654 | else | |
4655 | { | |
4656 | double t = iy / ry; | |
4657 | double d = ry * (1.0 + t * t); | |
4658 | return scm_make_complex ((rx + ix * t) / d, (ix - rx * t) / d); | |
4659 | } | |
4660 | } | |
f92e85f7 MV |
4661 | else if (SCM_FRACTIONP (y)) |
4662 | { | |
4663 | double yy = scm_i_fraction2double (y); | |
4664 | return scm_make_complex (rx / yy, ix / yy); | |
4665 | } | |
0aacf84e MD |
4666 | else |
4667 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f8de44c1 | 4668 | } |
f92e85f7 MV |
4669 | else if (SCM_FRACTIONP (x)) |
4670 | { | |
4671 | if (SCM_INUMP (y)) | |
4672 | { | |
4673 | long int yy = SCM_INUM (y); | |
4674 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO | |
4675 | if (yy == 0) | |
4676 | scm_num_overflow (s_divide); | |
4677 | else | |
4678 | #endif | |
4679 | return scm_make_ratio (SCM_FRACTION_NUMERATOR (x), | |
4680 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); | |
4681 | } | |
4682 | else if (SCM_BIGP (y)) | |
4683 | { | |
4684 | return scm_make_ratio (SCM_FRACTION_NUMERATOR (x), | |
4685 | scm_product (SCM_FRACTION_DENOMINATOR (x), y)); | |
4686 | } | |
4687 | else if (SCM_REALP (y)) | |
4688 | { | |
4689 | double yy = SCM_REAL_VALUE (y); | |
4690 | #ifndef ALLOW_DIVIDE_BY_ZERO | |
4691 | if (yy == 0.0) | |
4692 | scm_num_overflow (s_divide); | |
4693 | else | |
4694 | #endif | |
4695 | return scm_make_real (scm_i_fraction2double (x) / yy); | |
4696 | } | |
4697 | else if (SCM_COMPLEXP (y)) | |
4698 | { | |
4699 | a = scm_i_fraction2double (x); | |
4700 | goto complex_div; | |
4701 | } | |
4702 | else if (SCM_FRACTIONP (y)) | |
4703 | return scm_make_ratio (scm_product (SCM_FRACTION_NUMERATOR (x), SCM_FRACTION_DENOMINATOR (y)), | |
4704 | scm_product (SCM_FRACTION_NUMERATOR (y), SCM_FRACTION_DENOMINATOR (x))); | |
4705 | else | |
4706 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
4707 | } | |
0aacf84e | 4708 | else |
f8de44c1 | 4709 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); |
0f2d19dd | 4710 | } |
f92e85f7 MV |
4711 | |
4712 | SCM | |
4713 | scm_divide (SCM x, SCM y) | |
4714 | { | |
4715 | return scm_i_divide (x, y, 0); | |
4716 | } | |
4717 | ||
4718 | static SCM scm_divide2real (SCM x, SCM y) | |
4719 | { | |
4720 | return scm_i_divide (x, y, 1); | |
4721 | } | |
c05e97b7 | 4722 | #undef FUNC_NAME |
0f2d19dd | 4723 | |
fa605590 | 4724 | |
0f2d19dd | 4725 | double |
6e8d25a6 | 4726 | scm_asinh (double x) |
0f2d19dd | 4727 | { |
fa605590 KR |
4728 | #if HAVE_ASINH |
4729 | return asinh (x); | |
4730 | #else | |
4731 | #define asinh scm_asinh | |
f872b822 | 4732 | return log (x + sqrt (x * x + 1)); |
fa605590 | 4733 | #endif |
0f2d19dd | 4734 | } |
fa605590 KR |
4735 | SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_dsubr, (SCM (*)()) asinh, g_asinh); |
4736 | /* "Return the inverse hyperbolic sine of @var{x}." | |
4737 | */ | |
0f2d19dd JB |
4738 | |
4739 | ||
0f2d19dd | 4740 | double |
6e8d25a6 | 4741 | scm_acosh (double x) |
0f2d19dd | 4742 | { |
fa605590 KR |
4743 | #if HAVE_ACOSH |
4744 | return acosh (x); | |
4745 | #else | |
4746 | #define acosh scm_acosh | |
f872b822 | 4747 | return log (x + sqrt (x * x - 1)); |
fa605590 | 4748 | #endif |
0f2d19dd | 4749 | } |
fa605590 KR |
4750 | SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_dsubr, (SCM (*)()) acosh, g_acosh); |
4751 | /* "Return the inverse hyperbolic cosine of @var{x}." | |
4752 | */ | |
0f2d19dd JB |
4753 | |
4754 | ||
0f2d19dd | 4755 | double |
6e8d25a6 | 4756 | scm_atanh (double x) |
0f2d19dd | 4757 | { |
fa605590 KR |
4758 | #if HAVE_ATANH |
4759 | return atanh (x); | |
4760 | #else | |
4761 | #define atanh scm_atanh | |
f872b822 | 4762 | return 0.5 * log ((1 + x) / (1 - x)); |
fa605590 | 4763 | #endif |
0f2d19dd | 4764 | } |
fa605590 KR |
4765 | SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_dsubr, (SCM (*)()) atanh, g_atanh); |
4766 | /* "Return the inverse hyperbolic tangent of @var{x}." | |
4767 | */ | |
0f2d19dd JB |
4768 | |
4769 | ||
f92e85f7 MV |
4770 | /* XXX - eventually, we should remove this definition of scm_round and |
4771 | rename scm_round_number to scm_round. Likewise for scm_truncate | |
4772 | and scm_truncate_number. | |
4773 | */ | |
4774 | ||
0f2d19dd | 4775 | double |
6e8d25a6 | 4776 | scm_truncate (double x) |
0f2d19dd | 4777 | { |
fa605590 KR |
4778 | #if HAVE_TRUNC |
4779 | return trunc (x); | |
4780 | #else | |
4781 | #define trunc scm_truncate | |
f872b822 MD |
4782 | if (x < 0.0) |
4783 | return -floor (-x); | |
4784 | return floor (x); | |
fa605590 | 4785 | #endif |
0f2d19dd | 4786 | } |
0f2d19dd | 4787 | |
0f2d19dd | 4788 | double |
6e8d25a6 | 4789 | scm_round (double x) |
0f2d19dd JB |
4790 | { |
4791 | double plus_half = x + 0.5; | |
f872b822 | 4792 | double result = floor (plus_half); |
0f2d19dd | 4793 | /* Adjust so that the scm_round is towards even. */ |
0aacf84e MD |
4794 | return ((plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
4795 | ? result - 1 | |
4796 | : result); | |
0f2d19dd JB |
4797 | } |
4798 | ||
f92e85f7 MV |
4799 | SCM_DEFINE (scm_truncate_number, "truncate", 1, 0, 0, |
4800 | (SCM x), | |
4801 | "Round the number @var{x} towards zero.") | |
4802 | #define FUNC_NAME s_scm_truncate_number | |
4803 | { | |
4804 | if (SCM_FALSEP (scm_negative_p (x))) | |
4805 | return scm_floor (x); | |
4806 | else | |
4807 | return scm_ceiling (x); | |
4808 | } | |
4809 | #undef FUNC_NAME | |
4810 | ||
4811 | static SCM exactly_one_half; | |
4812 | ||
4813 | SCM_DEFINE (scm_round_number, "round", 1, 0, 0, | |
4814 | (SCM x), | |
4815 | "Round the number @var{x} towards the nearest integer. " | |
4816 | "When it is exactly halfway between two integers, " | |
4817 | "round towards the even one.") | |
4818 | #define FUNC_NAME s_scm_round_number | |
4819 | { | |
4820 | SCM plus_half = scm_sum (x, exactly_one_half); | |
4821 | SCM result = scm_floor (plus_half); | |
4822 | /* Adjust so that the scm_round is towards even. */ | |
4823 | if (!SCM_FALSEP (scm_num_eq_p (plus_half, result)) | |
4824 | && !SCM_FALSEP (scm_odd_p (result))) | |
4825 | return scm_difference (result, SCM_MAKINUM (1)); | |
4826 | else | |
4827 | return result; | |
4828 | } | |
4829 | #undef FUNC_NAME | |
4830 | ||
4831 | SCM_PRIMITIVE_GENERIC (scm_floor, "floor", 1, 0, 0, | |
4832 | (SCM x), | |
4833 | "Round the number @var{x} towards minus infinity.") | |
4834 | #define FUNC_NAME s_scm_floor | |
4835 | { | |
4836 | if (SCM_INUMP (x) || SCM_BIGP (x)) | |
4837 | return x; | |
4838 | else if (SCM_REALP (x)) | |
4839 | return scm_make_real (floor (SCM_REAL_VALUE (x))); | |
4840 | else if (SCM_FRACTIONP (x)) | |
4841 | { | |
4842 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
4843 | SCM_FRACTION_DENOMINATOR (x)); | |
4844 | if (SCM_FALSEP (scm_negative_p (x))) | |
4845 | { | |
4846 | /* For positive x, rounding towards zero is correct. */ | |
4847 | return q; | |
4848 | } | |
4849 | else | |
4850 | { | |
4851 | /* For negative x, we need to return q-1 unless x is an | |
4852 | integer. But fractions are never integer, per our | |
4853 | assumptions. */ | |
4854 | return scm_difference (q, SCM_MAKINUM (1)); | |
4855 | } | |
4856 | } | |
4857 | else | |
4858 | SCM_WTA_DISPATCH_1 (g_scm_floor, x, 1, s_scm_floor); | |
4859 | } | |
4860 | #undef FUNC_NAME | |
4861 | ||
4862 | SCM_PRIMITIVE_GENERIC (scm_ceiling, "ceiling", 1, 0, 0, | |
4863 | (SCM x), | |
4864 | "Round the number @var{x} towards infinity.") | |
4865 | #define FUNC_NAME s_scm_ceiling | |
4866 | { | |
4867 | if (SCM_INUMP (x) || SCM_BIGP (x)) | |
4868 | return x; | |
4869 | else if (SCM_REALP (x)) | |
4870 | return scm_make_real (ceil (SCM_REAL_VALUE (x))); | |
4871 | else if (SCM_FRACTIONP (x)) | |
4872 | { | |
4873 | SCM q = scm_quotient (SCM_FRACTION_NUMERATOR (x), | |
4874 | SCM_FRACTION_DENOMINATOR (x)); | |
4875 | if (SCM_FALSEP (scm_positive_p (x))) | |
4876 | { | |
4877 | /* For negative x, rounding towards zero is correct. */ | |
4878 | return q; | |
4879 | } | |
4880 | else | |
4881 | { | |
4882 | /* For positive x, we need to return q+1 unless x is an | |
4883 | integer. But fractions are never integer, per our | |
4884 | assumptions. */ | |
4885 | return scm_sum (q, SCM_MAKINUM (1)); | |
4886 | } | |
4887 | } | |
4888 | else | |
4889 | SCM_WTA_DISPATCH_1 (g_scm_ceiling, x, 1, s_scm_ceiling); | |
4890 | } | |
4891 | #undef FUNC_NAME | |
0f2d19dd | 4892 | |
14b18ed6 | 4893 | SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_dsubr, (SCM (*)()) sqrt, g_i_sqrt); |
942e5b91 MG |
4894 | /* "Return the square root of the real number @var{x}." |
4895 | */ | |
14b18ed6 | 4896 | SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_dsubr, (SCM (*)()) fabs, g_i_abs); |
942e5b91 MG |
4897 | /* "Return the absolute value of the real number @var{x}." |
4898 | */ | |
14b18ed6 | 4899 | SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_dsubr, (SCM (*)()) exp, g_i_exp); |
942e5b91 MG |
4900 | /* "Return the @var{x}th power of e." |
4901 | */ | |
14b18ed6 | 4902 | SCM_GPROC1 (s_i_log, "$log", scm_tc7_dsubr, (SCM (*)()) log, g_i_log); |
b3fcac34 | 4903 | /* "Return the natural logarithm of the real number @var{x}." |
942e5b91 | 4904 | */ |
14b18ed6 | 4905 | SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_dsubr, (SCM (*)()) sin, g_i_sin); |
942e5b91 MG |
4906 | /* "Return the sine of the real number @var{x}." |
4907 | */ | |
14b18ed6 | 4908 | SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_dsubr, (SCM (*)()) cos, g_i_cos); |
942e5b91 MG |
4909 | /* "Return the cosine of the real number @var{x}." |
4910 | */ | |
14b18ed6 | 4911 | SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_dsubr, (SCM (*)()) tan, g_i_tan); |
942e5b91 MG |
4912 | /* "Return the tangent of the real number @var{x}." |
4913 | */ | |
14b18ed6 | 4914 | SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_dsubr, (SCM (*)()) asin, g_i_asin); |
942e5b91 MG |
4915 | /* "Return the arc sine of the real number @var{x}." |
4916 | */ | |
14b18ed6 | 4917 | SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_dsubr, (SCM (*)()) acos, g_i_acos); |
942e5b91 MG |
4918 | /* "Return the arc cosine of the real number @var{x}." |
4919 | */ | |
14b18ed6 | 4920 | SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_dsubr, (SCM (*)()) atan, g_i_atan); |
942e5b91 MG |
4921 | /* "Return the arc tangent of the real number @var{x}." |
4922 | */ | |
14b18ed6 | 4923 | SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_dsubr, (SCM (*)()) sinh, g_i_sinh); |
942e5b91 MG |
4924 | /* "Return the hyperbolic sine of the real number @var{x}." |
4925 | */ | |
14b18ed6 | 4926 | SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_dsubr, (SCM (*)()) cosh, g_i_cosh); |
942e5b91 MG |
4927 | /* "Return the hyperbolic cosine of the real number @var{x}." |
4928 | */ | |
14b18ed6 | 4929 | SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_dsubr, (SCM (*)()) tanh, g_i_tanh); |
942e5b91 MG |
4930 | /* "Return the hyperbolic tangent of the real number @var{x}." |
4931 | */ | |
f872b822 MD |
4932 | |
4933 | struct dpair | |
4934 | { | |
4935 | double x, y; | |
4936 | }; | |
4937 | ||
27c37006 NJ |
4938 | static void scm_two_doubles (SCM x, |
4939 | SCM y, | |
3eeba8d4 JB |
4940 | const char *sstring, |
4941 | struct dpair * xy); | |
f872b822 MD |
4942 | |
4943 | static void | |
27c37006 NJ |
4944 | scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy) |
4945 | { | |
0aacf84e | 4946 | if (SCM_INUMP (x)) |
27c37006 | 4947 | xy->x = SCM_INUM (x); |
0aacf84e | 4948 | else if (SCM_BIGP (x)) |
1be6b49c | 4949 | xy->x = scm_i_big2dbl (x); |
0aacf84e | 4950 | else if (SCM_REALP (x)) |
27c37006 | 4951 | xy->x = SCM_REAL_VALUE (x); |
f92e85f7 MV |
4952 | else if (SCM_FRACTIONP (x)) |
4953 | xy->x = scm_i_fraction2double (x); | |
0aacf84e | 4954 | else |
27c37006 | 4955 | scm_wrong_type_arg (sstring, SCM_ARG1, x); |
98cb6e75 | 4956 | |
0aacf84e | 4957 | if (SCM_INUMP (y)) |
27c37006 | 4958 | xy->y = SCM_INUM (y); |
0aacf84e | 4959 | else if (SCM_BIGP (y)) |
1be6b49c | 4960 | xy->y = scm_i_big2dbl (y); |
0aacf84e | 4961 | else if (SCM_REALP (y)) |
27c37006 | 4962 | xy->y = SCM_REAL_VALUE (y); |
f92e85f7 MV |
4963 | else if (SCM_FRACTIONP (y)) |
4964 | xy->y = scm_i_fraction2double (y); | |
0aacf84e | 4965 | else |
27c37006 | 4966 | scm_wrong_type_arg (sstring, SCM_ARG2, y); |
0f2d19dd JB |
4967 | } |
4968 | ||
4969 | ||
a1ec6916 | 4970 | SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0, |
27c37006 NJ |
4971 | (SCM x, SCM y), |
4972 | "Return @var{x} raised to the power of @var{y}. This\n" | |
0137a31b | 4973 | "procedure does not accept complex arguments.") |
1bbd0b84 | 4974 | #define FUNC_NAME s_scm_sys_expt |
0f2d19dd JB |
4975 | { |
4976 | struct dpair xy; | |
27c37006 | 4977 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
f8de44c1 | 4978 | return scm_make_real (pow (xy.x, xy.y)); |
0f2d19dd | 4979 | } |
1bbd0b84 | 4980 | #undef FUNC_NAME |
0f2d19dd JB |
4981 | |
4982 | ||
a1ec6916 | 4983 | SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0, |
27c37006 NJ |
4984 | (SCM x, SCM y), |
4985 | "Return the arc tangent of the two arguments @var{x} and\n" | |
4986 | "@var{y}. This is similar to calculating the arc tangent of\n" | |
4987 | "@var{x} / @var{y}, except that the signs of both arguments\n" | |
0137a31b MG |
4988 | "are used to determine the quadrant of the result. This\n" |
4989 | "procedure does not accept complex arguments.") | |
1bbd0b84 | 4990 | #define FUNC_NAME s_scm_sys_atan2 |
0f2d19dd JB |
4991 | { |
4992 | struct dpair xy; | |
27c37006 | 4993 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
f8de44c1 | 4994 | return scm_make_real (atan2 (xy.x, xy.y)); |
0f2d19dd | 4995 | } |
1bbd0b84 | 4996 | #undef FUNC_NAME |
0f2d19dd JB |
4997 | |
4998 | ||
a1ec6916 | 4999 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
bb628794 | 5000 | (SCM real, SCM imaginary), |
942e5b91 MG |
5001 | "Return a complex number constructed of the given @var{real} and\n" |
5002 | "@var{imaginary} parts.") | |
1bbd0b84 | 5003 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd JB |
5004 | { |
5005 | struct dpair xy; | |
bb628794 | 5006 | scm_two_doubles (real, imaginary, FUNC_NAME, &xy); |
f8de44c1 | 5007 | return scm_make_complex (xy.x, xy.y); |
0f2d19dd | 5008 | } |
1bbd0b84 | 5009 | #undef FUNC_NAME |
0f2d19dd JB |
5010 | |
5011 | ||
5012 | ||
a1ec6916 | 5013 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 5014 | (SCM x, SCM y), |
942e5b91 | 5015 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 5016 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd JB |
5017 | { |
5018 | struct dpair xy; | |
6efadd7c | 5019 | double s, c; |
27c37006 | 5020 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
6efadd7c KR |
5021 | #if HAVE_SINCOS |
5022 | sincos (xy.y, &s, &c); | |
5023 | #else | |
5024 | s = sin (xy.y); | |
5025 | c = cos (xy.y); | |
5026 | #endif | |
5027 | return scm_make_complex (xy.x * c, xy.x * s); | |
0f2d19dd | 5028 | } |
1bbd0b84 | 5029 | #undef FUNC_NAME |
0f2d19dd JB |
5030 | |
5031 | ||
152f82bf | 5032 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
5033 | /* "Return the real part of the number @var{z}." |
5034 | */ | |
0f2d19dd | 5035 | SCM |
6e8d25a6 | 5036 | scm_real_part (SCM z) |
0f2d19dd | 5037 | { |
0aacf84e | 5038 | if (SCM_INUMP (z)) |
c2ff8ab0 | 5039 | return z; |
0aacf84e | 5040 | else if (SCM_BIGP (z)) |
c2ff8ab0 | 5041 | return z; |
0aacf84e | 5042 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5043 | return z; |
0aacf84e | 5044 | else if (SCM_COMPLEXP (z)) |
c2ff8ab0 | 5045 | return scm_make_real (SCM_COMPLEX_REAL (z)); |
f92e85f7 | 5046 | else if (SCM_FRACTIONP (z)) |
2fa2d879 | 5047 | return z; |
0aacf84e | 5048 | else |
c2ff8ab0 | 5049 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); |
0f2d19dd JB |
5050 | } |
5051 | ||
5052 | ||
152f82bf | 5053 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
5054 | /* "Return the imaginary part of the number @var{z}." |
5055 | */ | |
0f2d19dd | 5056 | SCM |
6e8d25a6 | 5057 | scm_imag_part (SCM z) |
0f2d19dd | 5058 | { |
0aacf84e | 5059 | if (SCM_INUMP (z)) |
f872b822 | 5060 | return SCM_INUM0; |
0aacf84e | 5061 | else if (SCM_BIGP (z)) |
f872b822 | 5062 | return SCM_INUM0; |
0aacf84e | 5063 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5064 | return scm_flo0; |
0aacf84e | 5065 | else if (SCM_COMPLEXP (z)) |
c2ff8ab0 | 5066 | return scm_make_real (SCM_COMPLEX_IMAG (z)); |
f92e85f7 MV |
5067 | else if (SCM_FRACTIONP (z)) |
5068 | return SCM_INUM0; | |
0aacf84e | 5069 | else |
c2ff8ab0 | 5070 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); |
0f2d19dd JB |
5071 | } |
5072 | ||
f92e85f7 MV |
5073 | SCM_GPROC (s_numerator, "numerator", 1, 0, 0, scm_numerator, g_numerator); |
5074 | /* "Return the numerator of the number @var{z}." | |
5075 | */ | |
5076 | SCM | |
5077 | scm_numerator (SCM z) | |
5078 | { | |
5079 | if (SCM_INUMP (z)) | |
5080 | return z; | |
5081 | else if (SCM_BIGP (z)) | |
5082 | return z; | |
5083 | else if (SCM_FRACTIONP (z)) | |
5084 | { | |
5085 | scm_i_fraction_reduce (z); | |
5086 | return SCM_FRACTION_NUMERATOR (z); | |
5087 | } | |
5088 | else if (SCM_REALP (z)) | |
5089 | return scm_exact_to_inexact (scm_numerator (scm_inexact_to_exact (z))); | |
5090 | else | |
5091 | SCM_WTA_DISPATCH_1 (g_numerator, z, SCM_ARG1, s_numerator); | |
5092 | } | |
5093 | ||
5094 | ||
5095 | SCM_GPROC (s_denominator, "denominator", 1, 0, 0, scm_denominator, g_denominator); | |
5096 | /* "Return the denominator of the number @var{z}." | |
5097 | */ | |
5098 | SCM | |
5099 | scm_denominator (SCM z) | |
5100 | { | |
5101 | if (SCM_INUMP (z)) | |
5102 | return SCM_MAKINUM (1); | |
5103 | else if (SCM_BIGP (z)) | |
5104 | return SCM_MAKINUM (1); | |
5105 | else if (SCM_FRACTIONP (z)) | |
5106 | { | |
5107 | scm_i_fraction_reduce (z); | |
5108 | return SCM_FRACTION_DENOMINATOR (z); | |
5109 | } | |
5110 | else if (SCM_REALP (z)) | |
5111 | return scm_exact_to_inexact (scm_denominator (scm_inexact_to_exact (z))); | |
5112 | else | |
5113 | SCM_WTA_DISPATCH_1 (g_denominator, z, SCM_ARG1, s_denominator); | |
5114 | } | |
0f2d19dd | 5115 | |
9de33deb | 5116 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
5117 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
5118 | * "@code{abs} for real arguments, but also allows complex numbers." | |
5119 | */ | |
0f2d19dd | 5120 | SCM |
6e8d25a6 | 5121 | scm_magnitude (SCM z) |
0f2d19dd | 5122 | { |
0aacf84e MD |
5123 | if (SCM_INUMP (z)) |
5124 | { | |
5125 | long int zz = SCM_INUM (z); | |
5126 | if (zz >= 0) | |
5127 | return z; | |
5128 | else if (SCM_POSFIXABLE (-zz)) | |
5129 | return SCM_MAKINUM (-zz); | |
5130 | else | |
5131 | return scm_i_long2big (-zz); | |
5986c47d | 5132 | } |
0aacf84e MD |
5133 | else if (SCM_BIGP (z)) |
5134 | { | |
5135 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5136 | scm_remember_upto_here_1 (z); | |
5137 | if (sgn < 0) | |
5138 | return scm_i_clonebig (z, 0); | |
5139 | else | |
5140 | return z; | |
5986c47d | 5141 | } |
0aacf84e | 5142 | else if (SCM_REALP (z)) |
c2ff8ab0 | 5143 | return scm_make_real (fabs (SCM_REAL_VALUE (z))); |
0aacf84e | 5144 | else if (SCM_COMPLEXP (z)) |
6efadd7c | 5145 | return scm_make_real (hypot (SCM_COMPLEX_REAL (z), SCM_COMPLEX_IMAG (z))); |
f92e85f7 MV |
5146 | else if (SCM_FRACTIONP (z)) |
5147 | { | |
5148 | if (SCM_FALSEP (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) | |
5149 | return z; | |
5150 | return scm_make_ratio (scm_difference (SCM_FRACTION_NUMERATOR (z), SCM_UNDEFINED), | |
5151 | SCM_FRACTION_DENOMINATOR (z)); | |
5152 | } | |
0aacf84e | 5153 | else |
c2ff8ab0 | 5154 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); |
0f2d19dd JB |
5155 | } |
5156 | ||
5157 | ||
9de33deb | 5158 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
5159 | /* "Return the angle of the complex number @var{z}." |
5160 | */ | |
0f2d19dd | 5161 | SCM |
6e8d25a6 | 5162 | scm_angle (SCM z) |
0f2d19dd | 5163 | { |
c8ae173e KR |
5164 | /* atan(0,-1) is pi and it'd be possible to have that as a constant like |
5165 | scm_flo0 to save allocating a new flonum with scm_make_real each time. | |
5166 | But if atan2 follows the floating point rounding mode, then the value | |
5167 | is not a constant. Maybe it'd be close enough though. */ | |
0aacf84e MD |
5168 | if (SCM_INUMP (z)) |
5169 | { | |
5170 | if (SCM_INUM (z) >= 0) | |
c8ae173e | 5171 | return scm_flo0; |
0aacf84e MD |
5172 | else |
5173 | return scm_make_real (atan2 (0.0, -1.0)); | |
f872b822 | 5174 | } |
0aacf84e MD |
5175 | else if (SCM_BIGP (z)) |
5176 | { | |
5177 | int sgn = mpz_sgn (SCM_I_BIG_MPZ (z)); | |
5178 | scm_remember_upto_here_1 (z); | |
5179 | if (sgn < 0) | |
5180 | return scm_make_real (atan2 (0.0, -1.0)); | |
5181 | else | |
c8ae173e | 5182 | return scm_flo0; |
0f2d19dd | 5183 | } |
0aacf84e | 5184 | else if (SCM_REALP (z)) |
c8ae173e KR |
5185 | { |
5186 | if (SCM_REAL_VALUE (z) >= 0) | |
5187 | return scm_flo0; | |
5188 | else | |
5189 | return scm_make_real (atan2 (0.0, -1.0)); | |
5190 | } | |
0aacf84e | 5191 | else if (SCM_COMPLEXP (z)) |
f4c627b3 | 5192 | return scm_make_real (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); |
f92e85f7 MV |
5193 | else if (SCM_FRACTIONP (z)) |
5194 | { | |
5195 | if (SCM_FALSEP (scm_negative_p (SCM_FRACTION_NUMERATOR (z)))) | |
5196 | return scm_flo0; | |
5197 | else return scm_make_real (atan2 (0.0, -1.0)); | |
5198 | } | |
0aacf84e | 5199 | else |
f4c627b3 | 5200 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); |
0f2d19dd JB |
5201 | } |
5202 | ||
5203 | ||
3c9a524f DH |
5204 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
5205 | /* Convert the number @var{x} to its inexact representation.\n" | |
5206 | */ | |
5207 | SCM | |
5208 | scm_exact_to_inexact (SCM z) | |
5209 | { | |
5210 | if (SCM_INUMP (z)) | |
5211 | return scm_make_real ((double) SCM_INUM (z)); | |
5212 | else if (SCM_BIGP (z)) | |
5213 | return scm_make_real (scm_i_big2dbl (z)); | |
f92e85f7 MV |
5214 | else if (SCM_FRACTIONP (z)) |
5215 | return scm_make_real (scm_i_fraction2double (z)); | |
3c9a524f DH |
5216 | else if (SCM_INEXACTP (z)) |
5217 | return z; | |
5218 | else | |
5219 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
5220 | } | |
5221 | ||
5222 | ||
a1ec6916 | 5223 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 5224 | (SCM z), |
1e6808ea | 5225 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 5226 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 5227 | { |
0aacf84e | 5228 | if (SCM_INUMP (z)) |
f872b822 | 5229 | return z; |
0aacf84e | 5230 | else if (SCM_BIGP (z)) |
f872b822 | 5231 | return z; |
0aacf84e MD |
5232 | else if (SCM_REALP (z)) |
5233 | { | |
f92e85f7 MV |
5234 | if (xisinf (SCM_REAL_VALUE (z)) || xisnan (SCM_REAL_VALUE (z))) |
5235 | SCM_OUT_OF_RANGE (1, z); | |
2be24db4 | 5236 | else |
f92e85f7 MV |
5237 | { |
5238 | mpq_t frac; | |
5239 | SCM q; | |
5240 | ||
5241 | mpq_init (frac); | |
5242 | mpq_set_d (frac, SCM_REAL_VALUE (z)); | |
5243 | q = scm_make_ratio (scm_i_mpz2num (mpq_numref (frac)), | |
5244 | scm_i_mpz2num (mpq_denref (frac))); | |
5245 | ||
5246 | /* When scm_make_ratio throws, we leak the memory allocated | |
5247 | for frac... | |
5248 | */ | |
5249 | mpq_clear (frac); | |
5250 | return q; | |
5251 | } | |
c2ff8ab0 | 5252 | } |
f92e85f7 MV |
5253 | else if (SCM_FRACTIONP (z)) |
5254 | return z; | |
0aacf84e | 5255 | else |
c2ff8ab0 | 5256 | SCM_WRONG_TYPE_ARG (1, z); |
0f2d19dd | 5257 | } |
1bbd0b84 | 5258 | #undef FUNC_NAME |
0f2d19dd | 5259 | |
f92e85f7 MV |
5260 | SCM_DEFINE (scm_rationalize, "rationalize", 2, 0, 0, |
5261 | (SCM x, SCM err), | |
5262 | "Return an exact number that is within @var{err} of @var{x}.") | |
5263 | #define FUNC_NAME s_scm_rationalize | |
5264 | { | |
5265 | if (SCM_INUMP (x)) | |
5266 | return x; | |
5267 | else if (SCM_BIGP (x)) | |
5268 | return x; | |
5269 | else if ((SCM_REALP (x)) || SCM_FRACTIONP (x)) | |
5270 | { | |
5271 | /* Use continued fractions to find closest ratio. All | |
5272 | arithmetic is done with exact numbers. | |
5273 | */ | |
5274 | ||
5275 | SCM ex = scm_inexact_to_exact (x); | |
5276 | SCM int_part = scm_floor (ex); | |
5277 | SCM tt = SCM_MAKINUM (1); | |
5278 | SCM a1 = SCM_MAKINUM (0), a2 = SCM_MAKINUM (1), a = SCM_MAKINUM (0); | |
5279 | SCM b1 = SCM_MAKINUM (1), b2 = SCM_MAKINUM (0), b = SCM_MAKINUM (0); | |
5280 | SCM rx; | |
5281 | int i = 0; | |
5282 | ||
5283 | if (!SCM_FALSEP (scm_num_eq_p (ex, int_part))) | |
5284 | return ex; | |
5285 | ||
5286 | ex = scm_difference (ex, int_part); /* x = x-int_part */ | |
5287 | rx = scm_divide (ex, SCM_UNDEFINED); /* rx = 1/x */ | |
5288 | ||
5289 | /* We stop after a million iterations just to be absolutely sure | |
5290 | that we don't go into an infinite loop. The process normally | |
5291 | converges after less than a dozen iterations. | |
5292 | */ | |
5293 | ||
5294 | err = scm_abs (err); | |
5295 | while (++i < 1000000) | |
5296 | { | |
5297 | a = scm_sum (scm_product (a1, tt), a2); /* a = a1*tt + a2 */ | |
5298 | b = scm_sum (scm_product (b1, tt), b2); /* b = b1*tt + b2 */ | |
5299 | if (SCM_FALSEP (scm_zero_p (b)) && /* b != 0 */ | |
5300 | SCM_FALSEP | |
5301 | (scm_gr_p (scm_abs (scm_difference (ex, scm_divide (a, b))), | |
5302 | err))) /* abs(x-a/b) <= err */ | |
02164269 MV |
5303 | { |
5304 | SCM res = scm_sum (int_part, scm_divide (a, b)); | |
5305 | if (SCM_FALSEP (scm_exact_p (x)) | |
5306 | || SCM_FALSEP (scm_exact_p (err))) | |
5307 | return scm_exact_to_inexact (res); | |
5308 | else | |
5309 | return res; | |
5310 | } | |
f92e85f7 MV |
5311 | rx = scm_divide (scm_difference (rx, tt), /* rx = 1/(rx - tt) */ |
5312 | SCM_UNDEFINED); | |
5313 | tt = scm_floor (rx); /* tt = floor (rx) */ | |
5314 | a2 = a1; | |
5315 | b2 = b1; | |
5316 | a1 = a; | |
5317 | b1 = b; | |
5318 | } | |
5319 | scm_num_overflow (s_scm_rationalize); | |
5320 | } | |
5321 | else | |
5322 | SCM_WRONG_TYPE_ARG (1, x); | |
5323 | } | |
5324 | #undef FUNC_NAME | |
5325 | ||
87617347 | 5326 | /* if you need to change this, change test-num2integral.c as well */ |
ee33d62a | 5327 | #if SCM_SIZEOF_LONG_LONG != 0 |
1be6b49c ML |
5328 | # ifndef LLONG_MAX |
5329 | # define ULLONG_MAX ((unsigned long long) (-1)) | |
5330 | # define LLONG_MAX ((long long) (ULLONG_MAX >> 1)) | |
5331 | # define LLONG_MIN (~LLONG_MAX) | |
5332 | # endif | |
f872b822 | 5333 | #endif |
0f2d19dd | 5334 | |
3d2e8ceb MV |
5335 | /* Parameters for creating integer conversion routines. |
5336 | ||
5337 | Define the following preprocessor macros before including | |
5338 | "libguile/num2integral.i.c": | |
5339 | ||
5340 | NUM2INTEGRAL - the name of the function for converting from a | |
ca46fb90 RB |
5341 | Scheme object to the integral type. This function will be |
5342 | defined when including "num2integral.i.c". | |
3d2e8ceb MV |
5343 | |
5344 | INTEGRAL2NUM - the name of the function for converting from the | |
ca46fb90 | 5345 | integral type to a Scheme object. This function will be defined. |
3d2e8ceb MV |
5346 | |
5347 | INTEGRAL2BIG - the name of an internal function that createas a | |
ca46fb90 RB |
5348 | bignum from the integral type. This function will be defined. |
5349 | The name should start with "scm_i_". | |
5350 | ||
5351 | ITYPE - the name of the integral type. | |
5352 | ||
9dd023e1 MV |
5353 | UNSIGNED - Define this to 1 when ITYPE is an unsigned type. Define |
5354 | it to 0 otherwise. | |
ca46fb90 RB |
5355 | |
5356 | UNSIGNED_ITYPE - the name of the the unsigned variant of the | |
5357 | integral type. If you don't define this, it defaults to | |
5358 | "unsigned ITYPE" for signed types and simply "ITYPE" for unsigned | |
5359 | ones. | |
5360 | ||
5361 | SIZEOF_ITYPE - an expression giving the size of the integral type | |
5362 | in bytes. This expression must be computable by the | |
5363 | preprocessor. (SIZEOF_FOO values are calculated by configure.in | |
5364 | for common types). | |
5365 | ||
3d2e8ceb MV |
5366 | */ |
5367 | ||
1be6b49c ML |
5368 | #define NUM2INTEGRAL scm_num2short |
5369 | #define INTEGRAL2NUM scm_short2num | |
5370 | #define INTEGRAL2BIG scm_i_short2big | |
ca46fb90 | 5371 | #define UNSIGNED 0 |
1be6b49c | 5372 | #define ITYPE short |
3d2e8ceb | 5373 | #define SIZEOF_ITYPE SIZEOF_SHORT |
1be6b49c ML |
5374 | #include "libguile/num2integral.i.c" |
5375 | ||
5376 | #define NUM2INTEGRAL scm_num2ushort | |
5377 | #define INTEGRAL2NUM scm_ushort2num | |
5378 | #define INTEGRAL2BIG scm_i_ushort2big | |
ca46fb90 | 5379 | #define UNSIGNED 1 |
1be6b49c | 5380 | #define ITYPE unsigned short |
ca46fb90 | 5381 | #define SIZEOF_ITYPE SIZEOF_UNSIGNED_SHORT |
1be6b49c ML |
5382 | #include "libguile/num2integral.i.c" |
5383 | ||
5384 | #define NUM2INTEGRAL scm_num2int | |
5385 | #define INTEGRAL2NUM scm_int2num | |
5386 | #define INTEGRAL2BIG scm_i_int2big | |
ca46fb90 | 5387 | #define UNSIGNED 0 |
1be6b49c | 5388 | #define ITYPE int |
3d2e8ceb | 5389 | #define SIZEOF_ITYPE SIZEOF_INT |
1be6b49c ML |
5390 | #include "libguile/num2integral.i.c" |
5391 | ||
5392 | #define NUM2INTEGRAL scm_num2uint | |
5393 | #define INTEGRAL2NUM scm_uint2num | |
5394 | #define INTEGRAL2BIG scm_i_uint2big | |
ca46fb90 | 5395 | #define UNSIGNED 1 |
1be6b49c | 5396 | #define ITYPE unsigned int |
ca46fb90 | 5397 | #define SIZEOF_ITYPE SIZEOF_UNSIGNED_INT |
1be6b49c ML |
5398 | #include "libguile/num2integral.i.c" |
5399 | ||
5400 | #define NUM2INTEGRAL scm_num2long | |
5401 | #define INTEGRAL2NUM scm_long2num | |
5402 | #define INTEGRAL2BIG scm_i_long2big | |
ca46fb90 | 5403 | #define UNSIGNED 0 |
1be6b49c | 5404 | #define ITYPE long |
3d2e8ceb | 5405 | #define SIZEOF_ITYPE SIZEOF_LONG |
1be6b49c ML |
5406 | #include "libguile/num2integral.i.c" |
5407 | ||
5408 | #define NUM2INTEGRAL scm_num2ulong | |
5409 | #define INTEGRAL2NUM scm_ulong2num | |
5410 | #define INTEGRAL2BIG scm_i_ulong2big | |
ca46fb90 | 5411 | #define UNSIGNED 1 |
1be6b49c | 5412 | #define ITYPE unsigned long |
ca46fb90 | 5413 | #define SIZEOF_ITYPE SIZEOF_UNSIGNED_LONG |
1be6b49c ML |
5414 | #include "libguile/num2integral.i.c" |
5415 | ||
1be6b49c ML |
5416 | #define NUM2INTEGRAL scm_num2ptrdiff |
5417 | #define INTEGRAL2NUM scm_ptrdiff2num | |
5418 | #define INTEGRAL2BIG scm_i_ptrdiff2big | |
ca46fb90 | 5419 | #define UNSIGNED 0 |
ee33d62a | 5420 | #define ITYPE scm_t_ptrdiff |
3d2e8ceb | 5421 | #define UNSIGNED_ITYPE size_t |
ee33d62a | 5422 | #define SIZEOF_ITYPE SCM_SIZEOF_SCM_T_PTRDIFF |
1be6b49c ML |
5423 | #include "libguile/num2integral.i.c" |
5424 | ||
5425 | #define NUM2INTEGRAL scm_num2size | |
5426 | #define INTEGRAL2NUM scm_size2num | |
5427 | #define INTEGRAL2BIG scm_i_size2big | |
ca46fb90 | 5428 | #define UNSIGNED 1 |
1be6b49c | 5429 | #define ITYPE size_t |
3d2e8ceb | 5430 | #define SIZEOF_ITYPE SIZEOF_SIZE_T |
1be6b49c | 5431 | #include "libguile/num2integral.i.c" |
0f2d19dd | 5432 | |
ee33d62a | 5433 | #if SCM_SIZEOF_LONG_LONG != 0 |
1cc91f1b | 5434 | |
caf08e65 MV |
5435 | #ifndef ULONG_LONG_MAX |
5436 | #define ULONG_LONG_MAX (~0ULL) | |
5437 | #endif | |
5438 | ||
1be6b49c ML |
5439 | #define NUM2INTEGRAL scm_num2long_long |
5440 | #define INTEGRAL2NUM scm_long_long2num | |
5441 | #define INTEGRAL2BIG scm_i_long_long2big | |
ca46fb90 | 5442 | #define UNSIGNED 0 |
1be6b49c | 5443 | #define ITYPE long long |
3d2e8ceb | 5444 | #define SIZEOF_ITYPE SIZEOF_LONG_LONG |
1be6b49c ML |
5445 | #include "libguile/num2integral.i.c" |
5446 | ||
5447 | #define NUM2INTEGRAL scm_num2ulong_long | |
5448 | #define INTEGRAL2NUM scm_ulong_long2num | |
5449 | #define INTEGRAL2BIG scm_i_ulong_long2big | |
ca46fb90 | 5450 | #define UNSIGNED 1 |
1be6b49c | 5451 | #define ITYPE unsigned long long |
ca46fb90 | 5452 | #define SIZEOF_ITYPE SIZEOF_UNSIGNED_LONG_LONG |
1be6b49c | 5453 | #include "libguile/num2integral.i.c" |
0f2d19dd | 5454 | |
ee33d62a | 5455 | #endif /* SCM_SIZEOF_LONG_LONG != 0 */ |
caf08e65 | 5456 | |
5437598b MD |
5457 | #define NUM2FLOAT scm_num2float |
5458 | #define FLOAT2NUM scm_float2num | |
5459 | #define FTYPE float | |
5460 | #include "libguile/num2float.i.c" | |
5461 | ||
5462 | #define NUM2FLOAT scm_num2double | |
5463 | #define FLOAT2NUM scm_double2num | |
5464 | #define FTYPE double | |
5465 | #include "libguile/num2float.i.c" | |
5466 | ||
1be6b49c | 5467 | #ifdef GUILE_DEBUG |
caf08e65 | 5468 | |
6063dc1d SJ |
5469 | #ifndef SIZE_MAX |
5470 | #define SIZE_MAX ((size_t) (-1)) | |
5471 | #endif | |
5472 | #ifndef PTRDIFF_MIN | |
5473 | #define PTRDIFF_MIN \ | |
b4fb7de8 RB |
5474 | ((scm_t_ptrdiff) ((scm_t_ptrdiff) 1 \ |
5475 | << ((sizeof (scm_t_ptrdiff) * SCM_CHAR_BIT) - 1))) | |
6063dc1d SJ |
5476 | #endif |
5477 | #ifndef PTRDIFF_MAX | |
5478 | #define PTRDIFF_MAX (~ PTRDIFF_MIN) | |
5479 | #endif | |
5480 | ||
0aacf84e MD |
5481 | #define CHECK(type, v) \ |
5482 | do \ | |
5483 | { \ | |
5484 | if ((v) != scm_num2##type (scm_##type##2num (v), 1, "check_sanity")) \ | |
5485 | abort (); \ | |
5486 | } \ | |
5487 | while (0) | |
caf08e65 | 5488 | |
1be6b49c ML |
5489 | static void |
5490 | check_sanity () | |
5491 | { | |
5492 | CHECK (short, 0); | |
5493 | CHECK (ushort, 0U); | |
5494 | CHECK (int, 0); | |
5495 | CHECK (uint, 0U); | |
5496 | CHECK (long, 0L); | |
5497 | CHECK (ulong, 0UL); | |
5498 | CHECK (size, 0); | |
5499 | CHECK (ptrdiff, 0); | |
5500 | ||
5501 | CHECK (short, -1); | |
5502 | CHECK (int, -1); | |
5503 | CHECK (long, -1L); | |
5504 | CHECK (ptrdiff, -1); | |
5505 | ||
5506 | CHECK (short, SHRT_MAX); | |
5507 | CHECK (short, SHRT_MIN); | |
5508 | CHECK (ushort, USHRT_MAX); | |
5509 | CHECK (int, INT_MAX); | |
5510 | CHECK (int, INT_MIN); | |
5511 | CHECK (uint, UINT_MAX); | |
5512 | CHECK (long, LONG_MAX); | |
5513 | CHECK (long, LONG_MIN); | |
5514 | CHECK (ulong, ULONG_MAX); | |
5515 | CHECK (size, SIZE_MAX); | |
5516 | CHECK (ptrdiff, PTRDIFF_MAX); | |
5517 | CHECK (ptrdiff, PTRDIFF_MIN); | |
0f2d19dd | 5518 | |
ee33d62a | 5519 | #if SCM_SIZEOF_LONG_LONG != 0 |
1be6b49c ML |
5520 | CHECK (long_long, 0LL); |
5521 | CHECK (ulong_long, 0ULL); | |
1be6b49c | 5522 | CHECK (long_long, -1LL); |
1be6b49c ML |
5523 | CHECK (long_long, LLONG_MAX); |
5524 | CHECK (long_long, LLONG_MIN); | |
5525 | CHECK (ulong_long, ULLONG_MAX); | |
5526 | #endif | |
0f2d19dd JB |
5527 | } |
5528 | ||
b10586f0 ML |
5529 | #undef CHECK |
5530 | ||
5531 | #define CHECK \ | |
5532 | scm_internal_catch (SCM_BOOL_T, check_body, &data, check_handler, &data); \ | |
5533 | if (!SCM_FALSEP (data)) abort(); | |
5534 | ||
5535 | static SCM | |
5536 | check_body (void *data) | |
5537 | { | |
5538 | SCM num = *(SCM *) data; | |
5539 | scm_num2ulong (num, 1, NULL); | |
5540 | ||
5541 | return SCM_UNSPECIFIED; | |
5542 | } | |
5543 | ||
5544 | static SCM | |
5545 | check_handler (void *data, SCM tag, SCM throw_args) | |
5546 | { | |
5547 | SCM *num = (SCM *) data; | |
5548 | *num = SCM_BOOL_F; | |
5549 | ||
5550 | return SCM_UNSPECIFIED; | |
5551 | } | |
5552 | ||
5553 | SCM_DEFINE (scm_sys_check_number_conversions, "%check-number-conversions", 0, 0, 0, | |
b4e15479 | 5554 | (void), |
b10586f0 ML |
5555 | "Number conversion sanity checking.") |
5556 | #define FUNC_NAME s_scm_sys_check_number_conversions | |
5557 | { | |
5558 | SCM data = SCM_MAKINUM (-1); | |
5559 | CHECK; | |
5560 | data = scm_int2num (INT_MIN); | |
5561 | CHECK; | |
5562 | data = scm_ulong2num (ULONG_MAX); | |
5563 | data = scm_difference (SCM_INUM0, data); | |
5564 | CHECK; | |
5565 | data = scm_ulong2num (ULONG_MAX); | |
5566 | data = scm_sum (SCM_MAKINUM (1), data); data = scm_difference (SCM_INUM0, data); | |
5567 | CHECK; | |
5568 | data = scm_int2num (-10000); data = scm_product (data, data); data = scm_product (data, data); | |
5569 | CHECK; | |
5570 | ||
5571 | return SCM_UNSPECIFIED; | |
5572 | } | |
5573 | #undef FUNC_NAME | |
5574 | ||
1be6b49c | 5575 | #endif |
0f2d19dd | 5576 | |
0f2d19dd JB |
5577 | void |
5578 | scm_init_numbers () | |
0f2d19dd | 5579 | { |
1be6b49c | 5580 | abs_most_negative_fixnum = scm_i_long2big (- SCM_MOST_NEGATIVE_FIXNUM); |
ac0c002c DH |
5581 | scm_permanent_object (abs_most_negative_fixnum); |
5582 | ||
713a4259 KR |
5583 | mpz_init_set_si (z_negative_one, -1); |
5584 | ||
a261c0e9 DH |
5585 | /* It may be possible to tune the performance of some algorithms by using |
5586 | * the following constants to avoid the creation of bignums. Please, before | |
5587 | * using these values, remember the two rules of program optimization: | |
5588 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe MV |
5589 | scm_c_define ("most-positive-fixnum", |
5590 | SCM_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); | |
5591 | scm_c_define ("most-negative-fixnum", | |
5592 | SCM_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); | |
a261c0e9 | 5593 | |
f3ae5d60 MD |
5594 | scm_add_feature ("complex"); |
5595 | scm_add_feature ("inexact"); | |
5986c47d | 5596 | scm_flo0 = scm_make_real (0.0); |
f872b822 | 5597 | #ifdef DBL_DIG |
0f2d19dd | 5598 | scm_dblprec = (DBL_DIG > 20) ? 20 : DBL_DIG; |
f872b822 | 5599 | #else |
0f2d19dd JB |
5600 | { /* determine floating point precision */ |
5601 | double f = 0.1; | |
f872b822 | 5602 | double fsum = 1.0 + f; |
0aacf84e MD |
5603 | while (fsum != 1.0) |
5604 | { | |
5605 | if (++scm_dblprec > 20) | |
5606 | fsum = 1.0; | |
5607 | else | |
5608 | { | |
5609 | f /= 10.0; | |
5610 | fsum = f + 1.0; | |
5611 | } | |
f872b822 MD |
5612 | } |
5613 | scm_dblprec = scm_dblprec - 1; | |
0f2d19dd | 5614 | } |
f872b822 | 5615 | #endif /* DBL_DIG */ |
1be6b49c ML |
5616 | |
5617 | #ifdef GUILE_DEBUG | |
5618 | check_sanity (); | |
5619 | #endif | |
f92e85f7 MV |
5620 | |
5621 | exactly_one_half = scm_permanent_object (scm_divide (SCM_MAKINUM (1), | |
5622 | SCM_MAKINUM (2))); | |
a0599745 | 5623 | #include "libguile/numbers.x" |
0f2d19dd | 5624 | } |
89e00824 ML |
5625 | |
5626 | /* | |
5627 | Local Variables: | |
5628 | c-file-style: "gnu" | |
5629 | End: | |
5630 | */ |