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a48d60b1 | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001,2002, 2003 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 | * |
0f2d19dd JB |
7 | * This program is free software; you can redistribute it and/or modify |
8 | * it under the terms of the GNU General Public License as published by | |
9 | * the Free Software Foundation; either version 2, or (at your option) | |
10 | * any later version. | |
11 | * | |
12 | * This program 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 | |
15 | * GNU General Public License for more details. | |
16 | * | |
17 | * You should have received a copy of the GNU General Public License | |
18 | * along with this software; see the file COPYING. If not, write to | |
82892bed JB |
19 | * the Free Software Foundation, Inc., 59 Temple Place, Suite 330, |
20 | * Boston, MA 02111-1307 USA | |
0f2d19dd JB |
21 | * |
22 | * As a special exception, the Free Software Foundation gives permission | |
23 | * for additional uses of the text contained in its release of GUILE. | |
24 | * | |
25 | * The exception is that, if you link the GUILE library with other files | |
26 | * to produce an executable, this does not by itself cause the | |
27 | * resulting executable to be covered by the GNU General Public License. | |
28 | * Your use of that executable is in no way restricted on account of | |
29 | * linking the GUILE library code into it. | |
30 | * | |
31 | * This exception does not however invalidate any other reasons why | |
32 | * the executable file might be covered by the GNU General Public License. | |
33 | * | |
34 | * This exception applies only to the code released by the | |
35 | * Free Software Foundation under the name GUILE. If you copy | |
36 | * code from other Free Software Foundation releases into a copy of | |
37 | * GUILE, as the General Public License permits, the exception does | |
38 | * not apply to the code that you add in this way. To avoid misleading | |
39 | * anyone as to the status of such modified files, you must delete | |
40 | * this exception notice from them. | |
41 | * | |
42 | * If you write modifications of your own for GUILE, it is your choice | |
43 | * whether to permit this exception to apply to your modifications. | |
82892bed | 44 | * If you do not wish that, delete this exception notice. */ |
1bbd0b84 | 45 | |
0f2d19dd JB |
46 | \f |
47 | ||
0f2d19dd | 48 | #include <math.h> |
3c9a524f | 49 | #include <ctype.h> |
fc194577 | 50 | #include <string.h> |
a0599745 | 51 | #include "libguile/_scm.h" |
a0599745 MD |
52 | #include "libguile/feature.h" |
53 | #include "libguile/ports.h" | |
54 | #include "libguile/root.h" | |
55 | #include "libguile/smob.h" | |
56 | #include "libguile/strings.h" | |
a0599745 MD |
57 | |
58 | #include "libguile/validate.h" | |
59 | #include "libguile/numbers.h" | |
1be6b49c | 60 | #include "libguile/deprecation.h" |
f4c627b3 | 61 | |
0f2d19dd | 62 | \f |
f4c627b3 | 63 | |
1be6b49c | 64 | static SCM scm_divbigbig (SCM_BIGDIG *x, size_t nx, SCM_BIGDIG *y, size_t ny, int sgn, int modes); |
f4c627b3 DH |
65 | static SCM scm_divbigint (SCM x, long z, int sgn, int mode); |
66 | ||
67 | ||
34d19ef6 | 68 | #define SCM_SWAP(x, y) do { SCM __t = x; x = y; y = __t; } while (0) |
09fb7599 DH |
69 | |
70 | ||
56e55ac7 | 71 | /* FLOBUFLEN is the maximum number of characters neccessary for the |
3a9809df DH |
72 | * printed or scm_string representation of an inexact number. |
73 | */ | |
56e55ac7 | 74 | #define FLOBUFLEN (10+2*(sizeof(double)/sizeof(char)*SCM_CHAR_BIT*3+9)/10) |
3a9809df | 75 | |
7351e207 MV |
76 | #if defined (SCO) |
77 | #if ! defined (HAVE_ISNAN) | |
78 | #define HAVE_ISNAN | |
79 | static int | |
80 | isnan (double x) | |
81 | { | |
82 | return (IsNANorINF (x) && NaN (x) && ! IsINF (x)) ? 1 : 0; | |
83 | } | |
0f2d19dd | 84 | #endif |
7351e207 MV |
85 | #if ! defined (HAVE_ISINF) |
86 | #define HAVE_ISINF | |
87 | static int | |
88 | isinf (double x) | |
89 | { | |
90 | return (IsNANorINF (x) && IsINF (x)) ? 1 : 0; | |
91 | } | |
0f2d19dd | 92 | |
7351e207 | 93 | #endif |
e6f3ef58 MD |
94 | #endif |
95 | ||
0f2d19dd JB |
96 | \f |
97 | ||
ac0c002c DH |
98 | static SCM abs_most_negative_fixnum; |
99 | ||
100 | \f | |
101 | ||
f872b822 | 102 | |
a1ec6916 | 103 | SCM_DEFINE (scm_exact_p, "exact?", 1, 0, 0, |
1bbd0b84 | 104 | (SCM x), |
942e5b91 MG |
105 | "Return @code{#t} if @var{x} is an exact number, @code{#f}\n" |
106 | "otherwise.") | |
1bbd0b84 | 107 | #define FUNC_NAME s_scm_exact_p |
0f2d19dd | 108 | { |
4219f20d | 109 | if (SCM_INUMP (x)) { |
f872b822 | 110 | return SCM_BOOL_T; |
4219f20d | 111 | } else if (SCM_BIGP (x)) { |
f872b822 | 112 | return SCM_BOOL_T; |
4219f20d DH |
113 | } else { |
114 | return SCM_BOOL_F; | |
115 | } | |
0f2d19dd | 116 | } |
1bbd0b84 | 117 | #undef FUNC_NAME |
0f2d19dd | 118 | |
4219f20d | 119 | |
a1ec6916 | 120 | SCM_DEFINE (scm_odd_p, "odd?", 1, 0, 0, |
1bbd0b84 | 121 | (SCM n), |
942e5b91 MG |
122 | "Return @code{#t} if @var{n} is an odd number, @code{#f}\n" |
123 | "otherwise.") | |
1bbd0b84 | 124 | #define FUNC_NAME s_scm_odd_p |
0f2d19dd | 125 | { |
4219f20d DH |
126 | if (SCM_INUMP (n)) { |
127 | return SCM_BOOL ((4 & SCM_UNPACK (n)) != 0); | |
4219f20d DH |
128 | } else if (SCM_BIGP (n)) { |
129 | return SCM_BOOL ((1 & SCM_BDIGITS (n) [0]) != 0); | |
7351e207 MV |
130 | } else if (scm_inf_p (n)) { |
131 | return SCM_BOOL_T; | |
4219f20d | 132 | } else { |
a1a33b0f | 133 | SCM_WRONG_TYPE_ARG (1, n); |
4219f20d | 134 | } |
0f2d19dd | 135 | } |
1bbd0b84 | 136 | #undef FUNC_NAME |
0f2d19dd | 137 | |
4219f20d | 138 | |
a1ec6916 | 139 | SCM_DEFINE (scm_even_p, "even?", 1, 0, 0, |
1bbd0b84 | 140 | (SCM n), |
942e5b91 MG |
141 | "Return @code{#t} if @var{n} is an even number, @code{#f}\n" |
142 | "otherwise.") | |
1bbd0b84 | 143 | #define FUNC_NAME s_scm_even_p |
0f2d19dd | 144 | { |
4219f20d DH |
145 | if (SCM_INUMP (n)) { |
146 | return SCM_BOOL ((4 & SCM_UNPACK (n)) == 0); | |
4219f20d DH |
147 | } else if (SCM_BIGP (n)) { |
148 | return SCM_BOOL ((1 & SCM_BDIGITS (n) [0]) == 0); | |
7351e207 MV |
149 | } else if (scm_inf_p (n)) { |
150 | return SCM_BOOL_T; | |
4219f20d | 151 | } else { |
a1a33b0f | 152 | SCM_WRONG_TYPE_ARG (1, n); |
4219f20d | 153 | } |
0f2d19dd | 154 | } |
1bbd0b84 | 155 | #undef FUNC_NAME |
0f2d19dd | 156 | |
7351e207 MV |
157 | static int |
158 | xisinf (double x) | |
159 | { | |
160 | #if defined (HAVE_ISINF) | |
161 | return isinf (x); | |
162 | #elif defined (HAVE_FINITE) && defined (HAVE_ISNAN) | |
163 | return (! (finite (x) || isnan (x))); | |
164 | #else | |
165 | return 0; | |
166 | #endif | |
167 | } | |
168 | ||
169 | static int | |
170 | xisnan (double x) | |
171 | { | |
172 | #if defined (HAVE_ISNAN) | |
173 | return isnan (x); | |
174 | #else | |
175 | return 0; | |
176 | #endif | |
177 | } | |
178 | ||
179 | #define isfinite(x) (! xisinf (x)) | |
180 | ||
181 | SCM_DEFINE (scm_inf_p, "inf?", 1, 0, 0, | |
182 | (SCM n), | |
183 | "Return @code{#t} if @var{n} is infinite, @code{#f}\n" | |
184 | "otherwise.") | |
185 | #define FUNC_NAME s_scm_inf_p | |
186 | { | |
187 | if (SCM_REALP (n)) { | |
188 | return SCM_BOOL (xisinf (SCM_REAL_VALUE (n))); | |
189 | } else if (SCM_COMPLEXP (n)) { | |
190 | return SCM_BOOL (xisinf (SCM_COMPLEX_REAL (n)) | |
191 | || xisinf (SCM_COMPLEX_IMAG (n))); | |
192 | } else { | |
193 | return SCM_BOOL_F; | |
194 | } | |
195 | } | |
196 | #undef FUNC_NAME | |
197 | ||
198 | SCM_DEFINE (scm_nan_p, "nan?", 1, 0, 0, | |
199 | (SCM n), | |
200 | "Return @code{#t} if @var{n} is a NaN, @code{#f}\n" | |
201 | "otherwise.") | |
202 | #define FUNC_NAME s_scm_nan_p | |
203 | { | |
204 | if (SCM_REALP (n)) { | |
205 | return SCM_BOOL (xisnan (SCM_REAL_VALUE (n))); | |
206 | } else if (SCM_COMPLEXP (n)) { | |
207 | return SCM_BOOL (xisnan (SCM_COMPLEX_REAL (n)) | |
208 | || xisnan (SCM_COMPLEX_IMAG (n))); | |
209 | } else { | |
210 | return SCM_BOOL_F; | |
211 | } | |
212 | } | |
213 | #undef FUNC_NAME | |
214 | ||
215 | /* Guile's idea of infinity. */ | |
216 | static double guile_Inf; | |
217 | ||
218 | /* Guile's idea of not a number. */ | |
219 | static double guile_NaN; | |
220 | ||
221 | static void | |
222 | guile_ieee_init (void) | |
223 | { | |
224 | #if defined (HAVE_ISINF) || defined (HAVE_FINITE) | |
225 | ||
226 | /* Some version of gcc on some old version of Linux used to crash when | |
227 | trying to make Inf and NaN. */ | |
228 | ||
229 | #if defined (SCO) | |
230 | double tmp = 1.0; | |
231 | guile_Inf = 1.0 / (tmp - tmp); | |
232 | #elif defined (__alpha__) && ! defined (linux) | |
233 | extern unsigned int DINFINITY[2]; | |
234 | guile_Inf = (*(X_CAST(double *, DINFINITY))); | |
235 | #else | |
236 | double tmp = 1e+10; | |
237 | guile_Inf = tmp; | |
238 | for (;;) | |
239 | { | |
240 | guile_Inf *= 1e+10; | |
241 | if (guile_Inf == tmp) | |
242 | break; | |
243 | tmp = guile_Inf; | |
244 | } | |
245 | #endif | |
246 | ||
247 | #endif | |
248 | ||
249 | #if defined (HAVE_ISNAN) | |
250 | ||
251 | #if defined (__alpha__) && ! defined (linux) | |
252 | extern unsigned int DQNAN[2]; | |
253 | guile_NaN = (*(X_CAST(double *, DQNAN))); | |
254 | #else | |
255 | guile_NaN = guile_Inf / guile_Inf; | |
256 | #endif | |
257 | ||
258 | #endif | |
259 | } | |
260 | ||
261 | SCM_DEFINE (scm_inf, "inf", 0, 0, 0, | |
262 | (void), | |
263 | "Return Inf.") | |
264 | #define FUNC_NAME s_scm_inf | |
265 | { | |
266 | static int initialized = 0; | |
267 | if (! initialized) | |
268 | { | |
269 | guile_ieee_init (); | |
270 | initialized = 1; | |
271 | } | |
272 | return scm_make_real (guile_Inf); | |
273 | } | |
274 | #undef FUNC_NAME | |
275 | ||
276 | SCM_DEFINE (scm_nan, "nan", 0, 0, 0, | |
277 | (void), | |
278 | "Return NaN.") | |
279 | #define FUNC_NAME s_scm_nan | |
280 | { | |
281 | static int initialized = 0; | |
282 | if (! initialized) | |
283 | { | |
284 | guile_ieee_init (); | |
285 | initialized = 1; | |
286 | } | |
287 | return scm_make_real (guile_NaN); | |
288 | } | |
289 | #undef FUNC_NAME | |
290 | ||
4219f20d | 291 | |
a48d60b1 MD |
292 | SCM_PRIMITIVE_GENERIC (scm_abs, "abs", 1, 0, 0, |
293 | (SCM x), | |
294 | "Return the absolute value of @var{x}.") | |
295 | #define FUNC_NAME | |
0f2d19dd | 296 | { |
4219f20d DH |
297 | if (SCM_INUMP (x)) { |
298 | long int xx = SCM_INUM (x); | |
299 | if (xx >= 0) { | |
300 | return x; | |
301 | } else if (SCM_POSFIXABLE (-xx)) { | |
302 | return SCM_MAKINUM (-xx); | |
303 | } else { | |
0f2d19dd | 304 | #ifdef SCM_BIGDIG |
1be6b49c | 305 | return scm_i_long2big (-xx); |
0f2d19dd | 306 | #else |
4219f20d | 307 | scm_num_overflow (s_abs); |
0f2d19dd | 308 | #endif |
4219f20d | 309 | } |
4219f20d DH |
310 | } else if (SCM_BIGP (x)) { |
311 | if (!SCM_BIGSIGN (x)) { | |
312 | return x; | |
313 | } else { | |
1be6b49c | 314 | return scm_i_copybig (x, 0); |
4219f20d | 315 | } |
5986c47d DH |
316 | } else if (SCM_REALP (x)) { |
317 | return scm_make_real (fabs (SCM_REAL_VALUE (x))); | |
4219f20d | 318 | } else { |
a48d60b1 | 319 | SCM_WTA_DISPATCH_1 (g_scm_abs, x, 1, s_scm_abs); |
4219f20d | 320 | } |
0f2d19dd | 321 | } |
a48d60b1 | 322 | #undef FUNC_NAME |
0f2d19dd | 323 | |
4219f20d | 324 | |
9de33deb | 325 | SCM_GPROC (s_quotient, "quotient", 2, 0, 0, scm_quotient, g_quotient); |
942e5b91 MG |
326 | /* "Return the quotient of the numbers @var{x} and @var{y}." |
327 | */ | |
0f2d19dd | 328 | SCM |
6e8d25a6 | 329 | scm_quotient (SCM x, SCM y) |
0f2d19dd | 330 | { |
828865c3 DH |
331 | if (SCM_INUMP (x)) { |
332 | long xx = SCM_INUM (x); | |
333 | if (SCM_INUMP (y)) { | |
334 | long yy = SCM_INUM (y); | |
335 | if (yy == 0) { | |
336 | scm_num_overflow (s_quotient); | |
337 | } else { | |
338 | long z = xx / yy; | |
4219f20d DH |
339 | if (SCM_FIXABLE (z)) { |
340 | return SCM_MAKINUM (z); | |
341 | } else { | |
828865c3 | 342 | #ifdef SCM_BIGDIG |
1be6b49c | 343 | return scm_i_long2big (z); |
828865c3 DH |
344 | #else |
345 | scm_num_overflow (s_quotient); | |
346 | #endif | |
828865c3 DH |
347 | } |
348 | } | |
4219f20d | 349 | } else if (SCM_BIGP (y)) { |
ac0c002c DH |
350 | if (SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM |
351 | && scm_bigcomp (abs_most_negative_fixnum, y) == 0) | |
352 | { | |
353 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
354 | return SCM_MAKINUM (-1); | |
355 | } | |
356 | else | |
357 | return SCM_MAKINUM (0); | |
4219f20d DH |
358 | } else { |
359 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); | |
828865c3 | 360 | } |
4219f20d DH |
361 | } else if (SCM_BIGP (x)) { |
362 | if (SCM_INUMP (y)) { | |
828865c3 DH |
363 | long yy = SCM_INUM (y); |
364 | if (yy == 0) { | |
365 | scm_num_overflow (s_quotient); | |
366 | } else if (yy == 1) { | |
f872b822 | 367 | return x; |
828865c3 DH |
368 | } else { |
369 | long z = yy < 0 ? -yy : yy; | |
370 | ||
371 | if (z < SCM_BIGRAD) { | |
1be6b49c | 372 | SCM sw = scm_i_copybig (x, SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0)); |
c209c88e | 373 | scm_divbigdig (SCM_BDIGITS (sw), SCM_NUMDIGS (sw), (SCM_BIGDIG) z); |
1be6b49c | 374 | return scm_i_normbig (sw); |
828865c3 | 375 | } else { |
0f2d19dd | 376 | #ifndef SCM_DIGSTOOBIG |
828865c3 DH |
377 | long w = scm_pseudolong (z); |
378 | return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
379 | (SCM_BIGDIG *) & w, SCM_DIGSPERLONG, | |
380 | SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0), 2); | |
0f2d19dd | 381 | #else |
828865c3 DH |
382 | SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; |
383 | scm_longdigs (z, zdigs); | |
384 | return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
385 | zdigs, SCM_DIGSPERLONG, | |
386 | SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0), 2); | |
f872b822 | 387 | #endif |
f872b822 | 388 | } |
828865c3 | 389 | } |
4219f20d DH |
390 | } else if (SCM_BIGP (y)) { |
391 | return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
392 | SCM_BDIGITS (y), SCM_NUMDIGS (y), | |
393 | SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y), 2); | |
394 | } else { | |
395 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG2, s_quotient); | |
f872b822 | 396 | } |
4219f20d | 397 | } else { |
89a7e495 | 398 | SCM_WTA_DISPATCH_2 (g_quotient, x, y, SCM_ARG1, s_quotient); |
0f2d19dd | 399 | } |
0f2d19dd JB |
400 | } |
401 | ||
4219f20d | 402 | |
9de33deb | 403 | SCM_GPROC (s_remainder, "remainder", 2, 0, 0, scm_remainder, g_remainder); |
942e5b91 MG |
404 | /* "Return the remainder of the numbers @var{x} and @var{y}.\n" |
405 | * "@lisp\n" | |
406 | * "(remainder 13 4) @result{} 1\n" | |
407 | * "(remainder -13 4) @result{} -1\n" | |
408 | * "@end lisp" | |
409 | */ | |
0f2d19dd | 410 | SCM |
6e8d25a6 | 411 | scm_remainder (SCM x, SCM y) |
0f2d19dd | 412 | { |
89a7e495 DH |
413 | if (SCM_INUMP (x)) { |
414 | if (SCM_INUMP (y)) { | |
415 | long yy = SCM_INUM (y); | |
416 | if (yy == 0) { | |
417 | scm_num_overflow (s_remainder); | |
418 | } else { | |
89a7e495 | 419 | long z = SCM_INUM (x) % yy; |
89a7e495 DH |
420 | return SCM_MAKINUM (z); |
421 | } | |
89a7e495 | 422 | } else if (SCM_BIGP (y)) { |
ac0c002c DH |
423 | if (SCM_INUM (x) == SCM_MOST_NEGATIVE_FIXNUM |
424 | && scm_bigcomp (abs_most_negative_fixnum, y) == 0) | |
425 | { | |
426 | /* Special case: x == fixnum-min && y == abs (fixnum-min) */ | |
427 | return SCM_MAKINUM (0); | |
428 | } | |
429 | else | |
430 | return x; | |
89a7e495 DH |
431 | } else { |
432 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); | |
433 | } | |
89a7e495 DH |
434 | } else if (SCM_BIGP (x)) { |
435 | if (SCM_INUMP (y)) { | |
436 | long yy = SCM_INUM (y); | |
437 | if (yy == 0) { | |
438 | scm_num_overflow (s_remainder); | |
439 | } else { | |
440 | return scm_divbigint (x, yy, SCM_BIGSIGN (x), 0); | |
441 | } | |
442 | } else if (SCM_BIGP (y)) { | |
443 | return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
444 | SCM_BDIGITS (y), SCM_NUMDIGS (y), | |
445 | SCM_BIGSIGN (x), 0); | |
446 | } else { | |
447 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG2, s_remainder); | |
f872b822 | 448 | } |
89a7e495 DH |
449 | } else { |
450 | SCM_WTA_DISPATCH_2 (g_remainder, x, y, SCM_ARG1, s_remainder); | |
451 | } | |
0f2d19dd JB |
452 | } |
453 | ||
89a7e495 | 454 | |
9de33deb | 455 | SCM_GPROC (s_modulo, "modulo", 2, 0, 0, scm_modulo, g_modulo); |
942e5b91 MG |
456 | /* "Return the modulo of the numbers @var{x} and @var{y}.\n" |
457 | * "@lisp\n" | |
458 | * "(modulo 13 4) @result{} 1\n" | |
459 | * "(modulo -13 4) @result{} 3\n" | |
460 | * "@end lisp" | |
461 | */ | |
0f2d19dd | 462 | SCM |
6e8d25a6 | 463 | scm_modulo (SCM x, SCM y) |
0f2d19dd | 464 | { |
828865c3 DH |
465 | if (SCM_INUMP (x)) { |
466 | long xx = SCM_INUM (x); | |
467 | if (SCM_INUMP (y)) { | |
468 | long yy = SCM_INUM (y); | |
469 | if (yy == 0) { | |
470 | scm_num_overflow (s_modulo); | |
471 | } else { | |
828865c3 | 472 | long z = xx % yy; |
828865c3 DH |
473 | return SCM_MAKINUM (((yy < 0) ? (z > 0) : (z < 0)) ? z + yy : z); |
474 | } | |
09fb7599 DH |
475 | } else if (SCM_BIGP (y)) { |
476 | return (SCM_BIGSIGN (y) ? (xx > 0) : (xx < 0)) ? scm_sum (x, y) : x; | |
09fb7599 DH |
477 | } else { |
478 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
f872b822 | 479 | } |
09fb7599 DH |
480 | } else if (SCM_BIGP (x)) { |
481 | if (SCM_INUMP (y)) { | |
828865c3 DH |
482 | long yy = SCM_INUM (y); |
483 | if (yy == 0) { | |
484 | scm_num_overflow (s_modulo); | |
485 | } else { | |
486 | return scm_divbigint (x, yy, yy < 0, | |
487 | (SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0)) ? 1 : 0); | |
488 | } | |
09fb7599 DH |
489 | } else if (SCM_BIGP (y)) { |
490 | return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
491 | SCM_BDIGITS (y), SCM_NUMDIGS (y), | |
492 | SCM_BIGSIGN (y), | |
493 | (SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y)) ? 1 : 0); | |
494 | } else { | |
495 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG2, s_modulo); | |
828865c3 | 496 | } |
09fb7599 DH |
497 | } else { |
498 | SCM_WTA_DISPATCH_2 (g_modulo, x, y, SCM_ARG1, s_modulo); | |
828865c3 | 499 | } |
0f2d19dd JB |
500 | } |
501 | ||
09fb7599 | 502 | |
9de33deb | 503 | SCM_GPROC1 (s_gcd, "gcd", scm_tc7_asubr, scm_gcd, g_gcd); |
942e5b91 MG |
504 | /* "Return the greatest common divisor of all arguments.\n" |
505 | * "If called without arguments, 0 is returned." | |
506 | */ | |
0f2d19dd | 507 | SCM |
6e8d25a6 | 508 | scm_gcd (SCM x, SCM y) |
0f2d19dd | 509 | { |
09fb7599 DH |
510 | if (SCM_UNBNDP (y)) { |
511 | if (SCM_UNBNDP (x)) { | |
512 | return SCM_INUM0; | |
513 | } else { | |
514 | return x; | |
515 | } | |
516 | } | |
f8de44c1 | 517 | |
0f2d19dd | 518 | tailrec: |
09fb7599 DH |
519 | if (SCM_INUMP (x)) { |
520 | if (SCM_INUMP (y)) { | |
521 | long xx = SCM_INUM (x); | |
522 | long yy = SCM_INUM (y); | |
523 | long u = xx < 0 ? -xx : xx; | |
524 | long v = yy < 0 ? -yy : yy; | |
525 | long result; | |
526 | ||
527 | if (xx == 0) { | |
528 | result = v; | |
529 | } else if (yy == 0) { | |
530 | result = u; | |
531 | } else { | |
1aaa208e | 532 | long k = 1; |
09fb7599 DH |
533 | long t; |
534 | ||
535 | /* Determine a common factor 2^k */ | |
536 | while (!(1 & (u | v))) { | |
537 | k <<= 1; | |
538 | u >>= 1; | |
539 | v >>= 1; | |
f872b822 | 540 | } |
09fb7599 DH |
541 | |
542 | /* Now, any factor 2^n can be eliminated */ | |
543 | if (u & 1) { | |
544 | t = -v; | |
545 | } else { | |
546 | t = u; | |
547 | b3: | |
548 | t = SCM_SRS (t, 1); | |
549 | } | |
550 | if (!(1 & t)) | |
551 | goto b3; | |
552 | if (t > 0) | |
553 | u = t; | |
554 | else | |
555 | v = -t; | |
556 | t = u - v; | |
557 | if (t != 0) | |
558 | goto b3; | |
559 | ||
560 | result = u * k; | |
561 | } | |
562 | if (SCM_POSFIXABLE (result)) { | |
563 | return SCM_MAKINUM (result); | |
564 | } else { | |
565 | #ifdef SCM_BIGDIG | |
1be6b49c | 566 | return scm_i_long2big (result); |
f872b822 | 567 | #else |
09fb7599 DH |
568 | scm_num_overflow (s_gcd); |
569 | #endif | |
570 | } | |
09fb7599 DH |
571 | } else if (SCM_BIGP (y)) { |
572 | SCM_SWAP (x, y); | |
573 | goto big_gcd; | |
09fb7599 DH |
574 | } else { |
575 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
f872b822 | 576 | } |
09fb7599 DH |
577 | } else if (SCM_BIGP (x)) { |
578 | big_gcd: | |
579 | if (SCM_BIGSIGN (x)) | |
1be6b49c | 580 | x = scm_i_copybig (x, 0); |
09fb7599 DH |
581 | newy: |
582 | if (SCM_INUMP (y)) { | |
583 | if (SCM_EQ_P (y, SCM_INUM0)) { | |
584 | return x; | |
585 | } else { | |
586 | goto swaprec; | |
587 | } | |
588 | } else if (SCM_BIGP (y)) { | |
589 | if (SCM_BIGSIGN (y)) | |
1be6b49c | 590 | y = scm_i_copybig (y, 0); |
09fb7599 DH |
591 | switch (scm_bigcomp (x, y)) |
592 | { | |
593 | case -1: /* x > y */ | |
594 | swaprec: | |
595 | { | |
596 | SCM t = scm_remainder (x, y); | |
597 | x = y; | |
598 | y = t; | |
599 | } | |
600 | goto tailrec; | |
601 | case 1: /* x < y */ | |
602 | y = scm_remainder (y, x); | |
603 | goto newy; | |
604 | default: /* x == y */ | |
605 | return x; | |
606 | } | |
607 | /* instead of the switch, we could just | |
608 | return scm_gcd (y, scm_modulo (x, y)); */ | |
609 | } else { | |
610 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG2, s_gcd); | |
611 | } | |
09fb7599 DH |
612 | } else { |
613 | SCM_WTA_DISPATCH_2 (g_gcd, x, y, SCM_ARG1, s_gcd); | |
614 | } | |
0f2d19dd JB |
615 | } |
616 | ||
09fb7599 | 617 | |
9de33deb | 618 | SCM_GPROC1 (s_lcm, "lcm", scm_tc7_asubr, scm_lcm, g_lcm); |
942e5b91 MG |
619 | /* "Return the least common multiple of the arguments.\n" |
620 | * "If called without arguments, 1 is returned." | |
621 | */ | |
0f2d19dd | 622 | SCM |
6e8d25a6 | 623 | scm_lcm (SCM n1, SCM n2) |
0f2d19dd | 624 | { |
09fb7599 DH |
625 | if (SCM_UNBNDP (n2)) { |
626 | if (SCM_UNBNDP (n1)) { | |
627 | return SCM_MAKINUM (1L); | |
628 | } else { | |
629 | n2 = SCM_MAKINUM (1L); | |
630 | } | |
631 | }; | |
632 | ||
02a3305a | 633 | #ifndef SCM_BIGDIG |
09fb7599 DH |
634 | SCM_GASSERT2 (SCM_INUMP (n1), g_lcm, n1, n2, SCM_ARG1, s_lcm); |
635 | SCM_GASSERT2 (SCM_INUMP (n2), g_lcm, n1, n2, SCM_ARGn, s_lcm); | |
9de33deb | 636 | #else |
09fb7599 | 637 | SCM_GASSERT2 (SCM_INUMP (n1) || SCM_BIGP (n1), |
9de33deb | 638 | g_lcm, n1, n2, SCM_ARG1, s_lcm); |
09fb7599 | 639 | SCM_GASSERT2 (SCM_INUMP (n2) || SCM_BIGP (n2), |
9de33deb MD |
640 | g_lcm, n1, n2, SCM_ARGn, s_lcm); |
641 | #endif | |
09fb7599 DH |
642 | |
643 | { | |
644 | SCM d = scm_gcd (n1, n2); | |
645 | if (SCM_EQ_P (d, SCM_INUM0)) { | |
646 | return d; | |
647 | } else { | |
648 | return scm_abs (scm_product (n1, scm_quotient (n2, d))); | |
f872b822 | 649 | } |
09fb7599 | 650 | } |
0f2d19dd JB |
651 | } |
652 | ||
09fb7599 | 653 | |
0f2d19dd | 654 | #ifndef scm_long2num |
c1bfcf60 GB |
655 | #define SCM_LOGOP_RETURN(x) scm_ulong2num(x) |
656 | #else | |
657 | #define SCM_LOGOP_RETURN(x) SCM_MAKINUM(x) | |
658 | #endif | |
659 | ||
8a525303 GB |
660 | |
661 | /* Emulating 2's complement bignums with sign magnitude arithmetic: | |
662 | ||
663 | Logand: | |
664 | X Y Result Method: | |
665 | (len) | |
666 | + + + x (map digit:logand X Y) | |
667 | + - + x (map digit:logand X (lognot (+ -1 Y))) | |
668 | - + + y (map digit:logand (lognot (+ -1 X)) Y) | |
669 | - - - (+ 1 (map digit:logior (+ -1 X) (+ -1 Y))) | |
670 | ||
671 | Logior: | |
672 | X Y Result Method: | |
673 | ||
674 | + + + (map digit:logior X Y) | |
675 | + - - y (+ 1 (map digit:logand (lognot X) (+ -1 Y))) | |
676 | - + - x (+ 1 (map digit:logand (+ -1 X) (lognot Y))) | |
677 | - - - x (+ 1 (map digit:logand (+ -1 X) (+ -1 Y))) | |
678 | ||
679 | Logxor: | |
680 | X Y Result Method: | |
681 | ||
682 | + + + (map digit:logxor X Y) | |
683 | + - - (+ 1 (map digit:logxor X (+ -1 Y))) | |
684 | - + - (+ 1 (map digit:logxor (+ -1 X) Y)) | |
685 | - - + (map digit:logxor (+ -1 X) (+ -1 Y)) | |
686 | ||
687 | Logtest: | |
688 | X Y Result | |
689 | ||
690 | + + (any digit:logand X Y) | |
691 | + - (any digit:logand X (lognot (+ -1 Y))) | |
692 | - + (any digit:logand (lognot (+ -1 X)) Y) | |
693 | - - #t | |
694 | ||
695 | */ | |
696 | ||
697 | #ifdef SCM_BIGDIG | |
698 | ||
699 | SCM scm_copy_big_dec(SCM b, int sign); | |
1be6b49c ML |
700 | SCM scm_copy_smaller(SCM_BIGDIG *x, size_t nx, int zsgn); |
701 | SCM scm_big_ior(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy); | |
702 | SCM scm_big_xor(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy); | |
703 | SCM scm_big_and(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy, int zsgn); | |
704 | SCM scm_big_test(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy); | |
8a525303 GB |
705 | |
706 | SCM scm_copy_big_dec(SCM b, int sign) | |
707 | { | |
708 | long num = -1; | |
1be6b49c ML |
709 | size_t nx = SCM_NUMDIGS(b); |
710 | size_t i = 0; | |
711 | SCM ans = scm_i_mkbig(nx, sign); | |
8a525303 GB |
712 | SCM_BIGDIG *src = SCM_BDIGITS(b), *dst = SCM_BDIGITS(ans); |
713 | if SCM_BIGSIGN(b) do { | |
714 | num += src[i]; | |
715 | if (num < 0) {dst[i] = num + SCM_BIGRAD; num = -1;} | |
716 | else {dst[i] = SCM_BIGLO(num); num = 0;} | |
717 | } while (++i < nx); | |
718 | else | |
719 | while (nx--) dst[nx] = src[nx]; | |
720 | return ans; | |
721 | } | |
722 | ||
1be6b49c | 723 | SCM scm_copy_smaller(SCM_BIGDIG *x, size_t nx, int zsgn) |
8a525303 GB |
724 | { |
725 | long num = -1; | |
1be6b49c ML |
726 | size_t i = 0; |
727 | SCM z = scm_i_mkbig(nx, zsgn); | |
8a525303 GB |
728 | SCM_BIGDIG *zds = SCM_BDIGITS(z); |
729 | if (zsgn) do { | |
730 | num += x[i]; | |
731 | if (num < 0) {zds[i] = num + SCM_BIGRAD; num = -1;} | |
732 | else {zds[i] = SCM_BIGLO(num); num = 0;} | |
733 | } while (++i < nx); | |
734 | else do zds[i] = x[i]; while (++i < nx); | |
735 | return z; | |
736 | } | |
737 | ||
1be6b49c | 738 | SCM scm_big_ior(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy) |
8a525303 | 739 | /* Assumes nx <= SCM_NUMDIGS(bigy) */ |
f3ae5d60 | 740 | /* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */ |
8a525303 GB |
741 | { |
742 | long num = -1; | |
1be6b49c | 743 | size_t i = 0, ny = SCM_NUMDIGS(bigy); |
f3ae5d60 | 744 | SCM z = scm_copy_big_dec (bigy, xsgn & SCM_BIGSIGN (bigy)); |
8a525303 GB |
745 | SCM_BIGDIG *zds = SCM_BDIGITS(z); |
746 | if (xsgn) { | |
747 | do { | |
748 | num += x[i]; | |
749 | if (num < 0) {zds[i] |= num + SCM_BIGRAD; num = -1;} | |
750 | else {zds[i] |= SCM_BIGLO(num); num = 0;} | |
751 | } while (++i < nx); | |
752 | /* ========= Need to increment zds now =========== */ | |
753 | i = 0; num = 1; | |
754 | while (i < ny) { | |
755 | num += zds[i]; | |
756 | zds[i++] = SCM_BIGLO(num); | |
757 | num = SCM_BIGDN(num); | |
758 | if (!num) return z; | |
759 | } | |
1be6b49c | 760 | scm_i_adjbig(z, 1 + ny); /* OOPS, overflowed into next digit. */ |
8a525303 GB |
761 | SCM_BDIGITS(z)[ny] = 1; |
762 | return z; | |
763 | } | |
764 | else do zds[i] = zds[i] | x[i]; while (++i < nx); | |
765 | return z; | |
766 | } | |
767 | ||
1be6b49c | 768 | SCM scm_big_xor(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy) |
8a525303 | 769 | /* Assumes nx <= SCM_NUMDIGS(bigy) */ |
f3ae5d60 | 770 | /* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */ |
8a525303 GB |
771 | { |
772 | long num = -1; | |
1be6b49c | 773 | size_t i = 0, ny = SCM_NUMDIGS(bigy); |
8a525303 GB |
774 | SCM z = scm_copy_big_dec(bigy, xsgn ^ SCM_BIGSIGN(bigy)); |
775 | SCM_BIGDIG *zds = SCM_BDIGITS(z); | |
776 | if (xsgn) do { | |
777 | num += x[i]; | |
778 | if (num < 0) {zds[i] ^= num + SCM_BIGRAD; num = -1;} | |
779 | else {zds[i] ^= SCM_BIGLO(num); num = 0;} | |
780 | } while (++i < nx); | |
781 | else do { | |
782 | zds[i] = zds[i] ^ x[i]; | |
783 | } while (++i < nx); | |
784 | ||
785 | if (xsgn ^ SCM_BIGSIGN(bigy)) { | |
786 | /* ========= Need to increment zds now =========== */ | |
787 | i = 0; num = 1; | |
788 | while (i < ny) { | |
789 | num += zds[i]; | |
790 | zds[i++] = SCM_BIGLO(num); | |
791 | num = SCM_BIGDN(num); | |
1be6b49c | 792 | if (!num) return scm_i_normbig(z); |
8a525303 GB |
793 | } |
794 | } | |
1be6b49c | 795 | return scm_i_normbig(z); |
8a525303 GB |
796 | } |
797 | ||
1be6b49c | 798 | SCM scm_big_and(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy, int zsgn) |
8a525303 | 799 | /* Assumes nx <= SCM_NUMDIGS(bigy) */ |
f3ae5d60 MD |
800 | /* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */ |
801 | /* return sign equals either 0 or SCM_BIGSIGNFLAG */ | |
8a525303 GB |
802 | { |
803 | long num = -1; | |
1be6b49c | 804 | size_t i = 0; |
8a525303 GB |
805 | SCM z; |
806 | SCM_BIGDIG *zds; | |
807 | if (xsgn==zsgn) { | |
808 | z = scm_copy_smaller(x, nx, zsgn); | |
809 | x = SCM_BDIGITS(bigy); | |
810 | xsgn = SCM_BIGSIGN(bigy); | |
811 | } | |
812 | else z = scm_copy_big_dec(bigy, zsgn); | |
813 | zds = SCM_BDIGITS(z); | |
814 | ||
815 | if (zsgn) { | |
816 | if (xsgn) do { | |
817 | num += x[i]; | |
818 | if (num < 0) {zds[i] &= num + SCM_BIGRAD; num = -1;} | |
819 | else {zds[i] &= SCM_BIGLO(num); num = 0;} | |
820 | } while (++i < nx); | |
821 | else do zds[i] = zds[i] & ~x[i]; while (++i < nx); | |
822 | /* ========= need to increment zds now =========== */ | |
823 | i = 0; num = 1; | |
824 | while (i < nx) { | |
825 | num += zds[i]; | |
826 | zds[i++] = SCM_BIGLO(num); | |
827 | num = SCM_BIGDN(num); | |
1be6b49c | 828 | if (!num) return scm_i_normbig(z); |
8a525303 GB |
829 | } |
830 | } | |
ac0c002c DH |
831 | else if (xsgn) { |
832 | unsigned long int carry = 1; | |
833 | do { | |
834 | unsigned long int mask = (SCM_BIGDIG) ~x[i] + carry; | |
835 | zds[i] = zds[i] & (SCM_BIGDIG) mask; | |
836 | carry = (mask >= SCM_BIGRAD) ? 1 : 0; | |
837 | } while (++i < nx); | |
838 | } else do zds[i] = zds[i] & x[i]; while (++i < nx); | |
1be6b49c | 839 | return scm_i_normbig(z); |
8a525303 GB |
840 | } |
841 | ||
1be6b49c | 842 | SCM scm_big_test(SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy) |
8a525303 | 843 | /* Assumes nx <= SCM_NUMDIGS(bigy) */ |
f3ae5d60 | 844 | /* Assumes xsgn equals either 0 or SCM_BIGSIGNFLAG */ |
8a525303 GB |
845 | { |
846 | SCM_BIGDIG *y; | |
1be6b49c | 847 | size_t i = 0; |
8a525303 GB |
848 | long num = -1; |
849 | if (SCM_BIGSIGN(bigy) & xsgn) return SCM_BOOL_T; | |
850 | if (SCM_NUMDIGS(bigy) != nx && xsgn) return SCM_BOOL_T; | |
851 | y = SCM_BDIGITS(bigy); | |
852 | if (xsgn) | |
853 | do { | |
854 | num += x[i]; | |
855 | if (num < 0) { | |
856 | if (y[i] & ~(num + SCM_BIGRAD)) return SCM_BOOL_T; | |
857 | num = -1; | |
858 | } | |
859 | else { | |
860 | if (y[i] & ~SCM_BIGLO(num)) return SCM_BOOL_T; | |
861 | num = 0; | |
862 | } | |
863 | } while (++i < nx); | |
864 | else if SCM_BIGSIGN(bigy) | |
865 | do { | |
866 | num += y[i]; | |
867 | if (num < 0) { | |
868 | if (x[i] & ~(num + SCM_BIGRAD)) return SCM_BOOL_T; | |
869 | num = -1; | |
870 | } | |
871 | else { | |
872 | if (x[i] & ~SCM_BIGLO(num)) return SCM_BOOL_T; | |
873 | num = 0; | |
874 | } | |
875 | } while (++i < nx); | |
876 | else | |
877 | do if (x[i] & y[i]) return SCM_BOOL_T; | |
878 | while (++i < nx); | |
879 | return SCM_BOOL_F; | |
880 | } | |
881 | ||
882 | #endif | |
883 | ||
c3ee7520 | 884 | SCM_DEFINE1 (scm_logand, "logand", scm_tc7_asubr, |
1bbd0b84 | 885 | (SCM n1, SCM n2), |
3c3db128 GH |
886 | "Return the bitwise AND of the integer arguments.\n\n" |
887 | "@lisp\n" | |
888 | "(logand) @result{} -1\n" | |
889 | "(logand 7) @result{} 7\n" | |
890 | "(logand #b111 #b011 #\b001) @result{} 1\n" | |
891 | "@end lisp") | |
1bbd0b84 | 892 | #define FUNC_NAME s_scm_logand |
0f2d19dd | 893 | { |
9a00c9fc DH |
894 | long int nn1; |
895 | ||
09fb7599 DH |
896 | if (SCM_UNBNDP (n2)) { |
897 | if (SCM_UNBNDP (n1)) { | |
898 | return SCM_MAKINUM (-1); | |
899 | } else if (!SCM_NUMBERP (n1)) { | |
900 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
09fb7599 | 901 | } else if (SCM_NUMBERP (n1)) { |
d28da049 | 902 | return n1; |
09fb7599 DH |
903 | } else { |
904 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 905 | } |
8a525303 | 906 | } |
09fb7599 DH |
907 | |
908 | if (SCM_INUMP (n1)) { | |
9a00c9fc | 909 | nn1 = SCM_INUM (n1); |
09fb7599 DH |
910 | if (SCM_INUMP (n2)) { |
911 | long nn2 = SCM_INUM (n2); | |
912 | return SCM_MAKINUM (nn1 & nn2); | |
09fb7599 DH |
913 | } else if SCM_BIGP (n2) { |
914 | intbig: | |
915 | { | |
8a525303 | 916 | # ifndef SCM_DIGSTOOBIG |
09fb7599 DH |
917 | long z = scm_pseudolong (nn1); |
918 | if ((nn1 < 0) && SCM_BIGSIGN (n2)) { | |
919 | return scm_big_ior ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
920 | SCM_BIGSIGNFLAG, n2); | |
921 | } else { | |
922 | return scm_big_and ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
923 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, 0); | |
924 | } | |
8a525303 | 925 | # else |
09fb7599 DH |
926 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
927 | scm_longdigs (nn1, zdigs); | |
928 | if ((nn1 < 0) && SCM_BIGSIGN (n2)) { | |
929 | return scm_big_ior (zdigs, SCM_DIGSPERLONG, SCM_BIGSIGNFLAG, n2); | |
930 | } else { | |
931 | return scm_big_and (zdigs, SCM_DIGSPERLONG, | |
932 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, 0); | |
933 | } | |
8a525303 | 934 | # endif |
09fb7599 | 935 | } |
09fb7599 DH |
936 | } else { |
937 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
938 | } | |
09fb7599 DH |
939 | } else if (SCM_BIGP (n1)) { |
940 | if (SCM_INUMP (n2)) { | |
941 | SCM_SWAP (n1, n2); | |
9a00c9fc | 942 | nn1 = SCM_INUM (n1); |
09fb7599 DH |
943 | goto intbig; |
944 | } else if (SCM_BIGP (n2)) { | |
945 | if (SCM_NUMDIGS (n1) > SCM_NUMDIGS (n2)) { | |
946 | SCM_SWAP (n1, n2); | |
947 | }; | |
948 | if ((SCM_BIGSIGN (n1)) && SCM_BIGSIGN (n2)) { | |
949 | return scm_big_ior (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), | |
950 | SCM_BIGSIGNFLAG, n2); | |
951 | } else { | |
952 | return scm_big_and (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), | |
953 | SCM_BIGSIGN (n1), n2, 0); | |
954 | } | |
955 | } else { | |
956 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
957 | } | |
09fb7599 DH |
958 | } else { |
959 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
960 | } | |
0f2d19dd | 961 | } |
1bbd0b84 | 962 | #undef FUNC_NAME |
0f2d19dd | 963 | |
09fb7599 | 964 | |
c3ee7520 | 965 | SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr, |
1bbd0b84 | 966 | (SCM n1, SCM n2), |
3c3db128 GH |
967 | "Return the bitwise OR of the integer arguments.\n\n" |
968 | "@lisp\n" | |
969 | "(logior) @result{} 0\n" | |
970 | "(logior 7) @result{} 7\n" | |
971 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1e6808ea | 972 | "@end lisp") |
1bbd0b84 | 973 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 974 | { |
9a00c9fc DH |
975 | long int nn1; |
976 | ||
09fb7599 DH |
977 | if (SCM_UNBNDP (n2)) { |
978 | if (SCM_UNBNDP (n1)) { | |
979 | return SCM_INUM0; | |
09fb7599 | 980 | } else if (SCM_NUMBERP (n1)) { |
d28da049 | 981 | return n1; |
09fb7599 DH |
982 | } else { |
983 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 984 | } |
8a525303 | 985 | } |
09fb7599 DH |
986 | |
987 | if (SCM_INUMP (n1)) { | |
9a00c9fc | 988 | nn1 = SCM_INUM (n1); |
09fb7599 DH |
989 | if (SCM_INUMP (n2)) { |
990 | long nn2 = SCM_INUM (n2); | |
991 | return SCM_MAKINUM (nn1 | nn2); | |
09fb7599 DH |
992 | } else if (SCM_BIGP (n2)) { |
993 | intbig: | |
994 | { | |
8a525303 | 995 | # ifndef SCM_DIGSTOOBIG |
09fb7599 DH |
996 | long z = scm_pseudolong (nn1); |
997 | if ((!(nn1 < 0)) && !SCM_BIGSIGN (n2)) { | |
998 | return scm_big_ior ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
999 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); | |
1000 | } else { | |
1001 | return scm_big_and ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
1002 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, SCM_BIGSIGNFLAG); | |
1003 | } | |
8a525303 | 1004 | # else |
5fa20751 | 1005 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
09fb7599 DH |
1006 | scm_longdigs (nn1, zdigs); |
1007 | if ((!(nn1 < 0)) && !SCM_BIGSIGN (n2)) { | |
1008 | return scm_big_ior (zdigs, SCM_DIGSPERLONG, | |
1009 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); | |
1010 | } else { | |
1011 | return scm_big_and (zdigs, SCM_DIGSPERLONG, | |
1012 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, SCM_BIGSIGNFLAG); | |
1013 | } | |
8a525303 | 1014 | # endif |
09fb7599 | 1015 | } |
09fb7599 DH |
1016 | } else { |
1017 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1018 | } | |
09fb7599 DH |
1019 | } else if (SCM_BIGP (n1)) { |
1020 | if (SCM_INUMP (n2)) { | |
1021 | SCM_SWAP (n1, n2); | |
9a00c9fc | 1022 | nn1 = SCM_INUM (n1); |
09fb7599 DH |
1023 | goto intbig; |
1024 | } else if (SCM_BIGP (n2)) { | |
1025 | if (SCM_NUMDIGS (n1) > SCM_NUMDIGS (n2)) { | |
1026 | SCM_SWAP (n1, n2); | |
1027 | }; | |
1028 | if ((!SCM_BIGSIGN (n1)) && !SCM_BIGSIGN (n2)) { | |
1029 | return scm_big_ior (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), | |
1030 | SCM_BIGSIGN (n1), n2); | |
1031 | } else { | |
1032 | return scm_big_and (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), | |
1033 | SCM_BIGSIGN (n1), n2, SCM_BIGSIGNFLAG); | |
1034 | } | |
1035 | } else { | |
1036 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1037 | } | |
09fb7599 DH |
1038 | } else { |
1039 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1040 | } | |
0f2d19dd | 1041 | } |
1bbd0b84 | 1042 | #undef FUNC_NAME |
0f2d19dd | 1043 | |
09fb7599 | 1044 | |
c3ee7520 | 1045 | SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr, |
1bbd0b84 | 1046 | (SCM n1, SCM n2), |
3c3db128 GH |
1047 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1048 | "set in the result if it is set in an odd number of arguments.\n" | |
1049 | "@lisp\n" | |
1050 | "(logxor) @result{} 0\n" | |
1051 | "(logxor 7) @result{} 7\n" | |
1052 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1053 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1054 | "@end lisp") |
1bbd0b84 | 1055 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1056 | { |
9a00c9fc DH |
1057 | long int nn1; |
1058 | ||
09fb7599 DH |
1059 | if (SCM_UNBNDP (n2)) { |
1060 | if (SCM_UNBNDP (n1)) { | |
1061 | return SCM_INUM0; | |
09fb7599 DH |
1062 | } else if (SCM_NUMBERP (n1)) { |
1063 | return n1; | |
1064 | } else { | |
1065 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
d28da049 | 1066 | } |
8a525303 | 1067 | } |
09fb7599 DH |
1068 | |
1069 | if (SCM_INUMP (n1)) { | |
9a00c9fc | 1070 | nn1 = SCM_INUM (n1); |
09fb7599 DH |
1071 | if (SCM_INUMP (n2)) { |
1072 | long nn2 = SCM_INUM (n2); | |
1073 | return SCM_MAKINUM (nn1 ^ nn2); | |
09fb7599 DH |
1074 | } else if (SCM_BIGP (n2)) { |
1075 | intbig: | |
8a525303 GB |
1076 | { |
1077 | # ifndef SCM_DIGSTOOBIG | |
09fb7599 DH |
1078 | long z = scm_pseudolong (nn1); |
1079 | return scm_big_xor ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
1080 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); | |
8a525303 | 1081 | # else |
09fb7599 DH |
1082 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
1083 | scm_longdigs (nn1, zdigs); | |
1084 | return scm_big_xor (zdigs, SCM_DIGSPERLONG, | |
1085 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); | |
8a525303 GB |
1086 | # endif |
1087 | } | |
09fb7599 DH |
1088 | } else { |
1089 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1090 | } | |
09fb7599 DH |
1091 | } else if (SCM_BIGP (n1)) { |
1092 | if (SCM_INUMP (n2)) { | |
1093 | SCM_SWAP (n1, n2); | |
9a00c9fc | 1094 | nn1 = SCM_INUM (n1); |
09fb7599 DH |
1095 | goto intbig; |
1096 | } else if (SCM_BIGP (n2)) { | |
1097 | if (SCM_NUMDIGS(n1) > SCM_NUMDIGS(n2)) { | |
1098 | SCM_SWAP (n1, n2); | |
1099 | } | |
1100 | return scm_big_xor (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), | |
1101 | SCM_BIGSIGN (n1), n2); | |
1102 | } else { | |
1103 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1104 | } | |
09fb7599 DH |
1105 | } else { |
1106 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1107 | } | |
0f2d19dd | 1108 | } |
1bbd0b84 | 1109 | #undef FUNC_NAME |
0f2d19dd | 1110 | |
09fb7599 | 1111 | |
a1ec6916 | 1112 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea MG |
1113 | (SCM j, SCM k), |
1114 | "@lisp\n" | |
b380b885 MD |
1115 | "(logtest j k) @equiv{} (not (zero? (logand j k)))\n\n" |
1116 | "(logtest #b0100 #b1011) @result{} #f\n" | |
1117 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1118 | "@end lisp") |
1bbd0b84 | 1119 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1120 | { |
1e6808ea | 1121 | long int nj; |
9a00c9fc | 1122 | |
1e6808ea MG |
1123 | if (SCM_INUMP (j)) { |
1124 | nj = SCM_INUM (j); | |
1125 | if (SCM_INUMP (k)) { | |
1126 | long nk = SCM_INUM (k); | |
1127 | return SCM_BOOL (nj & nk); | |
1128 | } else if (SCM_BIGP (k)) { | |
f8de44c1 DH |
1129 | intbig: |
1130 | { | |
8a525303 | 1131 | # ifndef SCM_DIGSTOOBIG |
1e6808ea | 1132 | long z = scm_pseudolong (nj); |
f8de44c1 | 1133 | return scm_big_test ((SCM_BIGDIG *)&z, SCM_DIGSPERLONG, |
1e6808ea | 1134 | (nj < 0) ? SCM_BIGSIGNFLAG : 0, k); |
8a525303 | 1135 | # else |
f8de44c1 | 1136 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
1e6808ea | 1137 | scm_longdigs (nj, zdigs); |
f8de44c1 | 1138 | return scm_big_test (zdigs, SCM_DIGSPERLONG, |
1e6808ea | 1139 | (nj < 0) ? SCM_BIGSIGNFLAG : 0, k); |
8a525303 | 1140 | # endif |
f8de44c1 | 1141 | } |
f8de44c1 | 1142 | } else { |
1e6808ea | 1143 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); |
f8de44c1 | 1144 | } |
1e6808ea MG |
1145 | } else if (SCM_BIGP (j)) { |
1146 | if (SCM_INUMP (k)) { | |
1147 | SCM_SWAP (j, k); | |
1148 | nj = SCM_INUM (j); | |
f8de44c1 | 1149 | goto intbig; |
1e6808ea MG |
1150 | } else if (SCM_BIGP (k)) { |
1151 | if (SCM_NUMDIGS (j) > SCM_NUMDIGS (k)) { | |
1152 | SCM_SWAP (j, k); | |
f8de44c1 | 1153 | } |
1e6808ea MG |
1154 | return scm_big_test (SCM_BDIGITS (j), SCM_NUMDIGS (j), |
1155 | SCM_BIGSIGN (j), k); | |
f8de44c1 | 1156 | } else { |
1e6808ea | 1157 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); |
f8de44c1 | 1158 | } |
f8de44c1 | 1159 | } else { |
1e6808ea | 1160 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); |
f8de44c1 | 1161 | } |
0f2d19dd | 1162 | } |
1bbd0b84 | 1163 | #undef FUNC_NAME |
0f2d19dd | 1164 | |
c1bfcf60 | 1165 | |
a1ec6916 | 1166 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1167 | (SCM index, SCM j), |
1e6808ea | 1168 | "@lisp\n" |
b380b885 MD |
1169 | "(logbit? index j) @equiv{} (logtest (integer-expt 2 index) j)\n\n" |
1170 | "(logbit? 0 #b1101) @result{} #t\n" | |
1171 | "(logbit? 1 #b1101) @result{} #f\n" | |
1172 | "(logbit? 2 #b1101) @result{} #t\n" | |
1173 | "(logbit? 3 #b1101) @result{} #t\n" | |
1174 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1175 | "@end lisp") |
1bbd0b84 | 1176 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1177 | { |
78166ad5 DH |
1178 | unsigned long int iindex; |
1179 | ||
1180 | SCM_VALIDATE_INUM_MIN (SCM_ARG1, index, 0); | |
1181 | iindex = (unsigned long int) SCM_INUM (index); | |
1182 | ||
1183 | if (SCM_INUMP (j)) { | |
1184 | return SCM_BOOL ((1L << iindex) & SCM_INUM (j)); | |
1185 | } else if (SCM_BIGP (j)) { | |
1186 | if (SCM_NUMDIGS (j) * SCM_BITSPERDIG < iindex) { | |
1187 | return SCM_BOOL_F; | |
1188 | } else if (SCM_BIGSIGN (j)) { | |
8a525303 | 1189 | long num = -1; |
1be6b49c | 1190 | size_t i = 0; |
78166ad5 | 1191 | SCM_BIGDIG * x = SCM_BDIGITS (j); |
1be6b49c | 1192 | size_t nx = iindex / SCM_BITSPERDIG; |
78166ad5 | 1193 | while (1) { |
8a525303 | 1194 | num += x[i]; |
78166ad5 DH |
1195 | if (nx == i++) { |
1196 | return SCM_BOOL (((1L << (iindex % SCM_BITSPERDIG)) & num) == 0); | |
1197 | } else if (num < 0) { | |
1198 | num = -1; | |
1199 | } else { | |
1200 | num = 0; | |
1201 | } | |
8a525303 | 1202 | } |
78166ad5 DH |
1203 | } else { |
1204 | return SCM_BOOL (SCM_BDIGITS (j) [iindex / SCM_BITSPERDIG] | |
1205 | & (1L << (iindex % SCM_BITSPERDIG))); | |
8a525303 | 1206 | } |
78166ad5 DH |
1207 | } else { |
1208 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); | |
8a525303 | 1209 | } |
0f2d19dd | 1210 | } |
1bbd0b84 | 1211 | #undef FUNC_NAME |
0f2d19dd | 1212 | |
78166ad5 | 1213 | |
a1ec6916 | 1214 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1215 | (SCM n), |
1e6808ea MG |
1216 | "Return the integer which is the 2s-complement of the integer\n" |
1217 | "argument.\n" | |
1218 | "\n" | |
b380b885 MD |
1219 | "@lisp\n" |
1220 | "(number->string (lognot #b10000000) 2)\n" | |
1221 | " @result{} \"-10000001\"\n" | |
1222 | "(number->string (lognot #b0) 2)\n" | |
1223 | " @result{} \"-1\"\n" | |
1e6808ea | 1224 | "@end lisp") |
1bbd0b84 | 1225 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1226 | { |
f872b822 | 1227 | return scm_difference (SCM_MAKINUM (-1L), n); |
0f2d19dd | 1228 | } |
1bbd0b84 | 1229 | #undef FUNC_NAME |
0f2d19dd | 1230 | |
a1ec6916 | 1231 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1232 | (SCM n, SCM k), |
1e6808ea MG |
1233 | "Return @var{n} raised to the non-negative integer exponent\n" |
1234 | "@var{k}.\n" | |
1235 | "\n" | |
b380b885 MD |
1236 | "@lisp\n" |
1237 | "(integer-expt 2 5)\n" | |
1238 | " @result{} 32\n" | |
1239 | "(integer-expt -3 3)\n" | |
1240 | " @result{} -27\n" | |
1241 | "@end lisp") | |
1bbd0b84 | 1242 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1243 | { |
f872b822 | 1244 | SCM acc = SCM_MAKINUM (1L); |
1bbd0b84 | 1245 | int i2; |
0f2d19dd | 1246 | #ifdef SCM_BIGDIG |
d57ed702 | 1247 | /* 0^0 == 1 according to R5RS */ |
4260a7fc | 1248 | if (SCM_EQ_P (n, SCM_INUM0) || SCM_EQ_P (n, acc)) |
7b3381f4 | 1249 | return SCM_FALSEP (scm_zero_p(k)) ? n : acc; |
4260a7fc DH |
1250 | else if (SCM_EQ_P (n, SCM_MAKINUM (-1L))) |
1251 | return SCM_FALSEP (scm_even_p (k)) ? n : acc; | |
0f2d19dd | 1252 | #endif |
2830fd91 MD |
1253 | if (SCM_REALP (k)) |
1254 | { | |
1255 | double r = SCM_REAL_VALUE (k); | |
1256 | i2 = r; | |
1257 | if (i2 != r) | |
1258 | SCM_WRONG_TYPE_ARG (2, k); | |
1259 | } | |
1260 | else | |
34d19ef6 | 1261 | SCM_VALIDATE_ULONG_COPY (2, k, i2); |
1bbd0b84 | 1262 | if (i2 < 0) |
f872b822 | 1263 | { |
1bbd0b84 | 1264 | i2 = -i2; |
2cd04b42 | 1265 | n = scm_divide (n, SCM_UNDEFINED); |
f872b822 MD |
1266 | } |
1267 | while (1) | |
1268 | { | |
1bbd0b84 | 1269 | if (0 == i2) |
f872b822 | 1270 | return acc; |
1bbd0b84 | 1271 | if (1 == i2) |
2cd04b42 | 1272 | return scm_product (acc, n); |
1bbd0b84 | 1273 | if (i2 & 1) |
2cd04b42 GB |
1274 | acc = scm_product (acc, n); |
1275 | n = scm_product (n, n); | |
1bbd0b84 | 1276 | i2 >>= 1; |
f872b822 | 1277 | } |
0f2d19dd | 1278 | } |
1bbd0b84 | 1279 | #undef FUNC_NAME |
0f2d19dd | 1280 | |
a1ec6916 | 1281 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1282 | (SCM n, SCM cnt), |
1e6808ea MG |
1283 | "The function ash performs an arithmetic shift left by @var{cnt}\n" |
1284 | "bits (or shift right, if @var{cnt} is negative). 'Arithmetic'\n" | |
1285 | "means, that the function does not guarantee to keep the bit\n" | |
1286 | "structure of @var{n}, but rather guarantees that the result\n" | |
1287 | "will always be rounded towards minus infinity. Therefore, the\n" | |
1288 | "results of ash and a corresponding bitwise shift will differ if\n" | |
1289 | "@var{n} is negative.\n" | |
1290 | "\n" | |
3ab9f56e | 1291 | "Formally, the function returns an integer equivalent to\n" |
1e6808ea MG |
1292 | "@code{(inexact->exact (floor (* @var{n} (expt 2 @var{cnt}))))}.\n" |
1293 | "\n" | |
b380b885 | 1294 | "@lisp\n" |
1e6808ea MG |
1295 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1296 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
a3c8b9fc | 1297 | "@end lisp") |
1bbd0b84 | 1298 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1299 | { |
3ab9f56e DH |
1300 | long bits_to_shift; |
1301 | ||
1302 | #ifndef SCM_BIGDIG | |
1303 | SCM_VALIDATE_INUM (1, n) | |
1304 | #endif | |
1305 | SCM_VALIDATE_INUM (2, cnt); | |
1306 | ||
1307 | bits_to_shift = SCM_INUM (cnt); | |
0f2d19dd | 1308 | #ifdef SCM_BIGDIG |
3ab9f56e DH |
1309 | if (bits_to_shift < 0) { |
1310 | /* Shift right by abs(cnt) bits. This is realized as a division by | |
1311 | div:=2^abs(cnt). However, to guarantee the floor rounding, negative | |
1312 | values require some special treatment. | |
1313 | */ | |
1314 | SCM div = scm_integer_expt (SCM_MAKINUM (2), SCM_MAKINUM (-bits_to_shift)); | |
1315 | if (SCM_FALSEP (scm_negative_p (n))) | |
1316 | return scm_quotient (n, div); | |
1317 | else | |
1318 | return scm_sum (SCM_MAKINUM (-1L), | |
1319 | scm_quotient (scm_sum (SCM_MAKINUM (1L), n), div)); | |
1320 | } else | |
1321 | /* Shift left is done by multiplication with 2^CNT */ | |
f872b822 | 1322 | return scm_product (n, scm_integer_expt (SCM_MAKINUM (2), cnt)); |
0f2d19dd | 1323 | #else |
3ab9f56e DH |
1324 | if (bits_to_shift < 0) |
1325 | /* Signed right shift (SCM_SRS does it right) by abs(cnt) bits. */ | |
1326 | return SCM_MAKINUM (SCM_SRS (SCM_INUM (n), -bits_to_shift)); | |
1327 | else { | |
1328 | /* Shift left, but make sure not to leave the range of inums */ | |
1329 | SCM res = SCM_MAKINUM (SCM_INUM (n) << cnt); | |
1330 | if (SCM_INUM (res) >> cnt != SCM_INUM (n)) | |
1331 | scm_num_overflow (FUNC_NAME); | |
1332 | return res; | |
1333 | } | |
0f2d19dd JB |
1334 | #endif |
1335 | } | |
1bbd0b84 | 1336 | #undef FUNC_NAME |
0f2d19dd | 1337 | |
3c9f20f8 | 1338 | |
a1ec6916 | 1339 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 1340 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
1341 | "Return the integer composed of the @var{start} (inclusive)\n" |
1342 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
1343 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
1344 | "\n" | |
b380b885 MD |
1345 | "@lisp\n" |
1346 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
1347 | " @result{} \"1010\"\n" | |
1348 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
1349 | " @result{} \"10110\"\n" | |
1350 | "@end lisp") | |
1bbd0b84 | 1351 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 1352 | { |
ac0c002c | 1353 | unsigned long int istart, iend; |
34d19ef6 | 1354 | SCM_VALIDATE_INUM_MIN_COPY (2, start,0, istart); |
c1bfcf60 GB |
1355 | SCM_VALIDATE_INUM_MIN_COPY (3, end, 0, iend); |
1356 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); | |
78166ad5 DH |
1357 | |
1358 | if (SCM_INUMP (n)) { | |
ac0c002c DH |
1359 | long int in = SCM_INUM (n); |
1360 | unsigned long int bits = iend - istart; | |
1361 | ||
1be6b49c | 1362 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
ac0c002c DH |
1363 | { |
1364 | /* Since we emulate two's complement encoded numbers, this special | |
1365 | * case requires us to produce a result that has more bits than can be | |
1366 | * stored in a fixnum. Thus, we fall back to the more general | |
1367 | * algorithm that is used for bignums. | |
1368 | */ | |
1369 | goto generalcase; | |
1370 | } | |
1371 | ||
1be6b49c | 1372 | if (istart < SCM_I_FIXNUM_BIT) |
ac0c002c DH |
1373 | { |
1374 | in = in >> istart; | |
1be6b49c | 1375 | if (bits < SCM_I_FIXNUM_BIT) |
ac0c002c DH |
1376 | return SCM_MAKINUM (in & ((1L << bits) - 1)); |
1377 | else /* we know: in >= 0 */ | |
1378 | return SCM_MAKINUM (in); | |
1379 | } | |
1380 | else if (in < 0) | |
1381 | { | |
1382 | return SCM_MAKINUM (-1L & ((1L << bits) - 1)); | |
1383 | } | |
1384 | else | |
1385 | { | |
1386 | return SCM_MAKINUM (0); | |
1387 | } | |
78166ad5 | 1388 | } else if (SCM_BIGP (n)) { |
ac0c002c DH |
1389 | generalcase: |
1390 | { | |
1391 | SCM num1 = SCM_MAKINUM (1L); | |
1392 | SCM num2 = SCM_MAKINUM (2L); | |
1393 | SCM bits = SCM_MAKINUM (iend - istart); | |
1394 | SCM mask = scm_difference (scm_integer_expt (num2, bits), num1); | |
1395 | return scm_logand (mask, scm_ash (n, SCM_MAKINUM (-istart))); | |
1396 | } | |
78166ad5 DH |
1397 | } else { |
1398 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1399 | } | |
0f2d19dd | 1400 | } |
1bbd0b84 | 1401 | #undef FUNC_NAME |
0f2d19dd | 1402 | |
3c9f20f8 | 1403 | |
e4755e5c JB |
1404 | static const char scm_logtab[] = { |
1405 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
1406 | }; | |
1cc91f1b | 1407 | |
a1ec6916 | 1408 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 1409 | (SCM n), |
1e6808ea MG |
1410 | "Return the number of bits in integer @var{n}. If integer is\n" |
1411 | "positive, the 1-bits in its binary representation are counted.\n" | |
1412 | "If negative, the 0-bits in its two's-complement binary\n" | |
1413 | "representation are counted. If 0, 0 is returned.\n" | |
1414 | "\n" | |
b380b885 MD |
1415 | "@lisp\n" |
1416 | "(logcount #b10101010)\n" | |
1417 | " @result{} 4\n" | |
1418 | "(logcount 0)\n" | |
1419 | " @result{} 0\n" | |
1420 | "(logcount -2)\n" | |
1421 | " @result{} 1\n" | |
1422 | "@end lisp") | |
1bbd0b84 | 1423 | #define FUNC_NAME s_scm_logcount |
0f2d19dd | 1424 | { |
3c9f20f8 DH |
1425 | if (SCM_INUMP (n)) { |
1426 | unsigned long int c = 0; | |
1427 | long int nn = SCM_INUM (n); | |
1428 | if (nn < 0) { | |
1429 | nn = -1 - nn; | |
1430 | }; | |
1431 | while (nn) { | |
1432 | c += scm_logtab[15 & nn]; | |
1433 | nn >>= 4; | |
1434 | }; | |
1435 | return SCM_MAKINUM (c); | |
1436 | } else if (SCM_BIGP (n)) { | |
1437 | if (SCM_BIGSIGN (n)) { | |
1438 | return scm_logcount (scm_difference (SCM_MAKINUM (-1L), n)); | |
1439 | } else { | |
1440 | unsigned long int c = 0; | |
1be6b49c | 1441 | size_t i = SCM_NUMDIGS (n); |
3c9f20f8 DH |
1442 | SCM_BIGDIG * ds = SCM_BDIGITS (n); |
1443 | while (i--) { | |
1444 | SCM_BIGDIG d; | |
1445 | for (d = ds[i]; d; d >>= 4) { | |
f872b822 | 1446 | c += scm_logtab[15 & d]; |
3c9f20f8 DH |
1447 | } |
1448 | } | |
f872b822 MD |
1449 | return SCM_MAKINUM (c); |
1450 | } | |
3c9f20f8 DH |
1451 | } else { |
1452 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1453 | } | |
0f2d19dd | 1454 | } |
1bbd0b84 GB |
1455 | #undef FUNC_NAME |
1456 | ||
0f2d19dd | 1457 | |
e4755e5c JB |
1458 | static const char scm_ilentab[] = { |
1459 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
1460 | }; | |
1cc91f1b | 1461 | |
a1ec6916 | 1462 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
1bbd0b84 | 1463 | (SCM n), |
bb2c02f2 | 1464 | "Return the number of bits necessary to represent @var{n}.\n" |
1e6808ea | 1465 | "\n" |
b380b885 MD |
1466 | "@lisp\n" |
1467 | "(integer-length #b10101010)\n" | |
1468 | " @result{} 8\n" | |
1469 | "(integer-length 0)\n" | |
1470 | " @result{} 0\n" | |
1471 | "(integer-length #b1111)\n" | |
1472 | " @result{} 4\n" | |
1473 | "@end lisp") | |
1bbd0b84 | 1474 | #define FUNC_NAME s_scm_integer_length |
0f2d19dd | 1475 | { |
3c9f20f8 DH |
1476 | if (SCM_INUMP (n)) { |
1477 | unsigned long int c = 0; | |
1478 | unsigned int l = 4; | |
1479 | long int nn = SCM_INUM (n); | |
1480 | if (nn < 0) { | |
1481 | nn = -1 - nn; | |
1482 | }; | |
1483 | while (nn) { | |
f872b822 | 1484 | c += 4; |
3c9f20f8 DH |
1485 | l = scm_ilentab [15 & nn]; |
1486 | nn >>= 4; | |
1487 | }; | |
1488 | return SCM_MAKINUM (c - 4 + l); | |
1489 | } else if (SCM_BIGP (n)) { | |
1490 | if (SCM_BIGSIGN (n)) { | |
1491 | return scm_integer_length (scm_difference (SCM_MAKINUM (-1L), n)); | |
1492 | } else { | |
1493 | unsigned long int digs = SCM_NUMDIGS (n) - 1; | |
1494 | unsigned long int c = digs * SCM_BITSPERDIG; | |
1495 | unsigned int l = 4; | |
1496 | SCM_BIGDIG * ds = SCM_BDIGITS (n); | |
1497 | SCM_BIGDIG d = ds [digs]; | |
1498 | while (d) { | |
1499 | c += 4; | |
1500 | l = scm_ilentab [15 & d]; | |
1501 | d >>= 4; | |
1502 | }; | |
1503 | return SCM_MAKINUM (c - 4 + l); | |
f872b822 | 1504 | } |
3c9f20f8 DH |
1505 | } else { |
1506 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1507 | } | |
0f2d19dd | 1508 | } |
1bbd0b84 | 1509 | #undef FUNC_NAME |
0f2d19dd JB |
1510 | |
1511 | ||
1512 | #ifdef SCM_BIGDIG | |
e4755e5c | 1513 | static const char s_bignum[] = "bignum"; |
1cc91f1b | 1514 | |
0f2d19dd | 1515 | SCM |
1be6b49c | 1516 | scm_i_mkbig (size_t nlen, int sign) |
0f2d19dd | 1517 | { |
c209c88e | 1518 | SCM v; |
5843e5c9 DH |
1519 | SCM_BIGDIG *base; |
1520 | ||
1521 | if (((nlen << SCM_BIGSIZEFIELD) >> SCM_BIGSIZEFIELD) != nlen) | |
2500356c | 1522 | scm_memory_error (s_bignum); |
5843e5c9 | 1523 | |
4c9419ac | 1524 | base = scm_gc_malloc (nlen * sizeof (SCM_BIGDIG), s_bignum); |
5843e5c9 | 1525 | |
228a24ef | 1526 | v = scm_cell (SCM_MAKE_BIGNUM_TAG (nlen, sign), (scm_t_bits) base); |
0f2d19dd JB |
1527 | return v; |
1528 | } | |
1529 | ||
0f2d19dd | 1530 | SCM |
1be6b49c | 1531 | scm_i_big2inum (SCM b, size_t l) |
0f2d19dd JB |
1532 | { |
1533 | unsigned long num = 0; | |
f872b822 MD |
1534 | SCM_BIGDIG *tmp = SCM_BDIGITS (b); |
1535 | while (l--) | |
1536 | num = SCM_BIGUP (num) + tmp[l]; | |
f3ae5d60 | 1537 | if (!SCM_BIGSIGN (b)) |
f872b822 MD |
1538 | { |
1539 | if (SCM_POSFIXABLE (num)) | |
1540 | return SCM_MAKINUM (num); | |
1541 | } | |
894a712b | 1542 | else if (num <= -SCM_MOST_NEGATIVE_FIXNUM) |
f872b822 | 1543 | return SCM_MAKINUM (-num); |
0f2d19dd JB |
1544 | return b; |
1545 | } | |
1546 | ||
1be6b49c | 1547 | static const char s_adjbig[] = "scm_i_adjbig"; |
1cc91f1b | 1548 | |
0f2d19dd | 1549 | SCM |
1be6b49c | 1550 | scm_i_adjbig (SCM b, size_t nlen) |
0f2d19dd | 1551 | { |
1be6b49c | 1552 | size_t nsiz = nlen; |
f3ae5d60 | 1553 | if (((nsiz << SCM_BIGSIZEFIELD) >> SCM_BIGSIZEFIELD) != nlen) |
2500356c | 1554 | scm_memory_error (s_adjbig); |
2bf746cc | 1555 | |
0f2d19dd | 1556 | SCM_DEFER_INTS; |
2bf746cc JB |
1557 | { |
1558 | SCM_BIGDIG *digits | |
1559 | = ((SCM_BIGDIG *) | |
4c9419ac MV |
1560 | scm_gc_realloc (SCM_BDIGITS (b), |
1561 | SCM_NUMDIGS (b) * sizeof (SCM_BIGDIG), | |
1562 | nsiz * sizeof (SCM_BIGDIG), s_bignum)); | |
2bf746cc | 1563 | |
6a0476fd | 1564 | SCM_SET_BIGNUM_BASE (b, digits); |
f3ae5d60 | 1565 | SCM_SETNUMDIGS (b, nsiz, SCM_BIGSIGN (b)); |
2bf746cc | 1566 | } |
0f2d19dd JB |
1567 | SCM_ALLOW_INTS; |
1568 | return b; | |
1569 | } | |
1570 | ||
0f2d19dd | 1571 | SCM |
1be6b49c | 1572 | scm_i_normbig (SCM b) |
0f2d19dd | 1573 | { |
f872b822 | 1574 | #ifndef _UNICOS |
1be6b49c | 1575 | size_t nlen = SCM_NUMDIGS (b); |
0f2d19dd | 1576 | #else |
f872b822 | 1577 | int nlen = SCM_NUMDIGS (b); /* unsigned nlen breaks on Cray when nlen => 0 */ |
0f2d19dd | 1578 | #endif |
f872b822 MD |
1579 | SCM_BIGDIG *zds = SCM_BDIGITS (b); |
1580 | while (nlen-- && !zds[nlen]); | |
1581 | nlen++; | |
1582 | if (nlen * SCM_BITSPERDIG / SCM_CHAR_BIT <= sizeof (SCM)) | |
1be6b49c | 1583 | if (SCM_INUMP (b = scm_i_big2inum (b, (size_t) nlen))) |
f872b822 MD |
1584 | return b; |
1585 | if (SCM_NUMDIGS (b) == nlen) | |
1586 | return b; | |
1be6b49c | 1587 | return scm_i_adjbig (b, (size_t) nlen); |
0f2d19dd JB |
1588 | } |
1589 | ||
0f2d19dd | 1590 | SCM |
1be6b49c | 1591 | scm_i_copybig (SCM b, int sign) |
0f2d19dd | 1592 | { |
1be6b49c ML |
1593 | size_t i = SCM_NUMDIGS (b); |
1594 | SCM ans = scm_i_mkbig (i, sign); | |
f872b822 MD |
1595 | SCM_BIGDIG *src = SCM_BDIGITS (b), *dst = SCM_BDIGITS (ans); |
1596 | while (i--) | |
1597 | dst[i] = src[i]; | |
0f2d19dd JB |
1598 | return ans; |
1599 | } | |
1600 | ||
0f2d19dd | 1601 | int |
1bbd0b84 | 1602 | scm_bigcomp (SCM x, SCM y) |
0f2d19dd | 1603 | { |
f872b822 MD |
1604 | int xsign = SCM_BIGSIGN (x); |
1605 | int ysign = SCM_BIGSIGN (y); | |
1be6b49c | 1606 | size_t xlen, ylen; |
2bf746cc JB |
1607 | |
1608 | /* Look at the signs, first. */ | |
f872b822 MD |
1609 | if (ysign < xsign) |
1610 | return 1; | |
1611 | if (ysign > xsign) | |
1612 | return -1; | |
2bf746cc JB |
1613 | |
1614 | /* They're the same sign, so see which one has more digits. Note | |
1615 | that, if they are negative, the longer number is the lesser. */ | |
f872b822 MD |
1616 | ylen = SCM_NUMDIGS (y); |
1617 | xlen = SCM_NUMDIGS (x); | |
2bf746cc JB |
1618 | if (ylen > xlen) |
1619 | return (xsign) ? -1 : 1; | |
f872b822 MD |
1620 | if (ylen < xlen) |
1621 | return (xsign) ? 1 : -1; | |
2bf746cc JB |
1622 | |
1623 | /* They have the same number of digits, so find the most significant | |
1624 | digit where they differ. */ | |
1625 | while (xlen) | |
1626 | { | |
1627 | --xlen; | |
1628 | if (SCM_BDIGITS (y)[xlen] != SCM_BDIGITS (x)[xlen]) | |
1629 | /* Make the discrimination based on the digit that differs. */ | |
f872b822 MD |
1630 | return ((SCM_BDIGITS (y)[xlen] > SCM_BDIGITS (x)[xlen]) |
1631 | ? (xsign ? -1 : 1) | |
1632 | : (xsign ? 1 : -1)); | |
2bf746cc JB |
1633 | } |
1634 | ||
1635 | /* The numbers are identical. */ | |
1636 | return 0; | |
0f2d19dd JB |
1637 | } |
1638 | ||
1639 | #ifndef SCM_DIGSTOOBIG | |
1640 | ||
1cc91f1b | 1641 | |
0f2d19dd | 1642 | long |
1bbd0b84 | 1643 | scm_pseudolong (long x) |
0f2d19dd | 1644 | { |
f872b822 MD |
1645 | union |
1646 | { | |
0f2d19dd JB |
1647 | long l; |
1648 | SCM_BIGDIG bd[SCM_DIGSPERLONG]; | |
f872b822 MD |
1649 | } |
1650 | p; | |
1be6b49c | 1651 | size_t i = 0; |
f872b822 MD |
1652 | if (x < 0) |
1653 | x = -x; | |
1654 | while (i < SCM_DIGSPERLONG) | |
1655 | { | |
1656 | p.bd[i++] = SCM_BIGLO (x); | |
1657 | x = SCM_BIGDN (x); | |
1658 | } | |
0f2d19dd JB |
1659 | /* p.bd[0] = SCM_BIGLO(x); p.bd[1] = SCM_BIGDN(x); */ |
1660 | return p.l; | |
1661 | } | |
1662 | ||
1663 | #else | |
1664 | ||
1cc91f1b | 1665 | |
0f2d19dd | 1666 | void |
1bbd0b84 | 1667 | scm_longdigs (long x, SCM_BIGDIG digs[]) |
0f2d19dd | 1668 | { |
1be6b49c | 1669 | size_t i = 0; |
f872b822 MD |
1670 | if (x < 0) |
1671 | x = -x; | |
1672 | while (i < SCM_DIGSPERLONG) | |
1673 | { | |
1674 | digs[i++] = SCM_BIGLO (x); | |
1675 | x = SCM_BIGDN (x); | |
1676 | } | |
0f2d19dd JB |
1677 | } |
1678 | #endif | |
1679 | ||
1680 | ||
1cc91f1b | 1681 | |
0f2d19dd | 1682 | SCM |
1be6b49c | 1683 | scm_addbig (SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy, int sgny) |
0f2d19dd JB |
1684 | { |
1685 | /* Assumes nx <= SCM_NUMDIGS(bigy) */ | |
f3ae5d60 | 1686 | /* Assumes xsgn and sgny scm_equal either 0 or SCM_BIGSIGNFLAG */ |
0f2d19dd | 1687 | long num = 0; |
1be6b49c ML |
1688 | size_t i = 0, ny = SCM_NUMDIGS (bigy); |
1689 | SCM z = scm_i_copybig (bigy, SCM_BIGSIGN (bigy) ^ sgny); | |
f872b822 MD |
1690 | SCM_BIGDIG *zds = SCM_BDIGITS (z); |
1691 | if (xsgn ^ SCM_BIGSIGN (z)) | |
1692 | { | |
1693 | do | |
1694 | { | |
1695 | num += (long) zds[i] - x[i]; | |
1696 | if (num < 0) | |
1697 | { | |
1698 | zds[i] = num + SCM_BIGRAD; | |
1699 | num = -1; | |
1700 | } | |
1701 | else | |
1702 | { | |
1703 | zds[i] = SCM_BIGLO (num); | |
1704 | num = 0; | |
1705 | } | |
1706 | } | |
1707 | while (++i < nx); | |
1708 | if (num && nx == ny) | |
1709 | { | |
1710 | num = 1; | |
1711 | i = 0; | |
4260a7fc | 1712 | SCM_SET_CELL_WORD_0 (z, SCM_CELL_WORD_0 (z) ^ SCM_BIGSIGNFLAG); |
f872b822 MD |
1713 | do |
1714 | { | |
1715 | num += (SCM_BIGRAD - 1) - zds[i]; | |
1716 | zds[i++] = SCM_BIGLO (num); | |
1717 | num = SCM_BIGDN (num); | |
1718 | } | |
1719 | while (i < ny); | |
1720 | } | |
1721 | else | |
1722 | while (i < ny) | |
1723 | { | |
1724 | num += zds[i]; | |
1725 | if (num < 0) | |
1726 | { | |
1727 | zds[i++] = num + SCM_BIGRAD; | |
1728 | num = -1; | |
1729 | } | |
1730 | else | |
1731 | { | |
1732 | zds[i++] = SCM_BIGLO (num); | |
1733 | num = 0; | |
1734 | } | |
1735 | } | |
1736 | } | |
1737 | else | |
1738 | { | |
1739 | do | |
1740 | { | |
1741 | num += (long) zds[i] + x[i]; | |
1742 | zds[i++] = SCM_BIGLO (num); | |
1743 | num = SCM_BIGDN (num); | |
1744 | } | |
1745 | while (i < nx); | |
1746 | if (!num) | |
1747 | return z; | |
1748 | while (i < ny) | |
1749 | { | |
1750 | num += zds[i]; | |
1751 | zds[i++] = SCM_BIGLO (num); | |
1752 | num = SCM_BIGDN (num); | |
1753 | if (!num) | |
1754 | return z; | |
1755 | } | |
1756 | if (num) | |
1757 | { | |
1be6b49c | 1758 | z = scm_i_adjbig (z, ny + 1); |
f872b822 MD |
1759 | SCM_BDIGITS (z)[ny] = num; |
1760 | return z; | |
1761 | } | |
1762 | } | |
1be6b49c | 1763 | return scm_i_normbig (z); |
0f2d19dd JB |
1764 | } |
1765 | ||
1cc91f1b | 1766 | |
0f2d19dd | 1767 | SCM |
1be6b49c | 1768 | scm_mulbig (SCM_BIGDIG *x, size_t nx, SCM_BIGDIG *y, size_t ny, int sgn) |
0f2d19dd | 1769 | { |
1be6b49c | 1770 | size_t i = 0, j = nx + ny; |
0f2d19dd | 1771 | unsigned long n = 0; |
1be6b49c | 1772 | SCM z = scm_i_mkbig (j, sgn); |
f872b822 MD |
1773 | SCM_BIGDIG *zds = SCM_BDIGITS (z); |
1774 | while (j--) | |
1775 | zds[j] = 0; | |
1776 | do | |
1777 | { | |
1778 | j = 0; | |
1779 | if (x[i]) | |
1780 | { | |
1781 | do | |
1782 | { | |
1783 | n += zds[i + j] + ((unsigned long) x[i] * y[j]); | |
1784 | zds[i + j++] = SCM_BIGLO (n); | |
1785 | n = SCM_BIGDN (n); | |
1786 | } | |
1787 | while (j < ny); | |
1788 | if (n) | |
1789 | { | |
1790 | zds[i + j] = n; | |
1791 | n = 0; | |
1792 | } | |
1793 | } | |
0f2d19dd | 1794 | } |
f872b822 | 1795 | while (++i < nx); |
1be6b49c | 1796 | return scm_i_normbig (z); |
0f2d19dd JB |
1797 | } |
1798 | ||
1cc91f1b | 1799 | |
0f2d19dd | 1800 | unsigned int |
1be6b49c | 1801 | scm_divbigdig (SCM_BIGDIG * ds, size_t h, SCM_BIGDIG div) |
0f2d19dd JB |
1802 | { |
1803 | register unsigned long t2 = 0; | |
f872b822 MD |
1804 | while (h--) |
1805 | { | |
1806 | t2 = SCM_BIGUP (t2) + ds[h]; | |
1807 | ds[h] = t2 / div; | |
1808 | t2 %= div; | |
1809 | } | |
0f2d19dd JB |
1810 | return t2; |
1811 | } | |
1812 | ||
1813 | ||
1cc91f1b | 1814 | |
f4c627b3 | 1815 | static SCM |
1bbd0b84 | 1816 | scm_divbigint (SCM x, long z, int sgn, int mode) |
0f2d19dd | 1817 | { |
f872b822 MD |
1818 | if (z < 0) |
1819 | z = -z; | |
1820 | if (z < SCM_BIGRAD) | |
1821 | { | |
1822 | register unsigned long t2 = 0; | |
1823 | register SCM_BIGDIG *ds = SCM_BDIGITS (x); | |
1be6b49c | 1824 | size_t nd = SCM_NUMDIGS (x); |
f872b822 MD |
1825 | while (nd--) |
1826 | t2 = (SCM_BIGUP (t2) + ds[nd]) % z; | |
1827 | if (mode && t2) | |
1828 | t2 = z - t2; | |
1829 | return SCM_MAKINUM (sgn ? -t2 : t2); | |
1830 | } | |
0f2d19dd JB |
1831 | { |
1832 | #ifndef SCM_DIGSTOOBIG | |
f872b822 MD |
1833 | unsigned long t2 = scm_pseudolong (z); |
1834 | return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
1835 | (SCM_BIGDIG *) & t2, SCM_DIGSPERLONG, | |
1836 | sgn, mode); | |
0f2d19dd JB |
1837 | #else |
1838 | SCM_BIGDIG t2[SCM_DIGSPERLONG]; | |
f872b822 MD |
1839 | scm_longdigs (z, t2); |
1840 | return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
1841 | t2, SCM_DIGSPERLONG, | |
1842 | sgn, mode); | |
0f2d19dd JB |
1843 | #endif |
1844 | } | |
1845 | } | |
1846 | ||
1cc91f1b | 1847 | |
f4c627b3 | 1848 | static SCM |
1be6b49c | 1849 | scm_divbigbig (SCM_BIGDIG *x, size_t nx, SCM_BIGDIG *y, size_t ny, int sgn, int modes) |
0f2d19dd JB |
1850 | { |
1851 | /* modes description | |
f872b822 MD |
1852 | 0 remainder |
1853 | 1 scm_modulo | |
1854 | 2 quotient | |
f4c627b3 | 1855 | 3 quotient but returns SCM_UNDEFINED if division is not exact. */ |
1be6b49c | 1856 | size_t i = 0, j = 0; |
0f2d19dd JB |
1857 | long num = 0; |
1858 | unsigned long t2 = 0; | |
1859 | SCM z, newy; | |
f872b822 | 1860 | SCM_BIGDIG d = 0, qhat, *zds, *yds; |
0f2d19dd JB |
1861 | /* algorithm requires nx >= ny */ |
1862 | if (nx < ny) | |
f872b822 MD |
1863 | switch (modes) |
1864 | { | |
1865 | case 0: /* remainder -- just return x */ | |
1be6b49c | 1866 | z = scm_i_mkbig (nx, sgn); |
f872b822 MD |
1867 | zds = SCM_BDIGITS (z); |
1868 | do | |
1869 | { | |
1870 | zds[i] = x[i]; | |
1871 | } | |
1872 | while (++i < nx); | |
1873 | return z; | |
1874 | case 1: /* scm_modulo -- return y-x */ | |
1be6b49c | 1875 | z = scm_i_mkbig (ny, sgn); |
f872b822 MD |
1876 | zds = SCM_BDIGITS (z); |
1877 | do | |
1878 | { | |
1879 | num += (long) y[i] - x[i]; | |
1880 | if (num < 0) | |
1881 | { | |
1882 | zds[i] = num + SCM_BIGRAD; | |
1883 | num = -1; | |
1884 | } | |
1885 | else | |
1886 | { | |
1887 | zds[i] = num; | |
1888 | num = 0; | |
1889 | } | |
1890 | } | |
1891 | while (++i < nx); | |
1892 | while (i < ny) | |
1893 | { | |
1894 | num += y[i]; | |
1895 | if (num < 0) | |
1896 | { | |
1897 | zds[i++] = num + SCM_BIGRAD; | |
1898 | num = -1; | |
1899 | } | |
1900 | else | |
1901 | { | |
1902 | zds[i++] = num; | |
1903 | num = 0; | |
1904 | } | |
1905 | } | |
1906 | goto doadj; | |
1907 | case 2: | |
1908 | return SCM_INUM0; /* quotient is zero */ | |
1909 | case 3: | |
f4c627b3 | 1910 | return SCM_UNDEFINED; /* the division is not exact */ |
0f2d19dd | 1911 | } |
f872b822 | 1912 | |
1be6b49c | 1913 | z = scm_i_mkbig (nx == ny ? nx + 2 : nx + 1, sgn); |
f872b822 MD |
1914 | zds = SCM_BDIGITS (z); |
1915 | if (nx == ny) | |
1916 | zds[nx + 1] = 0; | |
1917 | while (!y[ny - 1]) | |
1918 | ny--; /* in case y came in as a psuedolong */ | |
1919 | if (y[ny - 1] < (SCM_BIGRAD >> 1)) | |
1920 | { /* normalize operands */ | |
1921 | d = SCM_BIGRAD / (y[ny - 1] + 1); | |
1be6b49c | 1922 | newy = scm_i_mkbig (ny, 0); |
f872b822 MD |
1923 | yds = SCM_BDIGITS (newy); |
1924 | while (j < ny) | |
1925 | { | |
1926 | t2 += (unsigned long) y[j] * d; | |
1927 | yds[j++] = SCM_BIGLO (t2); | |
1928 | t2 = SCM_BIGDN (t2); | |
1929 | } | |
1930 | y = yds; | |
1931 | j = 0; | |
1932 | t2 = 0; | |
1933 | while (j < nx) | |
1934 | { | |
1935 | t2 += (unsigned long) x[j] * d; | |
1936 | zds[j++] = SCM_BIGLO (t2); | |
1937 | t2 = SCM_BIGDN (t2); | |
1938 | } | |
1939 | zds[j] = t2; | |
1940 | } | |
1941 | else | |
1942 | { | |
1943 | zds[j = nx] = 0; | |
1944 | while (j--) | |
1945 | zds[j] = x[j]; | |
1946 | } | |
1947 | j = nx == ny ? nx + 1 : nx; /* dividend needs more digits than divisor */ | |
1948 | do | |
1949 | { /* loop over digits of quotient */ | |
1950 | if (zds[j] == y[ny - 1]) | |
1951 | qhat = SCM_BIGRAD - 1; | |
1952 | else | |
1953 | qhat = (SCM_BIGUP (zds[j]) + zds[j - 1]) / y[ny - 1]; | |
1954 | if (!qhat) | |
1955 | continue; | |
1956 | i = 0; | |
1957 | num = 0; | |
1958 | t2 = 0; | |
1959 | do | |
1960 | { /* multiply and subtract */ | |
1961 | t2 += (unsigned long) y[i] * qhat; | |
1962 | num += zds[j - ny + i] - SCM_BIGLO (t2); | |
1963 | if (num < 0) | |
1964 | { | |
1965 | zds[j - ny + i] = num + SCM_BIGRAD; | |
1966 | num = -1; | |
1967 | } | |
1968 | else | |
1969 | { | |
1970 | zds[j - ny + i] = num; | |
1971 | num = 0; | |
1972 | } | |
1973 | t2 = SCM_BIGDN (t2); | |
1974 | } | |
1975 | while (++i < ny); | |
1976 | num += zds[j - ny + i] - t2; /* borrow from high digit; don't update */ | |
1977 | while (num) | |
1978 | { /* "add back" required */ | |
1979 | i = 0; | |
1980 | num = 0; | |
1981 | qhat--; | |
1982 | do | |
1983 | { | |
1984 | num += (long) zds[j - ny + i] + y[i]; | |
1985 | zds[j - ny + i] = SCM_BIGLO (num); | |
1986 | num = SCM_BIGDN (num); | |
1987 | } | |
1988 | while (++i < ny); | |
1989 | num--; | |
1990 | } | |
1991 | if (modes & 2) | |
1992 | zds[j] = qhat; | |
1993 | } | |
1994 | while (--j >= ny); | |
1995 | switch (modes) | |
1996 | { | |
1997 | case 3: /* check that remainder==0 */ | |
1998 | for (j = ny; j && !zds[j - 1]; --j); | |
1999 | if (j) | |
f4c627b3 | 2000 | return SCM_UNDEFINED; |
f872b822 MD |
2001 | case 2: /* move quotient down in z */ |
2002 | j = (nx == ny ? nx + 2 : nx + 1) - ny; | |
2003 | for (i = 0; i < j; i++) | |
2004 | zds[i] = zds[i + ny]; | |
2005 | ny = i; | |
2006 | break; | |
2007 | case 1: /* subtract for scm_modulo */ | |
2008 | i = 0; | |
2009 | num = 0; | |
2010 | j = 0; | |
2011 | do | |
2012 | { | |
2013 | num += y[i] - zds[i]; | |
2014 | j = j | zds[i]; | |
2015 | if (num < 0) | |
2016 | { | |
2017 | zds[i] = num + SCM_BIGRAD; | |
2018 | num = -1; | |
2019 | } | |
2020 | else | |
2021 | { | |
2022 | zds[i] = num; | |
2023 | num = 0; | |
2024 | } | |
2025 | } | |
2026 | while (++i < ny); | |
2027 | if (!j) | |
2028 | return SCM_INUM0; | |
2029 | case 0: /* just normalize remainder */ | |
2030 | if (d) | |
2031 | scm_divbigdig (zds, ny, d); | |
2032 | } | |
0f2d19dd | 2033 | doadj: |
f872b822 MD |
2034 | for (j = ny; j && !zds[j - 1]; --j); |
2035 | if (j * SCM_BITSPERDIG <= sizeof (SCM) * SCM_CHAR_BIT) | |
1be6b49c | 2036 | if (SCM_INUMP (z = scm_i_big2inum (z, j))) |
f872b822 | 2037 | return z; |
1be6b49c | 2038 | return scm_i_adjbig (z, j); |
0f2d19dd JB |
2039 | } |
2040 | #endif | |
f872b822 | 2041 | \f |
0f2d19dd JB |
2042 | |
2043 | ||
2044 | ||
0f2d19dd JB |
2045 | |
2046 | /*** NUMBERS -> STRINGS ***/ | |
0f2d19dd | 2047 | int scm_dblprec; |
e4755e5c | 2048 | static const double fx[] = |
f872b822 MD |
2049 | { 0.0, 5e-1, 5e-2, 5e-3, 5e-4, 5e-5, |
2050 | 5e-6, 5e-7, 5e-8, 5e-9, 5e-10, | |
2051 | 5e-11, 5e-12, 5e-13, 5e-14, 5e-15, | |
2052 | 5e-16, 5e-17, 5e-18, 5e-19, 5e-20}; | |
0f2d19dd JB |
2053 | |
2054 | ||
2055 | ||
1cc91f1b | 2056 | |
1be6b49c | 2057 | static size_t |
1bbd0b84 | 2058 | idbl2str (double f, char *a) |
0f2d19dd JB |
2059 | { |
2060 | int efmt, dpt, d, i, wp = scm_dblprec; | |
1be6b49c | 2061 | size_t ch = 0; |
0f2d19dd JB |
2062 | int exp = 0; |
2063 | ||
f872b822 | 2064 | if (f == 0.0) |
abb7e44d MV |
2065 | { |
2066 | #ifdef HAVE_COPYSIGN | |
2067 | double sgn = copysign (1.0, f); | |
2068 | ||
2069 | if (sgn < 0.0) | |
2070 | a[ch++] = '-'; | |
2071 | #endif | |
2072 | ||
2073 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ | |
2074 | } | |
7351e207 MV |
2075 | |
2076 | if (xisinf (f)) | |
2077 | { | |
2078 | if (f < 0) | |
2079 | strcpy (a, "-inf.0"); | |
2080 | else | |
2081 | strcpy (a, "+inf.0"); | |
2082 | return ch+6; | |
2083 | } | |
2084 | else if (xisnan (f)) | |
2085 | { | |
2086 | strcpy (a, "+nan.0"); | |
2087 | return ch+6; | |
2088 | } | |
2089 | ||
f872b822 MD |
2090 | if (f < 0.0) |
2091 | { | |
2092 | f = -f; | |
2093 | a[ch++] = '-'; | |
2094 | } | |
7351e207 | 2095 | |
f872b822 MD |
2096 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
2097 | make-uniform-vector, from causing infinite loops. */ | |
2098 | while (f < 1.0) | |
2099 | { | |
2100 | f *= 10.0; | |
2101 | if (exp-- < DBL_MIN_10_EXP) | |
7351e207 MV |
2102 | { |
2103 | a[ch++] = '#'; | |
2104 | a[ch++] = '.'; | |
2105 | a[ch++] = '#'; | |
2106 | return ch; | |
2107 | } | |
f872b822 MD |
2108 | } |
2109 | while (f > 10.0) | |
2110 | { | |
2111 | f *= 0.10; | |
2112 | if (exp++ > DBL_MAX_10_EXP) | |
7351e207 MV |
2113 | { |
2114 | a[ch++] = '#'; | |
2115 | a[ch++] = '.'; | |
2116 | a[ch++] = '#'; | |
2117 | return ch; | |
2118 | } | |
f872b822 MD |
2119 | } |
2120 | #else | |
2121 | while (f < 1.0) | |
2122 | { | |
2123 | f *= 10.0; | |
2124 | exp--; | |
2125 | } | |
2126 | while (f > 10.0) | |
2127 | { | |
2128 | f /= 10.0; | |
2129 | exp++; | |
2130 | } | |
2131 | #endif | |
2132 | if (f + fx[wp] >= 10.0) | |
2133 | { | |
2134 | f = 1.0; | |
2135 | exp++; | |
2136 | } | |
0f2d19dd | 2137 | zero: |
f872b822 MD |
2138 | #ifdef ENGNOT |
2139 | dpt = (exp + 9999) % 3; | |
0f2d19dd JB |
2140 | exp -= dpt++; |
2141 | efmt = 1; | |
f872b822 MD |
2142 | #else |
2143 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 2144 | if (!efmt) |
cda139a7 MD |
2145 | { |
2146 | if (exp < 0) | |
2147 | { | |
2148 | a[ch++] = '0'; | |
2149 | a[ch++] = '.'; | |
2150 | dpt = exp; | |
f872b822 MD |
2151 | while (++dpt) |
2152 | a[ch++] = '0'; | |
cda139a7 MD |
2153 | } |
2154 | else | |
f872b822 | 2155 | dpt = exp + 1; |
cda139a7 | 2156 | } |
0f2d19dd JB |
2157 | else |
2158 | dpt = 1; | |
f872b822 MD |
2159 | #endif |
2160 | ||
2161 | do | |
2162 | { | |
2163 | d = f; | |
2164 | f -= d; | |
2165 | a[ch++] = d + '0'; | |
2166 | if (f < fx[wp]) | |
2167 | break; | |
2168 | if (f + fx[wp] >= 1.0) | |
2169 | { | |
2170 | a[ch - 1]++; | |
2171 | break; | |
2172 | } | |
2173 | f *= 10.0; | |
2174 | if (!(--dpt)) | |
2175 | a[ch++] = '.'; | |
0f2d19dd | 2176 | } |
f872b822 | 2177 | while (wp--); |
0f2d19dd JB |
2178 | |
2179 | if (dpt > 0) | |
cda139a7 | 2180 | { |
f872b822 | 2181 | #ifndef ENGNOT |
cda139a7 MD |
2182 | if ((dpt > 4) && (exp > 6)) |
2183 | { | |
f872b822 | 2184 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 2185 | for (i = ch++; i > d; i--) |
f872b822 | 2186 | a[i] = a[i - 1]; |
cda139a7 MD |
2187 | a[d] = '.'; |
2188 | efmt = 1; | |
2189 | } | |
2190 | else | |
f872b822 | 2191 | #endif |
cda139a7 | 2192 | { |
f872b822 MD |
2193 | while (--dpt) |
2194 | a[ch++] = '0'; | |
cda139a7 MD |
2195 | a[ch++] = '.'; |
2196 | } | |
2197 | } | |
f872b822 MD |
2198 | if (a[ch - 1] == '.') |
2199 | a[ch++] = '0'; /* trailing zero */ | |
2200 | if (efmt && exp) | |
2201 | { | |
2202 | a[ch++] = 'e'; | |
2203 | if (exp < 0) | |
2204 | { | |
2205 | exp = -exp; | |
2206 | a[ch++] = '-'; | |
2207 | } | |
2208 | for (i = 10; i <= exp; i *= 10); | |
2209 | for (i /= 10; i; i /= 10) | |
2210 | { | |
2211 | a[ch++] = exp / i + '0'; | |
2212 | exp %= i; | |
2213 | } | |
0f2d19dd | 2214 | } |
0f2d19dd JB |
2215 | return ch; |
2216 | } | |
2217 | ||
1cc91f1b | 2218 | |
1be6b49c | 2219 | static size_t |
1bbd0b84 | 2220 | iflo2str (SCM flt, char *str) |
0f2d19dd | 2221 | { |
1be6b49c | 2222 | size_t i; |
3c9a524f | 2223 | if (SCM_REALP (flt)) |
f3ae5d60 | 2224 | i = idbl2str (SCM_REAL_VALUE (flt), str); |
0f2d19dd | 2225 | else |
f872b822 | 2226 | { |
f3ae5d60 MD |
2227 | i = idbl2str (SCM_COMPLEX_REAL (flt), str); |
2228 | if (SCM_COMPLEX_IMAG (flt) != 0.0) | |
2229 | { | |
7351e207 MV |
2230 | double imag = SCM_COMPLEX_IMAG (flt); |
2231 | /* Don't output a '+' for negative numbers or for Inf and | |
2232 | NaN. They will provide their own sign. */ | |
2233 | if (0 <= imag && !xisinf (imag) && !xisnan (imag)) | |
f3ae5d60 | 2234 | str[i++] = '+'; |
7351e207 | 2235 | i += idbl2str (imag, &str[i]); |
f3ae5d60 MD |
2236 | str[i++] = 'i'; |
2237 | } | |
f872b822 | 2238 | } |
0f2d19dd JB |
2239 | return i; |
2240 | } | |
0f2d19dd | 2241 | |
5c11cc9d | 2242 | /* convert a long to a string (unterminated). returns the number of |
1bbd0b84 GB |
2243 | characters in the result. |
2244 | rad is output base | |
2245 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2246 | size_t |
1bbd0b84 | 2247 | scm_iint2str (long num, int rad, char *p) |
0f2d19dd | 2248 | { |
1be6b49c ML |
2249 | size_t j = 1; |
2250 | size_t i; | |
5c11cc9d GH |
2251 | unsigned long n = (num < 0) ? -num : num; |
2252 | ||
f872b822 | 2253 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2254 | j++; |
2255 | ||
2256 | i = j; | |
2257 | if (num < 0) | |
f872b822 | 2258 | { |
f872b822 | 2259 | *p++ = '-'; |
5c11cc9d GH |
2260 | j++; |
2261 | n = -num; | |
f872b822 | 2262 | } |
5c11cc9d GH |
2263 | else |
2264 | n = num; | |
f872b822 MD |
2265 | while (i--) |
2266 | { | |
5c11cc9d GH |
2267 | int d = n % rad; |
2268 | ||
f872b822 MD |
2269 | n /= rad; |
2270 | p[i] = d + ((d < 10) ? '0' : 'a' - 10); | |
2271 | } | |
0f2d19dd JB |
2272 | return j; |
2273 | } | |
2274 | ||
2275 | ||
2276 | #ifdef SCM_BIGDIG | |
1cc91f1b | 2277 | |
0f2d19dd | 2278 | static SCM |
1bbd0b84 | 2279 | big2str (SCM b, unsigned int radix) |
0f2d19dd | 2280 | { |
1be6b49c | 2281 | SCM t = scm_i_copybig (b, 0); /* sign of temp doesn't matter */ |
f872b822 | 2282 | register SCM_BIGDIG *ds = SCM_BDIGITS (t); |
1be6b49c ML |
2283 | size_t i = SCM_NUMDIGS (t); |
2284 | size_t j = radix == 16 ? (SCM_BITSPERDIG * i) / 4 + 2 | |
f872b822 MD |
2285 | : radix >= 10 ? (SCM_BITSPERDIG * i * 241L) / 800 + 2 |
2286 | : (SCM_BITSPERDIG * i) + 2; | |
1be6b49c ML |
2287 | size_t k = 0; |
2288 | size_t radct = 0; | |
0f2d19dd | 2289 | SCM_BIGDIG radpow = 1, radmod = 0; |
be54b15d | 2290 | SCM ss = scm_allocate_string (j); |
9eb364fc | 2291 | char *s = SCM_STRING_CHARS (ss), c; |
c8a1bdc4 HWN |
2292 | |
2293 | if (i == 0) | |
2294 | { | |
2295 | return scm_makfrom0str ("0"); | |
2296 | } | |
2297 | ||
f872b822 MD |
2298 | while ((long) radpow * radix < SCM_BIGRAD) |
2299 | { | |
2300 | radpow *= radix; | |
2301 | radct++; | |
2302 | } | |
f872b822 MD |
2303 | while ((i || radmod) && j) |
2304 | { | |
2305 | if (k == 0) | |
2306 | { | |
2307 | radmod = (SCM_BIGDIG) scm_divbigdig (ds, i, radpow); | |
2308 | k = radct; | |
2309 | if (!ds[i - 1]) | |
2310 | i--; | |
2311 | } | |
2312 | c = radmod % radix; | |
2313 | radmod /= radix; | |
2314 | k--; | |
2315 | s[--j] = c < 10 ? c + '0' : c + 'a' - 10; | |
2316 | } | |
aa3188a7 DH |
2317 | |
2318 | if (SCM_BIGSIGN (b)) | |
2319 | s[--j] = '-'; | |
2320 | ||
2321 | if (j > 0) | |
2322 | { | |
2323 | /* The pre-reserved string length was too large. */ | |
2324 | unsigned long int length = SCM_STRING_LENGTH (ss); | |
2325 | ss = scm_substring (ss, SCM_MAKINUM (j), SCM_MAKINUM (length)); | |
f872b822 | 2326 | } |
b098016b JB |
2327 | |
2328 | return scm_return_first (ss, t); | |
0f2d19dd JB |
2329 | } |
2330 | #endif | |
2331 | ||
2332 | ||
a1ec6916 | 2333 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2334 | (SCM n, SCM radix), |
2335 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2336 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2337 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2338 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2339 | { |
1bbd0b84 | 2340 | int base; |
98cb6e75 DH |
2341 | |
2342 | if (SCM_UNBNDP (radix)) { | |
2343 | base = 10; | |
2344 | } else { | |
2345 | SCM_VALIDATE_INUM (2, radix); | |
2346 | base = SCM_INUM (radix); | |
2347 | SCM_ASSERT_RANGE (2, radix, base >= 2); | |
2348 | } | |
2349 | ||
bb628794 | 2350 | if (SCM_INUMP (n)) { |
98cb6e75 | 2351 | char num_buf [SCM_INTBUFLEN]; |
1be6b49c | 2352 | size_t length = scm_iint2str (SCM_INUM (n), base, num_buf); |
36284627 | 2353 | return scm_mem2string (num_buf, length); |
bb628794 DH |
2354 | } else if (SCM_BIGP (n)) { |
2355 | return big2str (n, (unsigned int) base); | |
2356 | } else if (SCM_INEXACTP (n)) { | |
56e55ac7 | 2357 | char num_buf [FLOBUFLEN]; |
36284627 | 2358 | return scm_mem2string (num_buf, iflo2str (n, num_buf)); |
98cb6e75 | 2359 | } else { |
bb628794 | 2360 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd JB |
2361 | } |
2362 | } | |
1bbd0b84 | 2363 | #undef FUNC_NAME |
0f2d19dd JB |
2364 | |
2365 | ||
2366 | /* These print routines are stubbed here so that scm_repl.c doesn't need | |
f3ae5d60 | 2367 | SCM_BIGDIG conditionals */ |
1cc91f1b | 2368 | |
0f2d19dd | 2369 | int |
e81d98ec | 2370 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2371 | { |
56e55ac7 | 2372 | char num_buf[FLOBUFLEN]; |
f872b822 | 2373 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port); |
0f2d19dd JB |
2374 | return !0; |
2375 | } | |
2376 | ||
f3ae5d60 | 2377 | int |
e81d98ec | 2378 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f3ae5d60 | 2379 | { |
56e55ac7 | 2380 | char num_buf[FLOBUFLEN]; |
f3ae5d60 MD |
2381 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port); |
2382 | return !0; | |
2383 | } | |
1cc91f1b | 2384 | |
0f2d19dd | 2385 | int |
e81d98ec | 2386 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd JB |
2387 | { |
2388 | #ifdef SCM_BIGDIG | |
f872b822 | 2389 | exp = big2str (exp, (unsigned int) 10); |
1be6b49c | 2390 | scm_lfwrite (SCM_STRING_CHARS (exp), (size_t) SCM_STRING_LENGTH (exp), port); |
0f2d19dd | 2391 | #else |
f872b822 | 2392 | scm_ipruk ("bignum", exp, port); |
0f2d19dd JB |
2393 | #endif |
2394 | return !0; | |
2395 | } | |
2396 | /*** END nums->strs ***/ | |
2397 | ||
3c9a524f | 2398 | |
0f2d19dd | 2399 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2400 | |
3c9a524f DH |
2401 | /* The following functions implement the conversion from strings to numbers. |
2402 | * The implementation somehow follows the grammar for numbers as it is given | |
2403 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2404 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2405 | * points should be noted about the implementation: | |
2406 | * * Each function keeps a local index variable 'idx' that points at the | |
2407 | * current position within the parsed string. The global index is only | |
2408 | * updated if the function could parse the corresponding syntactic unit | |
2409 | * successfully. | |
2410 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2411 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2412 | * global exactness information is only updated after each part has been | |
2413 | * successfully parsed. | |
2414 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2415 | * Only if these fixnums would overflow, the result variables are updated | |
2416 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2417 | * the temporary variables holding the fixnums are cleared, and the process | |
2418 | * starts over again. If for example fixnums were able to store five decimal | |
2419 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2420 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2421 | * only every five digits two bignum operations were performed. | |
2422 | */ | |
2423 | ||
2424 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2425 | ||
2426 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2427 | ||
2428 | /* In non ASCII-style encodings the following macro might not work. */ | |
2429 | #define XDIGIT2UINT(d) (isdigit (d) ? (d) - '0' : tolower (d) - 'a' + 10) | |
2430 | ||
2a8fecee | 2431 | static SCM |
3c9a524f DH |
2432 | mem2uinteger (const char* mem, size_t len, unsigned int *p_idx, |
2433 | unsigned int radix, enum t_exactness *p_exactness) | |
2a8fecee | 2434 | { |
3c9a524f DH |
2435 | unsigned int idx = *p_idx; |
2436 | unsigned int hash_seen = 0; | |
2437 | scm_t_bits shift = 1; | |
2438 | scm_t_bits add = 0; | |
2439 | unsigned int digit_value; | |
2440 | SCM result; | |
2441 | char c; | |
2442 | ||
2443 | if (idx == len) | |
2444 | return SCM_BOOL_F; | |
2a8fecee | 2445 | |
3c9a524f DH |
2446 | c = mem[idx]; |
2447 | if (!isxdigit (c)) | |
2448 | return SCM_BOOL_F; | |
2449 | digit_value = XDIGIT2UINT (c); | |
2450 | if (digit_value >= radix) | |
2451 | return SCM_BOOL_F; | |
2452 | ||
2453 | idx++; | |
2454 | result = SCM_MAKINUM (digit_value); | |
2455 | while (idx != len) | |
f872b822 | 2456 | { |
3c9a524f DH |
2457 | char c = mem[idx]; |
2458 | if (isxdigit (c)) | |
f872b822 | 2459 | { |
3c9a524f | 2460 | if (hash_seen) |
1fe5e088 | 2461 | break; |
3c9a524f DH |
2462 | digit_value = XDIGIT2UINT (c); |
2463 | if (digit_value >= radix) | |
1fe5e088 | 2464 | break; |
f872b822 | 2465 | } |
3c9a524f DH |
2466 | else if (c == '#') |
2467 | { | |
2468 | hash_seen = 1; | |
2469 | digit_value = 0; | |
2470 | } | |
2471 | else | |
2472 | break; | |
2473 | ||
2474 | idx++; | |
2475 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2476 | { | |
2477 | result = scm_product (result, SCM_MAKINUM (shift)); | |
2478 | if (add > 0) | |
2479 | result = scm_sum (result, SCM_MAKINUM (add)); | |
2480 | ||
2481 | shift = radix; | |
2482 | add = digit_value; | |
2483 | } | |
2484 | else | |
2485 | { | |
2486 | shift = shift * radix; | |
2487 | add = add * radix + digit_value; | |
2488 | } | |
2489 | }; | |
2490 | ||
2491 | if (shift > 1) | |
2492 | result = scm_product (result, SCM_MAKINUM (shift)); | |
2493 | if (add > 0) | |
2494 | result = scm_sum (result, SCM_MAKINUM (add)); | |
2495 | ||
2496 | *p_idx = idx; | |
2497 | if (hash_seen) | |
2498 | *p_exactness = INEXACT; | |
2499 | ||
2500 | return result; | |
2a8fecee JB |
2501 | } |
2502 | ||
2503 | ||
3c9a524f DH |
2504 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2505 | * covers the parts of the rules that start at a potential point. The value | |
2506 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2507 | * in variable result. The content of *p_exactness indicates, whether a hash |
2508 | * has already been seen in the digits before the point. | |
3c9a524f | 2509 | */ |
1cc91f1b | 2510 | |
3c9a524f DH |
2511 | /* In non ASCII-style encodings the following macro might not work. */ |
2512 | #define DIGIT2UINT(d) ((d) - '0') | |
2513 | ||
2514 | static SCM | |
79d34f68 | 2515 | mem2decimal_from_point (SCM result, const char* mem, size_t len, |
3c9a524f | 2516 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2517 | { |
3c9a524f DH |
2518 | unsigned int idx = *p_idx; |
2519 | enum t_exactness x = *p_exactness; | |
3c9a524f DH |
2520 | |
2521 | if (idx == len) | |
79d34f68 | 2522 | return result; |
3c9a524f DH |
2523 | |
2524 | if (mem[idx] == '.') | |
2525 | { | |
2526 | scm_t_bits shift = 1; | |
2527 | scm_t_bits add = 0; | |
2528 | unsigned int digit_value; | |
79d34f68 | 2529 | SCM big_shift = SCM_MAKINUM (1); |
3c9a524f DH |
2530 | |
2531 | idx++; | |
2532 | while (idx != len) | |
2533 | { | |
2534 | char c = mem[idx]; | |
2535 | if (isdigit (c)) | |
2536 | { | |
2537 | if (x == INEXACT) | |
2538 | return SCM_BOOL_F; | |
2539 | else | |
2540 | digit_value = DIGIT2UINT (c); | |
2541 | } | |
2542 | else if (c == '#') | |
2543 | { | |
2544 | x = INEXACT; | |
2545 | digit_value = 0; | |
2546 | } | |
2547 | else | |
2548 | break; | |
2549 | ||
2550 | idx++; | |
2551 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2552 | { | |
2553 | big_shift = scm_product (big_shift, SCM_MAKINUM (shift)); | |
79d34f68 | 2554 | result = scm_product (result, SCM_MAKINUM (shift)); |
3c9a524f | 2555 | if (add > 0) |
79d34f68 | 2556 | result = scm_sum (result, SCM_MAKINUM (add)); |
3c9a524f DH |
2557 | |
2558 | shift = 10; | |
2559 | add = digit_value; | |
2560 | } | |
2561 | else | |
2562 | { | |
2563 | shift = shift * 10; | |
2564 | add = add * 10 + digit_value; | |
2565 | } | |
2566 | }; | |
2567 | ||
2568 | if (add > 0) | |
2569 | { | |
2570 | big_shift = scm_product (big_shift, SCM_MAKINUM (shift)); | |
79d34f68 DH |
2571 | result = scm_product (result, SCM_MAKINUM (shift)); |
2572 | result = scm_sum (result, SCM_MAKINUM (add)); | |
3c9a524f DH |
2573 | } |
2574 | ||
79d34f68 DH |
2575 | result = scm_divide (result, big_shift); |
2576 | ||
3c9a524f DH |
2577 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2578 | x = INEXACT; | |
f872b822 | 2579 | } |
3c9a524f | 2580 | |
3c9a524f | 2581 | if (idx != len) |
f872b822 | 2582 | { |
3c9a524f DH |
2583 | int sign = 1; |
2584 | unsigned int start; | |
2585 | char c; | |
2586 | int exponent; | |
2587 | SCM e; | |
2588 | ||
2589 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2590 | ||
2591 | switch (mem[idx]) | |
f872b822 | 2592 | { |
3c9a524f DH |
2593 | case 'd': case 'D': |
2594 | case 'e': case 'E': | |
2595 | case 'f': case 'F': | |
2596 | case 'l': case 'L': | |
2597 | case 's': case 'S': | |
2598 | idx++; | |
2599 | start = idx; | |
2600 | c = mem[idx]; | |
2601 | if (c == '-') | |
2602 | { | |
2603 | idx++; | |
2604 | sign = -1; | |
2605 | c = mem[idx]; | |
2606 | } | |
2607 | else if (c == '+') | |
2608 | { | |
2609 | idx++; | |
2610 | sign = 1; | |
2611 | c = mem[idx]; | |
2612 | } | |
2613 | else | |
2614 | sign = 1; | |
2615 | ||
2616 | if (!isdigit (c)) | |
2617 | return SCM_BOOL_F; | |
2618 | ||
2619 | idx++; | |
2620 | exponent = DIGIT2UINT (c); | |
2621 | while (idx != len) | |
f872b822 | 2622 | { |
3c9a524f DH |
2623 | char c = mem[idx]; |
2624 | if (isdigit (c)) | |
2625 | { | |
2626 | idx++; | |
2627 | if (exponent <= SCM_MAXEXP) | |
2628 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2629 | } | |
2630 | else | |
2631 | break; | |
f872b822 | 2632 | } |
3c9a524f DH |
2633 | |
2634 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2635 | { |
3c9a524f DH |
2636 | size_t exp_len = idx - start; |
2637 | SCM exp_string = scm_mem2string (&mem[start], exp_len); | |
2638 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); | |
2639 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2640 | } |
3c9a524f DH |
2641 | |
2642 | e = scm_integer_expt (SCM_MAKINUM (10), SCM_MAKINUM (exponent)); | |
2643 | if (sign == 1) | |
2644 | result = scm_product (result, e); | |
2645 | else | |
2646 | result = scm_divide (result, e); | |
2647 | ||
2648 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2649 | x = INEXACT; | |
2650 | ||
f872b822 | 2651 | break; |
3c9a524f | 2652 | |
f872b822 | 2653 | default: |
3c9a524f | 2654 | break; |
f872b822 | 2655 | } |
0f2d19dd | 2656 | } |
3c9a524f DH |
2657 | |
2658 | *p_idx = idx; | |
2659 | if (x == INEXACT) | |
2660 | *p_exactness = x; | |
2661 | ||
2662 | return result; | |
0f2d19dd | 2663 | } |
0f2d19dd | 2664 | |
3c9a524f DH |
2665 | |
2666 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2667 | ||
2668 | static SCM | |
2669 | mem2ureal (const char* mem, size_t len, unsigned int *p_idx, | |
2670 | unsigned int radix, enum t_exactness *p_exactness) | |
0f2d19dd | 2671 | { |
3c9a524f | 2672 | unsigned int idx = *p_idx; |
164d2481 | 2673 | SCM result; |
3c9a524f DH |
2674 | |
2675 | if (idx == len) | |
2676 | return SCM_BOOL_F; | |
2677 | ||
7351e207 MV |
2678 | if (idx+5 <= len && !strncmp (mem+idx, "inf.0", 5)) |
2679 | { | |
2680 | *p_idx = idx+5; | |
2681 | return scm_inf (); | |
2682 | } | |
2683 | ||
2684 | if (idx+4 < len && !strncmp (mem+idx, "nan.", 4)) | |
2685 | { | |
2686 | enum t_exactness x = EXACT; | |
2687 | ||
2688 | /* Cobble up the fraction. We might want to set the NaN's | |
2689 | mantissa from it. */ | |
2690 | idx += 4; | |
2691 | mem2uinteger (mem, len, &idx, 10, &x); | |
2692 | *p_idx = idx; | |
2693 | return scm_nan (); | |
2694 | } | |
2695 | ||
3c9a524f DH |
2696 | if (mem[idx] == '.') |
2697 | { | |
2698 | if (radix != 10) | |
2699 | return SCM_BOOL_F; | |
2700 | else if (idx + 1 == len) | |
2701 | return SCM_BOOL_F; | |
2702 | else if (!isdigit (mem[idx + 1])) | |
2703 | return SCM_BOOL_F; | |
2704 | else | |
164d2481 MV |
2705 | result = mem2decimal_from_point (SCM_MAKINUM (0), mem, len, |
2706 | p_idx, p_exactness); | |
f872b822 | 2707 | } |
3c9a524f DH |
2708 | else |
2709 | { | |
2710 | enum t_exactness x = EXACT; | |
2711 | SCM uinteger; | |
3c9a524f DH |
2712 | |
2713 | uinteger = mem2uinteger (mem, len, &idx, radix, &x); | |
2714 | if (SCM_FALSEP (uinteger)) | |
2715 | return SCM_BOOL_F; | |
2716 | ||
2717 | if (idx == len) | |
2718 | result = uinteger; | |
2719 | else if (mem[idx] == '/') | |
f872b822 | 2720 | { |
3c9a524f DH |
2721 | SCM divisor; |
2722 | ||
2723 | idx++; | |
2724 | ||
2725 | divisor = mem2uinteger (mem, len, &idx, radix, &x); | |
2726 | if (SCM_FALSEP (divisor)) | |
2727 | return SCM_BOOL_F; | |
2728 | ||
2729 | result = scm_divide (uinteger, divisor); | |
f872b822 | 2730 | } |
3c9a524f DH |
2731 | else if (radix == 10) |
2732 | { | |
2733 | result = mem2decimal_from_point (uinteger, mem, len, &idx, &x); | |
2734 | if (SCM_FALSEP (result)) | |
2735 | return SCM_BOOL_F; | |
2736 | } | |
2737 | else | |
2738 | result = uinteger; | |
2739 | ||
2740 | *p_idx = idx; | |
2741 | if (x == INEXACT) | |
2742 | *p_exactness = x; | |
f872b822 | 2743 | } |
164d2481 MV |
2744 | |
2745 | /* When returning an inexact zero, make sure it is represented as a | |
2746 | floating point value so that we can change its sign. | |
2747 | */ | |
2748 | if (SCM_EQ_P (result, SCM_MAKINUM(0)) && *p_exactness == INEXACT) | |
2749 | result = scm_make_real (0.0); | |
2750 | ||
2751 | return result; | |
3c9a524f | 2752 | } |
0f2d19dd | 2753 | |
0f2d19dd | 2754 | |
3c9a524f | 2755 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2756 | |
3c9a524f DH |
2757 | static SCM |
2758 | mem2complex (const char* mem, size_t len, unsigned int idx, | |
2759 | unsigned int radix, enum t_exactness *p_exactness) | |
2760 | { | |
2761 | char c; | |
2762 | int sign = 0; | |
2763 | SCM ureal; | |
2764 | ||
2765 | if (idx == len) | |
2766 | return SCM_BOOL_F; | |
2767 | ||
2768 | c = mem[idx]; | |
2769 | if (c == '+') | |
2770 | { | |
2771 | idx++; | |
2772 | sign = 1; | |
2773 | } | |
2774 | else if (c == '-') | |
2775 | { | |
2776 | idx++; | |
2777 | sign = -1; | |
0f2d19dd | 2778 | } |
0f2d19dd | 2779 | |
3c9a524f DH |
2780 | if (idx == len) |
2781 | return SCM_BOOL_F; | |
2782 | ||
2783 | ureal = mem2ureal (mem, len, &idx, radix, p_exactness); | |
2784 | if (SCM_FALSEP (ureal)) | |
f872b822 | 2785 | { |
3c9a524f DH |
2786 | /* input must be either +i or -i */ |
2787 | ||
2788 | if (sign == 0) | |
2789 | return SCM_BOOL_F; | |
2790 | ||
2791 | if (mem[idx] == 'i' || mem[idx] == 'I') | |
f872b822 | 2792 | { |
3c9a524f DH |
2793 | idx++; |
2794 | if (idx != len) | |
2795 | return SCM_BOOL_F; | |
2796 | ||
2797 | return scm_make_rectangular (SCM_MAKINUM (0), SCM_MAKINUM (sign)); | |
f872b822 | 2798 | } |
3c9a524f DH |
2799 | else |
2800 | return SCM_BOOL_F; | |
0f2d19dd | 2801 | } |
3c9a524f DH |
2802 | else |
2803 | { | |
fc194577 | 2804 | if (sign == -1 && SCM_FALSEP (scm_nan_p (ureal))) |
3c9a524f | 2805 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 2806 | |
3c9a524f DH |
2807 | if (idx == len) |
2808 | return ureal; | |
2809 | ||
2810 | c = mem[idx]; | |
2811 | switch (c) | |
f872b822 | 2812 | { |
3c9a524f DH |
2813 | case 'i': case 'I': |
2814 | /* either +<ureal>i or -<ureal>i */ | |
2815 | ||
2816 | idx++; | |
2817 | if (sign == 0) | |
2818 | return SCM_BOOL_F; | |
2819 | if (idx != len) | |
2820 | return SCM_BOOL_F; | |
2821 | return scm_make_rectangular (SCM_MAKINUM (0), ureal); | |
2822 | ||
2823 | case '@': | |
2824 | /* polar input: <real>@<real>. */ | |
2825 | ||
2826 | idx++; | |
2827 | if (idx == len) | |
2828 | return SCM_BOOL_F; | |
2829 | else | |
f872b822 | 2830 | { |
3c9a524f DH |
2831 | int sign; |
2832 | SCM angle; | |
2833 | SCM result; | |
2834 | ||
2835 | c = mem[idx]; | |
2836 | if (c == '+') | |
2837 | { | |
2838 | idx++; | |
2839 | sign = 1; | |
2840 | } | |
2841 | else if (c == '-') | |
2842 | { | |
2843 | idx++; | |
2844 | sign = -1; | |
2845 | } | |
2846 | else | |
2847 | sign = 1; | |
2848 | ||
2849 | angle = mem2ureal (mem, len, &idx, radix, p_exactness); | |
2850 | if (SCM_FALSEP (angle)) | |
2851 | return SCM_BOOL_F; | |
2852 | if (idx != len) | |
2853 | return SCM_BOOL_F; | |
2854 | ||
fc194577 | 2855 | if (sign == -1 && SCM_FALSEP (scm_nan_p (ureal))) |
3c9a524f DH |
2856 | angle = scm_difference (angle, SCM_UNDEFINED); |
2857 | ||
2858 | result = scm_make_polar (ureal, angle); | |
2859 | return result; | |
f872b822 | 2860 | } |
3c9a524f DH |
2861 | case '+': |
2862 | case '-': | |
2863 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 2864 | |
3c9a524f DH |
2865 | idx++; |
2866 | if (idx == len) | |
2867 | return SCM_BOOL_F; | |
2868 | else | |
2869 | { | |
2870 | int sign = (c == '+') ? 1 : -1; | |
2871 | SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness); | |
0f2d19dd | 2872 | |
3c9a524f DH |
2873 | if (SCM_FALSEP (imag)) |
2874 | imag = SCM_MAKINUM (sign); | |
fc194577 | 2875 | else if (sign == -1 && SCM_FALSEP (scm_nan_p (ureal))) |
1fe5e088 | 2876 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 2877 | |
3c9a524f DH |
2878 | if (idx == len) |
2879 | return SCM_BOOL_F; | |
2880 | if (mem[idx] != 'i' && mem[idx] != 'I') | |
2881 | return SCM_BOOL_F; | |
0f2d19dd | 2882 | |
3c9a524f DH |
2883 | idx++; |
2884 | if (idx != len) | |
2885 | return SCM_BOOL_F; | |
0f2d19dd | 2886 | |
1fe5e088 | 2887 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
2888 | } |
2889 | default: | |
2890 | return SCM_BOOL_F; | |
2891 | } | |
2892 | } | |
0f2d19dd | 2893 | } |
0f2d19dd JB |
2894 | |
2895 | ||
3c9a524f DH |
2896 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
2897 | ||
2898 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 2899 | |
0f2d19dd | 2900 | SCM |
3c9a524f | 2901 | scm_i_mem2number (const char* mem, size_t len, unsigned int default_radix) |
0f2d19dd | 2902 | { |
3c9a524f DH |
2903 | unsigned int idx = 0; |
2904 | unsigned int radix = NO_RADIX; | |
2905 | enum t_exactness forced_x = NO_EXACTNESS; | |
2906 | enum t_exactness implicit_x = EXACT; | |
2907 | SCM result; | |
2908 | ||
2909 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
2910 | while (idx + 2 < len && mem[idx] == '#') | |
2911 | { | |
2912 | switch (mem[idx + 1]) | |
2913 | { | |
2914 | case 'b': case 'B': | |
2915 | if (radix != NO_RADIX) | |
2916 | return SCM_BOOL_F; | |
2917 | radix = DUAL; | |
2918 | break; | |
2919 | case 'd': case 'D': | |
2920 | if (radix != NO_RADIX) | |
2921 | return SCM_BOOL_F; | |
2922 | radix = DEC; | |
2923 | break; | |
2924 | case 'i': case 'I': | |
2925 | if (forced_x != NO_EXACTNESS) | |
2926 | return SCM_BOOL_F; | |
2927 | forced_x = INEXACT; | |
2928 | break; | |
2929 | case 'e': case 'E': | |
2930 | if (forced_x != NO_EXACTNESS) | |
2931 | return SCM_BOOL_F; | |
2932 | forced_x = EXACT; | |
2933 | break; | |
2934 | case 'o': case 'O': | |
2935 | if (radix != NO_RADIX) | |
2936 | return SCM_BOOL_F; | |
2937 | radix = OCT; | |
2938 | break; | |
2939 | case 'x': case 'X': | |
2940 | if (radix != NO_RADIX) | |
2941 | return SCM_BOOL_F; | |
2942 | radix = HEX; | |
2943 | break; | |
2944 | default: | |
f872b822 | 2945 | return SCM_BOOL_F; |
3c9a524f DH |
2946 | } |
2947 | idx += 2; | |
2948 | } | |
2949 | ||
2950 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
2951 | if (radix == NO_RADIX) | |
2952 | result = mem2complex (mem, len, idx, default_radix, &implicit_x); | |
2953 | else | |
2954 | result = mem2complex (mem, len, idx, (unsigned int) radix, &implicit_x); | |
2955 | ||
2956 | if (SCM_FALSEP (result)) | |
2957 | return SCM_BOOL_F; | |
f872b822 | 2958 | |
3c9a524f | 2959 | switch (forced_x) |
f872b822 | 2960 | { |
3c9a524f DH |
2961 | case EXACT: |
2962 | if (SCM_INEXACTP (result)) | |
2963 | /* FIXME: This may change the value. */ | |
2964 | return scm_inexact_to_exact (result); | |
2965 | else | |
2966 | return result; | |
2967 | case INEXACT: | |
2968 | if (SCM_INEXACTP (result)) | |
2969 | return result; | |
2970 | else | |
2971 | return scm_exact_to_inexact (result); | |
2972 | case NO_EXACTNESS: | |
2973 | default: | |
2974 | if (implicit_x == INEXACT) | |
2975 | { | |
2976 | if (SCM_INEXACTP (result)) | |
2977 | return result; | |
2978 | else | |
2979 | return scm_exact_to_inexact (result); | |
2980 | } | |
2981 | else | |
2982 | return result; | |
f872b822 | 2983 | } |
0f2d19dd JB |
2984 | } |
2985 | ||
2986 | ||
a1ec6916 | 2987 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 2988 | (SCM string, SCM radix), |
1e6808ea | 2989 | "Return a number of the maximally precise representation\n" |
942e5b91 | 2990 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
2991 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
2992 | "is a default radix that may be overridden by an explicit radix\n" | |
2993 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
2994 | "supplied, then the default radix is 10. If string is not a\n" | |
2995 | "syntactically valid notation for a number, then\n" | |
2996 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 2997 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
2998 | { |
2999 | SCM answer; | |
1bbd0b84 | 3000 | int base; |
a6d9e5ab | 3001 | SCM_VALIDATE_STRING (1, string); |
34d19ef6 | 3002 | SCM_VALIDATE_INUM_MIN_DEF_COPY (2, radix,2,10, base); |
3c9a524f DH |
3003 | answer = scm_i_mem2number (SCM_STRING_CHARS (string), |
3004 | SCM_STRING_LENGTH (string), | |
3005 | base); | |
bb628794 | 3006 | return scm_return_first (answer, string); |
0f2d19dd | 3007 | } |
1bbd0b84 | 3008 | #undef FUNC_NAME |
3c9a524f DH |
3009 | |
3010 | ||
0f2d19dd JB |
3011 | /*** END strs->nums ***/ |
3012 | ||
5986c47d | 3013 | |
0f2d19dd | 3014 | SCM |
f3ae5d60 | 3015 | scm_make_real (double x) |
0f2d19dd | 3016 | { |
3553e1d1 GH |
3017 | SCM z = scm_double_cell (scm_tc16_real, 0, 0, 0); |
3018 | ||
3a9809df | 3019 | SCM_REAL_VALUE (z) = x; |
0f2d19dd JB |
3020 | return z; |
3021 | } | |
0f2d19dd | 3022 | |
5986c47d | 3023 | |
f3ae5d60 MD |
3024 | SCM |
3025 | scm_make_complex (double x, double y) | |
3026 | { | |
3a9809df DH |
3027 | if (y == 0.0) { |
3028 | return scm_make_real (x); | |
3029 | } else { | |
3030 | SCM z; | |
4c9419ac MV |
3031 | SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (2*sizeof (double), |
3032 | "complex")); | |
3a9809df DH |
3033 | SCM_COMPLEX_REAL (z) = x; |
3034 | SCM_COMPLEX_IMAG (z) = y; | |
3035 | return z; | |
3036 | } | |
f3ae5d60 | 3037 | } |
1cc91f1b | 3038 | |
5986c47d | 3039 | |
0f2d19dd | 3040 | SCM |
1bbd0b84 | 3041 | scm_bigequal (SCM x, SCM y) |
0f2d19dd JB |
3042 | { |
3043 | #ifdef SCM_BIGDIG | |
f872b822 MD |
3044 | if (0 == scm_bigcomp (x, y)) |
3045 | return SCM_BOOL_T; | |
0f2d19dd JB |
3046 | #endif |
3047 | return SCM_BOOL_F; | |
3048 | } | |
3049 | ||
0f2d19dd | 3050 | SCM |
f3ae5d60 | 3051 | scm_real_equalp (SCM x, SCM y) |
0f2d19dd | 3052 | { |
f3ae5d60 | 3053 | return SCM_BOOL (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0f2d19dd JB |
3054 | } |
3055 | ||
f3ae5d60 MD |
3056 | SCM |
3057 | scm_complex_equalp (SCM x, SCM y) | |
3058 | { | |
3059 | return SCM_BOOL (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) | |
3060 | && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); | |
3061 | } | |
0f2d19dd JB |
3062 | |
3063 | ||
3064 | ||
1bbd0b84 | 3065 | SCM_REGISTER_PROC (s_number_p, "number?", 1, 0, 0, scm_number_p); |
942e5b91 MG |
3066 | /* "Return @code{#t} if @var{x} is a number, @code{#f}\n" |
3067 | * "else. Note that the sets of complex, real, rational and\n" | |
3068 | * "integer values form subsets of the set of numbers, i. e. the\n" | |
3069 | * "predicate will be fulfilled for any number." | |
3070 | */ | |
a1ec6916 | 3071 | SCM_DEFINE (scm_number_p, "complex?", 1, 0, 0, |
1bbd0b84 | 3072 | (SCM x), |
942e5b91 | 3073 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 3074 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
3075 | "values form subsets of the set of complex numbers, i. e. the\n" |
3076 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
3077 | "rational or integer number.") | |
1bbd0b84 | 3078 | #define FUNC_NAME s_scm_number_p |
0f2d19dd | 3079 | { |
bb628794 | 3080 | return SCM_BOOL (SCM_NUMBERP (x)); |
0f2d19dd | 3081 | } |
1bbd0b84 | 3082 | #undef FUNC_NAME |
0f2d19dd JB |
3083 | |
3084 | ||
1bbd0b84 | 3085 | SCM_REGISTER_PROC (s_real_p, "real?", 1, 0, 0, scm_real_p); |
942e5b91 MG |
3086 | /* "Return @code{#t} if @var{x} is a real number, @code{#f} else.\n" |
3087 | * "Note that the sets of integer and rational values form a subset\n" | |
3088 | * "of the set of real numbers, i. e. the predicate will also\n" | |
3089 | * "be fulfilled if @var{x} is an integer or a rational number." | |
3090 | */ | |
a1ec6916 | 3091 | SCM_DEFINE (scm_real_p, "rational?", 1, 0, 0, |
1bbd0b84 | 3092 | (SCM x), |
942e5b91 | 3093 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 3094 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 MG |
3095 | "the set of rational numbers, i. e. the predicate will also be\n" |
3096 | "fulfilled if @var{x} is an integer number. Real numbers\n" | |
3097 | "will also satisfy this predicate, because of their limited\n" | |
3098 | "precision.") | |
1bbd0b84 | 3099 | #define FUNC_NAME s_scm_real_p |
0f2d19dd | 3100 | { |
bb628794 | 3101 | if (SCM_INUMP (x)) { |
0f2d19dd | 3102 | return SCM_BOOL_T; |
bb628794 | 3103 | } else if (SCM_IMP (x)) { |
0f2d19dd | 3104 | return SCM_BOOL_F; |
3c9a524f | 3105 | } else if (SCM_REALP (x)) { |
0f2d19dd | 3106 | return SCM_BOOL_T; |
bb628794 | 3107 | } else if (SCM_BIGP (x)) { |
0f2d19dd | 3108 | return SCM_BOOL_T; |
bb628794 DH |
3109 | } else { |
3110 | return SCM_BOOL_F; | |
3111 | } | |
0f2d19dd | 3112 | } |
1bbd0b84 | 3113 | #undef FUNC_NAME |
0f2d19dd JB |
3114 | |
3115 | ||
a1ec6916 | 3116 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 3117 | (SCM x), |
942e5b91 MG |
3118 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
3119 | "else.") | |
1bbd0b84 | 3120 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd JB |
3121 | { |
3122 | double r; | |
f872b822 MD |
3123 | if (SCM_INUMP (x)) |
3124 | return SCM_BOOL_T; | |
3125 | if (SCM_IMP (x)) | |
3126 | return SCM_BOOL_F; | |
f872b822 MD |
3127 | if (SCM_BIGP (x)) |
3128 | return SCM_BOOL_T; | |
3c9a524f | 3129 | if (!SCM_INEXACTP (x)) |
f872b822 | 3130 | return SCM_BOOL_F; |
3c9a524f | 3131 | if (SCM_COMPLEXP (x)) |
f872b822 | 3132 | return SCM_BOOL_F; |
5986c47d | 3133 | r = SCM_REAL_VALUE (x); |
f872b822 MD |
3134 | if (r == floor (r)) |
3135 | return SCM_BOOL_T; | |
0f2d19dd JB |
3136 | return SCM_BOOL_F; |
3137 | } | |
1bbd0b84 | 3138 | #undef FUNC_NAME |
0f2d19dd JB |
3139 | |
3140 | ||
a1ec6916 | 3141 | SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, |
1bbd0b84 | 3142 | (SCM x), |
942e5b91 MG |
3143 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" |
3144 | "else.") | |
1bbd0b84 | 3145 | #define FUNC_NAME s_scm_inexact_p |
0f2d19dd | 3146 | { |
f4c627b3 | 3147 | return SCM_BOOL (SCM_INEXACTP (x)); |
0f2d19dd | 3148 | } |
1bbd0b84 | 3149 | #undef FUNC_NAME |
0f2d19dd JB |
3150 | |
3151 | ||
152f82bf | 3152 | SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p); |
942e5b91 | 3153 | /* "Return @code{#t} if all parameters are numerically equal." */ |
0f2d19dd | 3154 | SCM |
6e8d25a6 | 3155 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 3156 | { |
f4c627b3 DH |
3157 | if (SCM_INUMP (x)) { |
3158 | long xx = SCM_INUM (x); | |
3159 | if (SCM_INUMP (y)) { | |
3160 | long yy = SCM_INUM (y); | |
3161 | return SCM_BOOL (xx == yy); | |
3162 | } else if (SCM_BIGP (y)) { | |
3163 | return SCM_BOOL_F; | |
3164 | } else if (SCM_REALP (y)) { | |
3165 | return SCM_BOOL ((double) xx == SCM_REAL_VALUE (y)); | |
3166 | } else if (SCM_COMPLEXP (y)) { | |
3167 | return SCM_BOOL (((double) xx == SCM_COMPLEX_REAL (y)) | |
3168 | && (0.0 == SCM_COMPLEX_IMAG (y))); | |
3169 | } else { | |
3170 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3171 | } |
f4c627b3 DH |
3172 | } else if (SCM_BIGP (x)) { |
3173 | if (SCM_INUMP (y)) { | |
3174 | return SCM_BOOL_F; | |
3175 | } else if (SCM_BIGP (y)) { | |
3176 | return SCM_BOOL (0 == scm_bigcomp (x, y)); | |
3177 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3178 | return SCM_BOOL (scm_i_big2dbl (x) == SCM_REAL_VALUE (y)); |
f4c627b3 | 3179 | } else if (SCM_COMPLEXP (y)) { |
1be6b49c | 3180 | return SCM_BOOL ((scm_i_big2dbl (x) == SCM_COMPLEX_REAL (y)) |
f4c627b3 DH |
3181 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
3182 | } else { | |
3183 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
3184 | } | |
3185 | } else if (SCM_REALP (x)) { | |
3186 | if (SCM_INUMP (y)) { | |
3187 | return SCM_BOOL (SCM_REAL_VALUE (x) == (double) SCM_INUM (y)); | |
3188 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3189 | return SCM_BOOL (SCM_REAL_VALUE (x) == scm_i_big2dbl (y)); |
f4c627b3 DH |
3190 | } else if (SCM_REALP (y)) { |
3191 | return SCM_BOOL (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); | |
3192 | } else if (SCM_COMPLEXP (y)) { | |
3193 | return SCM_BOOL ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) | |
3194 | && (0.0 == SCM_COMPLEX_IMAG (y))); | |
3195 | } else { | |
3196 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3197 | } |
f4c627b3 DH |
3198 | } else if (SCM_COMPLEXP (x)) { |
3199 | if (SCM_INUMP (y)) { | |
3200 | return SCM_BOOL ((SCM_COMPLEX_REAL (x) == (double) SCM_INUM (y)) | |
3201 | && (SCM_COMPLEX_IMAG (x) == 0.0)); | |
3202 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3203 | return SCM_BOOL ((SCM_COMPLEX_REAL (x) == scm_i_big2dbl (y)) |
f4c627b3 DH |
3204 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3205 | } else if (SCM_REALP (y)) { | |
3206 | return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) | |
3207 | && (SCM_COMPLEX_IMAG (x) == 0.0)); | |
3208 | } else if (SCM_COMPLEXP (y)) { | |
3209 | return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) | |
3210 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); | |
3211 | } else { | |
3212 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
3213 | } | |
3214 | } else { | |
3215 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p); | |
3216 | } | |
0f2d19dd JB |
3217 | } |
3218 | ||
3219 | ||
152f82bf | 3220 | SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p); |
942e5b91 MG |
3221 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3222 | * "increasing." | |
3223 | */ | |
0f2d19dd | 3224 | SCM |
6e8d25a6 | 3225 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3226 | { |
f4c627b3 DH |
3227 | if (SCM_INUMP (x)) { |
3228 | long xx = SCM_INUM (x); | |
3229 | if (SCM_INUMP (y)) { | |
3230 | long yy = SCM_INUM (y); | |
3231 | return SCM_BOOL (xx < yy); | |
3232 | } else if (SCM_BIGP (y)) { | |
3233 | return SCM_BOOL (!SCM_BIGSIGN (y)); | |
3234 | } else if (SCM_REALP (y)) { | |
3235 | return SCM_BOOL ((double) xx < SCM_REAL_VALUE (y)); | |
3236 | } else { | |
3237 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3238 | } |
f4c627b3 DH |
3239 | } else if (SCM_BIGP (x)) { |
3240 | if (SCM_INUMP (y)) { | |
3241 | return SCM_BOOL (SCM_BIGSIGN (x)); | |
3242 | } else if (SCM_BIGP (y)) { | |
3243 | return SCM_BOOL (1 == scm_bigcomp (x, y)); | |
3244 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3245 | return SCM_BOOL (scm_i_big2dbl (x) < SCM_REAL_VALUE (y)); |
f4c627b3 DH |
3246 | } else { |
3247 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
3248 | } | |
3249 | } else if (SCM_REALP (x)) { | |
3250 | if (SCM_INUMP (y)) { | |
3251 | return SCM_BOOL (SCM_REAL_VALUE (x) < (double) SCM_INUM (y)); | |
3252 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3253 | return SCM_BOOL (SCM_REAL_VALUE (x) < scm_i_big2dbl (y)); |
f4c627b3 DH |
3254 | } else if (SCM_REALP (y)) { |
3255 | return SCM_BOOL (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); | |
3256 | } else { | |
3257 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3258 | } |
f4c627b3 DH |
3259 | } else { |
3260 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p); | |
3261 | } | |
0f2d19dd JB |
3262 | } |
3263 | ||
3264 | ||
c76b1eaf | 3265 | SCM_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p); |
942e5b91 MG |
3266 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3267 | * "decreasing." | |
c76b1eaf | 3268 | */ |
1bbd0b84 | 3269 | #define FUNC_NAME s_scm_gr_p |
c76b1eaf MD |
3270 | SCM |
3271 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3272 | { |
c76b1eaf MD |
3273 | if (!SCM_NUMBERP (x)) |
3274 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME); | |
3275 | else if (!SCM_NUMBERP (y)) | |
3276 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME); | |
3277 | else | |
3278 | return scm_less_p (y, x); | |
0f2d19dd | 3279 | } |
1bbd0b84 | 3280 | #undef FUNC_NAME |
0f2d19dd JB |
3281 | |
3282 | ||
c76b1eaf | 3283 | SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p); |
942e5b91 | 3284 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3285 | * "non-decreasing." |
3286 | */ | |
1bbd0b84 | 3287 | #define FUNC_NAME s_scm_leq_p |
c76b1eaf MD |
3288 | SCM |
3289 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3290 | { |
c76b1eaf MD |
3291 | if (!SCM_NUMBERP (x)) |
3292 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3293 | else if (!SCM_NUMBERP (y)) | |
3294 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME); | |
fc194577 MV |
3295 | else if (SCM_NFALSEP (scm_nan_p (x)) || SCM_NFALSEP (scm_nan_p (y))) |
3296 | return SCM_BOOL_F; | |
c76b1eaf MD |
3297 | else |
3298 | return SCM_BOOL_NOT (scm_less_p (y, x)); | |
0f2d19dd | 3299 | } |
1bbd0b84 | 3300 | #undef FUNC_NAME |
0f2d19dd JB |
3301 | |
3302 | ||
c76b1eaf | 3303 | SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p); |
942e5b91 | 3304 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3305 | * "non-increasing." |
3306 | */ | |
1bbd0b84 | 3307 | #define FUNC_NAME s_scm_geq_p |
c76b1eaf MD |
3308 | SCM |
3309 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3310 | { |
c76b1eaf MD |
3311 | if (!SCM_NUMBERP (x)) |
3312 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3313 | else if (!SCM_NUMBERP (y)) | |
3314 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME); | |
fc194577 MV |
3315 | else if (SCM_NFALSEP (scm_nan_p (x)) || SCM_NFALSEP (scm_nan_p (y))) |
3316 | return SCM_BOOL_F; | |
c76b1eaf | 3317 | else |
fc194577 | 3318 | return SCM_BOOL_NOT (scm_less_p (x, y)); |
0f2d19dd | 3319 | } |
1bbd0b84 | 3320 | #undef FUNC_NAME |
0f2d19dd JB |
3321 | |
3322 | ||
152f82bf | 3323 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3324 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3325 | * "zero." | |
3326 | */ | |
0f2d19dd | 3327 | SCM |
6e8d25a6 | 3328 | scm_zero_p (SCM z) |
0f2d19dd | 3329 | { |
c2ff8ab0 DH |
3330 | if (SCM_INUMP (z)) { |
3331 | return SCM_BOOL (SCM_EQ_P (z, SCM_INUM0)); | |
3332 | } else if (SCM_BIGP (z)) { | |
3333 | return SCM_BOOL_F; | |
3334 | } else if (SCM_REALP (z)) { | |
3335 | return SCM_BOOL (SCM_REAL_VALUE (z) == 0.0); | |
3336 | } else if (SCM_COMPLEXP (z)) { | |
3337 | return SCM_BOOL (SCM_COMPLEX_REAL (z) == 0.0 | |
3338 | && SCM_COMPLEX_IMAG (z) == 0.0); | |
3339 | } else { | |
3340 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); | |
3341 | } | |
0f2d19dd JB |
3342 | } |
3343 | ||
3344 | ||
152f82bf | 3345 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3346 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3347 | * "zero." | |
3348 | */ | |
0f2d19dd | 3349 | SCM |
6e8d25a6 | 3350 | scm_positive_p (SCM x) |
0f2d19dd | 3351 | { |
c2ff8ab0 DH |
3352 | if (SCM_INUMP (x)) { |
3353 | return SCM_BOOL (SCM_INUM (x) > 0); | |
3354 | } else if (SCM_BIGP (x)) { | |
3355 | return SCM_BOOL (!SCM_BIGSIGN (x)); | |
3356 | } else if (SCM_REALP (x)) { | |
3357 | return SCM_BOOL(SCM_REAL_VALUE (x) > 0.0); | |
3358 | } else { | |
3359 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); | |
3360 | } | |
0f2d19dd JB |
3361 | } |
3362 | ||
3363 | ||
152f82bf | 3364 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3365 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3366 | * "zero." | |
3367 | */ | |
0f2d19dd | 3368 | SCM |
6e8d25a6 | 3369 | scm_negative_p (SCM x) |
0f2d19dd | 3370 | { |
c2ff8ab0 DH |
3371 | if (SCM_INUMP (x)) { |
3372 | return SCM_BOOL (SCM_INUM (x) < 0); | |
3373 | } else if (SCM_BIGP (x)) { | |
3374 | return SCM_BOOL (SCM_BIGSIGN (x)); | |
3375 | } else if (SCM_REALP (x)) { | |
3376 | return SCM_BOOL(SCM_REAL_VALUE (x) < 0.0); | |
3377 | } else { | |
3378 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); | |
3379 | } | |
0f2d19dd JB |
3380 | } |
3381 | ||
3382 | ||
9de33deb | 3383 | SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max); |
942e5b91 MG |
3384 | /* "Return the maximum of all parameter values." |
3385 | */ | |
0f2d19dd | 3386 | SCM |
6e8d25a6 | 3387 | scm_max (SCM x, SCM y) |
0f2d19dd | 3388 | { |
f4c627b3 DH |
3389 | if (SCM_UNBNDP (y)) { |
3390 | if (SCM_UNBNDP (x)) { | |
c05e97b7 | 3391 | SCM_WTA_DISPATCH_0 (g_max, s_max); |
f4c627b3 | 3392 | } else if (SCM_NUMBERP (x)) { |
f872b822 | 3393 | return x; |
f4c627b3 DH |
3394 | } else { |
3395 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3396 | } |
f4c627b3 DH |
3397 | } |
3398 | ||
3399 | if (SCM_INUMP (x)) { | |
3400 | long xx = SCM_INUM (x); | |
3401 | if (SCM_INUMP (y)) { | |
3402 | long yy = SCM_INUM (y); | |
3403 | return (xx < yy) ? y : x; | |
3404 | } else if (SCM_BIGP (y)) { | |
3405 | return SCM_BIGSIGN (y) ? x : y; | |
3406 | } else if (SCM_REALP (y)) { | |
3407 | double z = xx; | |
3408 | return (z <= SCM_REAL_VALUE (y)) ? y : scm_make_real (z); | |
3409 | } else { | |
3410 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3411 | } |
f4c627b3 DH |
3412 | } else if (SCM_BIGP (x)) { |
3413 | if (SCM_INUMP (y)) { | |
3414 | return SCM_BIGSIGN (x) ? y : x; | |
3415 | } else if (SCM_BIGP (y)) { | |
3416 | return (1 == scm_bigcomp (x, y)) ? y : x; | |
3417 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3418 | double z = scm_i_big2dbl (x); |
f4c627b3 DH |
3419 | return (z <= SCM_REAL_VALUE (y)) ? y : scm_make_real (z); |
3420 | } else { | |
3421 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3422 | } | |
3423 | } else if (SCM_REALP (x)) { | |
3424 | if (SCM_INUMP (y)) { | |
3425 | double z = SCM_INUM (y); | |
3426 | return (SCM_REAL_VALUE (x) < z) ? scm_make_real (z) : x; | |
3427 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3428 | double z = scm_i_big2dbl (y); |
f4c627b3 DH |
3429 | return (SCM_REAL_VALUE (x) < z) ? scm_make_real (z) : x; |
3430 | } else if (SCM_REALP (y)) { | |
3431 | return (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)) ? y : x; | |
3432 | } else { | |
3433 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3434 | } |
f4c627b3 DH |
3435 | } else { |
3436 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); | |
3437 | } | |
0f2d19dd JB |
3438 | } |
3439 | ||
3440 | ||
9de33deb | 3441 | SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min); |
942e5b91 MG |
3442 | /* "Return the minium of all parameter values." |
3443 | */ | |
0f2d19dd | 3444 | SCM |
6e8d25a6 | 3445 | scm_min (SCM x, SCM y) |
0f2d19dd | 3446 | { |
f4c627b3 DH |
3447 | if (SCM_UNBNDP (y)) { |
3448 | if (SCM_UNBNDP (x)) { | |
c05e97b7 | 3449 | SCM_WTA_DISPATCH_0 (g_min, s_min); |
f4c627b3 | 3450 | } else if (SCM_NUMBERP (x)) { |
f872b822 | 3451 | return x; |
f4c627b3 DH |
3452 | } else { |
3453 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 3454 | } |
f4c627b3 DH |
3455 | } |
3456 | ||
3457 | if (SCM_INUMP (x)) { | |
3458 | long xx = SCM_INUM (x); | |
3459 | if (SCM_INUMP (y)) { | |
3460 | long yy = SCM_INUM (y); | |
3461 | return (xx < yy) ? x : y; | |
3462 | } else if (SCM_BIGP (y)) { | |
3463 | return SCM_BIGSIGN (y) ? y : x; | |
3464 | } else if (SCM_REALP (y)) { | |
3465 | double z = xx; | |
3466 | return (z < SCM_REAL_VALUE (y)) ? scm_make_real (z) : y; | |
3467 | } else { | |
3468 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3469 | } |
f4c627b3 DH |
3470 | } else if (SCM_BIGP (x)) { |
3471 | if (SCM_INUMP (y)) { | |
3472 | return SCM_BIGSIGN (x) ? x : y; | |
3473 | } else if (SCM_BIGP (y)) { | |
3474 | return (-1 == scm_bigcomp (x, y)) ? y : x; | |
3475 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3476 | double z = scm_i_big2dbl (x); |
f4c627b3 DH |
3477 | return (z < SCM_REAL_VALUE (y)) ? scm_make_real (z) : y; |
3478 | } else { | |
3479 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
3480 | } | |
3481 | } else if (SCM_REALP (x)) { | |
3482 | if (SCM_INUMP (y)) { | |
3483 | double z = SCM_INUM (y); | |
3484 | return (SCM_REAL_VALUE (x) <= z) ? x : scm_make_real (z); | |
3485 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3486 | double z = scm_i_big2dbl (y); |
f4c627b3 DH |
3487 | return (SCM_REAL_VALUE (x) <= z) ? x : scm_make_real (z); |
3488 | } else if (SCM_REALP (y)) { | |
3489 | return (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)) ? x : y; | |
3490 | } else { | |
3491 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3492 | } |
f4c627b3 DH |
3493 | } else { |
3494 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); | |
3495 | } | |
0f2d19dd JB |
3496 | } |
3497 | ||
3498 | ||
9de33deb | 3499 | SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum); |
942e5b91 MG |
3500 | /* "Return the sum of all parameter values. Return 0 if called without\n" |
3501 | * "any parameters." | |
3502 | */ | |
0f2d19dd | 3503 | SCM |
6e8d25a6 | 3504 | scm_sum (SCM x, SCM y) |
0f2d19dd | 3505 | { |
98cb6e75 DH |
3506 | if (SCM_UNBNDP (y)) { |
3507 | if (SCM_UNBNDP (x)) { | |
3508 | return SCM_INUM0; | |
3509 | } else if (SCM_NUMBERP (x)) { | |
f872b822 | 3510 | return x; |
98cb6e75 DH |
3511 | } else { |
3512 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); | |
f872b822 | 3513 | } |
98cb6e75 | 3514 | } |
c209c88e | 3515 | |
98cb6e75 DH |
3516 | if (SCM_INUMP (x)) { |
3517 | long int xx = SCM_INUM (x); | |
3518 | if (SCM_INUMP (y)) { | |
3519 | long int yy = SCM_INUM (y); | |
3520 | long int z = xx + yy; | |
3521 | if (SCM_FIXABLE (z)) { | |
3522 | return SCM_MAKINUM (z); | |
3523 | } else { | |
3524 | #ifdef SCM_BIGDIG | |
1be6b49c | 3525 | return scm_i_long2big (z); |
98cb6e75 DH |
3526 | #else /* SCM_BIGDIG */ |
3527 | return scm_make_real ((double) z); | |
3528 | #endif /* SCM_BIGDIG */ | |
3529 | } | |
3530 | } else if (SCM_BIGP (y)) { | |
3531 | intbig: | |
f872b822 | 3532 | { |
98cb6e75 DH |
3533 | long int xx = SCM_INUM (x); |
3534 | #ifndef SCM_DIGSTOOBIG | |
3535 | long z = scm_pseudolong (xx); | |
3536 | return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
3537 | (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, 0); | |
3538 | #else /* SCM_DIGSTOOBIG */ | |
3539 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; | |
3540 | scm_longdigs (xx, zdigs); | |
3541 | return scm_addbig (zdigs, SCM_DIGSPERLONG, | |
3542 | (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, 0); | |
3543 | #endif /* SCM_DIGSTOOBIG */ | |
0f2d19dd | 3544 | } |
98cb6e75 DH |
3545 | } else if (SCM_REALP (y)) { |
3546 | return scm_make_real (xx + SCM_REAL_VALUE (y)); | |
3547 | } else if (SCM_COMPLEXP (y)) { | |
3548 | return scm_make_complex (xx + SCM_COMPLEX_REAL (y), | |
3549 | SCM_COMPLEX_IMAG (y)); | |
3550 | } else { | |
3551 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 3552 | } |
98cb6e75 DH |
3553 | } else if (SCM_BIGP (x)) { |
3554 | if (SCM_INUMP (y)) { | |
3555 | SCM_SWAP (x, y); | |
3556 | goto intbig; | |
3557 | } else if (SCM_BIGP (y)) { | |
3558 | if (SCM_NUMDIGS (x) > SCM_NUMDIGS (y)) { | |
3559 | SCM_SWAP (x, y); | |
3560 | } | |
3561 | return scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
3562 | SCM_BIGSIGN (x), y, 0); | |
3563 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3564 | return scm_make_real (scm_i_big2dbl (x) + SCM_REAL_VALUE (y)); |
98cb6e75 | 3565 | } else if (SCM_COMPLEXP (y)) { |
1be6b49c | 3566 | return scm_make_complex (scm_i_big2dbl (x) + SCM_COMPLEX_REAL (y), |
98cb6e75 DH |
3567 | SCM_COMPLEX_IMAG (y)); |
3568 | } else { | |
3569 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 3570 | } |
98cb6e75 DH |
3571 | } else if (SCM_REALP (x)) { |
3572 | if (SCM_INUMP (y)) { | |
3573 | return scm_make_real (SCM_REAL_VALUE (x) + SCM_INUM (y)); | |
3574 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3575 | return scm_make_real (SCM_REAL_VALUE (x) + scm_i_big2dbl (y)); |
98cb6e75 DH |
3576 | } else if (SCM_REALP (y)) { |
3577 | return scm_make_real (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); | |
3578 | } else if (SCM_COMPLEXP (y)) { | |
3579 | return scm_make_complex (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), | |
3580 | SCM_COMPLEX_IMAG (y)); | |
3581 | } else { | |
3582 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
3583 | } | |
3584 | } else if (SCM_COMPLEXP (x)) { | |
3585 | if (SCM_INUMP (y)) { | |
3586 | return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_INUM (y), | |
3587 | SCM_COMPLEX_IMAG (x)); | |
3588 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3589 | return scm_make_complex (SCM_COMPLEX_REAL (x) + scm_i_big2dbl (y), |
98cb6e75 DH |
3590 | SCM_COMPLEX_IMAG (x)); |
3591 | } else if (SCM_REALP (y)) { | |
3592 | return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), | |
3593 | SCM_COMPLEX_IMAG (x)); | |
3594 | } else if (SCM_COMPLEXP (y)) { | |
3595 | return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), | |
3596 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); | |
3597 | } else { | |
3598 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
3599 | } | |
3600 | } else { | |
3601 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); | |
3602 | } | |
0f2d19dd JB |
3603 | } |
3604 | ||
3605 | ||
9de33deb | 3606 | SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference); |
609c3d30 MG |
3607 | /* If called with one argument @var{z1}, -@var{z1} returned. Otherwise |
3608 | * the sum of all but the first argument are subtracted from the first | |
3609 | * argument. */ | |
c05e97b7 | 3610 | #define FUNC_NAME s_difference |
0f2d19dd | 3611 | SCM |
6e8d25a6 | 3612 | scm_difference (SCM x, SCM y) |
0f2d19dd | 3613 | { |
98cb6e75 | 3614 | if (SCM_UNBNDP (y)) { |
c05e97b7 MV |
3615 | if (SCM_UNBNDP (x)) { |
3616 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
3617 | } else if (SCM_INUMP (x)) { | |
98cb6e75 DH |
3618 | long xx = -SCM_INUM (x); |
3619 | if (SCM_FIXABLE (xx)) { | |
3620 | return SCM_MAKINUM (xx); | |
3621 | } else { | |
f872b822 | 3622 | #ifdef SCM_BIGDIG |
1be6b49c | 3623 | return scm_i_long2big (xx); |
f3ae5d60 | 3624 | #else |
98cb6e75 | 3625 | return scm_make_real ((double) xx); |
f3ae5d60 | 3626 | #endif |
f3ae5d60 | 3627 | } |
98cb6e75 | 3628 | } else if (SCM_BIGP (x)) { |
1be6b49c | 3629 | SCM z = scm_i_copybig (x, !SCM_BIGSIGN (x)); |
98cb6e75 DH |
3630 | unsigned int digs = SCM_NUMDIGS (z); |
3631 | unsigned int size = digs * SCM_BITSPERDIG / SCM_CHAR_BIT; | |
1be6b49c | 3632 | return size <= sizeof (SCM) ? scm_i_big2inum (z, digs) : z; |
98cb6e75 DH |
3633 | } else if (SCM_REALP (x)) { |
3634 | return scm_make_real (-SCM_REAL_VALUE (x)); | |
3635 | } else if (SCM_COMPLEXP (x)) { | |
3636 | return scm_make_complex (-SCM_COMPLEX_REAL (x), -SCM_COMPLEX_IMAG (x)); | |
3637 | } else { | |
3638 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 3639 | } |
98cb6e75 DH |
3640 | } |
3641 | ||
3642 | if (SCM_INUMP (x)) { | |
3643 | long int xx = SCM_INUM (x); | |
3644 | if (SCM_INUMP (y)) { | |
3645 | long int yy = SCM_INUM (y); | |
3646 | long int z = xx - yy; | |
3647 | if (SCM_FIXABLE (z)) { | |
3648 | return SCM_MAKINUM (z); | |
3649 | } else { | |
f872b822 | 3650 | #ifdef SCM_BIGDIG |
1be6b49c | 3651 | return scm_i_long2big (z); |
f872b822 | 3652 | #else |
98cb6e75 | 3653 | return scm_make_real ((double) z); |
f872b822 | 3654 | #endif |
98cb6e75 DH |
3655 | } |
3656 | } else if (SCM_BIGP (y)) { | |
3657 | #ifndef SCM_DIGSTOOBIG | |
3658 | long z = scm_pseudolong (xx); | |
3659 | return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
3660 | (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, SCM_BIGSIGNFLAG); | |
f872b822 | 3661 | #else |
98cb6e75 DH |
3662 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
3663 | scm_longdigs (xx, zdigs); | |
3664 | return scm_addbig (zdigs, SCM_DIGSPERLONG, | |
3665 | (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, SCM_BIGSIGNFLAG); | |
f872b822 | 3666 | #endif |
98cb6e75 DH |
3667 | } else if (SCM_REALP (y)) { |
3668 | return scm_make_real (xx - SCM_REAL_VALUE (y)); | |
3669 | } else if (SCM_COMPLEXP (y)) { | |
3670 | return scm_make_complex (xx - SCM_COMPLEX_REAL (y), | |
3671 | -SCM_COMPLEX_IMAG (y)); | |
3672 | } else { | |
3673 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 3674 | } |
98cb6e75 DH |
3675 | } else if (SCM_BIGP (x)) { |
3676 | if (SCM_INUMP (y)) { | |
3677 | long int yy = SCM_INUM (y); | |
3678 | #ifndef SCM_DIGSTOOBIG | |
3679 | long z = scm_pseudolong (yy); | |
3680 | return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
3681 | (yy < 0) ? 0 : SCM_BIGSIGNFLAG, x, 0); | |
f872b822 | 3682 | #else |
98cb6e75 DH |
3683 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
3684 | scm_longdigs (yy, zdigs); | |
3685 | return scm_addbig (zdigs, SCM_DIGSPERLONG, | |
3686 | (yy < 0) ? 0 : SCM_BIGSIGNFLAG, x, 0); | |
0f2d19dd | 3687 | #endif |
98cb6e75 DH |
3688 | } else if (SCM_BIGP (y)) { |
3689 | return (SCM_NUMDIGS (x) < SCM_NUMDIGS (y)) | |
3690 | ? scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
3691 | SCM_BIGSIGN (x), y, SCM_BIGSIGNFLAG) | |
3692 | : scm_addbig (SCM_BDIGITS (y), SCM_NUMDIGS (y), | |
3693 | SCM_BIGSIGN (y) ^ SCM_BIGSIGNFLAG, x, 0); | |
3694 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3695 | return scm_make_real (scm_i_big2dbl (x) - SCM_REAL_VALUE (y)); |
98cb6e75 | 3696 | } else if (SCM_COMPLEXP (y)) { |
1be6b49c | 3697 | return scm_make_complex (scm_i_big2dbl (x) - SCM_COMPLEX_REAL (y), |
98cb6e75 DH |
3698 | - SCM_COMPLEX_IMAG (y)); |
3699 | } else { | |
3700 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
3701 | } | |
3702 | } else if (SCM_REALP (x)) { | |
3703 | if (SCM_INUMP (y)) { | |
3704 | return scm_make_real (SCM_REAL_VALUE (x) - SCM_INUM (y)); | |
3705 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3706 | return scm_make_real (SCM_REAL_VALUE (x) - scm_i_big2dbl (y)); |
98cb6e75 DH |
3707 | } else if (SCM_REALP (y)) { |
3708 | return scm_make_real (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); | |
3709 | } else if (SCM_COMPLEXP (y)) { | |
3710 | return scm_make_complex (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), | |
3711 | -SCM_COMPLEX_IMAG (y)); | |
3712 | } else { | |
3713 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
3714 | } | |
3715 | } else if (SCM_COMPLEXP (x)) { | |
3716 | if (SCM_INUMP (y)) { | |
3717 | return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_INUM (y), | |
3718 | SCM_COMPLEX_IMAG (x)); | |
3719 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3720 | return scm_make_complex (SCM_COMPLEX_REAL (x) - scm_i_big2dbl (y), |
98cb6e75 DH |
3721 | SCM_COMPLEX_IMAG (x)); |
3722 | } else if (SCM_REALP (y)) { | |
3723 | return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), | |
3724 | SCM_COMPLEX_IMAG (x)); | |
3725 | } else if (SCM_COMPLEXP (y)) { | |
3726 | return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), | |
3727 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); | |
3728 | } else { | |
3729 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
3730 | } | |
3731 | } else { | |
3732 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); | |
3733 | } | |
0f2d19dd | 3734 | } |
c05e97b7 | 3735 | #undef FUNC_NAME |
0f2d19dd | 3736 | |
9de33deb | 3737 | SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product); |
942e5b91 MG |
3738 | /* "Return the product of all arguments. If called without arguments,\n" |
3739 | * "1 is returned." | |
3740 | */ | |
0f2d19dd | 3741 | SCM |
6e8d25a6 | 3742 | scm_product (SCM x, SCM y) |
0f2d19dd | 3743 | { |
f4c627b3 DH |
3744 | if (SCM_UNBNDP (y)) { |
3745 | if (SCM_UNBNDP (x)) { | |
3746 | return SCM_MAKINUM (1L); | |
3747 | } else if (SCM_NUMBERP (x)) { | |
f872b822 | 3748 | return x; |
f4c627b3 DH |
3749 | } else { |
3750 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 3751 | } |
f4c627b3 DH |
3752 | } |
3753 | ||
3754 | if (SCM_INUMP (x)) { | |
3755 | long xx; | |
3756 | ||
3757 | intbig: | |
3758 | xx = SCM_INUM (x); | |
3759 | ||
3760 | if (xx == 0) { | |
f872b822 | 3761 | return x; |
f4c627b3 DH |
3762 | } else if (xx == 1) { |
3763 | return y; | |
3764 | } | |
3765 | ||
3766 | if (SCM_INUMP (y)) { | |
3767 | long yy = SCM_INUM (y); | |
3768 | long kk = xx * yy; | |
3769 | SCM k = SCM_MAKINUM (kk); | |
3770 | if (kk != SCM_INUM (k) || kk / xx != yy) { | |
f872b822 | 3771 | #ifdef SCM_BIGDIG |
f4c627b3 | 3772 | int sgn = (xx < 0) ^ (yy < 0); |
f872b822 | 3773 | #ifndef SCM_DIGSTOOBIG |
f4c627b3 DH |
3774 | long i = scm_pseudolong (xx); |
3775 | long j = scm_pseudolong (yy); | |
f872b822 MD |
3776 | return scm_mulbig ((SCM_BIGDIG *) & i, SCM_DIGSPERLONG, |
3777 | (SCM_BIGDIG *) & j, SCM_DIGSPERLONG, sgn); | |
3778 | #else /* SCM_DIGSTOOBIG */ | |
f4c627b3 DH |
3779 | SCM_BIGDIG xdigs [SCM_DIGSPERLONG]; |
3780 | SCM_BIGDIG ydigs [SCM_DIGSPERLONG]; | |
3781 | scm_longdigs (xx, xdigs); | |
3782 | scm_longdigs (yy, ydigs); | |
3783 | return scm_mulbig (xdigs, SCM_DIGSPERLONG, | |
3784 | ydigs, SCM_DIGSPERLONG, | |
f872b822 MD |
3785 | sgn); |
3786 | #endif | |
f4c627b3 DH |
3787 | #else |
3788 | return scm_make_real (((double) xx) * ((double) yy)); | |
3789 | #endif | |
3790 | } else { | |
3791 | return k; | |
0f2d19dd | 3792 | } |
f4c627b3 DH |
3793 | } else if (SCM_BIGP (y)) { |
3794 | #ifndef SCM_DIGSTOOBIG | |
3795 | long z = scm_pseudolong (xx); | |
3796 | return scm_mulbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
3797 | SCM_BDIGITS (y), SCM_NUMDIGS (y), | |
3798 | SCM_BIGSIGN (y) ? (xx > 0) : (xx < 0)); | |
0f2d19dd | 3799 | #else |
f4c627b3 DH |
3800 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
3801 | scm_longdigs (xx, zdigs); | |
3802 | return scm_mulbig (zdigs, SCM_DIGSPERLONG, | |
3803 | SCM_BDIGITS (y), SCM_NUMDIGS (y), | |
3804 | SCM_BIGSIGN (y) ? (xx > 0) : (xx < 0)); | |
0f2d19dd | 3805 | #endif |
f4c627b3 DH |
3806 | } else if (SCM_REALP (y)) { |
3807 | return scm_make_real (xx * SCM_REAL_VALUE (y)); | |
3808 | } else if (SCM_COMPLEXP (y)) { | |
3809 | return scm_make_complex (xx * SCM_COMPLEX_REAL (y), | |
3810 | xx * SCM_COMPLEX_IMAG (y)); | |
3811 | } else { | |
3812 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
3813 | } | |
3814 | } else if (SCM_BIGP (x)) { | |
3815 | if (SCM_INUMP (y)) { | |
3816 | SCM_SWAP (x, y); | |
3817 | goto intbig; | |
3818 | } else if (SCM_BIGP (y)) { | |
3819 | return scm_mulbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
3820 | SCM_BDIGITS (y), SCM_NUMDIGS (y), | |
3821 | SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y)); | |
3822 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3823 | return scm_make_real (scm_i_big2dbl (x) * SCM_REAL_VALUE (y)); |
f4c627b3 | 3824 | } else if (SCM_COMPLEXP (y)) { |
1be6b49c | 3825 | double z = scm_i_big2dbl (x); |
f4c627b3 DH |
3826 | return scm_make_complex (z * SCM_COMPLEX_REAL (y), |
3827 | z * SCM_COMPLEX_IMAG (y)); | |
3828 | } else { | |
3829 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
3830 | } | |
3831 | } else if (SCM_REALP (x)) { | |
3832 | if (SCM_INUMP (y)) { | |
3833 | return scm_make_real (SCM_INUM (y) * SCM_REAL_VALUE (x)); | |
3834 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3835 | return scm_make_real (scm_i_big2dbl (y) * SCM_REAL_VALUE (x)); |
f4c627b3 DH |
3836 | } else if (SCM_REALP (y)) { |
3837 | return scm_make_real (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); | |
3838 | } else if (SCM_COMPLEXP (y)) { | |
3839 | return scm_make_complex (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), | |
3840 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); | |
3841 | } else { | |
3842 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
3843 | } | |
3844 | } else if (SCM_COMPLEXP (x)) { | |
3845 | if (SCM_INUMP (y)) { | |
3846 | return scm_make_complex (SCM_INUM (y) * SCM_COMPLEX_REAL (x), | |
3847 | SCM_INUM (y) * SCM_COMPLEX_IMAG (x)); | |
3848 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3849 | double z = scm_i_big2dbl (y); |
f4c627b3 DH |
3850 | return scm_make_complex (z * SCM_COMPLEX_REAL (x), |
3851 | z * SCM_COMPLEX_IMAG (x)); | |
3852 | } else if (SCM_REALP (y)) { | |
3853 | return scm_make_complex (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), | |
3854 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); | |
3855 | } else if (SCM_COMPLEXP (y)) { | |
3856 | return scm_make_complex (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) | |
3857 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), | |
3858 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
3859 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
3860 | } else { | |
3861 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
3862 | } | |
3863 | } else { | |
3864 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); | |
0f2d19dd JB |
3865 | } |
3866 | } | |
3867 | ||
3868 | ||
0f2d19dd | 3869 | double |
6e8d25a6 | 3870 | scm_num2dbl (SCM a, const char *why) |
f4c627b3 | 3871 | #define FUNC_NAME why |
0f2d19dd | 3872 | { |
f4c627b3 | 3873 | if (SCM_INUMP (a)) { |
0f2d19dd | 3874 | return (double) SCM_INUM (a); |
f4c627b3 | 3875 | } else if (SCM_BIGP (a)) { |
1be6b49c | 3876 | return scm_i_big2dbl (a); |
f4c627b3 DH |
3877 | } else if (SCM_REALP (a)) { |
3878 | return (SCM_REAL_VALUE (a)); | |
3879 | } else { | |
3880 | SCM_WRONG_TYPE_ARG (SCM_ARGn, a); | |
3881 | } | |
0f2d19dd | 3882 | } |
f4c627b3 | 3883 | #undef FUNC_NAME |
0f2d19dd | 3884 | |
7351e207 MV |
3885 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
3886 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
3887 | #define ALLOW_DIVIDE_BY_ZERO | |
3888 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
3889 | #endif | |
0f2d19dd | 3890 | |
ba74ef4e MV |
3891 | /* The code below for complex division is adapted from the GNU |
3892 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
3893 | this copyright: */ | |
3894 | ||
3895 | /**************************************************************** | |
3896 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
3897 | ||
3898 | Permission to use, copy, modify, and distribute this software | |
3899 | and its documentation for any purpose and without fee is hereby | |
3900 | granted, provided that the above copyright notice appear in all | |
3901 | copies and that both that the copyright notice and this | |
3902 | permission notice and warranty disclaimer appear in supporting | |
3903 | documentation, and that the names of AT&T Bell Laboratories or | |
3904 | Bellcore or any of their entities not be used in advertising or | |
3905 | publicity pertaining to distribution of the software without | |
3906 | specific, written prior permission. | |
3907 | ||
3908 | AT&T and Bellcore disclaim all warranties with regard to this | |
3909 | software, including all implied warranties of merchantability | |
3910 | and fitness. In no event shall AT&T or Bellcore be liable for | |
3911 | any special, indirect or consequential damages or any damages | |
3912 | whatsoever resulting from loss of use, data or profits, whether | |
3913 | in an action of contract, negligence or other tortious action, | |
3914 | arising out of or in connection with the use or performance of | |
3915 | this software. | |
3916 | ****************************************************************/ | |
3917 | ||
9de33deb | 3918 | SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide); |
609c3d30 MG |
3919 | /* Divide the first argument by the product of the remaining |
3920 | arguments. If called with one argument @var{z1}, 1/@var{z1} is | |
3921 | returned. */ | |
c05e97b7 | 3922 | #define FUNC_NAME s_divide |
0f2d19dd | 3923 | SCM |
6e8d25a6 | 3924 | scm_divide (SCM x, SCM y) |
0f2d19dd | 3925 | { |
f8de44c1 DH |
3926 | double a; |
3927 | ||
3928 | if (SCM_UNBNDP (y)) { | |
3929 | if (SCM_UNBNDP (x)) { | |
c05e97b7 | 3930 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); |
f8de44c1 | 3931 | } else if (SCM_INUMP (x)) { |
164826d3 DH |
3932 | long xx = SCM_INUM (x); |
3933 | if (xx == 1 || xx == -1) { | |
f8de44c1 | 3934 | return x; |
7351e207 | 3935 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
164826d3 DH |
3936 | } else if (xx == 0) { |
3937 | scm_num_overflow (s_divide); | |
7351e207 | 3938 | #endif |
f8de44c1 | 3939 | } else { |
164826d3 | 3940 | return scm_make_real (1.0 / (double) xx); |
f8de44c1 | 3941 | } |
f8de44c1 | 3942 | } else if (SCM_BIGP (x)) { |
1be6b49c | 3943 | return scm_make_real (1.0 / scm_i_big2dbl (x)); |
f8de44c1 | 3944 | } else if (SCM_REALP (x)) { |
5eec27e9 | 3945 | double xx = SCM_REAL_VALUE (x); |
7351e207 | 3946 | #ifndef ALLOW_DIVIDE_BY_ZERO |
5eec27e9 DH |
3947 | if (xx == 0.0) |
3948 | scm_num_overflow (s_divide); | |
3949 | else | |
7351e207 | 3950 | #endif |
5eec27e9 | 3951 | return scm_make_real (1.0 / xx); |
f8de44c1 DH |
3952 | } else if (SCM_COMPLEXP (x)) { |
3953 | double r = SCM_COMPLEX_REAL (x); | |
3954 | double i = SCM_COMPLEX_IMAG (x); | |
ba74ef4e MV |
3955 | if (r <= i) { |
3956 | double t = r / i; | |
3957 | double d = i * (1.0 + t * t); | |
3958 | return scm_make_complex (t / d, -1.0 / d); | |
3959 | } else { | |
3960 | double t = i / r; | |
3961 | double d = r * (1.0 + t * t); | |
3962 | return scm_make_complex (1.0 / d, -t / d); | |
3963 | } | |
f8de44c1 DH |
3964 | } else { |
3965 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
3966 | } | |
3967 | } | |
3968 | ||
3969 | if (SCM_INUMP (x)) { | |
3970 | long xx = SCM_INUM (x); | |
3971 | if (SCM_INUMP (y)) { | |
3972 | long yy = SCM_INUM (y); | |
3973 | if (yy == 0) { | |
7351e207 | 3974 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
f4c627b3 | 3975 | scm_num_overflow (s_divide); |
7351e207 MV |
3976 | #else |
3977 | return scm_make_real ((double) xx / (double) yy); | |
3978 | #endif | |
f8de44c1 DH |
3979 | } else if (xx % yy != 0) { |
3980 | return scm_make_real ((double) xx / (double) yy); | |
3981 | } else { | |
3982 | long z = xx / yy; | |
3983 | if (SCM_FIXABLE (z)) { | |
3984 | return SCM_MAKINUM (z); | |
3985 | } else { | |
f872b822 | 3986 | #ifdef SCM_BIGDIG |
1be6b49c | 3987 | return scm_i_long2big (z); |
f872b822 | 3988 | #else |
f8de44c1 | 3989 | return scm_make_real ((double) xx / (double) yy); |
f872b822 | 3990 | #endif |
f872b822 | 3991 | } |
f8de44c1 | 3992 | } |
f8de44c1 | 3993 | } else if (SCM_BIGP (y)) { |
1be6b49c | 3994 | return scm_make_real ((double) xx / scm_i_big2dbl (y)); |
f8de44c1 | 3995 | } else if (SCM_REALP (y)) { |
5eec27e9 | 3996 | double yy = SCM_REAL_VALUE (y); |
7351e207 | 3997 | #ifndef ALLOW_DIVIDE_BY_ZERO |
5eec27e9 DH |
3998 | if (yy == 0.0) |
3999 | scm_num_overflow (s_divide); | |
4000 | else | |
7351e207 | 4001 | #endif |
5eec27e9 | 4002 | return scm_make_real ((double) xx / yy); |
f8de44c1 DH |
4003 | } else if (SCM_COMPLEXP (y)) { |
4004 | a = xx; | |
4005 | complex_div: /* y _must_ be a complex number */ | |
4006 | { | |
4007 | double r = SCM_COMPLEX_REAL (y); | |
4008 | double i = SCM_COMPLEX_IMAG (y); | |
ba74ef4e MV |
4009 | if (r <= i) { |
4010 | double t = r / i; | |
4011 | double d = i * (1.0 + t * t); | |
4012 | return scm_make_complex ((a * t) / d, -a / d); | |
4013 | } else { | |
4014 | double t = i / r; | |
4015 | double d = r * (1.0 + t * t); | |
4016 | return scm_make_complex (a / d, -(a * t) / d); | |
4017 | } | |
f8de44c1 DH |
4018 | } |
4019 | } else { | |
4020 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
4021 | } | |
f8de44c1 DH |
4022 | } else if (SCM_BIGP (x)) { |
4023 | if (SCM_INUMP (y)) { | |
4024 | long int yy = SCM_INUM (y); | |
4025 | if (yy == 0) { | |
7351e207 | 4026 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
f8de44c1 | 4027 | scm_num_overflow (s_divide); |
7351e207 MV |
4028 | #else |
4029 | if (scm_bigcomp (x, scm_i_int2big (0)) == 0) | |
4030 | return scm_nan (); | |
4031 | else | |
4032 | return scm_inf (); | |
4033 | #endif | |
f8de44c1 DH |
4034 | } else if (yy == 1) { |
4035 | return x; | |
4036 | } else { | |
4037 | long z = yy < 0 ? -yy : yy; | |
4038 | if (z < SCM_BIGRAD) { | |
1be6b49c | 4039 | SCM w = scm_i_copybig (x, SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0)); |
f8de44c1 DH |
4040 | return scm_divbigdig (SCM_BDIGITS (w), SCM_NUMDIGS (w), |
4041 | (SCM_BIGDIG) z) | |
1be6b49c ML |
4042 | ? scm_make_real (scm_i_big2dbl (x) / (double) yy) |
4043 | : scm_i_normbig (w); | |
f8de44c1 DH |
4044 | } else { |
4045 | SCM w; | |
4046 | #ifndef SCM_DIGSTOOBIG | |
4047 | z = scm_pseudolong (z); | |
4048 | w = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
4049 | (SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
4050 | SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0), 3); | |
f872b822 | 4051 | #else |
f8de44c1 DH |
4052 | SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; |
4053 | scm_longdigs (z, zdigs); | |
4054 | w = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
4055 | zdigs, SCM_DIGSPERLONG, | |
4056 | SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0), 3); | |
f872b822 | 4057 | #endif |
f4c627b3 DH |
4058 | return (!SCM_UNBNDP (w)) |
4059 | ? w | |
1be6b49c | 4060 | : scm_make_real (scm_i_big2dbl (x) / (double) yy); |
f872b822 | 4061 | } |
f8de44c1 DH |
4062 | } |
4063 | } else if (SCM_BIGP (y)) { | |
4064 | SCM w = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
4065 | SCM_BDIGITS (y), SCM_NUMDIGS (y), | |
4066 | SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y), 3); | |
f4c627b3 DH |
4067 | return (!SCM_UNBNDP (w)) |
4068 | ? w | |
1be6b49c | 4069 | : scm_make_real (scm_i_big2dbl (x) / scm_i_big2dbl (y)); |
f8de44c1 | 4070 | } else if (SCM_REALP (y)) { |
5eec27e9 | 4071 | double yy = SCM_REAL_VALUE (y); |
7351e207 | 4072 | #ifndef ALLOW_DIVIDE_BY_ZERO |
5eec27e9 DH |
4073 | if (yy == 0.0) |
4074 | scm_num_overflow (s_divide); | |
4075 | else | |
7351e207 | 4076 | #endif |
5eec27e9 | 4077 | return scm_make_real (scm_i_big2dbl (x) / yy); |
f8de44c1 | 4078 | } else if (SCM_COMPLEXP (y)) { |
1be6b49c | 4079 | a = scm_i_big2dbl (x); |
f8de44c1 DH |
4080 | goto complex_div; |
4081 | } else { | |
4082 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4083 | } |
f8de44c1 DH |
4084 | } else if (SCM_REALP (x)) { |
4085 | double rx = SCM_REAL_VALUE (x); | |
4086 | if (SCM_INUMP (y)) { | |
5eec27e9 | 4087 | long int yy = SCM_INUM (y); |
7351e207 MV |
4088 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
4089 | if (yy == 0) | |
5eec27e9 | 4090 | scm_num_overflow (s_divide); |
7351e207 MV |
4091 | else |
4092 | #endif | |
5eec27e9 | 4093 | return scm_make_real (rx / (double) yy); |
f8de44c1 | 4094 | } else if (SCM_BIGP (y)) { |
1be6b49c | 4095 | return scm_make_real (rx / scm_i_big2dbl (y)); |
f8de44c1 | 4096 | } else if (SCM_REALP (y)) { |
5eec27e9 | 4097 | double yy = SCM_REAL_VALUE (y); |
7351e207 | 4098 | #ifndef ALLOW_DIVIDE_BY_ZERO |
5eec27e9 DH |
4099 | if (yy == 0.0) |
4100 | scm_num_overflow (s_divide); | |
4101 | else | |
7351e207 | 4102 | #endif |
5eec27e9 | 4103 | return scm_make_real (rx / yy); |
f8de44c1 DH |
4104 | } else if (SCM_COMPLEXP (y)) { |
4105 | a = rx; | |
4106 | goto complex_div; | |
4107 | } else { | |
4108 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4109 | } |
f8de44c1 DH |
4110 | } else if (SCM_COMPLEXP (x)) { |
4111 | double rx = SCM_COMPLEX_REAL (x); | |
4112 | double ix = SCM_COMPLEX_IMAG (x); | |
4113 | if (SCM_INUMP (y)) { | |
5eec27e9 | 4114 | long int yy = SCM_INUM (y); |
7351e207 MV |
4115 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
4116 | if (yy == 0) | |
5eec27e9 | 4117 | scm_num_overflow (s_divide); |
7351e207 MV |
4118 | else |
4119 | #endif | |
4120 | { | |
5eec27e9 DH |
4121 | double d = yy; |
4122 | return scm_make_complex (rx / d, ix / d); | |
4123 | } | |
f8de44c1 | 4124 | } else if (SCM_BIGP (y)) { |
1be6b49c | 4125 | double d = scm_i_big2dbl (y); |
f8de44c1 | 4126 | return scm_make_complex (rx / d, ix / d); |
f8de44c1 | 4127 | } else if (SCM_REALP (y)) { |
5eec27e9 | 4128 | double yy = SCM_REAL_VALUE (y); |
7351e207 | 4129 | #ifndef ALLOW_DIVIDE_BY_ZERO |
5eec27e9 DH |
4130 | if (yy == 0.0) |
4131 | scm_num_overflow (s_divide); | |
4132 | else | |
7351e207 | 4133 | #endif |
5eec27e9 | 4134 | return scm_make_complex (rx / yy, ix / yy); |
f8de44c1 DH |
4135 | } else if (SCM_COMPLEXP (y)) { |
4136 | double ry = SCM_COMPLEX_REAL (y); | |
4137 | double iy = SCM_COMPLEX_IMAG (y); | |
ba74ef4e MV |
4138 | if (ry <= iy) { |
4139 | double t = ry / iy; | |
4140 | double d = iy * (1.0 + t * t); | |
4141 | return scm_make_complex ((rx * t + ix) / d, (ix * t - rx) / d); | |
4142 | } else { | |
4143 | double t = iy / ry; | |
4144 | double d = ry * (1.0 + t * t); | |
4145 | return scm_make_complex ((rx + ix * t) / d, (ix - rx * t) / d); | |
4146 | } | |
f8de44c1 DH |
4147 | } else { |
4148 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
4149 | } | |
4150 | } else { | |
4151 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); | |
0f2d19dd JB |
4152 | } |
4153 | } | |
c05e97b7 | 4154 | #undef FUNC_NAME |
0f2d19dd | 4155 | |
9de33deb | 4156 | SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_cxr, (SCM (*)()) scm_asinh, g_asinh); |
942e5b91 MG |
4157 | /* "Return the inverse hyperbolic sine of @var{x}." |
4158 | */ | |
0f2d19dd | 4159 | double |
6e8d25a6 | 4160 | scm_asinh (double x) |
0f2d19dd | 4161 | { |
f872b822 | 4162 | return log (x + sqrt (x * x + 1)); |
0f2d19dd JB |
4163 | } |
4164 | ||
4165 | ||
4166 | ||
4167 | ||
9de33deb | 4168 | SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_cxr, (SCM (*)()) scm_acosh, g_acosh); |
942e5b91 MG |
4169 | /* "Return the inverse hyperbolic cosine of @var{x}." |
4170 | */ | |
0f2d19dd | 4171 | double |
6e8d25a6 | 4172 | scm_acosh (double x) |
0f2d19dd | 4173 | { |
f872b822 | 4174 | return log (x + sqrt (x * x - 1)); |
0f2d19dd JB |
4175 | } |
4176 | ||
4177 | ||
4178 | ||
4179 | ||
9de33deb | 4180 | SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_cxr, (SCM (*)()) scm_atanh, g_atanh); |
942e5b91 MG |
4181 | /* "Return the inverse hyperbolic tangent of @var{x}." |
4182 | */ | |
0f2d19dd | 4183 | double |
6e8d25a6 | 4184 | scm_atanh (double x) |
0f2d19dd | 4185 | { |
f872b822 | 4186 | return 0.5 * log ((1 + x) / (1 - x)); |
0f2d19dd JB |
4187 | } |
4188 | ||
4189 | ||
4190 | ||
4191 | ||
9de33deb | 4192 | SCM_GPROC1 (s_truncate, "truncate", scm_tc7_cxr, (SCM (*)()) scm_truncate, g_truncate); |
942e5b91 MG |
4193 | /* "Round the inexact number @var{x} towards zero." |
4194 | */ | |
0f2d19dd | 4195 | double |
6e8d25a6 | 4196 | scm_truncate (double x) |
0f2d19dd | 4197 | { |
f872b822 MD |
4198 | if (x < 0.0) |
4199 | return -floor (-x); | |
4200 | return floor (x); | |
0f2d19dd JB |
4201 | } |
4202 | ||
4203 | ||
4204 | ||
9de33deb | 4205 | SCM_GPROC1 (s_round, "round", scm_tc7_cxr, (SCM (*)()) scm_round, g_round); |
942e5b91 MG |
4206 | /* "Round the inexact number @var{x}. If @var{x} is halfway between two\n" |
4207 | * "numbers, round towards even." | |
4208 | */ | |
0f2d19dd | 4209 | double |
6e8d25a6 | 4210 | scm_round (double x) |
0f2d19dd JB |
4211 | { |
4212 | double plus_half = x + 0.5; | |
f872b822 | 4213 | double result = floor (plus_half); |
0f2d19dd | 4214 | /* Adjust so that the scm_round is towards even. */ |
f872b822 | 4215 | return (plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
0f2d19dd JB |
4216 | ? result - 1 : result; |
4217 | } | |
4218 | ||
4219 | ||
9de33deb | 4220 | SCM_GPROC1 (s_i_floor, "floor", scm_tc7_cxr, (SCM (*)()) floor, g_i_floor); |
942e5b91 MG |
4221 | /* "Round the number @var{x} towards minus infinity." |
4222 | */ | |
9de33deb | 4223 | SCM_GPROC1 (s_i_ceil, "ceiling", scm_tc7_cxr, (SCM (*)()) ceil, g_i_ceil); |
942e5b91 MG |
4224 | /* "Round the number @var{x} towards infinity." |
4225 | */ | |
9de33deb | 4226 | SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_cxr, (SCM (*)()) sqrt, g_i_sqrt); |
942e5b91 MG |
4227 | /* "Return the square root of the real number @var{x}." |
4228 | */ | |
9de33deb | 4229 | SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_cxr, (SCM (*)()) fabs, g_i_abs); |
942e5b91 MG |
4230 | /* "Return the absolute value of the real number @var{x}." |
4231 | */ | |
9de33deb | 4232 | SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_cxr, (SCM (*)()) exp, g_i_exp); |
942e5b91 MG |
4233 | /* "Return the @var{x}th power of e." |
4234 | */ | |
9de33deb | 4235 | SCM_GPROC1 (s_i_log, "$log", scm_tc7_cxr, (SCM (*)()) log, g_i_log); |
b3fcac34 | 4236 | /* "Return the natural logarithm of the real number @var{x}." |
942e5b91 | 4237 | */ |
9de33deb | 4238 | SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_cxr, (SCM (*)()) sin, g_i_sin); |
942e5b91 MG |
4239 | /* "Return the sine of the real number @var{x}." |
4240 | */ | |
9de33deb | 4241 | SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_cxr, (SCM (*)()) cos, g_i_cos); |
942e5b91 MG |
4242 | /* "Return the cosine of the real number @var{x}." |
4243 | */ | |
9de33deb | 4244 | SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_cxr, (SCM (*)()) tan, g_i_tan); |
942e5b91 MG |
4245 | /* "Return the tangent of the real number @var{x}." |
4246 | */ | |
9de33deb | 4247 | SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_cxr, (SCM (*)()) asin, g_i_asin); |
942e5b91 MG |
4248 | /* "Return the arc sine of the real number @var{x}." |
4249 | */ | |
9de33deb | 4250 | SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_cxr, (SCM (*)()) acos, g_i_acos); |
942e5b91 MG |
4251 | /* "Return the arc cosine of the real number @var{x}." |
4252 | */ | |
9de33deb | 4253 | SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_cxr, (SCM (*)()) atan, g_i_atan); |
942e5b91 MG |
4254 | /* "Return the arc tangent of the real number @var{x}." |
4255 | */ | |
9de33deb | 4256 | SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_cxr, (SCM (*)()) sinh, g_i_sinh); |
942e5b91 MG |
4257 | /* "Return the hyperbolic sine of the real number @var{x}." |
4258 | */ | |
9de33deb | 4259 | SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_cxr, (SCM (*)()) cosh, g_i_cosh); |
942e5b91 MG |
4260 | /* "Return the hyperbolic cosine of the real number @var{x}." |
4261 | */ | |
9de33deb | 4262 | SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_cxr, (SCM (*)()) tanh, g_i_tanh); |
942e5b91 MG |
4263 | /* "Return the hyperbolic tangent of the real number @var{x}." |
4264 | */ | |
f872b822 MD |
4265 | |
4266 | struct dpair | |
4267 | { | |
4268 | double x, y; | |
4269 | }; | |
4270 | ||
27c37006 NJ |
4271 | static void scm_two_doubles (SCM x, |
4272 | SCM y, | |
3eeba8d4 JB |
4273 | const char *sstring, |
4274 | struct dpair * xy); | |
f872b822 MD |
4275 | |
4276 | static void | |
27c37006 NJ |
4277 | scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy) |
4278 | { | |
4279 | if (SCM_INUMP (x)) { | |
4280 | xy->x = SCM_INUM (x); | |
4281 | } else if (SCM_BIGP (x)) { | |
1be6b49c | 4282 | xy->x = scm_i_big2dbl (x); |
27c37006 NJ |
4283 | } else if (SCM_REALP (x)) { |
4284 | xy->x = SCM_REAL_VALUE (x); | |
98cb6e75 | 4285 | } else { |
27c37006 | 4286 | scm_wrong_type_arg (sstring, SCM_ARG1, x); |
98cb6e75 DH |
4287 | } |
4288 | ||
27c37006 NJ |
4289 | if (SCM_INUMP (y)) { |
4290 | xy->y = SCM_INUM (y); | |
4291 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 4292 | xy->y = scm_i_big2dbl (y); |
27c37006 NJ |
4293 | } else if (SCM_REALP (y)) { |
4294 | xy->y = SCM_REAL_VALUE (y); | |
98cb6e75 | 4295 | } else { |
27c37006 | 4296 | scm_wrong_type_arg (sstring, SCM_ARG2, y); |
98cb6e75 | 4297 | } |
0f2d19dd JB |
4298 | } |
4299 | ||
4300 | ||
a1ec6916 | 4301 | SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0, |
27c37006 NJ |
4302 | (SCM x, SCM y), |
4303 | "Return @var{x} raised to the power of @var{y}. This\n" | |
0137a31b | 4304 | "procedure does not accept complex arguments.") |
1bbd0b84 | 4305 | #define FUNC_NAME s_scm_sys_expt |
0f2d19dd JB |
4306 | { |
4307 | struct dpair xy; | |
27c37006 | 4308 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
f8de44c1 | 4309 | return scm_make_real (pow (xy.x, xy.y)); |
0f2d19dd | 4310 | } |
1bbd0b84 | 4311 | #undef FUNC_NAME |
0f2d19dd JB |
4312 | |
4313 | ||
a1ec6916 | 4314 | SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0, |
27c37006 NJ |
4315 | (SCM x, SCM y), |
4316 | "Return the arc tangent of the two arguments @var{x} and\n" | |
4317 | "@var{y}. This is similar to calculating the arc tangent of\n" | |
4318 | "@var{x} / @var{y}, except that the signs of both arguments\n" | |
0137a31b MG |
4319 | "are used to determine the quadrant of the result. This\n" |
4320 | "procedure does not accept complex arguments.") | |
1bbd0b84 | 4321 | #define FUNC_NAME s_scm_sys_atan2 |
0f2d19dd JB |
4322 | { |
4323 | struct dpair xy; | |
27c37006 | 4324 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
f8de44c1 | 4325 | return scm_make_real (atan2 (xy.x, xy.y)); |
0f2d19dd | 4326 | } |
1bbd0b84 | 4327 | #undef FUNC_NAME |
0f2d19dd JB |
4328 | |
4329 | ||
a1ec6916 | 4330 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
bb628794 | 4331 | (SCM real, SCM imaginary), |
942e5b91 MG |
4332 | "Return a complex number constructed of the given @var{real} and\n" |
4333 | "@var{imaginary} parts.") | |
1bbd0b84 | 4334 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd JB |
4335 | { |
4336 | struct dpair xy; | |
bb628794 | 4337 | scm_two_doubles (real, imaginary, FUNC_NAME, &xy); |
f8de44c1 | 4338 | return scm_make_complex (xy.x, xy.y); |
0f2d19dd | 4339 | } |
1bbd0b84 | 4340 | #undef FUNC_NAME |
0f2d19dd JB |
4341 | |
4342 | ||
4343 | ||
a1ec6916 | 4344 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 4345 | (SCM x, SCM y), |
942e5b91 | 4346 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 4347 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd JB |
4348 | { |
4349 | struct dpair xy; | |
27c37006 | 4350 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
f8de44c1 | 4351 | return scm_make_complex (xy.x * cos (xy.y), xy.x * sin (xy.y)); |
0f2d19dd | 4352 | } |
1bbd0b84 | 4353 | #undef FUNC_NAME |
0f2d19dd JB |
4354 | |
4355 | ||
152f82bf | 4356 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
4357 | /* "Return the real part of the number @var{z}." |
4358 | */ | |
0f2d19dd | 4359 | SCM |
6e8d25a6 | 4360 | scm_real_part (SCM z) |
0f2d19dd | 4361 | { |
c2ff8ab0 DH |
4362 | if (SCM_INUMP (z)) { |
4363 | return z; | |
4364 | } else if (SCM_BIGP (z)) { | |
4365 | return z; | |
4366 | } else if (SCM_REALP (z)) { | |
4367 | return z; | |
4368 | } else if (SCM_COMPLEXP (z)) { | |
4369 | return scm_make_real (SCM_COMPLEX_REAL (z)); | |
4370 | } else { | |
4371 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); | |
4372 | } | |
0f2d19dd JB |
4373 | } |
4374 | ||
4375 | ||
152f82bf | 4376 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
4377 | /* "Return the imaginary part of the number @var{z}." |
4378 | */ | |
0f2d19dd | 4379 | SCM |
6e8d25a6 | 4380 | scm_imag_part (SCM z) |
0f2d19dd | 4381 | { |
c2ff8ab0 | 4382 | if (SCM_INUMP (z)) { |
f872b822 | 4383 | return SCM_INUM0; |
c2ff8ab0 | 4384 | } else if (SCM_BIGP (z)) { |
f872b822 | 4385 | return SCM_INUM0; |
c2ff8ab0 DH |
4386 | } else if (SCM_REALP (z)) { |
4387 | return scm_flo0; | |
4388 | } else if (SCM_COMPLEXP (z)) { | |
4389 | return scm_make_real (SCM_COMPLEX_IMAG (z)); | |
4390 | } else { | |
4391 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); | |
4392 | } | |
0f2d19dd JB |
4393 | } |
4394 | ||
4395 | ||
9de33deb | 4396 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
4397 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
4398 | * "@code{abs} for real arguments, but also allows complex numbers." | |
4399 | */ | |
0f2d19dd | 4400 | SCM |
6e8d25a6 | 4401 | scm_magnitude (SCM z) |
0f2d19dd | 4402 | { |
c2ff8ab0 | 4403 | if (SCM_INUMP (z)) { |
5986c47d DH |
4404 | long int zz = SCM_INUM (z); |
4405 | if (zz >= 0) { | |
4406 | return z; | |
4407 | } else if (SCM_POSFIXABLE (-zz)) { | |
4408 | return SCM_MAKINUM (-zz); | |
4409 | } else { | |
4410 | #ifdef SCM_BIGDIG | |
1be6b49c | 4411 | return scm_i_long2big (-zz); |
5986c47d DH |
4412 | #else |
4413 | scm_num_overflow (s_magnitude); | |
4414 | #endif | |
4415 | } | |
c2ff8ab0 | 4416 | } else if (SCM_BIGP (z)) { |
5986c47d DH |
4417 | if (!SCM_BIGSIGN (z)) { |
4418 | return z; | |
4419 | } else { | |
1be6b49c | 4420 | return scm_i_copybig (z, 0); |
5986c47d | 4421 | } |
c2ff8ab0 DH |
4422 | } else if (SCM_REALP (z)) { |
4423 | return scm_make_real (fabs (SCM_REAL_VALUE (z))); | |
4424 | } else if (SCM_COMPLEXP (z)) { | |
4425 | double r = SCM_COMPLEX_REAL (z); | |
4426 | double i = SCM_COMPLEX_IMAG (z); | |
4427 | return scm_make_real (sqrt (i * i + r * r)); | |
4428 | } else { | |
4429 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); | |
4430 | } | |
0f2d19dd JB |
4431 | } |
4432 | ||
4433 | ||
9de33deb | 4434 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
4435 | /* "Return the angle of the complex number @var{z}." |
4436 | */ | |
0f2d19dd | 4437 | SCM |
6e8d25a6 | 4438 | scm_angle (SCM z) |
0f2d19dd | 4439 | { |
f4c627b3 DH |
4440 | if (SCM_INUMP (z)) { |
4441 | if (SCM_INUM (z) >= 0) { | |
4442 | return scm_make_real (atan2 (0.0, 1.0)); | |
4443 | } else { | |
4444 | return scm_make_real (atan2 (0.0, -1.0)); | |
f872b822 | 4445 | } |
f4c627b3 DH |
4446 | } else if (SCM_BIGP (z)) { |
4447 | if (SCM_BIGSIGN (z)) { | |
4448 | return scm_make_real (atan2 (0.0, -1.0)); | |
4449 | } else { | |
4450 | return scm_make_real (atan2 (0.0, 1.0)); | |
0f2d19dd | 4451 | } |
f4c627b3 DH |
4452 | } else if (SCM_REALP (z)) { |
4453 | return scm_make_real (atan2 (0.0, SCM_REAL_VALUE (z))); | |
4454 | } else if (SCM_COMPLEXP (z)) { | |
4455 | return scm_make_real (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); | |
4456 | } else { | |
4457 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); | |
4458 | } | |
0f2d19dd JB |
4459 | } |
4460 | ||
4461 | ||
3c9a524f DH |
4462 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
4463 | /* Convert the number @var{x} to its inexact representation.\n" | |
4464 | */ | |
4465 | SCM | |
4466 | scm_exact_to_inexact (SCM z) | |
4467 | { | |
4468 | if (SCM_INUMP (z)) | |
4469 | return scm_make_real ((double) SCM_INUM (z)); | |
4470 | else if (SCM_BIGP (z)) | |
4471 | return scm_make_real (scm_i_big2dbl (z)); | |
4472 | else if (SCM_INEXACTP (z)) | |
4473 | return z; | |
4474 | else | |
4475 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
4476 | } | |
4477 | ||
4478 | ||
a1ec6916 | 4479 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 4480 | (SCM z), |
1e6808ea | 4481 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 4482 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 4483 | { |
c2ff8ab0 | 4484 | if (SCM_INUMP (z)) { |
f872b822 | 4485 | return z; |
c2ff8ab0 | 4486 | } else if (SCM_BIGP (z)) { |
f872b822 | 4487 | return z; |
c2ff8ab0 DH |
4488 | } else if (SCM_REALP (z)) { |
4489 | double u = floor (SCM_REAL_VALUE (z) + 0.5); | |
4490 | long lu = (long) u; | |
4491 | if (SCM_FIXABLE (lu)) { | |
4492 | return SCM_MAKINUM (lu); | |
f872b822 | 4493 | #ifdef SCM_BIGDIG |
fc194577 | 4494 | } else if (isfinite (u) && !xisnan (u)) { |
1be6b49c | 4495 | return scm_i_dbl2big (u); |
f872b822 | 4496 | #endif |
c2ff8ab0 DH |
4497 | } else { |
4498 | scm_num_overflow (s_scm_inexact_to_exact); | |
4499 | } | |
4500 | } else { | |
4501 | SCM_WRONG_TYPE_ARG (1, z); | |
4502 | } | |
0f2d19dd | 4503 | } |
1bbd0b84 | 4504 | #undef FUNC_NAME |
0f2d19dd JB |
4505 | |
4506 | ||
0f2d19dd | 4507 | #ifdef SCM_BIGDIG |
0f2d19dd | 4508 | /* d must be integer */ |
1cc91f1b | 4509 | |
0f2d19dd | 4510 | SCM |
1be6b49c | 4511 | scm_i_dbl2big (double d) |
0f2d19dd | 4512 | { |
1be6b49c | 4513 | size_t i = 0; |
0f2d19dd JB |
4514 | long c; |
4515 | SCM_BIGDIG *digits; | |
4516 | SCM ans; | |
f872b822 MD |
4517 | double u = (d < 0) ? -d : d; |
4518 | while (0 != floor (u)) | |
4519 | { | |
4520 | u /= SCM_BIGRAD; | |
4521 | i++; | |
4522 | } | |
1be6b49c | 4523 | ans = scm_i_mkbig (i, d < 0); |
f872b822 MD |
4524 | digits = SCM_BDIGITS (ans); |
4525 | while (i--) | |
4526 | { | |
4527 | u *= SCM_BIGRAD; | |
4528 | c = floor (u); | |
4529 | u -= c; | |
4530 | digits[i] = c; | |
4531 | } | |
e1724d20 | 4532 | if (u != 0) |
52859adf | 4533 | scm_num_overflow ("dbl2big"); |
0f2d19dd JB |
4534 | return ans; |
4535 | } | |
4536 | ||
0f2d19dd | 4537 | double |
1be6b49c | 4538 | scm_i_big2dbl (SCM b) |
0f2d19dd JB |
4539 | { |
4540 | double ans = 0.0; | |
1be6b49c | 4541 | size_t i = SCM_NUMDIGS (b); |
f872b822 MD |
4542 | SCM_BIGDIG *digits = SCM_BDIGITS (b); |
4543 | while (i--) | |
4544 | ans = digits[i] + SCM_BIGRAD * ans; | |
f3ae5d60 MD |
4545 | if (SCM_BIGSIGN (b)) |
4546 | return - ans; | |
0f2d19dd JB |
4547 | return ans; |
4548 | } | |
1cc91f1b | 4549 | |
f872b822 | 4550 | #endif |
0f2d19dd | 4551 | |
5c11cc9d | 4552 | #ifdef HAVE_LONG_LONGS |
1be6b49c ML |
4553 | # ifndef LLONG_MAX |
4554 | # define ULLONG_MAX ((unsigned long long) (-1)) | |
4555 | # define LLONG_MAX ((long long) (ULLONG_MAX >> 1)) | |
4556 | # define LLONG_MIN (~LLONG_MAX) | |
4557 | # endif | |
f872b822 | 4558 | #endif |
0f2d19dd | 4559 | |
3d2e8ceb MV |
4560 | /* Parameters for creating integer conversion routines. |
4561 | ||
4562 | Define the following preprocessor macros before including | |
4563 | "libguile/num2integral.i.c": | |
4564 | ||
4565 | NUM2INTEGRAL - the name of the function for converting from a | |
4566 | Scheme object to the integral type. This function | |
4567 | will be defined when including "num2integral.i.c". | |
4568 | ||
4569 | INTEGRAL2NUM - the name of the function for converting from the | |
4570 | integral type to a Scheme object. This function | |
4571 | will be defined. | |
4572 | ||
4573 | INTEGRAL2BIG - the name of an internal function that createas a | |
4574 | bignum from the integral type. This function will | |
4575 | be defined. The name should start with "scm_i_". | |
4576 | ||
4577 | ITYPE - the name of the integral type. | |
4578 | ||
4579 | UNSIGNED - Define this when ITYPE is an unsigned type. Do not | |
4580 | define it otherwise. | |
4581 | ||
4582 | UNSIGNED_ITYPE | |
4583 | - the name of the the unsigned variant of the | |
4584 | integral type. If you don't define this, it defaults | |
4585 | to "unsigned ITYPE" for signed types and simply "ITYPE" | |
4586 | for unsigned ones. | |
4587 | ||
4588 | SIZEOF_ITYPE - an expression giving the size of the integral type in | |
4589 | bytes. This expression must be computable by the | |
4590 | preprocessor. If you don't know a value for this, | |
4591 | don't define it. The purpose of this parameter is | |
4592 | mainly to suppress some warnings. The generated | |
4593 | code will work correctly without it. | |
4594 | */ | |
4595 | ||
1be6b49c ML |
4596 | #define NUM2INTEGRAL scm_num2short |
4597 | #define INTEGRAL2NUM scm_short2num | |
4598 | #define INTEGRAL2BIG scm_i_short2big | |
4599 | #define ITYPE short | |
3d2e8ceb | 4600 | #define SIZEOF_ITYPE SIZEOF_SHORT |
1be6b49c ML |
4601 | #include "libguile/num2integral.i.c" |
4602 | ||
4603 | #define NUM2INTEGRAL scm_num2ushort | |
4604 | #define INTEGRAL2NUM scm_ushort2num | |
4605 | #define INTEGRAL2BIG scm_i_ushort2big | |
4606 | #define UNSIGNED | |
4607 | #define ITYPE unsigned short | |
3d2e8ceb | 4608 | #define SIZEOF_ITYPE SIZEOF_SHORT |
1be6b49c ML |
4609 | #include "libguile/num2integral.i.c" |
4610 | ||
4611 | #define NUM2INTEGRAL scm_num2int | |
4612 | #define INTEGRAL2NUM scm_int2num | |
4613 | #define INTEGRAL2BIG scm_i_int2big | |
4614 | #define ITYPE int | |
3d2e8ceb | 4615 | #define SIZEOF_ITYPE SIZEOF_INT |
1be6b49c ML |
4616 | #include "libguile/num2integral.i.c" |
4617 | ||
4618 | #define NUM2INTEGRAL scm_num2uint | |
4619 | #define INTEGRAL2NUM scm_uint2num | |
4620 | #define INTEGRAL2BIG scm_i_uint2big | |
4621 | #define UNSIGNED | |
4622 | #define ITYPE unsigned int | |
3d2e8ceb | 4623 | #define SIZEOF_ITYPE SIZEOF_INT |
1be6b49c ML |
4624 | #include "libguile/num2integral.i.c" |
4625 | ||
4626 | #define NUM2INTEGRAL scm_num2long | |
4627 | #define INTEGRAL2NUM scm_long2num | |
4628 | #define INTEGRAL2BIG scm_i_long2big | |
4629 | #define ITYPE long | |
3d2e8ceb | 4630 | #define SIZEOF_ITYPE SIZEOF_LONG |
1be6b49c ML |
4631 | #include "libguile/num2integral.i.c" |
4632 | ||
4633 | #define NUM2INTEGRAL scm_num2ulong | |
4634 | #define INTEGRAL2NUM scm_ulong2num | |
4635 | #define INTEGRAL2BIG scm_i_ulong2big | |
4636 | #define UNSIGNED | |
4637 | #define ITYPE unsigned long | |
3d2e8ceb | 4638 | #define SIZEOF_ITYPE SIZEOF_LONG |
1be6b49c ML |
4639 | #include "libguile/num2integral.i.c" |
4640 | ||
1be6b49c ML |
4641 | #define NUM2INTEGRAL scm_num2ptrdiff |
4642 | #define INTEGRAL2NUM scm_ptrdiff2num | |
4643 | #define INTEGRAL2BIG scm_i_ptrdiff2big | |
4644 | #define ITYPE ptrdiff_t | |
3d2e8ceb MV |
4645 | #define UNSIGNED_ITYPE size_t |
4646 | #define SIZEOF_ITYPE SIZEOF_PTRDIFF_T | |
1be6b49c ML |
4647 | #include "libguile/num2integral.i.c" |
4648 | ||
4649 | #define NUM2INTEGRAL scm_num2size | |
4650 | #define INTEGRAL2NUM scm_size2num | |
4651 | #define INTEGRAL2BIG scm_i_size2big | |
4652 | #define UNSIGNED | |
4653 | #define ITYPE size_t | |
3d2e8ceb | 4654 | #define SIZEOF_ITYPE SIZEOF_SIZE_T |
1be6b49c | 4655 | #include "libguile/num2integral.i.c" |
0f2d19dd | 4656 | |
5c11cc9d | 4657 | #ifdef HAVE_LONG_LONGS |
1cc91f1b | 4658 | |
caf08e65 MV |
4659 | #ifndef ULONG_LONG_MAX |
4660 | #define ULONG_LONG_MAX (~0ULL) | |
4661 | #endif | |
4662 | ||
1be6b49c ML |
4663 | #define NUM2INTEGRAL scm_num2long_long |
4664 | #define INTEGRAL2NUM scm_long_long2num | |
4665 | #define INTEGRAL2BIG scm_i_long_long2big | |
4666 | #define ITYPE long long | |
3d2e8ceb | 4667 | #define SIZEOF_ITYPE SIZEOF_LONG_LONG |
1be6b49c ML |
4668 | #include "libguile/num2integral.i.c" |
4669 | ||
4670 | #define NUM2INTEGRAL scm_num2ulong_long | |
4671 | #define INTEGRAL2NUM scm_ulong_long2num | |
4672 | #define INTEGRAL2BIG scm_i_ulong_long2big | |
4673 | #define UNSIGNED | |
4674 | #define ITYPE unsigned long long | |
3d2e8ceb | 4675 | #define SIZEOF_ITYPE SIZEOF_LONG_LONG |
1be6b49c | 4676 | #include "libguile/num2integral.i.c" |
0f2d19dd | 4677 | |
1be6b49c | 4678 | #endif /* HAVE_LONG_LONGS */ |
caf08e65 | 4679 | |
5437598b MD |
4680 | #define NUM2FLOAT scm_num2float |
4681 | #define FLOAT2NUM scm_float2num | |
4682 | #define FTYPE float | |
4683 | #include "libguile/num2float.i.c" | |
4684 | ||
4685 | #define NUM2FLOAT scm_num2double | |
4686 | #define FLOAT2NUM scm_double2num | |
4687 | #define FTYPE double | |
4688 | #include "libguile/num2float.i.c" | |
4689 | ||
1be6b49c | 4690 | #ifdef GUILE_DEBUG |
caf08e65 | 4691 | |
6063dc1d SJ |
4692 | #ifndef SIZE_MAX |
4693 | #define SIZE_MAX ((size_t) (-1)) | |
4694 | #endif | |
4695 | #ifndef PTRDIFF_MIN | |
4696 | #define PTRDIFF_MIN \ | |
4697 | ((ptrdiff_t) ((ptrdiff_t) 1 << (sizeof (ptrdiff_t) * 8 - 1))) | |
4698 | #endif | |
4699 | #ifndef PTRDIFF_MAX | |
4700 | #define PTRDIFF_MAX (~ PTRDIFF_MIN) | |
4701 | #endif | |
4702 | ||
1be6b49c ML |
4703 | #define CHECK(type, v) \ |
4704 | do { \ | |
4705 | if ((v) != scm_num2##type (scm_##type##2num (v), 1, "check_sanity")) \ | |
4706 | abort (); \ | |
4707 | } while (0); | |
caf08e65 | 4708 | |
1be6b49c ML |
4709 | static void |
4710 | check_sanity () | |
4711 | { | |
4712 | CHECK (short, 0); | |
4713 | CHECK (ushort, 0U); | |
4714 | CHECK (int, 0); | |
4715 | CHECK (uint, 0U); | |
4716 | CHECK (long, 0L); | |
4717 | CHECK (ulong, 0UL); | |
4718 | CHECK (size, 0); | |
4719 | CHECK (ptrdiff, 0); | |
4720 | ||
4721 | CHECK (short, -1); | |
4722 | CHECK (int, -1); | |
4723 | CHECK (long, -1L); | |
4724 | CHECK (ptrdiff, -1); | |
4725 | ||
4726 | CHECK (short, SHRT_MAX); | |
4727 | CHECK (short, SHRT_MIN); | |
4728 | CHECK (ushort, USHRT_MAX); | |
4729 | CHECK (int, INT_MAX); | |
4730 | CHECK (int, INT_MIN); | |
4731 | CHECK (uint, UINT_MAX); | |
4732 | CHECK (long, LONG_MAX); | |
4733 | CHECK (long, LONG_MIN); | |
4734 | CHECK (ulong, ULONG_MAX); | |
4735 | CHECK (size, SIZE_MAX); | |
4736 | CHECK (ptrdiff, PTRDIFF_MAX); | |
4737 | CHECK (ptrdiff, PTRDIFF_MIN); | |
0f2d19dd | 4738 | |
1be6b49c ML |
4739 | #ifdef HAVE_LONG_LONGS |
4740 | CHECK (long_long, 0LL); | |
4741 | CHECK (ulong_long, 0ULL); | |
1be6b49c | 4742 | CHECK (long_long, -1LL); |
1be6b49c ML |
4743 | CHECK (long_long, LLONG_MAX); |
4744 | CHECK (long_long, LLONG_MIN); | |
4745 | CHECK (ulong_long, ULLONG_MAX); | |
4746 | #endif | |
0f2d19dd JB |
4747 | } |
4748 | ||
b10586f0 ML |
4749 | #undef CHECK |
4750 | ||
4751 | #define CHECK \ | |
4752 | scm_internal_catch (SCM_BOOL_T, check_body, &data, check_handler, &data); \ | |
4753 | if (!SCM_FALSEP (data)) abort(); | |
4754 | ||
4755 | static SCM | |
4756 | check_body (void *data) | |
4757 | { | |
4758 | SCM num = *(SCM *) data; | |
4759 | scm_num2ulong (num, 1, NULL); | |
4760 | ||
4761 | return SCM_UNSPECIFIED; | |
4762 | } | |
4763 | ||
4764 | static SCM | |
4765 | check_handler (void *data, SCM tag, SCM throw_args) | |
4766 | { | |
4767 | SCM *num = (SCM *) data; | |
4768 | *num = SCM_BOOL_F; | |
4769 | ||
4770 | return SCM_UNSPECIFIED; | |
4771 | } | |
4772 | ||
4773 | SCM_DEFINE (scm_sys_check_number_conversions, "%check-number-conversions", 0, 0, 0, | |
b4e15479 | 4774 | (void), |
b10586f0 ML |
4775 | "Number conversion sanity checking.") |
4776 | #define FUNC_NAME s_scm_sys_check_number_conversions | |
4777 | { | |
4778 | SCM data = SCM_MAKINUM (-1); | |
4779 | CHECK; | |
4780 | data = scm_int2num (INT_MIN); | |
4781 | CHECK; | |
4782 | data = scm_ulong2num (ULONG_MAX); | |
4783 | data = scm_difference (SCM_INUM0, data); | |
4784 | CHECK; | |
4785 | data = scm_ulong2num (ULONG_MAX); | |
4786 | data = scm_sum (SCM_MAKINUM (1), data); data = scm_difference (SCM_INUM0, data); | |
4787 | CHECK; | |
4788 | data = scm_int2num (-10000); data = scm_product (data, data); data = scm_product (data, data); | |
4789 | CHECK; | |
4790 | ||
4791 | return SCM_UNSPECIFIED; | |
4792 | } | |
4793 | #undef FUNC_NAME | |
4794 | ||
1be6b49c | 4795 | #endif |
0f2d19dd | 4796 | |
0f2d19dd JB |
4797 | void |
4798 | scm_init_numbers () | |
0f2d19dd | 4799 | { |
1be6b49c | 4800 | abs_most_negative_fixnum = scm_i_long2big (- SCM_MOST_NEGATIVE_FIXNUM); |
ac0c002c DH |
4801 | scm_permanent_object (abs_most_negative_fixnum); |
4802 | ||
a261c0e9 DH |
4803 | /* It may be possible to tune the performance of some algorithms by using |
4804 | * the following constants to avoid the creation of bignums. Please, before | |
4805 | * using these values, remember the two rules of program optimization: | |
4806 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe MV |
4807 | scm_c_define ("most-positive-fixnum", |
4808 | SCM_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); | |
4809 | scm_c_define ("most-negative-fixnum", | |
4810 | SCM_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); | |
a261c0e9 | 4811 | |
f3ae5d60 MD |
4812 | scm_add_feature ("complex"); |
4813 | scm_add_feature ("inexact"); | |
5986c47d | 4814 | scm_flo0 = scm_make_real (0.0); |
f872b822 | 4815 | #ifdef DBL_DIG |
0f2d19dd | 4816 | scm_dblprec = (DBL_DIG > 20) ? 20 : DBL_DIG; |
f872b822 | 4817 | #else |
0f2d19dd JB |
4818 | { /* determine floating point precision */ |
4819 | double f = 0.1; | |
f872b822 | 4820 | double fsum = 1.0 + f; |
bb628794 DH |
4821 | while (fsum != 1.0) { |
4822 | if (++scm_dblprec > 20) { | |
4823 | fsum = 1.0; | |
4824 | } else { | |
f872b822 | 4825 | f /= 10.0; |
bb628794 | 4826 | fsum = f + 1.0; |
f872b822 | 4827 | } |
bb628794 | 4828 | } |
f872b822 | 4829 | scm_dblprec = scm_dblprec - 1; |
0f2d19dd | 4830 | } |
f872b822 | 4831 | #endif /* DBL_DIG */ |
1be6b49c ML |
4832 | |
4833 | #ifdef GUILE_DEBUG | |
4834 | check_sanity (); | |
4835 | #endif | |
4836 | ||
a0599745 | 4837 | #include "libguile/numbers.x" |
0f2d19dd | 4838 | } |
89e00824 ML |
4839 | |
4840 | /* | |
4841 | Local Variables: | |
4842 | c-file-style: "gnu" | |
4843 | End: | |
4844 | */ |