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be54b15d | 1 | /* Copyright (C) 1995,1996,1997,1998,1999,2000,2001 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 | ||
09fb7599 DH |
68 | #define SCM_SWAP(x,y) do { SCM __t = x; x = y; y = __t; } while (0) |
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 | |
9de33deb | 292 | SCM_GPROC (s_abs, "abs", 1, 0, 0, scm_abs, g_abs); |
942e5b91 MG |
293 | /* "Return the absolute value of @var{x}." |
294 | */ | |
0f2d19dd | 295 | SCM |
6e8d25a6 | 296 | scm_abs (SCM x) |
0f2d19dd | 297 | { |
4219f20d DH |
298 | if (SCM_INUMP (x)) { |
299 | long int xx = SCM_INUM (x); | |
300 | if (xx >= 0) { | |
301 | return x; | |
302 | } else if (SCM_POSFIXABLE (-xx)) { | |
303 | return SCM_MAKINUM (-xx); | |
304 | } else { | |
0f2d19dd | 305 | #ifdef SCM_BIGDIG |
1be6b49c | 306 | return scm_i_long2big (-xx); |
0f2d19dd | 307 | #else |
4219f20d | 308 | scm_num_overflow (s_abs); |
0f2d19dd | 309 | #endif |
4219f20d | 310 | } |
4219f20d DH |
311 | } else if (SCM_BIGP (x)) { |
312 | if (!SCM_BIGSIGN (x)) { | |
313 | return x; | |
314 | } else { | |
1be6b49c | 315 | return scm_i_copybig (x, 0); |
4219f20d | 316 | } |
5986c47d DH |
317 | } else if (SCM_REALP (x)) { |
318 | return scm_make_real (fabs (SCM_REAL_VALUE (x))); | |
4219f20d DH |
319 | } else { |
320 | SCM_WTA_DISPATCH_1 (g_abs, x, 1, s_abs); | |
321 | } | |
0f2d19dd JB |
322 | } |
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); | |
8a525303 | 901 | #ifndef SCM_RECKLESS |
09fb7599 | 902 | } else if (SCM_NUMBERP (n1)) { |
d28da049 | 903 | return n1; |
09fb7599 DH |
904 | } else { |
905 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
906 | #else | |
907 | } else { | |
908 | return n1; | |
909 | #endif | |
d28da049 | 910 | } |
8a525303 | 911 | } |
09fb7599 DH |
912 | |
913 | if (SCM_INUMP (n1)) { | |
9a00c9fc | 914 | nn1 = SCM_INUM (n1); |
09fb7599 DH |
915 | if (SCM_INUMP (n2)) { |
916 | long nn2 = SCM_INUM (n2); | |
917 | return SCM_MAKINUM (nn1 & nn2); | |
09fb7599 DH |
918 | } else if SCM_BIGP (n2) { |
919 | intbig: | |
920 | { | |
8a525303 | 921 | # ifndef SCM_DIGSTOOBIG |
09fb7599 DH |
922 | long z = scm_pseudolong (nn1); |
923 | if ((nn1 < 0) && SCM_BIGSIGN (n2)) { | |
924 | return scm_big_ior ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
925 | SCM_BIGSIGNFLAG, n2); | |
926 | } else { | |
927 | return scm_big_and ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
928 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, 0); | |
929 | } | |
8a525303 | 930 | # else |
09fb7599 DH |
931 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
932 | scm_longdigs (nn1, zdigs); | |
933 | if ((nn1 < 0) && SCM_BIGSIGN (n2)) { | |
934 | return scm_big_ior (zdigs, SCM_DIGSPERLONG, SCM_BIGSIGNFLAG, n2); | |
935 | } else { | |
936 | return scm_big_and (zdigs, SCM_DIGSPERLONG, | |
937 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, 0); | |
938 | } | |
8a525303 | 939 | # endif |
09fb7599 | 940 | } |
09fb7599 DH |
941 | } else { |
942 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
943 | } | |
09fb7599 DH |
944 | } else if (SCM_BIGP (n1)) { |
945 | if (SCM_INUMP (n2)) { | |
946 | SCM_SWAP (n1, n2); | |
9a00c9fc | 947 | nn1 = SCM_INUM (n1); |
09fb7599 DH |
948 | goto intbig; |
949 | } else if (SCM_BIGP (n2)) { | |
950 | if (SCM_NUMDIGS (n1) > SCM_NUMDIGS (n2)) { | |
951 | SCM_SWAP (n1, n2); | |
952 | }; | |
953 | if ((SCM_BIGSIGN (n1)) && SCM_BIGSIGN (n2)) { | |
954 | return scm_big_ior (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), | |
955 | SCM_BIGSIGNFLAG, n2); | |
956 | } else { | |
957 | return scm_big_and (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), | |
958 | SCM_BIGSIGN (n1), n2, 0); | |
959 | } | |
960 | } else { | |
961 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
962 | } | |
09fb7599 DH |
963 | } else { |
964 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
965 | } | |
0f2d19dd | 966 | } |
1bbd0b84 | 967 | #undef FUNC_NAME |
0f2d19dd | 968 | |
09fb7599 | 969 | |
c3ee7520 | 970 | SCM_DEFINE1 (scm_logior, "logior", scm_tc7_asubr, |
1bbd0b84 | 971 | (SCM n1, SCM n2), |
3c3db128 GH |
972 | "Return the bitwise OR of the integer arguments.\n\n" |
973 | "@lisp\n" | |
974 | "(logior) @result{} 0\n" | |
975 | "(logior 7) @result{} 7\n" | |
976 | "(logior #b000 #b001 #b011) @result{} 3\n" | |
1e6808ea | 977 | "@end lisp") |
1bbd0b84 | 978 | #define FUNC_NAME s_scm_logior |
0f2d19dd | 979 | { |
9a00c9fc DH |
980 | long int nn1; |
981 | ||
09fb7599 DH |
982 | if (SCM_UNBNDP (n2)) { |
983 | if (SCM_UNBNDP (n1)) { | |
984 | return SCM_INUM0; | |
8a525303 | 985 | #ifndef SCM_RECKLESS |
09fb7599 | 986 | } else if (SCM_NUMBERP (n1)) { |
d28da049 | 987 | return n1; |
09fb7599 DH |
988 | } else { |
989 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
990 | #else | |
991 | } else { | |
992 | return n1; | |
993 | #endif | |
d28da049 | 994 | } |
8a525303 | 995 | } |
09fb7599 DH |
996 | |
997 | if (SCM_INUMP (n1)) { | |
9a00c9fc | 998 | nn1 = SCM_INUM (n1); |
09fb7599 DH |
999 | if (SCM_INUMP (n2)) { |
1000 | long nn2 = SCM_INUM (n2); | |
1001 | return SCM_MAKINUM (nn1 | nn2); | |
09fb7599 DH |
1002 | } else if (SCM_BIGP (n2)) { |
1003 | intbig: | |
1004 | { | |
8a525303 | 1005 | # ifndef SCM_DIGSTOOBIG |
09fb7599 DH |
1006 | long z = scm_pseudolong (nn1); |
1007 | if ((!(nn1 < 0)) && !SCM_BIGSIGN (n2)) { | |
1008 | return scm_big_ior ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
1009 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); | |
1010 | } else { | |
1011 | return scm_big_and ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
1012 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, SCM_BIGSIGNFLAG); | |
1013 | } | |
8a525303 | 1014 | # else |
5fa20751 | 1015 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
09fb7599 DH |
1016 | scm_longdigs (nn1, zdigs); |
1017 | if ((!(nn1 < 0)) && !SCM_BIGSIGN (n2)) { | |
1018 | return scm_big_ior (zdigs, SCM_DIGSPERLONG, | |
1019 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); | |
1020 | } else { | |
1021 | return scm_big_and (zdigs, SCM_DIGSPERLONG, | |
1022 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2, SCM_BIGSIGNFLAG); | |
1023 | } | |
8a525303 | 1024 | # endif |
09fb7599 | 1025 | } |
09fb7599 DH |
1026 | } else { |
1027 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1028 | } | |
09fb7599 DH |
1029 | } else if (SCM_BIGP (n1)) { |
1030 | if (SCM_INUMP (n2)) { | |
1031 | SCM_SWAP (n1, n2); | |
9a00c9fc | 1032 | nn1 = SCM_INUM (n1); |
09fb7599 DH |
1033 | goto intbig; |
1034 | } else if (SCM_BIGP (n2)) { | |
1035 | if (SCM_NUMDIGS (n1) > SCM_NUMDIGS (n2)) { | |
1036 | SCM_SWAP (n1, n2); | |
1037 | }; | |
1038 | if ((!SCM_BIGSIGN (n1)) && !SCM_BIGSIGN (n2)) { | |
1039 | return scm_big_ior (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), | |
1040 | SCM_BIGSIGN (n1), n2); | |
1041 | } else { | |
1042 | return scm_big_and (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), | |
1043 | SCM_BIGSIGN (n1), n2, SCM_BIGSIGNFLAG); | |
1044 | } | |
1045 | } else { | |
1046 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1047 | } | |
09fb7599 DH |
1048 | } else { |
1049 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1050 | } | |
0f2d19dd | 1051 | } |
1bbd0b84 | 1052 | #undef FUNC_NAME |
0f2d19dd | 1053 | |
09fb7599 | 1054 | |
c3ee7520 | 1055 | SCM_DEFINE1 (scm_logxor, "logxor", scm_tc7_asubr, |
1bbd0b84 | 1056 | (SCM n1, SCM n2), |
3c3db128 GH |
1057 | "Return the bitwise XOR of the integer arguments. A bit is\n" |
1058 | "set in the result if it is set in an odd number of arguments.\n" | |
1059 | "@lisp\n" | |
1060 | "(logxor) @result{} 0\n" | |
1061 | "(logxor 7) @result{} 7\n" | |
1062 | "(logxor #b000 #b001 #b011) @result{} 2\n" | |
1063 | "(logxor #b000 #b001 #b011 #b011) @result{} 1\n" | |
1e6808ea | 1064 | "@end lisp") |
1bbd0b84 | 1065 | #define FUNC_NAME s_scm_logxor |
0f2d19dd | 1066 | { |
9a00c9fc DH |
1067 | long int nn1; |
1068 | ||
09fb7599 DH |
1069 | if (SCM_UNBNDP (n2)) { |
1070 | if (SCM_UNBNDP (n1)) { | |
1071 | return SCM_INUM0; | |
8a525303 | 1072 | #ifndef SCM_RECKLESS |
09fb7599 DH |
1073 | } else if (SCM_NUMBERP (n1)) { |
1074 | return n1; | |
1075 | } else { | |
1076 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1077 | #else | |
1078 | } else { | |
d28da049 | 1079 | return n1; |
09fb7599 | 1080 | #endif |
d28da049 | 1081 | } |
8a525303 | 1082 | } |
09fb7599 DH |
1083 | |
1084 | if (SCM_INUMP (n1)) { | |
9a00c9fc | 1085 | nn1 = SCM_INUM (n1); |
09fb7599 DH |
1086 | if (SCM_INUMP (n2)) { |
1087 | long nn2 = SCM_INUM (n2); | |
1088 | return SCM_MAKINUM (nn1 ^ nn2); | |
09fb7599 DH |
1089 | } else if (SCM_BIGP (n2)) { |
1090 | intbig: | |
8a525303 GB |
1091 | { |
1092 | # ifndef SCM_DIGSTOOBIG | |
09fb7599 DH |
1093 | long z = scm_pseudolong (nn1); |
1094 | return scm_big_xor ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
1095 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); | |
8a525303 | 1096 | # else |
09fb7599 DH |
1097 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
1098 | scm_longdigs (nn1, zdigs); | |
1099 | return scm_big_xor (zdigs, SCM_DIGSPERLONG, | |
1100 | (nn1 < 0) ? SCM_BIGSIGNFLAG : 0, n2); | |
8a525303 GB |
1101 | # endif |
1102 | } | |
09fb7599 DH |
1103 | } else { |
1104 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1105 | } | |
09fb7599 DH |
1106 | } else if (SCM_BIGP (n1)) { |
1107 | if (SCM_INUMP (n2)) { | |
1108 | SCM_SWAP (n1, n2); | |
9a00c9fc | 1109 | nn1 = SCM_INUM (n1); |
09fb7599 DH |
1110 | goto intbig; |
1111 | } else if (SCM_BIGP (n2)) { | |
1112 | if (SCM_NUMDIGS(n1) > SCM_NUMDIGS(n2)) { | |
1113 | SCM_SWAP (n1, n2); | |
1114 | } | |
1115 | return scm_big_xor (SCM_BDIGITS (n1), SCM_NUMDIGS (n1), | |
1116 | SCM_BIGSIGN (n1), n2); | |
1117 | } else { | |
1118 | SCM_WRONG_TYPE_ARG (SCM_ARG2, n2); | |
1119 | } | |
09fb7599 DH |
1120 | } else { |
1121 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n1); | |
1122 | } | |
0f2d19dd | 1123 | } |
1bbd0b84 | 1124 | #undef FUNC_NAME |
0f2d19dd | 1125 | |
09fb7599 | 1126 | |
a1ec6916 | 1127 | SCM_DEFINE (scm_logtest, "logtest", 2, 0, 0, |
1e6808ea MG |
1128 | (SCM j, SCM k), |
1129 | "@lisp\n" | |
b380b885 MD |
1130 | "(logtest j k) @equiv{} (not (zero? (logand j k)))\n\n" |
1131 | "(logtest #b0100 #b1011) @result{} #f\n" | |
1132 | "(logtest #b0100 #b0111) @result{} #t\n" | |
1e6808ea | 1133 | "@end lisp") |
1bbd0b84 | 1134 | #define FUNC_NAME s_scm_logtest |
0f2d19dd | 1135 | { |
1e6808ea | 1136 | long int nj; |
9a00c9fc | 1137 | |
1e6808ea MG |
1138 | if (SCM_INUMP (j)) { |
1139 | nj = SCM_INUM (j); | |
1140 | if (SCM_INUMP (k)) { | |
1141 | long nk = SCM_INUM (k); | |
1142 | return SCM_BOOL (nj & nk); | |
1143 | } else if (SCM_BIGP (k)) { | |
f8de44c1 DH |
1144 | intbig: |
1145 | { | |
8a525303 | 1146 | # ifndef SCM_DIGSTOOBIG |
1e6808ea | 1147 | long z = scm_pseudolong (nj); |
f8de44c1 | 1148 | return scm_big_test ((SCM_BIGDIG *)&z, SCM_DIGSPERLONG, |
1e6808ea | 1149 | (nj < 0) ? SCM_BIGSIGNFLAG : 0, k); |
8a525303 | 1150 | # else |
f8de44c1 | 1151 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
1e6808ea | 1152 | scm_longdigs (nj, zdigs); |
f8de44c1 | 1153 | return scm_big_test (zdigs, SCM_DIGSPERLONG, |
1e6808ea | 1154 | (nj < 0) ? SCM_BIGSIGNFLAG : 0, k); |
8a525303 | 1155 | # endif |
f8de44c1 | 1156 | } |
f8de44c1 | 1157 | } else { |
1e6808ea | 1158 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); |
f8de44c1 | 1159 | } |
1e6808ea MG |
1160 | } else if (SCM_BIGP (j)) { |
1161 | if (SCM_INUMP (k)) { | |
1162 | SCM_SWAP (j, k); | |
1163 | nj = SCM_INUM (j); | |
f8de44c1 | 1164 | goto intbig; |
1e6808ea MG |
1165 | } else if (SCM_BIGP (k)) { |
1166 | if (SCM_NUMDIGS (j) > SCM_NUMDIGS (k)) { | |
1167 | SCM_SWAP (j, k); | |
f8de44c1 | 1168 | } |
1e6808ea MG |
1169 | return scm_big_test (SCM_BDIGITS (j), SCM_NUMDIGS (j), |
1170 | SCM_BIGSIGN (j), k); | |
f8de44c1 | 1171 | } else { |
1e6808ea | 1172 | SCM_WRONG_TYPE_ARG (SCM_ARG2, k); |
f8de44c1 | 1173 | } |
f8de44c1 | 1174 | } else { |
1e6808ea | 1175 | SCM_WRONG_TYPE_ARG (SCM_ARG1, j); |
f8de44c1 | 1176 | } |
0f2d19dd | 1177 | } |
1bbd0b84 | 1178 | #undef FUNC_NAME |
0f2d19dd | 1179 | |
c1bfcf60 | 1180 | |
a1ec6916 | 1181 | SCM_DEFINE (scm_logbit_p, "logbit?", 2, 0, 0, |
2cd04b42 | 1182 | (SCM index, SCM j), |
1e6808ea | 1183 | "@lisp\n" |
b380b885 MD |
1184 | "(logbit? index j) @equiv{} (logtest (integer-expt 2 index) j)\n\n" |
1185 | "(logbit? 0 #b1101) @result{} #t\n" | |
1186 | "(logbit? 1 #b1101) @result{} #f\n" | |
1187 | "(logbit? 2 #b1101) @result{} #t\n" | |
1188 | "(logbit? 3 #b1101) @result{} #t\n" | |
1189 | "(logbit? 4 #b1101) @result{} #f\n" | |
1e6808ea | 1190 | "@end lisp") |
1bbd0b84 | 1191 | #define FUNC_NAME s_scm_logbit_p |
0f2d19dd | 1192 | { |
78166ad5 DH |
1193 | unsigned long int iindex; |
1194 | ||
1195 | SCM_VALIDATE_INUM_MIN (SCM_ARG1, index, 0); | |
1196 | iindex = (unsigned long int) SCM_INUM (index); | |
1197 | ||
1198 | if (SCM_INUMP (j)) { | |
1199 | return SCM_BOOL ((1L << iindex) & SCM_INUM (j)); | |
1200 | } else if (SCM_BIGP (j)) { | |
1201 | if (SCM_NUMDIGS (j) * SCM_BITSPERDIG < iindex) { | |
1202 | return SCM_BOOL_F; | |
1203 | } else if (SCM_BIGSIGN (j)) { | |
8a525303 | 1204 | long num = -1; |
1be6b49c | 1205 | size_t i = 0; |
78166ad5 | 1206 | SCM_BIGDIG * x = SCM_BDIGITS (j); |
1be6b49c | 1207 | size_t nx = iindex / SCM_BITSPERDIG; |
78166ad5 | 1208 | while (1) { |
8a525303 | 1209 | num += x[i]; |
78166ad5 DH |
1210 | if (nx == i++) { |
1211 | return SCM_BOOL (((1L << (iindex % SCM_BITSPERDIG)) & num) == 0); | |
1212 | } else if (num < 0) { | |
1213 | num = -1; | |
1214 | } else { | |
1215 | num = 0; | |
1216 | } | |
8a525303 | 1217 | } |
78166ad5 DH |
1218 | } else { |
1219 | return SCM_BOOL (SCM_BDIGITS (j) [iindex / SCM_BITSPERDIG] | |
1220 | & (1L << (iindex % SCM_BITSPERDIG))); | |
8a525303 | 1221 | } |
78166ad5 DH |
1222 | } else { |
1223 | SCM_WRONG_TYPE_ARG (SCM_ARG2, j); | |
8a525303 | 1224 | } |
0f2d19dd | 1225 | } |
1bbd0b84 | 1226 | #undef FUNC_NAME |
0f2d19dd | 1227 | |
78166ad5 | 1228 | |
a1ec6916 | 1229 | SCM_DEFINE (scm_lognot, "lognot", 1, 0, 0, |
1bbd0b84 | 1230 | (SCM n), |
1e6808ea MG |
1231 | "Return the integer which is the 2s-complement of the integer\n" |
1232 | "argument.\n" | |
1233 | "\n" | |
b380b885 MD |
1234 | "@lisp\n" |
1235 | "(number->string (lognot #b10000000) 2)\n" | |
1236 | " @result{} \"-10000001\"\n" | |
1237 | "(number->string (lognot #b0) 2)\n" | |
1238 | " @result{} \"-1\"\n" | |
1e6808ea | 1239 | "@end lisp") |
1bbd0b84 | 1240 | #define FUNC_NAME s_scm_lognot |
0f2d19dd | 1241 | { |
f872b822 | 1242 | return scm_difference (SCM_MAKINUM (-1L), n); |
0f2d19dd | 1243 | } |
1bbd0b84 | 1244 | #undef FUNC_NAME |
0f2d19dd | 1245 | |
a1ec6916 | 1246 | SCM_DEFINE (scm_integer_expt, "integer-expt", 2, 0, 0, |
2cd04b42 | 1247 | (SCM n, SCM k), |
1e6808ea MG |
1248 | "Return @var{n} raised to the non-negative integer exponent\n" |
1249 | "@var{k}.\n" | |
1250 | "\n" | |
b380b885 MD |
1251 | "@lisp\n" |
1252 | "(integer-expt 2 5)\n" | |
1253 | " @result{} 32\n" | |
1254 | "(integer-expt -3 3)\n" | |
1255 | " @result{} -27\n" | |
1256 | "@end lisp") | |
1bbd0b84 | 1257 | #define FUNC_NAME s_scm_integer_expt |
0f2d19dd | 1258 | { |
f872b822 | 1259 | SCM acc = SCM_MAKINUM (1L); |
1bbd0b84 | 1260 | int i2; |
0f2d19dd | 1261 | #ifdef SCM_BIGDIG |
4260a7fc | 1262 | if (SCM_EQ_P (n, SCM_INUM0) || SCM_EQ_P (n, acc)) |
2cd04b42 | 1263 | return n; |
4260a7fc DH |
1264 | else if (SCM_EQ_P (n, SCM_MAKINUM (-1L))) |
1265 | return SCM_FALSEP (scm_even_p (k)) ? n : acc; | |
0f2d19dd | 1266 | #endif |
2830fd91 MD |
1267 | if (SCM_REALP (k)) |
1268 | { | |
1269 | double r = SCM_REAL_VALUE (k); | |
1270 | i2 = r; | |
1271 | if (i2 != r) | |
1272 | SCM_WRONG_TYPE_ARG (2, k); | |
1273 | } | |
1274 | else | |
1275 | SCM_VALIDATE_ULONG_COPY (2,k,i2); | |
1bbd0b84 | 1276 | if (i2 < 0) |
f872b822 | 1277 | { |
1bbd0b84 | 1278 | i2 = -i2; |
2cd04b42 | 1279 | n = scm_divide (n, SCM_UNDEFINED); |
f872b822 MD |
1280 | } |
1281 | while (1) | |
1282 | { | |
1bbd0b84 | 1283 | if (0 == i2) |
f872b822 | 1284 | return acc; |
1bbd0b84 | 1285 | if (1 == i2) |
2cd04b42 | 1286 | return scm_product (acc, n); |
1bbd0b84 | 1287 | if (i2 & 1) |
2cd04b42 GB |
1288 | acc = scm_product (acc, n); |
1289 | n = scm_product (n, n); | |
1bbd0b84 | 1290 | i2 >>= 1; |
f872b822 | 1291 | } |
0f2d19dd | 1292 | } |
1bbd0b84 | 1293 | #undef FUNC_NAME |
0f2d19dd | 1294 | |
a1ec6916 | 1295 | SCM_DEFINE (scm_ash, "ash", 2, 0, 0, |
1bbd0b84 | 1296 | (SCM n, SCM cnt), |
1e6808ea MG |
1297 | "The function ash performs an arithmetic shift left by @var{cnt}\n" |
1298 | "bits (or shift right, if @var{cnt} is negative). 'Arithmetic'\n" | |
1299 | "means, that the function does not guarantee to keep the bit\n" | |
1300 | "structure of @var{n}, but rather guarantees that the result\n" | |
1301 | "will always be rounded towards minus infinity. Therefore, the\n" | |
1302 | "results of ash and a corresponding bitwise shift will differ if\n" | |
1303 | "@var{n} is negative.\n" | |
1304 | "\n" | |
3ab9f56e | 1305 | "Formally, the function returns an integer equivalent to\n" |
1e6808ea MG |
1306 | "@code{(inexact->exact (floor (* @var{n} (expt 2 @var{cnt}))))}.\n" |
1307 | "\n" | |
b380b885 | 1308 | "@lisp\n" |
1e6808ea MG |
1309 | "(number->string (ash #b1 3) 2) @result{} \"1000\"\n" |
1310 | "(number->string (ash #b1010 -1) 2) @result{} \"101\"\n" | |
a3c8b9fc | 1311 | "@end lisp") |
1bbd0b84 | 1312 | #define FUNC_NAME s_scm_ash |
0f2d19dd | 1313 | { |
3ab9f56e DH |
1314 | long bits_to_shift; |
1315 | ||
1316 | #ifndef SCM_BIGDIG | |
1317 | SCM_VALIDATE_INUM (1, n) | |
1318 | #endif | |
1319 | SCM_VALIDATE_INUM (2, cnt); | |
1320 | ||
1321 | bits_to_shift = SCM_INUM (cnt); | |
0f2d19dd | 1322 | #ifdef SCM_BIGDIG |
3ab9f56e DH |
1323 | if (bits_to_shift < 0) { |
1324 | /* Shift right by abs(cnt) bits. This is realized as a division by | |
1325 | div:=2^abs(cnt). However, to guarantee the floor rounding, negative | |
1326 | values require some special treatment. | |
1327 | */ | |
1328 | SCM div = scm_integer_expt (SCM_MAKINUM (2), SCM_MAKINUM (-bits_to_shift)); | |
1329 | if (SCM_FALSEP (scm_negative_p (n))) | |
1330 | return scm_quotient (n, div); | |
1331 | else | |
1332 | return scm_sum (SCM_MAKINUM (-1L), | |
1333 | scm_quotient (scm_sum (SCM_MAKINUM (1L), n), div)); | |
1334 | } else | |
1335 | /* Shift left is done by multiplication with 2^CNT */ | |
f872b822 | 1336 | return scm_product (n, scm_integer_expt (SCM_MAKINUM (2), cnt)); |
0f2d19dd | 1337 | #else |
3ab9f56e DH |
1338 | if (bits_to_shift < 0) |
1339 | /* Signed right shift (SCM_SRS does it right) by abs(cnt) bits. */ | |
1340 | return SCM_MAKINUM (SCM_SRS (SCM_INUM (n), -bits_to_shift)); | |
1341 | else { | |
1342 | /* Shift left, but make sure not to leave the range of inums */ | |
1343 | SCM res = SCM_MAKINUM (SCM_INUM (n) << cnt); | |
1344 | if (SCM_INUM (res) >> cnt != SCM_INUM (n)) | |
1345 | scm_num_overflow (FUNC_NAME); | |
1346 | return res; | |
1347 | } | |
0f2d19dd JB |
1348 | #endif |
1349 | } | |
1bbd0b84 | 1350 | #undef FUNC_NAME |
0f2d19dd | 1351 | |
3c9f20f8 | 1352 | |
a1ec6916 | 1353 | SCM_DEFINE (scm_bit_extract, "bit-extract", 3, 0, 0, |
1bbd0b84 | 1354 | (SCM n, SCM start, SCM end), |
1e6808ea MG |
1355 | "Return the integer composed of the @var{start} (inclusive)\n" |
1356 | "through @var{end} (exclusive) bits of @var{n}. The\n" | |
1357 | "@var{start}th bit becomes the 0-th bit in the result.\n" | |
1358 | "\n" | |
b380b885 MD |
1359 | "@lisp\n" |
1360 | "(number->string (bit-extract #b1101101010 0 4) 2)\n" | |
1361 | " @result{} \"1010\"\n" | |
1362 | "(number->string (bit-extract #b1101101010 4 9) 2)\n" | |
1363 | " @result{} \"10110\"\n" | |
1364 | "@end lisp") | |
1bbd0b84 | 1365 | #define FUNC_NAME s_scm_bit_extract |
0f2d19dd | 1366 | { |
ac0c002c | 1367 | unsigned long int istart, iend; |
c1bfcf60 GB |
1368 | SCM_VALIDATE_INUM_MIN_COPY (2,start,0,istart); |
1369 | SCM_VALIDATE_INUM_MIN_COPY (3, end, 0, iend); | |
1370 | SCM_ASSERT_RANGE (3, end, (iend >= istart)); | |
78166ad5 DH |
1371 | |
1372 | if (SCM_INUMP (n)) { | |
ac0c002c DH |
1373 | long int in = SCM_INUM (n); |
1374 | unsigned long int bits = iend - istart; | |
1375 | ||
1be6b49c | 1376 | if (in < 0 && bits >= SCM_I_FIXNUM_BIT) |
ac0c002c DH |
1377 | { |
1378 | /* Since we emulate two's complement encoded numbers, this special | |
1379 | * case requires us to produce a result that has more bits than can be | |
1380 | * stored in a fixnum. Thus, we fall back to the more general | |
1381 | * algorithm that is used for bignums. | |
1382 | */ | |
1383 | goto generalcase; | |
1384 | } | |
1385 | ||
1be6b49c | 1386 | if (istart < SCM_I_FIXNUM_BIT) |
ac0c002c DH |
1387 | { |
1388 | in = in >> istart; | |
1be6b49c | 1389 | if (bits < SCM_I_FIXNUM_BIT) |
ac0c002c DH |
1390 | return SCM_MAKINUM (in & ((1L << bits) - 1)); |
1391 | else /* we know: in >= 0 */ | |
1392 | return SCM_MAKINUM (in); | |
1393 | } | |
1394 | else if (in < 0) | |
1395 | { | |
1396 | return SCM_MAKINUM (-1L & ((1L << bits) - 1)); | |
1397 | } | |
1398 | else | |
1399 | { | |
1400 | return SCM_MAKINUM (0); | |
1401 | } | |
78166ad5 | 1402 | } else if (SCM_BIGP (n)) { |
ac0c002c DH |
1403 | generalcase: |
1404 | { | |
1405 | SCM num1 = SCM_MAKINUM (1L); | |
1406 | SCM num2 = SCM_MAKINUM (2L); | |
1407 | SCM bits = SCM_MAKINUM (iend - istart); | |
1408 | SCM mask = scm_difference (scm_integer_expt (num2, bits), num1); | |
1409 | return scm_logand (mask, scm_ash (n, SCM_MAKINUM (-istart))); | |
1410 | } | |
78166ad5 DH |
1411 | } else { |
1412 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1413 | } | |
0f2d19dd | 1414 | } |
1bbd0b84 | 1415 | #undef FUNC_NAME |
0f2d19dd | 1416 | |
3c9f20f8 | 1417 | |
e4755e5c JB |
1418 | static const char scm_logtab[] = { |
1419 | 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 | |
1420 | }; | |
1cc91f1b | 1421 | |
a1ec6916 | 1422 | SCM_DEFINE (scm_logcount, "logcount", 1, 0, 0, |
1bbd0b84 | 1423 | (SCM n), |
1e6808ea MG |
1424 | "Return the number of bits in integer @var{n}. If integer is\n" |
1425 | "positive, the 1-bits in its binary representation are counted.\n" | |
1426 | "If negative, the 0-bits in its two's-complement binary\n" | |
1427 | "representation are counted. If 0, 0 is returned.\n" | |
1428 | "\n" | |
b380b885 MD |
1429 | "@lisp\n" |
1430 | "(logcount #b10101010)\n" | |
1431 | " @result{} 4\n" | |
1432 | "(logcount 0)\n" | |
1433 | " @result{} 0\n" | |
1434 | "(logcount -2)\n" | |
1435 | " @result{} 1\n" | |
1436 | "@end lisp") | |
1bbd0b84 | 1437 | #define FUNC_NAME s_scm_logcount |
0f2d19dd | 1438 | { |
3c9f20f8 DH |
1439 | if (SCM_INUMP (n)) { |
1440 | unsigned long int c = 0; | |
1441 | long int nn = SCM_INUM (n); | |
1442 | if (nn < 0) { | |
1443 | nn = -1 - nn; | |
1444 | }; | |
1445 | while (nn) { | |
1446 | c += scm_logtab[15 & nn]; | |
1447 | nn >>= 4; | |
1448 | }; | |
1449 | return SCM_MAKINUM (c); | |
1450 | } else if (SCM_BIGP (n)) { | |
1451 | if (SCM_BIGSIGN (n)) { | |
1452 | return scm_logcount (scm_difference (SCM_MAKINUM (-1L), n)); | |
1453 | } else { | |
1454 | unsigned long int c = 0; | |
1be6b49c | 1455 | size_t i = SCM_NUMDIGS (n); |
3c9f20f8 DH |
1456 | SCM_BIGDIG * ds = SCM_BDIGITS (n); |
1457 | while (i--) { | |
1458 | SCM_BIGDIG d; | |
1459 | for (d = ds[i]; d; d >>= 4) { | |
f872b822 | 1460 | c += scm_logtab[15 & d]; |
3c9f20f8 DH |
1461 | } |
1462 | } | |
f872b822 MD |
1463 | return SCM_MAKINUM (c); |
1464 | } | |
3c9f20f8 DH |
1465 | } else { |
1466 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1467 | } | |
0f2d19dd | 1468 | } |
1bbd0b84 GB |
1469 | #undef FUNC_NAME |
1470 | ||
0f2d19dd | 1471 | |
e4755e5c JB |
1472 | static const char scm_ilentab[] = { |
1473 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 | |
1474 | }; | |
1cc91f1b | 1475 | |
a1ec6916 | 1476 | SCM_DEFINE (scm_integer_length, "integer-length", 1, 0, 0, |
1bbd0b84 | 1477 | (SCM n), |
bb2c02f2 | 1478 | "Return the number of bits necessary to represent @var{n}.\n" |
1e6808ea | 1479 | "\n" |
b380b885 MD |
1480 | "@lisp\n" |
1481 | "(integer-length #b10101010)\n" | |
1482 | " @result{} 8\n" | |
1483 | "(integer-length 0)\n" | |
1484 | " @result{} 0\n" | |
1485 | "(integer-length #b1111)\n" | |
1486 | " @result{} 4\n" | |
1487 | "@end lisp") | |
1bbd0b84 | 1488 | #define FUNC_NAME s_scm_integer_length |
0f2d19dd | 1489 | { |
3c9f20f8 DH |
1490 | if (SCM_INUMP (n)) { |
1491 | unsigned long int c = 0; | |
1492 | unsigned int l = 4; | |
1493 | long int nn = SCM_INUM (n); | |
1494 | if (nn < 0) { | |
1495 | nn = -1 - nn; | |
1496 | }; | |
1497 | while (nn) { | |
f872b822 | 1498 | c += 4; |
3c9f20f8 DH |
1499 | l = scm_ilentab [15 & nn]; |
1500 | nn >>= 4; | |
1501 | }; | |
1502 | return SCM_MAKINUM (c - 4 + l); | |
1503 | } else if (SCM_BIGP (n)) { | |
1504 | if (SCM_BIGSIGN (n)) { | |
1505 | return scm_integer_length (scm_difference (SCM_MAKINUM (-1L), n)); | |
1506 | } else { | |
1507 | unsigned long int digs = SCM_NUMDIGS (n) - 1; | |
1508 | unsigned long int c = digs * SCM_BITSPERDIG; | |
1509 | unsigned int l = 4; | |
1510 | SCM_BIGDIG * ds = SCM_BDIGITS (n); | |
1511 | SCM_BIGDIG d = ds [digs]; | |
1512 | while (d) { | |
1513 | c += 4; | |
1514 | l = scm_ilentab [15 & d]; | |
1515 | d >>= 4; | |
1516 | }; | |
1517 | return SCM_MAKINUM (c - 4 + l); | |
f872b822 | 1518 | } |
3c9f20f8 DH |
1519 | } else { |
1520 | SCM_WRONG_TYPE_ARG (SCM_ARG1, n); | |
1521 | } | |
0f2d19dd | 1522 | } |
1bbd0b84 | 1523 | #undef FUNC_NAME |
0f2d19dd JB |
1524 | |
1525 | ||
1526 | #ifdef SCM_BIGDIG | |
e4755e5c | 1527 | static const char s_bignum[] = "bignum"; |
1cc91f1b | 1528 | |
0f2d19dd | 1529 | SCM |
1be6b49c | 1530 | scm_i_mkbig (size_t nlen, int sign) |
0f2d19dd | 1531 | { |
c209c88e | 1532 | SCM v; |
5843e5c9 DH |
1533 | SCM_BIGDIG *base; |
1534 | ||
1535 | if (((nlen << SCM_BIGSIZEFIELD) >> SCM_BIGSIZEFIELD) != nlen) | |
2500356c | 1536 | scm_memory_error (s_bignum); |
5843e5c9 | 1537 | |
4c9419ac | 1538 | base = scm_gc_malloc (nlen * sizeof (SCM_BIGDIG), s_bignum); |
5843e5c9 | 1539 | |
228a24ef | 1540 | v = scm_cell (SCM_MAKE_BIGNUM_TAG (nlen, sign), (scm_t_bits) base); |
0f2d19dd JB |
1541 | return v; |
1542 | } | |
1543 | ||
0f2d19dd | 1544 | SCM |
1be6b49c | 1545 | scm_i_big2inum (SCM b, size_t l) |
0f2d19dd JB |
1546 | { |
1547 | unsigned long num = 0; | |
f872b822 MD |
1548 | SCM_BIGDIG *tmp = SCM_BDIGITS (b); |
1549 | while (l--) | |
1550 | num = SCM_BIGUP (num) + tmp[l]; | |
f3ae5d60 | 1551 | if (!SCM_BIGSIGN (b)) |
f872b822 MD |
1552 | { |
1553 | if (SCM_POSFIXABLE (num)) | |
1554 | return SCM_MAKINUM (num); | |
1555 | } | |
894a712b | 1556 | else if (num <= -SCM_MOST_NEGATIVE_FIXNUM) |
f872b822 | 1557 | return SCM_MAKINUM (-num); |
0f2d19dd JB |
1558 | return b; |
1559 | } | |
1560 | ||
1be6b49c | 1561 | static const char s_adjbig[] = "scm_i_adjbig"; |
1cc91f1b | 1562 | |
0f2d19dd | 1563 | SCM |
1be6b49c | 1564 | scm_i_adjbig (SCM b, size_t nlen) |
0f2d19dd | 1565 | { |
1be6b49c | 1566 | size_t nsiz = nlen; |
f3ae5d60 | 1567 | if (((nsiz << SCM_BIGSIZEFIELD) >> SCM_BIGSIZEFIELD) != nlen) |
2500356c | 1568 | scm_memory_error (s_adjbig); |
2bf746cc | 1569 | |
0f2d19dd | 1570 | SCM_DEFER_INTS; |
2bf746cc JB |
1571 | { |
1572 | SCM_BIGDIG *digits | |
1573 | = ((SCM_BIGDIG *) | |
4c9419ac MV |
1574 | scm_gc_realloc (SCM_BDIGITS (b), |
1575 | SCM_NUMDIGS (b) * sizeof (SCM_BIGDIG), | |
1576 | nsiz * sizeof (SCM_BIGDIG), s_bignum)); | |
2bf746cc | 1577 | |
6a0476fd | 1578 | SCM_SET_BIGNUM_BASE (b, digits); |
f3ae5d60 | 1579 | SCM_SETNUMDIGS (b, nsiz, SCM_BIGSIGN (b)); |
2bf746cc | 1580 | } |
0f2d19dd JB |
1581 | SCM_ALLOW_INTS; |
1582 | return b; | |
1583 | } | |
1584 | ||
0f2d19dd | 1585 | SCM |
1be6b49c | 1586 | scm_i_normbig (SCM b) |
0f2d19dd | 1587 | { |
f872b822 | 1588 | #ifndef _UNICOS |
1be6b49c | 1589 | size_t nlen = SCM_NUMDIGS (b); |
0f2d19dd | 1590 | #else |
f872b822 | 1591 | int nlen = SCM_NUMDIGS (b); /* unsigned nlen breaks on Cray when nlen => 0 */ |
0f2d19dd | 1592 | #endif |
f872b822 MD |
1593 | SCM_BIGDIG *zds = SCM_BDIGITS (b); |
1594 | while (nlen-- && !zds[nlen]); | |
1595 | nlen++; | |
1596 | if (nlen * SCM_BITSPERDIG / SCM_CHAR_BIT <= sizeof (SCM)) | |
1be6b49c | 1597 | if (SCM_INUMP (b = scm_i_big2inum (b, (size_t) nlen))) |
f872b822 MD |
1598 | return b; |
1599 | if (SCM_NUMDIGS (b) == nlen) | |
1600 | return b; | |
1be6b49c | 1601 | return scm_i_adjbig (b, (size_t) nlen); |
0f2d19dd JB |
1602 | } |
1603 | ||
0f2d19dd | 1604 | SCM |
1be6b49c | 1605 | scm_i_copybig (SCM b, int sign) |
0f2d19dd | 1606 | { |
1be6b49c ML |
1607 | size_t i = SCM_NUMDIGS (b); |
1608 | SCM ans = scm_i_mkbig (i, sign); | |
f872b822 MD |
1609 | SCM_BIGDIG *src = SCM_BDIGITS (b), *dst = SCM_BDIGITS (ans); |
1610 | while (i--) | |
1611 | dst[i] = src[i]; | |
0f2d19dd JB |
1612 | return ans; |
1613 | } | |
1614 | ||
0f2d19dd | 1615 | int |
1bbd0b84 | 1616 | scm_bigcomp (SCM x, SCM y) |
0f2d19dd | 1617 | { |
f872b822 MD |
1618 | int xsign = SCM_BIGSIGN (x); |
1619 | int ysign = SCM_BIGSIGN (y); | |
1be6b49c | 1620 | size_t xlen, ylen; |
2bf746cc JB |
1621 | |
1622 | /* Look at the signs, first. */ | |
f872b822 MD |
1623 | if (ysign < xsign) |
1624 | return 1; | |
1625 | if (ysign > xsign) | |
1626 | return -1; | |
2bf746cc JB |
1627 | |
1628 | /* They're the same sign, so see which one has more digits. Note | |
1629 | that, if they are negative, the longer number is the lesser. */ | |
f872b822 MD |
1630 | ylen = SCM_NUMDIGS (y); |
1631 | xlen = SCM_NUMDIGS (x); | |
2bf746cc JB |
1632 | if (ylen > xlen) |
1633 | return (xsign) ? -1 : 1; | |
f872b822 MD |
1634 | if (ylen < xlen) |
1635 | return (xsign) ? 1 : -1; | |
2bf746cc JB |
1636 | |
1637 | /* They have the same number of digits, so find the most significant | |
1638 | digit where they differ. */ | |
1639 | while (xlen) | |
1640 | { | |
1641 | --xlen; | |
1642 | if (SCM_BDIGITS (y)[xlen] != SCM_BDIGITS (x)[xlen]) | |
1643 | /* Make the discrimination based on the digit that differs. */ | |
f872b822 MD |
1644 | return ((SCM_BDIGITS (y)[xlen] > SCM_BDIGITS (x)[xlen]) |
1645 | ? (xsign ? -1 : 1) | |
1646 | : (xsign ? 1 : -1)); | |
2bf746cc JB |
1647 | } |
1648 | ||
1649 | /* The numbers are identical. */ | |
1650 | return 0; | |
0f2d19dd JB |
1651 | } |
1652 | ||
1653 | #ifndef SCM_DIGSTOOBIG | |
1654 | ||
1cc91f1b | 1655 | |
0f2d19dd | 1656 | long |
1bbd0b84 | 1657 | scm_pseudolong (long x) |
0f2d19dd | 1658 | { |
f872b822 MD |
1659 | union |
1660 | { | |
0f2d19dd JB |
1661 | long l; |
1662 | SCM_BIGDIG bd[SCM_DIGSPERLONG]; | |
f872b822 MD |
1663 | } |
1664 | p; | |
1be6b49c | 1665 | size_t i = 0; |
f872b822 MD |
1666 | if (x < 0) |
1667 | x = -x; | |
1668 | while (i < SCM_DIGSPERLONG) | |
1669 | { | |
1670 | p.bd[i++] = SCM_BIGLO (x); | |
1671 | x = SCM_BIGDN (x); | |
1672 | } | |
0f2d19dd JB |
1673 | /* p.bd[0] = SCM_BIGLO(x); p.bd[1] = SCM_BIGDN(x); */ |
1674 | return p.l; | |
1675 | } | |
1676 | ||
1677 | #else | |
1678 | ||
1cc91f1b | 1679 | |
0f2d19dd | 1680 | void |
1bbd0b84 | 1681 | scm_longdigs (long x, SCM_BIGDIG digs[]) |
0f2d19dd | 1682 | { |
1be6b49c | 1683 | size_t i = 0; |
f872b822 MD |
1684 | if (x < 0) |
1685 | x = -x; | |
1686 | while (i < SCM_DIGSPERLONG) | |
1687 | { | |
1688 | digs[i++] = SCM_BIGLO (x); | |
1689 | x = SCM_BIGDN (x); | |
1690 | } | |
0f2d19dd JB |
1691 | } |
1692 | #endif | |
1693 | ||
1694 | ||
1cc91f1b | 1695 | |
0f2d19dd | 1696 | SCM |
1be6b49c | 1697 | scm_addbig (SCM_BIGDIG *x, size_t nx, int xsgn, SCM bigy, int sgny) |
0f2d19dd JB |
1698 | { |
1699 | /* Assumes nx <= SCM_NUMDIGS(bigy) */ | |
f3ae5d60 | 1700 | /* Assumes xsgn and sgny scm_equal either 0 or SCM_BIGSIGNFLAG */ |
0f2d19dd | 1701 | long num = 0; |
1be6b49c ML |
1702 | size_t i = 0, ny = SCM_NUMDIGS (bigy); |
1703 | SCM z = scm_i_copybig (bigy, SCM_BIGSIGN (bigy) ^ sgny); | |
f872b822 MD |
1704 | SCM_BIGDIG *zds = SCM_BDIGITS (z); |
1705 | if (xsgn ^ SCM_BIGSIGN (z)) | |
1706 | { | |
1707 | do | |
1708 | { | |
1709 | num += (long) zds[i] - x[i]; | |
1710 | if (num < 0) | |
1711 | { | |
1712 | zds[i] = num + SCM_BIGRAD; | |
1713 | num = -1; | |
1714 | } | |
1715 | else | |
1716 | { | |
1717 | zds[i] = SCM_BIGLO (num); | |
1718 | num = 0; | |
1719 | } | |
1720 | } | |
1721 | while (++i < nx); | |
1722 | if (num && nx == ny) | |
1723 | { | |
1724 | num = 1; | |
1725 | i = 0; | |
4260a7fc | 1726 | SCM_SET_CELL_WORD_0 (z, SCM_CELL_WORD_0 (z) ^ SCM_BIGSIGNFLAG); |
f872b822 MD |
1727 | do |
1728 | { | |
1729 | num += (SCM_BIGRAD - 1) - zds[i]; | |
1730 | zds[i++] = SCM_BIGLO (num); | |
1731 | num = SCM_BIGDN (num); | |
1732 | } | |
1733 | while (i < ny); | |
1734 | } | |
1735 | else | |
1736 | while (i < ny) | |
1737 | { | |
1738 | num += zds[i]; | |
1739 | if (num < 0) | |
1740 | { | |
1741 | zds[i++] = num + SCM_BIGRAD; | |
1742 | num = -1; | |
1743 | } | |
1744 | else | |
1745 | { | |
1746 | zds[i++] = SCM_BIGLO (num); | |
1747 | num = 0; | |
1748 | } | |
1749 | } | |
1750 | } | |
1751 | else | |
1752 | { | |
1753 | do | |
1754 | { | |
1755 | num += (long) zds[i] + x[i]; | |
1756 | zds[i++] = SCM_BIGLO (num); | |
1757 | num = SCM_BIGDN (num); | |
1758 | } | |
1759 | while (i < nx); | |
1760 | if (!num) | |
1761 | return z; | |
1762 | while (i < ny) | |
1763 | { | |
1764 | num += zds[i]; | |
1765 | zds[i++] = SCM_BIGLO (num); | |
1766 | num = SCM_BIGDN (num); | |
1767 | if (!num) | |
1768 | return z; | |
1769 | } | |
1770 | if (num) | |
1771 | { | |
1be6b49c | 1772 | z = scm_i_adjbig (z, ny + 1); |
f872b822 MD |
1773 | SCM_BDIGITS (z)[ny] = num; |
1774 | return z; | |
1775 | } | |
1776 | } | |
1be6b49c | 1777 | return scm_i_normbig (z); |
0f2d19dd JB |
1778 | } |
1779 | ||
1cc91f1b | 1780 | |
0f2d19dd | 1781 | SCM |
1be6b49c | 1782 | scm_mulbig (SCM_BIGDIG *x, size_t nx, SCM_BIGDIG *y, size_t ny, int sgn) |
0f2d19dd | 1783 | { |
1be6b49c | 1784 | size_t i = 0, j = nx + ny; |
0f2d19dd | 1785 | unsigned long n = 0; |
1be6b49c | 1786 | SCM z = scm_i_mkbig (j, sgn); |
f872b822 MD |
1787 | SCM_BIGDIG *zds = SCM_BDIGITS (z); |
1788 | while (j--) | |
1789 | zds[j] = 0; | |
1790 | do | |
1791 | { | |
1792 | j = 0; | |
1793 | if (x[i]) | |
1794 | { | |
1795 | do | |
1796 | { | |
1797 | n += zds[i + j] + ((unsigned long) x[i] * y[j]); | |
1798 | zds[i + j++] = SCM_BIGLO (n); | |
1799 | n = SCM_BIGDN (n); | |
1800 | } | |
1801 | while (j < ny); | |
1802 | if (n) | |
1803 | { | |
1804 | zds[i + j] = n; | |
1805 | n = 0; | |
1806 | } | |
1807 | } | |
0f2d19dd | 1808 | } |
f872b822 | 1809 | while (++i < nx); |
1be6b49c | 1810 | return scm_i_normbig (z); |
0f2d19dd JB |
1811 | } |
1812 | ||
1cc91f1b | 1813 | |
0f2d19dd | 1814 | unsigned int |
1be6b49c | 1815 | scm_divbigdig (SCM_BIGDIG * ds, size_t h, SCM_BIGDIG div) |
0f2d19dd JB |
1816 | { |
1817 | register unsigned long t2 = 0; | |
f872b822 MD |
1818 | while (h--) |
1819 | { | |
1820 | t2 = SCM_BIGUP (t2) + ds[h]; | |
1821 | ds[h] = t2 / div; | |
1822 | t2 %= div; | |
1823 | } | |
0f2d19dd JB |
1824 | return t2; |
1825 | } | |
1826 | ||
1827 | ||
1cc91f1b | 1828 | |
f4c627b3 | 1829 | static SCM |
1bbd0b84 | 1830 | scm_divbigint (SCM x, long z, int sgn, int mode) |
0f2d19dd | 1831 | { |
f872b822 MD |
1832 | if (z < 0) |
1833 | z = -z; | |
1834 | if (z < SCM_BIGRAD) | |
1835 | { | |
1836 | register unsigned long t2 = 0; | |
1837 | register SCM_BIGDIG *ds = SCM_BDIGITS (x); | |
1be6b49c | 1838 | size_t nd = SCM_NUMDIGS (x); |
f872b822 MD |
1839 | while (nd--) |
1840 | t2 = (SCM_BIGUP (t2) + ds[nd]) % z; | |
1841 | if (mode && t2) | |
1842 | t2 = z - t2; | |
1843 | return SCM_MAKINUM (sgn ? -t2 : t2); | |
1844 | } | |
0f2d19dd JB |
1845 | { |
1846 | #ifndef SCM_DIGSTOOBIG | |
f872b822 MD |
1847 | unsigned long t2 = scm_pseudolong (z); |
1848 | return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
1849 | (SCM_BIGDIG *) & t2, SCM_DIGSPERLONG, | |
1850 | sgn, mode); | |
0f2d19dd JB |
1851 | #else |
1852 | SCM_BIGDIG t2[SCM_DIGSPERLONG]; | |
f872b822 MD |
1853 | scm_longdigs (z, t2); |
1854 | return scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
1855 | t2, SCM_DIGSPERLONG, | |
1856 | sgn, mode); | |
0f2d19dd JB |
1857 | #endif |
1858 | } | |
1859 | } | |
1860 | ||
1cc91f1b | 1861 | |
f4c627b3 | 1862 | static SCM |
1be6b49c | 1863 | scm_divbigbig (SCM_BIGDIG *x, size_t nx, SCM_BIGDIG *y, size_t ny, int sgn, int modes) |
0f2d19dd JB |
1864 | { |
1865 | /* modes description | |
f872b822 MD |
1866 | 0 remainder |
1867 | 1 scm_modulo | |
1868 | 2 quotient | |
f4c627b3 | 1869 | 3 quotient but returns SCM_UNDEFINED if division is not exact. */ |
1be6b49c | 1870 | size_t i = 0, j = 0; |
0f2d19dd JB |
1871 | long num = 0; |
1872 | unsigned long t2 = 0; | |
1873 | SCM z, newy; | |
f872b822 | 1874 | SCM_BIGDIG d = 0, qhat, *zds, *yds; |
0f2d19dd JB |
1875 | /* algorithm requires nx >= ny */ |
1876 | if (nx < ny) | |
f872b822 MD |
1877 | switch (modes) |
1878 | { | |
1879 | case 0: /* remainder -- just return x */ | |
1be6b49c | 1880 | z = scm_i_mkbig (nx, sgn); |
f872b822 MD |
1881 | zds = SCM_BDIGITS (z); |
1882 | do | |
1883 | { | |
1884 | zds[i] = x[i]; | |
1885 | } | |
1886 | while (++i < nx); | |
1887 | return z; | |
1888 | case 1: /* scm_modulo -- return y-x */ | |
1be6b49c | 1889 | z = scm_i_mkbig (ny, sgn); |
f872b822 MD |
1890 | zds = SCM_BDIGITS (z); |
1891 | do | |
1892 | { | |
1893 | num += (long) y[i] - x[i]; | |
1894 | if (num < 0) | |
1895 | { | |
1896 | zds[i] = num + SCM_BIGRAD; | |
1897 | num = -1; | |
1898 | } | |
1899 | else | |
1900 | { | |
1901 | zds[i] = num; | |
1902 | num = 0; | |
1903 | } | |
1904 | } | |
1905 | while (++i < nx); | |
1906 | while (i < ny) | |
1907 | { | |
1908 | num += y[i]; | |
1909 | if (num < 0) | |
1910 | { | |
1911 | zds[i++] = num + SCM_BIGRAD; | |
1912 | num = -1; | |
1913 | } | |
1914 | else | |
1915 | { | |
1916 | zds[i++] = num; | |
1917 | num = 0; | |
1918 | } | |
1919 | } | |
1920 | goto doadj; | |
1921 | case 2: | |
1922 | return SCM_INUM0; /* quotient is zero */ | |
1923 | case 3: | |
f4c627b3 | 1924 | return SCM_UNDEFINED; /* the division is not exact */ |
0f2d19dd | 1925 | } |
f872b822 | 1926 | |
1be6b49c | 1927 | z = scm_i_mkbig (nx == ny ? nx + 2 : nx + 1, sgn); |
f872b822 MD |
1928 | zds = SCM_BDIGITS (z); |
1929 | if (nx == ny) | |
1930 | zds[nx + 1] = 0; | |
1931 | while (!y[ny - 1]) | |
1932 | ny--; /* in case y came in as a psuedolong */ | |
1933 | if (y[ny - 1] < (SCM_BIGRAD >> 1)) | |
1934 | { /* normalize operands */ | |
1935 | d = SCM_BIGRAD / (y[ny - 1] + 1); | |
1be6b49c | 1936 | newy = scm_i_mkbig (ny, 0); |
f872b822 MD |
1937 | yds = SCM_BDIGITS (newy); |
1938 | while (j < ny) | |
1939 | { | |
1940 | t2 += (unsigned long) y[j] * d; | |
1941 | yds[j++] = SCM_BIGLO (t2); | |
1942 | t2 = SCM_BIGDN (t2); | |
1943 | } | |
1944 | y = yds; | |
1945 | j = 0; | |
1946 | t2 = 0; | |
1947 | while (j < nx) | |
1948 | { | |
1949 | t2 += (unsigned long) x[j] * d; | |
1950 | zds[j++] = SCM_BIGLO (t2); | |
1951 | t2 = SCM_BIGDN (t2); | |
1952 | } | |
1953 | zds[j] = t2; | |
1954 | } | |
1955 | else | |
1956 | { | |
1957 | zds[j = nx] = 0; | |
1958 | while (j--) | |
1959 | zds[j] = x[j]; | |
1960 | } | |
1961 | j = nx == ny ? nx + 1 : nx; /* dividend needs more digits than divisor */ | |
1962 | do | |
1963 | { /* loop over digits of quotient */ | |
1964 | if (zds[j] == y[ny - 1]) | |
1965 | qhat = SCM_BIGRAD - 1; | |
1966 | else | |
1967 | qhat = (SCM_BIGUP (zds[j]) + zds[j - 1]) / y[ny - 1]; | |
1968 | if (!qhat) | |
1969 | continue; | |
1970 | i = 0; | |
1971 | num = 0; | |
1972 | t2 = 0; | |
1973 | do | |
1974 | { /* multiply and subtract */ | |
1975 | t2 += (unsigned long) y[i] * qhat; | |
1976 | num += zds[j - ny + i] - SCM_BIGLO (t2); | |
1977 | if (num < 0) | |
1978 | { | |
1979 | zds[j - ny + i] = num + SCM_BIGRAD; | |
1980 | num = -1; | |
1981 | } | |
1982 | else | |
1983 | { | |
1984 | zds[j - ny + i] = num; | |
1985 | num = 0; | |
1986 | } | |
1987 | t2 = SCM_BIGDN (t2); | |
1988 | } | |
1989 | while (++i < ny); | |
1990 | num += zds[j - ny + i] - t2; /* borrow from high digit; don't update */ | |
1991 | while (num) | |
1992 | { /* "add back" required */ | |
1993 | i = 0; | |
1994 | num = 0; | |
1995 | qhat--; | |
1996 | do | |
1997 | { | |
1998 | num += (long) zds[j - ny + i] + y[i]; | |
1999 | zds[j - ny + i] = SCM_BIGLO (num); | |
2000 | num = SCM_BIGDN (num); | |
2001 | } | |
2002 | while (++i < ny); | |
2003 | num--; | |
2004 | } | |
2005 | if (modes & 2) | |
2006 | zds[j] = qhat; | |
2007 | } | |
2008 | while (--j >= ny); | |
2009 | switch (modes) | |
2010 | { | |
2011 | case 3: /* check that remainder==0 */ | |
2012 | for (j = ny; j && !zds[j - 1]; --j); | |
2013 | if (j) | |
f4c627b3 | 2014 | return SCM_UNDEFINED; |
f872b822 MD |
2015 | case 2: /* move quotient down in z */ |
2016 | j = (nx == ny ? nx + 2 : nx + 1) - ny; | |
2017 | for (i = 0; i < j; i++) | |
2018 | zds[i] = zds[i + ny]; | |
2019 | ny = i; | |
2020 | break; | |
2021 | case 1: /* subtract for scm_modulo */ | |
2022 | i = 0; | |
2023 | num = 0; | |
2024 | j = 0; | |
2025 | do | |
2026 | { | |
2027 | num += y[i] - zds[i]; | |
2028 | j = j | zds[i]; | |
2029 | if (num < 0) | |
2030 | { | |
2031 | zds[i] = num + SCM_BIGRAD; | |
2032 | num = -1; | |
2033 | } | |
2034 | else | |
2035 | { | |
2036 | zds[i] = num; | |
2037 | num = 0; | |
2038 | } | |
2039 | } | |
2040 | while (++i < ny); | |
2041 | if (!j) | |
2042 | return SCM_INUM0; | |
2043 | case 0: /* just normalize remainder */ | |
2044 | if (d) | |
2045 | scm_divbigdig (zds, ny, d); | |
2046 | } | |
0f2d19dd | 2047 | doadj: |
f872b822 MD |
2048 | for (j = ny; j && !zds[j - 1]; --j); |
2049 | if (j * SCM_BITSPERDIG <= sizeof (SCM) * SCM_CHAR_BIT) | |
1be6b49c | 2050 | if (SCM_INUMP (z = scm_i_big2inum (z, j))) |
f872b822 | 2051 | return z; |
1be6b49c | 2052 | return scm_i_adjbig (z, j); |
0f2d19dd JB |
2053 | } |
2054 | #endif | |
f872b822 | 2055 | \f |
0f2d19dd JB |
2056 | |
2057 | ||
2058 | ||
0f2d19dd JB |
2059 | |
2060 | /*** NUMBERS -> STRINGS ***/ | |
0f2d19dd | 2061 | int scm_dblprec; |
e4755e5c | 2062 | static const double fx[] = |
f872b822 MD |
2063 | { 0.0, 5e-1, 5e-2, 5e-3, 5e-4, 5e-5, |
2064 | 5e-6, 5e-7, 5e-8, 5e-9, 5e-10, | |
2065 | 5e-11, 5e-12, 5e-13, 5e-14, 5e-15, | |
2066 | 5e-16, 5e-17, 5e-18, 5e-19, 5e-20}; | |
0f2d19dd JB |
2067 | |
2068 | ||
2069 | ||
1cc91f1b | 2070 | |
1be6b49c | 2071 | static size_t |
1bbd0b84 | 2072 | idbl2str (double f, char *a) |
0f2d19dd JB |
2073 | { |
2074 | int efmt, dpt, d, i, wp = scm_dblprec; | |
1be6b49c | 2075 | size_t ch = 0; |
0f2d19dd JB |
2076 | int exp = 0; |
2077 | ||
f872b822 MD |
2078 | if (f == 0.0) |
2079 | goto zero; /*{a[0]='0'; a[1]='.'; a[2]='0'; return 3;} */ | |
7351e207 MV |
2080 | |
2081 | if (xisinf (f)) | |
2082 | { | |
2083 | if (f < 0) | |
2084 | strcpy (a, "-inf.0"); | |
2085 | else | |
2086 | strcpy (a, "+inf.0"); | |
2087 | return ch+6; | |
2088 | } | |
2089 | else if (xisnan (f)) | |
2090 | { | |
2091 | strcpy (a, "+nan.0"); | |
2092 | return ch+6; | |
2093 | } | |
2094 | ||
f872b822 MD |
2095 | if (f < 0.0) |
2096 | { | |
2097 | f = -f; | |
2098 | a[ch++] = '-'; | |
2099 | } | |
7351e207 | 2100 | |
f872b822 MD |
2101 | #ifdef DBL_MIN_10_EXP /* Prevent unnormalized values, as from |
2102 | make-uniform-vector, from causing infinite loops. */ | |
2103 | while (f < 1.0) | |
2104 | { | |
2105 | f *= 10.0; | |
2106 | if (exp-- < DBL_MIN_10_EXP) | |
7351e207 MV |
2107 | { |
2108 | a[ch++] = '#'; | |
2109 | a[ch++] = '.'; | |
2110 | a[ch++] = '#'; | |
2111 | return ch; | |
2112 | } | |
f872b822 MD |
2113 | } |
2114 | while (f > 10.0) | |
2115 | { | |
2116 | f *= 0.10; | |
2117 | if (exp++ > DBL_MAX_10_EXP) | |
7351e207 MV |
2118 | { |
2119 | a[ch++] = '#'; | |
2120 | a[ch++] = '.'; | |
2121 | a[ch++] = '#'; | |
2122 | return ch; | |
2123 | } | |
f872b822 MD |
2124 | } |
2125 | #else | |
2126 | while (f < 1.0) | |
2127 | { | |
2128 | f *= 10.0; | |
2129 | exp--; | |
2130 | } | |
2131 | while (f > 10.0) | |
2132 | { | |
2133 | f /= 10.0; | |
2134 | exp++; | |
2135 | } | |
2136 | #endif | |
2137 | if (f + fx[wp] >= 10.0) | |
2138 | { | |
2139 | f = 1.0; | |
2140 | exp++; | |
2141 | } | |
0f2d19dd | 2142 | zero: |
f872b822 MD |
2143 | #ifdef ENGNOT |
2144 | dpt = (exp + 9999) % 3; | |
0f2d19dd JB |
2145 | exp -= dpt++; |
2146 | efmt = 1; | |
f872b822 MD |
2147 | #else |
2148 | efmt = (exp < -3) || (exp > wp + 2); | |
0f2d19dd | 2149 | if (!efmt) |
cda139a7 MD |
2150 | { |
2151 | if (exp < 0) | |
2152 | { | |
2153 | a[ch++] = '0'; | |
2154 | a[ch++] = '.'; | |
2155 | dpt = exp; | |
f872b822 MD |
2156 | while (++dpt) |
2157 | a[ch++] = '0'; | |
cda139a7 MD |
2158 | } |
2159 | else | |
f872b822 | 2160 | dpt = exp + 1; |
cda139a7 | 2161 | } |
0f2d19dd JB |
2162 | else |
2163 | dpt = 1; | |
f872b822 MD |
2164 | #endif |
2165 | ||
2166 | do | |
2167 | { | |
2168 | d = f; | |
2169 | f -= d; | |
2170 | a[ch++] = d + '0'; | |
2171 | if (f < fx[wp]) | |
2172 | break; | |
2173 | if (f + fx[wp] >= 1.0) | |
2174 | { | |
2175 | a[ch - 1]++; | |
2176 | break; | |
2177 | } | |
2178 | f *= 10.0; | |
2179 | if (!(--dpt)) | |
2180 | a[ch++] = '.'; | |
0f2d19dd | 2181 | } |
f872b822 | 2182 | while (wp--); |
0f2d19dd JB |
2183 | |
2184 | if (dpt > 0) | |
cda139a7 | 2185 | { |
f872b822 | 2186 | #ifndef ENGNOT |
cda139a7 MD |
2187 | if ((dpt > 4) && (exp > 6)) |
2188 | { | |
f872b822 | 2189 | d = (a[0] == '-' ? 2 : 1); |
cda139a7 | 2190 | for (i = ch++; i > d; i--) |
f872b822 | 2191 | a[i] = a[i - 1]; |
cda139a7 MD |
2192 | a[d] = '.'; |
2193 | efmt = 1; | |
2194 | } | |
2195 | else | |
f872b822 | 2196 | #endif |
cda139a7 | 2197 | { |
f872b822 MD |
2198 | while (--dpt) |
2199 | a[ch++] = '0'; | |
cda139a7 MD |
2200 | a[ch++] = '.'; |
2201 | } | |
2202 | } | |
f872b822 MD |
2203 | if (a[ch - 1] == '.') |
2204 | a[ch++] = '0'; /* trailing zero */ | |
2205 | if (efmt && exp) | |
2206 | { | |
2207 | a[ch++] = 'e'; | |
2208 | if (exp < 0) | |
2209 | { | |
2210 | exp = -exp; | |
2211 | a[ch++] = '-'; | |
2212 | } | |
2213 | for (i = 10; i <= exp; i *= 10); | |
2214 | for (i /= 10; i; i /= 10) | |
2215 | { | |
2216 | a[ch++] = exp / i + '0'; | |
2217 | exp %= i; | |
2218 | } | |
0f2d19dd | 2219 | } |
0f2d19dd JB |
2220 | return ch; |
2221 | } | |
2222 | ||
1cc91f1b | 2223 | |
1be6b49c | 2224 | static size_t |
1bbd0b84 | 2225 | iflo2str (SCM flt, char *str) |
0f2d19dd | 2226 | { |
1be6b49c | 2227 | size_t i; |
3c9a524f | 2228 | if (SCM_REALP (flt)) |
f3ae5d60 | 2229 | i = idbl2str (SCM_REAL_VALUE (flt), str); |
0f2d19dd | 2230 | else |
f872b822 | 2231 | { |
f3ae5d60 MD |
2232 | i = idbl2str (SCM_COMPLEX_REAL (flt), str); |
2233 | if (SCM_COMPLEX_IMAG (flt) != 0.0) | |
2234 | { | |
7351e207 MV |
2235 | double imag = SCM_COMPLEX_IMAG (flt); |
2236 | /* Don't output a '+' for negative numbers or for Inf and | |
2237 | NaN. They will provide their own sign. */ | |
2238 | if (0 <= imag && !xisinf (imag) && !xisnan (imag)) | |
f3ae5d60 | 2239 | str[i++] = '+'; |
7351e207 | 2240 | i += idbl2str (imag, &str[i]); |
f3ae5d60 MD |
2241 | str[i++] = 'i'; |
2242 | } | |
f872b822 | 2243 | } |
0f2d19dd JB |
2244 | return i; |
2245 | } | |
0f2d19dd | 2246 | |
5c11cc9d | 2247 | /* convert a long to a string (unterminated). returns the number of |
1bbd0b84 GB |
2248 | characters in the result. |
2249 | rad is output base | |
2250 | p is destination: worst case (base 2) is SCM_INTBUFLEN */ | |
1be6b49c | 2251 | size_t |
1bbd0b84 | 2252 | scm_iint2str (long num, int rad, char *p) |
0f2d19dd | 2253 | { |
1be6b49c ML |
2254 | size_t j = 1; |
2255 | size_t i; | |
5c11cc9d GH |
2256 | unsigned long n = (num < 0) ? -num : num; |
2257 | ||
f872b822 | 2258 | for (n /= rad; n > 0; n /= rad) |
5c11cc9d GH |
2259 | j++; |
2260 | ||
2261 | i = j; | |
2262 | if (num < 0) | |
f872b822 | 2263 | { |
f872b822 | 2264 | *p++ = '-'; |
5c11cc9d GH |
2265 | j++; |
2266 | n = -num; | |
f872b822 | 2267 | } |
5c11cc9d GH |
2268 | else |
2269 | n = num; | |
f872b822 MD |
2270 | while (i--) |
2271 | { | |
5c11cc9d GH |
2272 | int d = n % rad; |
2273 | ||
f872b822 MD |
2274 | n /= rad; |
2275 | p[i] = d + ((d < 10) ? '0' : 'a' - 10); | |
2276 | } | |
0f2d19dd JB |
2277 | return j; |
2278 | } | |
2279 | ||
2280 | ||
2281 | #ifdef SCM_BIGDIG | |
1cc91f1b | 2282 | |
0f2d19dd | 2283 | static SCM |
1bbd0b84 | 2284 | big2str (SCM b, unsigned int radix) |
0f2d19dd | 2285 | { |
1be6b49c | 2286 | SCM t = scm_i_copybig (b, 0); /* sign of temp doesn't matter */ |
f872b822 | 2287 | register SCM_BIGDIG *ds = SCM_BDIGITS (t); |
1be6b49c ML |
2288 | size_t i = SCM_NUMDIGS (t); |
2289 | size_t j = radix == 16 ? (SCM_BITSPERDIG * i) / 4 + 2 | |
f872b822 MD |
2290 | : radix >= 10 ? (SCM_BITSPERDIG * i * 241L) / 800 + 2 |
2291 | : (SCM_BITSPERDIG * i) + 2; | |
1be6b49c ML |
2292 | size_t k = 0; |
2293 | size_t radct = 0; | |
0f2d19dd | 2294 | SCM_BIGDIG radpow = 1, radmod = 0; |
be54b15d | 2295 | SCM ss = scm_allocate_string (j); |
9eb364fc | 2296 | char *s = SCM_STRING_CHARS (ss), c; |
f872b822 MD |
2297 | while ((long) radpow * radix < SCM_BIGRAD) |
2298 | { | |
2299 | radpow *= radix; | |
2300 | radct++; | |
2301 | } | |
f872b822 MD |
2302 | while ((i || radmod) && j) |
2303 | { | |
2304 | if (k == 0) | |
2305 | { | |
2306 | radmod = (SCM_BIGDIG) scm_divbigdig (ds, i, radpow); | |
2307 | k = radct; | |
2308 | if (!ds[i - 1]) | |
2309 | i--; | |
2310 | } | |
2311 | c = radmod % radix; | |
2312 | radmod /= radix; | |
2313 | k--; | |
2314 | s[--j] = c < 10 ? c + '0' : c + 'a' - 10; | |
2315 | } | |
aa3188a7 DH |
2316 | |
2317 | if (SCM_BIGSIGN (b)) | |
2318 | s[--j] = '-'; | |
2319 | ||
2320 | if (j > 0) | |
2321 | { | |
2322 | /* The pre-reserved string length was too large. */ | |
2323 | unsigned long int length = SCM_STRING_LENGTH (ss); | |
2324 | ss = scm_substring (ss, SCM_MAKINUM (j), SCM_MAKINUM (length)); | |
f872b822 | 2325 | } |
b098016b JB |
2326 | |
2327 | return scm_return_first (ss, t); | |
0f2d19dd JB |
2328 | } |
2329 | #endif | |
2330 | ||
2331 | ||
a1ec6916 | 2332 | SCM_DEFINE (scm_number_to_string, "number->string", 1, 1, 0, |
bb628794 DH |
2333 | (SCM n, SCM radix), |
2334 | "Return a string holding the external representation of the\n" | |
942e5b91 MG |
2335 | "number @var{n} in the given @var{radix}. If @var{n} is\n" |
2336 | "inexact, a radix of 10 will be used.") | |
1bbd0b84 | 2337 | #define FUNC_NAME s_scm_number_to_string |
0f2d19dd | 2338 | { |
1bbd0b84 | 2339 | int base; |
98cb6e75 DH |
2340 | |
2341 | if (SCM_UNBNDP (radix)) { | |
2342 | base = 10; | |
2343 | } else { | |
2344 | SCM_VALIDATE_INUM (2, radix); | |
2345 | base = SCM_INUM (radix); | |
2346 | SCM_ASSERT_RANGE (2, radix, base >= 2); | |
2347 | } | |
2348 | ||
bb628794 | 2349 | if (SCM_INUMP (n)) { |
98cb6e75 | 2350 | char num_buf [SCM_INTBUFLEN]; |
1be6b49c | 2351 | size_t length = scm_iint2str (SCM_INUM (n), base, num_buf); |
36284627 | 2352 | return scm_mem2string (num_buf, length); |
bb628794 DH |
2353 | } else if (SCM_BIGP (n)) { |
2354 | return big2str (n, (unsigned int) base); | |
2355 | } else if (SCM_INEXACTP (n)) { | |
56e55ac7 | 2356 | char num_buf [FLOBUFLEN]; |
36284627 | 2357 | return scm_mem2string (num_buf, iflo2str (n, num_buf)); |
98cb6e75 | 2358 | } else { |
bb628794 | 2359 | SCM_WRONG_TYPE_ARG (1, n); |
0f2d19dd JB |
2360 | } |
2361 | } | |
1bbd0b84 | 2362 | #undef FUNC_NAME |
0f2d19dd JB |
2363 | |
2364 | ||
2365 | /* These print routines are stubbed here so that scm_repl.c doesn't need | |
f3ae5d60 | 2366 | SCM_BIGDIG conditionals */ |
1cc91f1b | 2367 | |
0f2d19dd | 2368 | int |
e81d98ec | 2369 | scm_print_real (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd | 2370 | { |
56e55ac7 | 2371 | char num_buf[FLOBUFLEN]; |
f872b822 | 2372 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port); |
0f2d19dd JB |
2373 | return !0; |
2374 | } | |
2375 | ||
f3ae5d60 | 2376 | int |
e81d98ec | 2377 | scm_print_complex (SCM sexp, SCM port, scm_print_state *pstate SCM_UNUSED) |
f3ae5d60 | 2378 | { |
56e55ac7 | 2379 | char num_buf[FLOBUFLEN]; |
f3ae5d60 MD |
2380 | scm_lfwrite (num_buf, iflo2str (sexp, num_buf), port); |
2381 | return !0; | |
2382 | } | |
1cc91f1b | 2383 | |
0f2d19dd | 2384 | int |
e81d98ec | 2385 | scm_bigprint (SCM exp, SCM port, scm_print_state *pstate SCM_UNUSED) |
0f2d19dd JB |
2386 | { |
2387 | #ifdef SCM_BIGDIG | |
f872b822 | 2388 | exp = big2str (exp, (unsigned int) 10); |
1be6b49c | 2389 | scm_lfwrite (SCM_STRING_CHARS (exp), (size_t) SCM_STRING_LENGTH (exp), port); |
0f2d19dd | 2390 | #else |
f872b822 | 2391 | scm_ipruk ("bignum", exp, port); |
0f2d19dd JB |
2392 | #endif |
2393 | return !0; | |
2394 | } | |
2395 | /*** END nums->strs ***/ | |
2396 | ||
3c9a524f | 2397 | |
0f2d19dd | 2398 | /*** STRINGS -> NUMBERS ***/ |
2a8fecee | 2399 | |
3c9a524f DH |
2400 | /* The following functions implement the conversion from strings to numbers. |
2401 | * The implementation somehow follows the grammar for numbers as it is given | |
2402 | * in R5RS. Thus, the functions resemble syntactic units (<ureal R>, | |
2403 | * <uinteger R>, ...) that are used to build up numbers in the grammar. Some | |
2404 | * points should be noted about the implementation: | |
2405 | * * Each function keeps a local index variable 'idx' that points at the | |
2406 | * current position within the parsed string. The global index is only | |
2407 | * updated if the function could parse the corresponding syntactic unit | |
2408 | * successfully. | |
2409 | * * Similarly, the functions keep track of indicators of inexactness ('#', | |
2410 | * '.' or exponents) using local variables ('hash_seen', 'x'). Again, the | |
2411 | * global exactness information is only updated after each part has been | |
2412 | * successfully parsed. | |
2413 | * * Sequences of digits are parsed into temporary variables holding fixnums. | |
2414 | * Only if these fixnums would overflow, the result variables are updated | |
2415 | * using the standard functions scm_add, scm_product, scm_divide etc. Then, | |
2416 | * the temporary variables holding the fixnums are cleared, and the process | |
2417 | * starts over again. If for example fixnums were able to store five decimal | |
2418 | * digits, a number 1234567890 would be parsed in two parts 12345 and 67890, | |
2419 | * and the result was computed as 12345 * 100000 + 67890. In other words, | |
2420 | * only every five digits two bignum operations were performed. | |
2421 | */ | |
2422 | ||
2423 | enum t_exactness {NO_EXACTNESS, INEXACT, EXACT}; | |
2424 | ||
2425 | /* R5RS, section 7.1.1, lexical structure of numbers: <uinteger R>. */ | |
2426 | ||
2427 | /* In non ASCII-style encodings the following macro might not work. */ | |
2428 | #define XDIGIT2UINT(d) (isdigit (d) ? (d) - '0' : tolower (d) - 'a' + 10) | |
2429 | ||
2a8fecee | 2430 | static SCM |
3c9a524f DH |
2431 | mem2uinteger (const char* mem, size_t len, unsigned int *p_idx, |
2432 | unsigned int radix, enum t_exactness *p_exactness) | |
2a8fecee | 2433 | { |
3c9a524f DH |
2434 | unsigned int idx = *p_idx; |
2435 | unsigned int hash_seen = 0; | |
2436 | scm_t_bits shift = 1; | |
2437 | scm_t_bits add = 0; | |
2438 | unsigned int digit_value; | |
2439 | SCM result; | |
2440 | char c; | |
2441 | ||
2442 | if (idx == len) | |
2443 | return SCM_BOOL_F; | |
2a8fecee | 2444 | |
3c9a524f DH |
2445 | c = mem[idx]; |
2446 | if (!isxdigit (c)) | |
2447 | return SCM_BOOL_F; | |
2448 | digit_value = XDIGIT2UINT (c); | |
2449 | if (digit_value >= radix) | |
2450 | return SCM_BOOL_F; | |
2451 | ||
2452 | idx++; | |
2453 | result = SCM_MAKINUM (digit_value); | |
2454 | while (idx != len) | |
f872b822 | 2455 | { |
3c9a524f DH |
2456 | char c = mem[idx]; |
2457 | if (isxdigit (c)) | |
f872b822 | 2458 | { |
3c9a524f | 2459 | if (hash_seen) |
1fe5e088 | 2460 | break; |
3c9a524f DH |
2461 | digit_value = XDIGIT2UINT (c); |
2462 | if (digit_value >= radix) | |
1fe5e088 | 2463 | break; |
f872b822 | 2464 | } |
3c9a524f DH |
2465 | else if (c == '#') |
2466 | { | |
2467 | hash_seen = 1; | |
2468 | digit_value = 0; | |
2469 | } | |
2470 | else | |
2471 | break; | |
2472 | ||
2473 | idx++; | |
2474 | if (SCM_MOST_POSITIVE_FIXNUM / radix < shift) | |
2475 | { | |
2476 | result = scm_product (result, SCM_MAKINUM (shift)); | |
2477 | if (add > 0) | |
2478 | result = scm_sum (result, SCM_MAKINUM (add)); | |
2479 | ||
2480 | shift = radix; | |
2481 | add = digit_value; | |
2482 | } | |
2483 | else | |
2484 | { | |
2485 | shift = shift * radix; | |
2486 | add = add * radix + digit_value; | |
2487 | } | |
2488 | }; | |
2489 | ||
2490 | if (shift > 1) | |
2491 | result = scm_product (result, SCM_MAKINUM (shift)); | |
2492 | if (add > 0) | |
2493 | result = scm_sum (result, SCM_MAKINUM (add)); | |
2494 | ||
2495 | *p_idx = idx; | |
2496 | if (hash_seen) | |
2497 | *p_exactness = INEXACT; | |
2498 | ||
2499 | return result; | |
2a8fecee JB |
2500 | } |
2501 | ||
2502 | ||
3c9a524f DH |
2503 | /* R5RS, section 7.1.1, lexical structure of numbers: <decimal 10>. Only |
2504 | * covers the parts of the rules that start at a potential point. The value | |
2505 | * of the digits up to the point have been parsed by the caller and are given | |
79d34f68 DH |
2506 | * in variable result. The content of *p_exactness indicates, whether a hash |
2507 | * has already been seen in the digits before the point. | |
3c9a524f | 2508 | */ |
1cc91f1b | 2509 | |
3c9a524f DH |
2510 | /* In non ASCII-style encodings the following macro might not work. */ |
2511 | #define DIGIT2UINT(d) ((d) - '0') | |
2512 | ||
2513 | static SCM | |
79d34f68 | 2514 | mem2decimal_from_point (SCM result, const char* mem, size_t len, |
3c9a524f | 2515 | unsigned int *p_idx, enum t_exactness *p_exactness) |
0f2d19dd | 2516 | { |
3c9a524f DH |
2517 | unsigned int idx = *p_idx; |
2518 | enum t_exactness x = *p_exactness; | |
3c9a524f DH |
2519 | |
2520 | if (idx == len) | |
79d34f68 | 2521 | return result; |
3c9a524f DH |
2522 | |
2523 | if (mem[idx] == '.') | |
2524 | { | |
2525 | scm_t_bits shift = 1; | |
2526 | scm_t_bits add = 0; | |
2527 | unsigned int digit_value; | |
79d34f68 | 2528 | SCM big_shift = SCM_MAKINUM (1); |
3c9a524f DH |
2529 | |
2530 | idx++; | |
2531 | while (idx != len) | |
2532 | { | |
2533 | char c = mem[idx]; | |
2534 | if (isdigit (c)) | |
2535 | { | |
2536 | if (x == INEXACT) | |
2537 | return SCM_BOOL_F; | |
2538 | else | |
2539 | digit_value = DIGIT2UINT (c); | |
2540 | } | |
2541 | else if (c == '#') | |
2542 | { | |
2543 | x = INEXACT; | |
2544 | digit_value = 0; | |
2545 | } | |
2546 | else | |
2547 | break; | |
2548 | ||
2549 | idx++; | |
2550 | if (SCM_MOST_POSITIVE_FIXNUM / 10 < shift) | |
2551 | { | |
2552 | big_shift = scm_product (big_shift, SCM_MAKINUM (shift)); | |
79d34f68 | 2553 | result = scm_product (result, SCM_MAKINUM (shift)); |
3c9a524f | 2554 | if (add > 0) |
79d34f68 | 2555 | result = scm_sum (result, SCM_MAKINUM (add)); |
3c9a524f DH |
2556 | |
2557 | shift = 10; | |
2558 | add = digit_value; | |
2559 | } | |
2560 | else | |
2561 | { | |
2562 | shift = shift * 10; | |
2563 | add = add * 10 + digit_value; | |
2564 | } | |
2565 | }; | |
2566 | ||
2567 | if (add > 0) | |
2568 | { | |
2569 | big_shift = scm_product (big_shift, SCM_MAKINUM (shift)); | |
79d34f68 DH |
2570 | result = scm_product (result, SCM_MAKINUM (shift)); |
2571 | result = scm_sum (result, SCM_MAKINUM (add)); | |
3c9a524f DH |
2572 | } |
2573 | ||
79d34f68 DH |
2574 | result = scm_divide (result, big_shift); |
2575 | ||
3c9a524f DH |
2576 | /* We've seen a decimal point, thus the value is implicitly inexact. */ |
2577 | x = INEXACT; | |
f872b822 | 2578 | } |
3c9a524f | 2579 | |
3c9a524f | 2580 | if (idx != len) |
f872b822 | 2581 | { |
3c9a524f DH |
2582 | int sign = 1; |
2583 | unsigned int start; | |
2584 | char c; | |
2585 | int exponent; | |
2586 | SCM e; | |
2587 | ||
2588 | /* R5RS, section 7.1.1, lexical structure of numbers: <suffix> */ | |
2589 | ||
2590 | switch (mem[idx]) | |
f872b822 | 2591 | { |
3c9a524f DH |
2592 | case 'd': case 'D': |
2593 | case 'e': case 'E': | |
2594 | case 'f': case 'F': | |
2595 | case 'l': case 'L': | |
2596 | case 's': case 'S': | |
2597 | idx++; | |
2598 | start = idx; | |
2599 | c = mem[idx]; | |
2600 | if (c == '-') | |
2601 | { | |
2602 | idx++; | |
2603 | sign = -1; | |
2604 | c = mem[idx]; | |
2605 | } | |
2606 | else if (c == '+') | |
2607 | { | |
2608 | idx++; | |
2609 | sign = 1; | |
2610 | c = mem[idx]; | |
2611 | } | |
2612 | else | |
2613 | sign = 1; | |
2614 | ||
2615 | if (!isdigit (c)) | |
2616 | return SCM_BOOL_F; | |
2617 | ||
2618 | idx++; | |
2619 | exponent = DIGIT2UINT (c); | |
2620 | while (idx != len) | |
f872b822 | 2621 | { |
3c9a524f DH |
2622 | char c = mem[idx]; |
2623 | if (isdigit (c)) | |
2624 | { | |
2625 | idx++; | |
2626 | if (exponent <= SCM_MAXEXP) | |
2627 | exponent = exponent * 10 + DIGIT2UINT (c); | |
2628 | } | |
2629 | else | |
2630 | break; | |
f872b822 | 2631 | } |
3c9a524f DH |
2632 | |
2633 | if (exponent > SCM_MAXEXP) | |
f872b822 | 2634 | { |
3c9a524f DH |
2635 | size_t exp_len = idx - start; |
2636 | SCM exp_string = scm_mem2string (&mem[start], exp_len); | |
2637 | SCM exp_num = scm_string_to_number (exp_string, SCM_UNDEFINED); | |
2638 | scm_out_of_range ("string->number", exp_num); | |
f872b822 | 2639 | } |
3c9a524f DH |
2640 | |
2641 | e = scm_integer_expt (SCM_MAKINUM (10), SCM_MAKINUM (exponent)); | |
2642 | if (sign == 1) | |
2643 | result = scm_product (result, e); | |
2644 | else | |
2645 | result = scm_divide (result, e); | |
2646 | ||
2647 | /* We've seen an exponent, thus the value is implicitly inexact. */ | |
2648 | x = INEXACT; | |
2649 | ||
f872b822 | 2650 | break; |
3c9a524f | 2651 | |
f872b822 | 2652 | default: |
3c9a524f | 2653 | break; |
f872b822 | 2654 | } |
0f2d19dd | 2655 | } |
3c9a524f DH |
2656 | |
2657 | *p_idx = idx; | |
2658 | if (x == INEXACT) | |
2659 | *p_exactness = x; | |
2660 | ||
2661 | return result; | |
0f2d19dd | 2662 | } |
0f2d19dd | 2663 | |
3c9a524f DH |
2664 | |
2665 | /* R5RS, section 7.1.1, lexical structure of numbers: <ureal R> */ | |
2666 | ||
2667 | static SCM | |
2668 | mem2ureal (const char* mem, size_t len, unsigned int *p_idx, | |
2669 | unsigned int radix, enum t_exactness *p_exactness) | |
0f2d19dd | 2670 | { |
3c9a524f DH |
2671 | unsigned int idx = *p_idx; |
2672 | ||
2673 | if (idx == len) | |
2674 | return SCM_BOOL_F; | |
2675 | ||
7351e207 MV |
2676 | if (idx+5 <= len && !strncmp (mem+idx, "inf.0", 5)) |
2677 | { | |
2678 | *p_idx = idx+5; | |
2679 | return scm_inf (); | |
2680 | } | |
2681 | ||
2682 | if (idx+4 < len && !strncmp (mem+idx, "nan.", 4)) | |
2683 | { | |
2684 | enum t_exactness x = EXACT; | |
2685 | ||
2686 | /* Cobble up the fraction. We might want to set the NaN's | |
2687 | mantissa from it. */ | |
2688 | idx += 4; | |
2689 | mem2uinteger (mem, len, &idx, 10, &x); | |
2690 | *p_idx = idx; | |
2691 | return scm_nan (); | |
2692 | } | |
2693 | ||
3c9a524f DH |
2694 | if (mem[idx] == '.') |
2695 | { | |
2696 | if (radix != 10) | |
2697 | return SCM_BOOL_F; | |
2698 | else if (idx + 1 == len) | |
2699 | return SCM_BOOL_F; | |
2700 | else if (!isdigit (mem[idx + 1])) | |
2701 | return SCM_BOOL_F; | |
2702 | else | |
2703 | return mem2decimal_from_point (SCM_MAKINUM (0), mem, len, | |
2704 | p_idx, p_exactness); | |
f872b822 | 2705 | } |
3c9a524f DH |
2706 | else |
2707 | { | |
2708 | enum t_exactness x = EXACT; | |
2709 | SCM uinteger; | |
2710 | SCM result; | |
2711 | ||
2712 | uinteger = mem2uinteger (mem, len, &idx, radix, &x); | |
2713 | if (SCM_FALSEP (uinteger)) | |
2714 | return SCM_BOOL_F; | |
2715 | ||
2716 | if (idx == len) | |
2717 | result = uinteger; | |
2718 | else if (mem[idx] == '/') | |
f872b822 | 2719 | { |
3c9a524f DH |
2720 | SCM divisor; |
2721 | ||
2722 | idx++; | |
2723 | ||
2724 | divisor = mem2uinteger (mem, len, &idx, radix, &x); | |
2725 | if (SCM_FALSEP (divisor)) | |
2726 | return SCM_BOOL_F; | |
2727 | ||
2728 | result = scm_divide (uinteger, divisor); | |
f872b822 | 2729 | } |
3c9a524f DH |
2730 | else if (radix == 10) |
2731 | { | |
2732 | result = mem2decimal_from_point (uinteger, mem, len, &idx, &x); | |
2733 | if (SCM_FALSEP (result)) | |
2734 | return SCM_BOOL_F; | |
2735 | } | |
2736 | else | |
2737 | result = uinteger; | |
2738 | ||
2739 | *p_idx = idx; | |
2740 | if (x == INEXACT) | |
2741 | *p_exactness = x; | |
2742 | ||
2743 | return result; | |
f872b822 | 2744 | } |
3c9a524f | 2745 | } |
0f2d19dd | 2746 | |
0f2d19dd | 2747 | |
3c9a524f | 2748 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ |
0f2d19dd | 2749 | |
3c9a524f DH |
2750 | static SCM |
2751 | mem2complex (const char* mem, size_t len, unsigned int idx, | |
2752 | unsigned int radix, enum t_exactness *p_exactness) | |
2753 | { | |
2754 | char c; | |
2755 | int sign = 0; | |
2756 | SCM ureal; | |
2757 | ||
2758 | if (idx == len) | |
2759 | return SCM_BOOL_F; | |
2760 | ||
2761 | c = mem[idx]; | |
2762 | if (c == '+') | |
2763 | { | |
2764 | idx++; | |
2765 | sign = 1; | |
2766 | } | |
2767 | else if (c == '-') | |
2768 | { | |
2769 | idx++; | |
2770 | sign = -1; | |
0f2d19dd | 2771 | } |
0f2d19dd | 2772 | |
3c9a524f DH |
2773 | if (idx == len) |
2774 | return SCM_BOOL_F; | |
2775 | ||
2776 | ureal = mem2ureal (mem, len, &idx, radix, p_exactness); | |
2777 | if (SCM_FALSEP (ureal)) | |
f872b822 | 2778 | { |
3c9a524f DH |
2779 | /* input must be either +i or -i */ |
2780 | ||
2781 | if (sign == 0) | |
2782 | return SCM_BOOL_F; | |
2783 | ||
2784 | if (mem[idx] == 'i' || mem[idx] == 'I') | |
f872b822 | 2785 | { |
3c9a524f DH |
2786 | idx++; |
2787 | if (idx != len) | |
2788 | return SCM_BOOL_F; | |
2789 | ||
2790 | return scm_make_rectangular (SCM_MAKINUM (0), SCM_MAKINUM (sign)); | |
f872b822 | 2791 | } |
3c9a524f DH |
2792 | else |
2793 | return SCM_BOOL_F; | |
0f2d19dd | 2794 | } |
3c9a524f DH |
2795 | else |
2796 | { | |
fc194577 | 2797 | if (sign == -1 && SCM_FALSEP (scm_nan_p (ureal))) |
3c9a524f | 2798 | ureal = scm_difference (ureal, SCM_UNDEFINED); |
f872b822 | 2799 | |
3c9a524f DH |
2800 | if (idx == len) |
2801 | return ureal; | |
2802 | ||
2803 | c = mem[idx]; | |
2804 | switch (c) | |
f872b822 | 2805 | { |
3c9a524f DH |
2806 | case 'i': case 'I': |
2807 | /* either +<ureal>i or -<ureal>i */ | |
2808 | ||
2809 | idx++; | |
2810 | if (sign == 0) | |
2811 | return SCM_BOOL_F; | |
2812 | if (idx != len) | |
2813 | return SCM_BOOL_F; | |
2814 | return scm_make_rectangular (SCM_MAKINUM (0), ureal); | |
2815 | ||
2816 | case '@': | |
2817 | /* polar input: <real>@<real>. */ | |
2818 | ||
2819 | idx++; | |
2820 | if (idx == len) | |
2821 | return SCM_BOOL_F; | |
2822 | else | |
f872b822 | 2823 | { |
3c9a524f DH |
2824 | int sign; |
2825 | SCM angle; | |
2826 | SCM result; | |
2827 | ||
2828 | c = mem[idx]; | |
2829 | if (c == '+') | |
2830 | { | |
2831 | idx++; | |
2832 | sign = 1; | |
2833 | } | |
2834 | else if (c == '-') | |
2835 | { | |
2836 | idx++; | |
2837 | sign = -1; | |
2838 | } | |
2839 | else | |
2840 | sign = 1; | |
2841 | ||
2842 | angle = mem2ureal (mem, len, &idx, radix, p_exactness); | |
2843 | if (SCM_FALSEP (angle)) | |
2844 | return SCM_BOOL_F; | |
2845 | if (idx != len) | |
2846 | return SCM_BOOL_F; | |
2847 | ||
fc194577 | 2848 | if (sign == -1 && SCM_FALSEP (scm_nan_p (ureal))) |
3c9a524f DH |
2849 | angle = scm_difference (angle, SCM_UNDEFINED); |
2850 | ||
2851 | result = scm_make_polar (ureal, angle); | |
2852 | return result; | |
f872b822 | 2853 | } |
3c9a524f DH |
2854 | case '+': |
2855 | case '-': | |
2856 | /* expecting input matching <real>[+-]<ureal>?i */ | |
0f2d19dd | 2857 | |
3c9a524f DH |
2858 | idx++; |
2859 | if (idx == len) | |
2860 | return SCM_BOOL_F; | |
2861 | else | |
2862 | { | |
2863 | int sign = (c == '+') ? 1 : -1; | |
2864 | SCM imag = mem2ureal (mem, len, &idx, radix, p_exactness); | |
0f2d19dd | 2865 | |
3c9a524f DH |
2866 | if (SCM_FALSEP (imag)) |
2867 | imag = SCM_MAKINUM (sign); | |
fc194577 | 2868 | else if (sign == -1 && SCM_FALSEP (scm_nan_p (ureal))) |
1fe5e088 | 2869 | imag = scm_difference (imag, SCM_UNDEFINED); |
0f2d19dd | 2870 | |
3c9a524f DH |
2871 | if (idx == len) |
2872 | return SCM_BOOL_F; | |
2873 | if (mem[idx] != 'i' && mem[idx] != 'I') | |
2874 | return SCM_BOOL_F; | |
0f2d19dd | 2875 | |
3c9a524f DH |
2876 | idx++; |
2877 | if (idx != len) | |
2878 | return SCM_BOOL_F; | |
0f2d19dd | 2879 | |
1fe5e088 | 2880 | return scm_make_rectangular (ureal, imag); |
3c9a524f DH |
2881 | } |
2882 | default: | |
2883 | return SCM_BOOL_F; | |
2884 | } | |
2885 | } | |
0f2d19dd | 2886 | } |
0f2d19dd JB |
2887 | |
2888 | ||
3c9a524f DH |
2889 | /* R5RS, section 7.1.1, lexical structure of numbers: <number> */ |
2890 | ||
2891 | enum t_radix {NO_RADIX=0, DUAL=2, OCT=8, DEC=10, HEX=16}; | |
1cc91f1b | 2892 | |
0f2d19dd | 2893 | SCM |
3c9a524f | 2894 | scm_i_mem2number (const char* mem, size_t len, unsigned int default_radix) |
0f2d19dd | 2895 | { |
3c9a524f DH |
2896 | unsigned int idx = 0; |
2897 | unsigned int radix = NO_RADIX; | |
2898 | enum t_exactness forced_x = NO_EXACTNESS; | |
2899 | enum t_exactness implicit_x = EXACT; | |
2900 | SCM result; | |
2901 | ||
2902 | /* R5RS, section 7.1.1, lexical structure of numbers: <prefix R> */ | |
2903 | while (idx + 2 < len && mem[idx] == '#') | |
2904 | { | |
2905 | switch (mem[idx + 1]) | |
2906 | { | |
2907 | case 'b': case 'B': | |
2908 | if (radix != NO_RADIX) | |
2909 | return SCM_BOOL_F; | |
2910 | radix = DUAL; | |
2911 | break; | |
2912 | case 'd': case 'D': | |
2913 | if (radix != NO_RADIX) | |
2914 | return SCM_BOOL_F; | |
2915 | radix = DEC; | |
2916 | break; | |
2917 | case 'i': case 'I': | |
2918 | if (forced_x != NO_EXACTNESS) | |
2919 | return SCM_BOOL_F; | |
2920 | forced_x = INEXACT; | |
2921 | break; | |
2922 | case 'e': case 'E': | |
2923 | if (forced_x != NO_EXACTNESS) | |
2924 | return SCM_BOOL_F; | |
2925 | forced_x = EXACT; | |
2926 | break; | |
2927 | case 'o': case 'O': | |
2928 | if (radix != NO_RADIX) | |
2929 | return SCM_BOOL_F; | |
2930 | radix = OCT; | |
2931 | break; | |
2932 | case 'x': case 'X': | |
2933 | if (radix != NO_RADIX) | |
2934 | return SCM_BOOL_F; | |
2935 | radix = HEX; | |
2936 | break; | |
2937 | default: | |
f872b822 | 2938 | return SCM_BOOL_F; |
3c9a524f DH |
2939 | } |
2940 | idx += 2; | |
2941 | } | |
2942 | ||
2943 | /* R5RS, section 7.1.1, lexical structure of numbers: <complex R> */ | |
2944 | if (radix == NO_RADIX) | |
2945 | result = mem2complex (mem, len, idx, default_radix, &implicit_x); | |
2946 | else | |
2947 | result = mem2complex (mem, len, idx, (unsigned int) radix, &implicit_x); | |
2948 | ||
2949 | if (SCM_FALSEP (result)) | |
2950 | return SCM_BOOL_F; | |
f872b822 | 2951 | |
3c9a524f | 2952 | switch (forced_x) |
f872b822 | 2953 | { |
3c9a524f DH |
2954 | case EXACT: |
2955 | if (SCM_INEXACTP (result)) | |
2956 | /* FIXME: This may change the value. */ | |
2957 | return scm_inexact_to_exact (result); | |
2958 | else | |
2959 | return result; | |
2960 | case INEXACT: | |
2961 | if (SCM_INEXACTP (result)) | |
2962 | return result; | |
2963 | else | |
2964 | return scm_exact_to_inexact (result); | |
2965 | case NO_EXACTNESS: | |
2966 | default: | |
2967 | if (implicit_x == INEXACT) | |
2968 | { | |
2969 | if (SCM_INEXACTP (result)) | |
2970 | return result; | |
2971 | else | |
2972 | return scm_exact_to_inexact (result); | |
2973 | } | |
2974 | else | |
2975 | return result; | |
f872b822 | 2976 | } |
0f2d19dd JB |
2977 | } |
2978 | ||
2979 | ||
a1ec6916 | 2980 | SCM_DEFINE (scm_string_to_number, "string->number", 1, 1, 0, |
bb628794 | 2981 | (SCM string, SCM radix), |
1e6808ea | 2982 | "Return a number of the maximally precise representation\n" |
942e5b91 | 2983 | "expressed by the given @var{string}. @var{radix} must be an\n" |
5352393c MG |
2984 | "exact integer, either 2, 8, 10, or 16. If supplied, @var{radix}\n" |
2985 | "is a default radix that may be overridden by an explicit radix\n" | |
2986 | "prefix in @var{string} (e.g. \"#o177\"). If @var{radix} is not\n" | |
2987 | "supplied, then the default radix is 10. If string is not a\n" | |
2988 | "syntactically valid notation for a number, then\n" | |
2989 | "@code{string->number} returns @code{#f}.") | |
1bbd0b84 | 2990 | #define FUNC_NAME s_scm_string_to_number |
0f2d19dd JB |
2991 | { |
2992 | SCM answer; | |
1bbd0b84 | 2993 | int base; |
a6d9e5ab | 2994 | SCM_VALIDATE_STRING (1, string); |
3b3b36dd | 2995 | SCM_VALIDATE_INUM_MIN_DEF_COPY (2,radix,2,10,base); |
3c9a524f DH |
2996 | answer = scm_i_mem2number (SCM_STRING_CHARS (string), |
2997 | SCM_STRING_LENGTH (string), | |
2998 | base); | |
bb628794 | 2999 | return scm_return_first (answer, string); |
0f2d19dd | 3000 | } |
1bbd0b84 | 3001 | #undef FUNC_NAME |
3c9a524f DH |
3002 | |
3003 | ||
0f2d19dd JB |
3004 | /*** END strs->nums ***/ |
3005 | ||
5986c47d | 3006 | |
0f2d19dd | 3007 | SCM |
f3ae5d60 | 3008 | scm_make_real (double x) |
0f2d19dd JB |
3009 | { |
3010 | SCM z; | |
228a24ef | 3011 | z = scm_double_cell (scm_tc16_real, 0, 0, 0); |
3a9809df | 3012 | SCM_REAL_VALUE (z) = x; |
0f2d19dd JB |
3013 | return z; |
3014 | } | |
0f2d19dd | 3015 | |
5986c47d | 3016 | |
f3ae5d60 MD |
3017 | SCM |
3018 | scm_make_complex (double x, double y) | |
3019 | { | |
3a9809df DH |
3020 | if (y == 0.0) { |
3021 | return scm_make_real (x); | |
3022 | } else { | |
3023 | SCM z; | |
4c9419ac MV |
3024 | SCM_NEWSMOB (z, scm_tc16_complex, scm_gc_malloc (2*sizeof (double), |
3025 | "complex")); | |
3a9809df DH |
3026 | SCM_COMPLEX_REAL (z) = x; |
3027 | SCM_COMPLEX_IMAG (z) = y; | |
3028 | return z; | |
3029 | } | |
f3ae5d60 | 3030 | } |
1cc91f1b | 3031 | |
5986c47d | 3032 | |
0f2d19dd | 3033 | SCM |
1bbd0b84 | 3034 | scm_bigequal (SCM x, SCM y) |
0f2d19dd JB |
3035 | { |
3036 | #ifdef SCM_BIGDIG | |
f872b822 MD |
3037 | if (0 == scm_bigcomp (x, y)) |
3038 | return SCM_BOOL_T; | |
0f2d19dd JB |
3039 | #endif |
3040 | return SCM_BOOL_F; | |
3041 | } | |
3042 | ||
0f2d19dd | 3043 | SCM |
f3ae5d60 | 3044 | scm_real_equalp (SCM x, SCM y) |
0f2d19dd | 3045 | { |
f3ae5d60 | 3046 | return SCM_BOOL (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); |
0f2d19dd JB |
3047 | } |
3048 | ||
f3ae5d60 MD |
3049 | SCM |
3050 | scm_complex_equalp (SCM x, SCM y) | |
3051 | { | |
3052 | return SCM_BOOL (SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y) | |
3053 | && SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y)); | |
3054 | } | |
0f2d19dd JB |
3055 | |
3056 | ||
3057 | ||
1bbd0b84 | 3058 | SCM_REGISTER_PROC (s_number_p, "number?", 1, 0, 0, scm_number_p); |
942e5b91 MG |
3059 | /* "Return @code{#t} if @var{x} is a number, @code{#f}\n" |
3060 | * "else. Note that the sets of complex, real, rational and\n" | |
3061 | * "integer values form subsets of the set of numbers, i. e. the\n" | |
3062 | * "predicate will be fulfilled for any number." | |
3063 | */ | |
a1ec6916 | 3064 | SCM_DEFINE (scm_number_p, "complex?", 1, 0, 0, |
1bbd0b84 | 3065 | (SCM x), |
942e5b91 | 3066 | "Return @code{#t} if @var{x} is a complex number, @code{#f}\n" |
bb2c02f2 | 3067 | "otherwise. Note that the sets of real, rational and integer\n" |
942e5b91 MG |
3068 | "values form subsets of the set of complex numbers, i. e. the\n" |
3069 | "predicate will also be fulfilled if @var{x} is a real,\n" | |
3070 | "rational or integer number.") | |
1bbd0b84 | 3071 | #define FUNC_NAME s_scm_number_p |
0f2d19dd | 3072 | { |
bb628794 | 3073 | return SCM_BOOL (SCM_NUMBERP (x)); |
0f2d19dd | 3074 | } |
1bbd0b84 | 3075 | #undef FUNC_NAME |
0f2d19dd JB |
3076 | |
3077 | ||
1bbd0b84 | 3078 | SCM_REGISTER_PROC (s_real_p, "real?", 1, 0, 0, scm_real_p); |
942e5b91 MG |
3079 | /* "Return @code{#t} if @var{x} is a real number, @code{#f} else.\n" |
3080 | * "Note that the sets of integer and rational values form a subset\n" | |
3081 | * "of the set of real numbers, i. e. the predicate will also\n" | |
3082 | * "be fulfilled if @var{x} is an integer or a rational number." | |
3083 | */ | |
a1ec6916 | 3084 | SCM_DEFINE (scm_real_p, "rational?", 1, 0, 0, |
1bbd0b84 | 3085 | (SCM x), |
942e5b91 | 3086 | "Return @code{#t} if @var{x} is a rational number, @code{#f}\n" |
bb2c02f2 | 3087 | "otherwise. Note that the set of integer values forms a subset of\n" |
942e5b91 MG |
3088 | "the set of rational numbers, i. e. the predicate will also be\n" |
3089 | "fulfilled if @var{x} is an integer number. Real numbers\n" | |
3090 | "will also satisfy this predicate, because of their limited\n" | |
3091 | "precision.") | |
1bbd0b84 | 3092 | #define FUNC_NAME s_scm_real_p |
0f2d19dd | 3093 | { |
bb628794 | 3094 | if (SCM_INUMP (x)) { |
0f2d19dd | 3095 | return SCM_BOOL_T; |
bb628794 | 3096 | } else if (SCM_IMP (x)) { |
0f2d19dd | 3097 | return SCM_BOOL_F; |
3c9a524f | 3098 | } else if (SCM_REALP (x)) { |
0f2d19dd | 3099 | return SCM_BOOL_T; |
bb628794 | 3100 | } else if (SCM_BIGP (x)) { |
0f2d19dd | 3101 | return SCM_BOOL_T; |
bb628794 DH |
3102 | } else { |
3103 | return SCM_BOOL_F; | |
3104 | } | |
0f2d19dd | 3105 | } |
1bbd0b84 | 3106 | #undef FUNC_NAME |
0f2d19dd JB |
3107 | |
3108 | ||
a1ec6916 | 3109 | SCM_DEFINE (scm_integer_p, "integer?", 1, 0, 0, |
1bbd0b84 | 3110 | (SCM x), |
942e5b91 MG |
3111 | "Return @code{#t} if @var{x} is an integer number, @code{#f}\n" |
3112 | "else.") | |
1bbd0b84 | 3113 | #define FUNC_NAME s_scm_integer_p |
0f2d19dd JB |
3114 | { |
3115 | double r; | |
f872b822 MD |
3116 | if (SCM_INUMP (x)) |
3117 | return SCM_BOOL_T; | |
3118 | if (SCM_IMP (x)) | |
3119 | return SCM_BOOL_F; | |
f872b822 MD |
3120 | if (SCM_BIGP (x)) |
3121 | return SCM_BOOL_T; | |
3c9a524f | 3122 | if (!SCM_INEXACTP (x)) |
f872b822 | 3123 | return SCM_BOOL_F; |
3c9a524f | 3124 | if (SCM_COMPLEXP (x)) |
f872b822 | 3125 | return SCM_BOOL_F; |
5986c47d | 3126 | r = SCM_REAL_VALUE (x); |
f872b822 MD |
3127 | if (r == floor (r)) |
3128 | return SCM_BOOL_T; | |
0f2d19dd JB |
3129 | return SCM_BOOL_F; |
3130 | } | |
1bbd0b84 | 3131 | #undef FUNC_NAME |
0f2d19dd JB |
3132 | |
3133 | ||
a1ec6916 | 3134 | SCM_DEFINE (scm_inexact_p, "inexact?", 1, 0, 0, |
1bbd0b84 | 3135 | (SCM x), |
942e5b91 MG |
3136 | "Return @code{#t} if @var{x} is an inexact number, @code{#f}\n" |
3137 | "else.") | |
1bbd0b84 | 3138 | #define FUNC_NAME s_scm_inexact_p |
0f2d19dd | 3139 | { |
f4c627b3 | 3140 | return SCM_BOOL (SCM_INEXACTP (x)); |
0f2d19dd | 3141 | } |
1bbd0b84 | 3142 | #undef FUNC_NAME |
0f2d19dd JB |
3143 | |
3144 | ||
152f82bf | 3145 | SCM_GPROC1 (s_eq_p, "=", scm_tc7_rpsubr, scm_num_eq_p, g_eq_p); |
942e5b91 | 3146 | /* "Return @code{#t} if all parameters are numerically equal." */ |
0f2d19dd | 3147 | SCM |
6e8d25a6 | 3148 | scm_num_eq_p (SCM x, SCM y) |
0f2d19dd | 3149 | { |
f4c627b3 DH |
3150 | if (SCM_INUMP (x)) { |
3151 | long xx = SCM_INUM (x); | |
3152 | if (SCM_INUMP (y)) { | |
3153 | long yy = SCM_INUM (y); | |
3154 | return SCM_BOOL (xx == yy); | |
3155 | } else if (SCM_BIGP (y)) { | |
3156 | return SCM_BOOL_F; | |
3157 | } else if (SCM_REALP (y)) { | |
3158 | return SCM_BOOL ((double) xx == SCM_REAL_VALUE (y)); | |
3159 | } else if (SCM_COMPLEXP (y)) { | |
3160 | return SCM_BOOL (((double) xx == SCM_COMPLEX_REAL (y)) | |
3161 | && (0.0 == SCM_COMPLEX_IMAG (y))); | |
3162 | } else { | |
3163 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3164 | } |
f4c627b3 DH |
3165 | } else if (SCM_BIGP (x)) { |
3166 | if (SCM_INUMP (y)) { | |
3167 | return SCM_BOOL_F; | |
3168 | } else if (SCM_BIGP (y)) { | |
3169 | return SCM_BOOL (0 == scm_bigcomp (x, y)); | |
3170 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3171 | return SCM_BOOL (scm_i_big2dbl (x) == SCM_REAL_VALUE (y)); |
f4c627b3 | 3172 | } else if (SCM_COMPLEXP (y)) { |
1be6b49c | 3173 | return SCM_BOOL ((scm_i_big2dbl (x) == SCM_COMPLEX_REAL (y)) |
f4c627b3 DH |
3174 | && (0.0 == SCM_COMPLEX_IMAG (y))); |
3175 | } else { | |
3176 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
3177 | } | |
3178 | } else if (SCM_REALP (x)) { | |
3179 | if (SCM_INUMP (y)) { | |
3180 | return SCM_BOOL (SCM_REAL_VALUE (x) == (double) SCM_INUM (y)); | |
3181 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3182 | return SCM_BOOL (SCM_REAL_VALUE (x) == scm_i_big2dbl (y)); |
f4c627b3 DH |
3183 | } else if (SCM_REALP (y)) { |
3184 | return SCM_BOOL (SCM_REAL_VALUE (x) == SCM_REAL_VALUE (y)); | |
3185 | } else if (SCM_COMPLEXP (y)) { | |
3186 | return SCM_BOOL ((SCM_REAL_VALUE (x) == SCM_COMPLEX_REAL (y)) | |
3187 | && (0.0 == SCM_COMPLEX_IMAG (y))); | |
3188 | } else { | |
3189 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
f872b822 | 3190 | } |
f4c627b3 DH |
3191 | } else if (SCM_COMPLEXP (x)) { |
3192 | if (SCM_INUMP (y)) { | |
3193 | return SCM_BOOL ((SCM_COMPLEX_REAL (x) == (double) SCM_INUM (y)) | |
3194 | && (SCM_COMPLEX_IMAG (x) == 0.0)); | |
3195 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3196 | return SCM_BOOL ((SCM_COMPLEX_REAL (x) == scm_i_big2dbl (y)) |
f4c627b3 DH |
3197 | && (SCM_COMPLEX_IMAG (x) == 0.0)); |
3198 | } else if (SCM_REALP (y)) { | |
3199 | return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_REAL_VALUE (y)) | |
3200 | && (SCM_COMPLEX_IMAG (x) == 0.0)); | |
3201 | } else if (SCM_COMPLEXP (y)) { | |
3202 | return SCM_BOOL ((SCM_COMPLEX_REAL (x) == SCM_COMPLEX_REAL (y)) | |
3203 | && (SCM_COMPLEX_IMAG (x) == SCM_COMPLEX_IMAG (y))); | |
3204 | } else { | |
3205 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARGn, s_eq_p); | |
3206 | } | |
3207 | } else { | |
3208 | SCM_WTA_DISPATCH_2 (g_eq_p, x, y, SCM_ARG1, s_eq_p); | |
3209 | } | |
0f2d19dd JB |
3210 | } |
3211 | ||
3212 | ||
152f82bf | 3213 | SCM_GPROC1 (s_less_p, "<", scm_tc7_rpsubr, scm_less_p, g_less_p); |
942e5b91 MG |
3214 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3215 | * "increasing." | |
3216 | */ | |
0f2d19dd | 3217 | SCM |
6e8d25a6 | 3218 | scm_less_p (SCM x, SCM y) |
0f2d19dd | 3219 | { |
f4c627b3 DH |
3220 | if (SCM_INUMP (x)) { |
3221 | long xx = SCM_INUM (x); | |
3222 | if (SCM_INUMP (y)) { | |
3223 | long yy = SCM_INUM (y); | |
3224 | return SCM_BOOL (xx < yy); | |
3225 | } else if (SCM_BIGP (y)) { | |
3226 | return SCM_BOOL (!SCM_BIGSIGN (y)); | |
3227 | } else if (SCM_REALP (y)) { | |
3228 | return SCM_BOOL ((double) xx < SCM_REAL_VALUE (y)); | |
3229 | } else { | |
3230 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3231 | } |
f4c627b3 DH |
3232 | } else if (SCM_BIGP (x)) { |
3233 | if (SCM_INUMP (y)) { | |
3234 | return SCM_BOOL (SCM_BIGSIGN (x)); | |
3235 | } else if (SCM_BIGP (y)) { | |
3236 | return SCM_BOOL (1 == scm_bigcomp (x, y)); | |
3237 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3238 | return SCM_BOOL (scm_i_big2dbl (x) < SCM_REAL_VALUE (y)); |
f4c627b3 DH |
3239 | } else { |
3240 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
3241 | } | |
3242 | } else if (SCM_REALP (x)) { | |
3243 | if (SCM_INUMP (y)) { | |
3244 | return SCM_BOOL (SCM_REAL_VALUE (x) < (double) SCM_INUM (y)); | |
3245 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3246 | return SCM_BOOL (SCM_REAL_VALUE (x) < scm_i_big2dbl (y)); |
f4c627b3 DH |
3247 | } else if (SCM_REALP (y)) { |
3248 | return SCM_BOOL (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)); | |
3249 | } else { | |
3250 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARGn, s_less_p); | |
f872b822 | 3251 | } |
f4c627b3 DH |
3252 | } else { |
3253 | SCM_WTA_DISPATCH_2 (g_less_p, x, y, SCM_ARG1, s_less_p); | |
3254 | } | |
0f2d19dd JB |
3255 | } |
3256 | ||
3257 | ||
c76b1eaf | 3258 | SCM_GPROC1 (s_scm_gr_p, ">", scm_tc7_rpsubr, scm_gr_p, g_gr_p); |
942e5b91 MG |
3259 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
3260 | * "decreasing." | |
c76b1eaf | 3261 | */ |
1bbd0b84 | 3262 | #define FUNC_NAME s_scm_gr_p |
c76b1eaf MD |
3263 | SCM |
3264 | scm_gr_p (SCM x, SCM y) | |
0f2d19dd | 3265 | { |
c76b1eaf MD |
3266 | if (!SCM_NUMBERP (x)) |
3267 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG1, FUNC_NAME); | |
3268 | else if (!SCM_NUMBERP (y)) | |
3269 | SCM_WTA_DISPATCH_2 (g_gr_p, x, y, SCM_ARG2, FUNC_NAME); | |
3270 | else | |
3271 | return scm_less_p (y, x); | |
0f2d19dd | 3272 | } |
1bbd0b84 | 3273 | #undef FUNC_NAME |
0f2d19dd JB |
3274 | |
3275 | ||
c76b1eaf | 3276 | SCM_GPROC1 (s_scm_leq_p, "<=", scm_tc7_rpsubr, scm_leq_p, g_leq_p); |
942e5b91 | 3277 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3278 | * "non-decreasing." |
3279 | */ | |
1bbd0b84 | 3280 | #define FUNC_NAME s_scm_leq_p |
c76b1eaf MD |
3281 | SCM |
3282 | scm_leq_p (SCM x, SCM y) | |
0f2d19dd | 3283 | { |
c76b1eaf MD |
3284 | if (!SCM_NUMBERP (x)) |
3285 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3286 | else if (!SCM_NUMBERP (y)) | |
3287 | SCM_WTA_DISPATCH_2 (g_leq_p, x, y, SCM_ARG2, FUNC_NAME); | |
fc194577 MV |
3288 | else if (SCM_NFALSEP (scm_nan_p (x)) || SCM_NFALSEP (scm_nan_p (y))) |
3289 | return SCM_BOOL_F; | |
c76b1eaf MD |
3290 | else |
3291 | return SCM_BOOL_NOT (scm_less_p (y, x)); | |
0f2d19dd | 3292 | } |
1bbd0b84 | 3293 | #undef FUNC_NAME |
0f2d19dd JB |
3294 | |
3295 | ||
c76b1eaf | 3296 | SCM_GPROC1 (s_scm_geq_p, ">=", scm_tc7_rpsubr, scm_geq_p, g_geq_p); |
942e5b91 | 3297 | /* "Return @code{#t} if the list of parameters is monotonically\n" |
c76b1eaf MD |
3298 | * "non-increasing." |
3299 | */ | |
1bbd0b84 | 3300 | #define FUNC_NAME s_scm_geq_p |
c76b1eaf MD |
3301 | SCM |
3302 | scm_geq_p (SCM x, SCM y) | |
0f2d19dd | 3303 | { |
c76b1eaf MD |
3304 | if (!SCM_NUMBERP (x)) |
3305 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG1, FUNC_NAME); | |
3306 | else if (!SCM_NUMBERP (y)) | |
3307 | SCM_WTA_DISPATCH_2 (g_geq_p, x, y, SCM_ARG2, FUNC_NAME); | |
fc194577 MV |
3308 | else if (SCM_NFALSEP (scm_nan_p (x)) || SCM_NFALSEP (scm_nan_p (y))) |
3309 | return SCM_BOOL_F; | |
c76b1eaf | 3310 | else |
fc194577 | 3311 | return SCM_BOOL_NOT (scm_less_p (x, y)); |
0f2d19dd | 3312 | } |
1bbd0b84 | 3313 | #undef FUNC_NAME |
0f2d19dd JB |
3314 | |
3315 | ||
152f82bf | 3316 | SCM_GPROC (s_zero_p, "zero?", 1, 0, 0, scm_zero_p, g_zero_p); |
942e5b91 MG |
3317 | /* "Return @code{#t} if @var{z} is an exact or inexact number equal to\n" |
3318 | * "zero." | |
3319 | */ | |
0f2d19dd | 3320 | SCM |
6e8d25a6 | 3321 | scm_zero_p (SCM z) |
0f2d19dd | 3322 | { |
c2ff8ab0 DH |
3323 | if (SCM_INUMP (z)) { |
3324 | return SCM_BOOL (SCM_EQ_P (z, SCM_INUM0)); | |
3325 | } else if (SCM_BIGP (z)) { | |
3326 | return SCM_BOOL_F; | |
3327 | } else if (SCM_REALP (z)) { | |
3328 | return SCM_BOOL (SCM_REAL_VALUE (z) == 0.0); | |
3329 | } else if (SCM_COMPLEXP (z)) { | |
3330 | return SCM_BOOL (SCM_COMPLEX_REAL (z) == 0.0 | |
3331 | && SCM_COMPLEX_IMAG (z) == 0.0); | |
3332 | } else { | |
3333 | SCM_WTA_DISPATCH_1 (g_zero_p, z, SCM_ARG1, s_zero_p); | |
3334 | } | |
0f2d19dd JB |
3335 | } |
3336 | ||
3337 | ||
152f82bf | 3338 | SCM_GPROC (s_positive_p, "positive?", 1, 0, 0, scm_positive_p, g_positive_p); |
942e5b91 MG |
3339 | /* "Return @code{#t} if @var{x} is an exact or inexact number greater than\n" |
3340 | * "zero." | |
3341 | */ | |
0f2d19dd | 3342 | SCM |
6e8d25a6 | 3343 | scm_positive_p (SCM x) |
0f2d19dd | 3344 | { |
c2ff8ab0 DH |
3345 | if (SCM_INUMP (x)) { |
3346 | return SCM_BOOL (SCM_INUM (x) > 0); | |
3347 | } else if (SCM_BIGP (x)) { | |
3348 | return SCM_BOOL (!SCM_BIGSIGN (x)); | |
3349 | } else if (SCM_REALP (x)) { | |
3350 | return SCM_BOOL(SCM_REAL_VALUE (x) > 0.0); | |
3351 | } else { | |
3352 | SCM_WTA_DISPATCH_1 (g_positive_p, x, SCM_ARG1, s_positive_p); | |
3353 | } | |
0f2d19dd JB |
3354 | } |
3355 | ||
3356 | ||
152f82bf | 3357 | SCM_GPROC (s_negative_p, "negative?", 1, 0, 0, scm_negative_p, g_negative_p); |
942e5b91 MG |
3358 | /* "Return @code{#t} if @var{x} is an exact or inexact number less than\n" |
3359 | * "zero." | |
3360 | */ | |
0f2d19dd | 3361 | SCM |
6e8d25a6 | 3362 | scm_negative_p (SCM x) |
0f2d19dd | 3363 | { |
c2ff8ab0 DH |
3364 | if (SCM_INUMP (x)) { |
3365 | return SCM_BOOL (SCM_INUM (x) < 0); | |
3366 | } else if (SCM_BIGP (x)) { | |
3367 | return SCM_BOOL (SCM_BIGSIGN (x)); | |
3368 | } else if (SCM_REALP (x)) { | |
3369 | return SCM_BOOL(SCM_REAL_VALUE (x) < 0.0); | |
3370 | } else { | |
3371 | SCM_WTA_DISPATCH_1 (g_negative_p, x, SCM_ARG1, s_negative_p); | |
3372 | } | |
0f2d19dd JB |
3373 | } |
3374 | ||
3375 | ||
9de33deb | 3376 | SCM_GPROC1 (s_max, "max", scm_tc7_asubr, scm_max, g_max); |
942e5b91 MG |
3377 | /* "Return the maximum of all parameter values." |
3378 | */ | |
0f2d19dd | 3379 | SCM |
6e8d25a6 | 3380 | scm_max (SCM x, SCM y) |
0f2d19dd | 3381 | { |
f4c627b3 DH |
3382 | if (SCM_UNBNDP (y)) { |
3383 | if (SCM_UNBNDP (x)) { | |
c05e97b7 | 3384 | SCM_WTA_DISPATCH_0 (g_max, s_max); |
f4c627b3 | 3385 | } else if (SCM_NUMBERP (x)) { |
f872b822 | 3386 | return x; |
f4c627b3 DH |
3387 | } else { |
3388 | SCM_WTA_DISPATCH_1 (g_max, x, SCM_ARG1, s_max); | |
f872b822 | 3389 | } |
f4c627b3 DH |
3390 | } |
3391 | ||
3392 | if (SCM_INUMP (x)) { | |
3393 | long xx = SCM_INUM (x); | |
3394 | if (SCM_INUMP (y)) { | |
3395 | long yy = SCM_INUM (y); | |
3396 | return (xx < yy) ? y : x; | |
3397 | } else if (SCM_BIGP (y)) { | |
3398 | return SCM_BIGSIGN (y) ? x : y; | |
3399 | } else if (SCM_REALP (y)) { | |
3400 | double z = xx; | |
3401 | return (z <= SCM_REAL_VALUE (y)) ? y : scm_make_real (z); | |
3402 | } else { | |
3403 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3404 | } |
f4c627b3 DH |
3405 | } else if (SCM_BIGP (x)) { |
3406 | if (SCM_INUMP (y)) { | |
3407 | return SCM_BIGSIGN (x) ? y : x; | |
3408 | } else if (SCM_BIGP (y)) { | |
3409 | return (1 == scm_bigcomp (x, y)) ? y : x; | |
3410 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3411 | double z = scm_i_big2dbl (x); |
f4c627b3 DH |
3412 | return (z <= SCM_REAL_VALUE (y)) ? y : scm_make_real (z); |
3413 | } else { | |
3414 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
3415 | } | |
3416 | } else if (SCM_REALP (x)) { | |
3417 | if (SCM_INUMP (y)) { | |
3418 | double z = SCM_INUM (y); | |
3419 | return (SCM_REAL_VALUE (x) < z) ? scm_make_real (z) : x; | |
3420 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3421 | double z = scm_i_big2dbl (y); |
f4c627b3 DH |
3422 | return (SCM_REAL_VALUE (x) < z) ? scm_make_real (z) : x; |
3423 | } else if (SCM_REALP (y)) { | |
3424 | return (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)) ? y : x; | |
3425 | } else { | |
3426 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARGn, s_max); | |
f872b822 | 3427 | } |
f4c627b3 DH |
3428 | } else { |
3429 | SCM_WTA_DISPATCH_2 (g_max, x, y, SCM_ARG1, s_max); | |
3430 | } | |
0f2d19dd JB |
3431 | } |
3432 | ||
3433 | ||
9de33deb | 3434 | SCM_GPROC1 (s_min, "min", scm_tc7_asubr, scm_min, g_min); |
942e5b91 MG |
3435 | /* "Return the minium of all parameter values." |
3436 | */ | |
0f2d19dd | 3437 | SCM |
6e8d25a6 | 3438 | scm_min (SCM x, SCM y) |
0f2d19dd | 3439 | { |
f4c627b3 DH |
3440 | if (SCM_UNBNDP (y)) { |
3441 | if (SCM_UNBNDP (x)) { | |
c05e97b7 | 3442 | SCM_WTA_DISPATCH_0 (g_min, s_min); |
f4c627b3 | 3443 | } else if (SCM_NUMBERP (x)) { |
f872b822 | 3444 | return x; |
f4c627b3 DH |
3445 | } else { |
3446 | SCM_WTA_DISPATCH_1 (g_min, x, SCM_ARG1, s_min); | |
f872b822 | 3447 | } |
f4c627b3 DH |
3448 | } |
3449 | ||
3450 | if (SCM_INUMP (x)) { | |
3451 | long xx = SCM_INUM (x); | |
3452 | if (SCM_INUMP (y)) { | |
3453 | long yy = SCM_INUM (y); | |
3454 | return (xx < yy) ? x : y; | |
3455 | } else if (SCM_BIGP (y)) { | |
3456 | return SCM_BIGSIGN (y) ? y : x; | |
3457 | } else if (SCM_REALP (y)) { | |
3458 | double z = xx; | |
3459 | return (z < SCM_REAL_VALUE (y)) ? scm_make_real (z) : y; | |
3460 | } else { | |
3461 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3462 | } |
f4c627b3 DH |
3463 | } else if (SCM_BIGP (x)) { |
3464 | if (SCM_INUMP (y)) { | |
3465 | return SCM_BIGSIGN (x) ? x : y; | |
3466 | } else if (SCM_BIGP (y)) { | |
3467 | return (-1 == scm_bigcomp (x, y)) ? y : x; | |
3468 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3469 | double z = scm_i_big2dbl (x); |
f4c627b3 DH |
3470 | return (z < SCM_REAL_VALUE (y)) ? scm_make_real (z) : y; |
3471 | } else { | |
3472 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
3473 | } | |
3474 | } else if (SCM_REALP (x)) { | |
3475 | if (SCM_INUMP (y)) { | |
3476 | double z = SCM_INUM (y); | |
3477 | return (SCM_REAL_VALUE (x) <= z) ? x : scm_make_real (z); | |
3478 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3479 | double z = scm_i_big2dbl (y); |
f4c627b3 DH |
3480 | return (SCM_REAL_VALUE (x) <= z) ? x : scm_make_real (z); |
3481 | } else if (SCM_REALP (y)) { | |
3482 | return (SCM_REAL_VALUE (x) < SCM_REAL_VALUE (y)) ? x : y; | |
3483 | } else { | |
3484 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARGn, s_min); | |
f872b822 | 3485 | } |
f4c627b3 DH |
3486 | } else { |
3487 | SCM_WTA_DISPATCH_2 (g_min, x, y, SCM_ARG1, s_min); | |
3488 | } | |
0f2d19dd JB |
3489 | } |
3490 | ||
3491 | ||
9de33deb | 3492 | SCM_GPROC1 (s_sum, "+", scm_tc7_asubr, scm_sum, g_sum); |
942e5b91 MG |
3493 | /* "Return the sum of all parameter values. Return 0 if called without\n" |
3494 | * "any parameters." | |
3495 | */ | |
0f2d19dd | 3496 | SCM |
6e8d25a6 | 3497 | scm_sum (SCM x, SCM y) |
0f2d19dd | 3498 | { |
98cb6e75 DH |
3499 | if (SCM_UNBNDP (y)) { |
3500 | if (SCM_UNBNDP (x)) { | |
3501 | return SCM_INUM0; | |
3502 | } else if (SCM_NUMBERP (x)) { | |
f872b822 | 3503 | return x; |
98cb6e75 DH |
3504 | } else { |
3505 | SCM_WTA_DISPATCH_1 (g_sum, x, SCM_ARG1, s_sum); | |
f872b822 | 3506 | } |
98cb6e75 | 3507 | } |
c209c88e | 3508 | |
98cb6e75 DH |
3509 | if (SCM_INUMP (x)) { |
3510 | long int xx = SCM_INUM (x); | |
3511 | if (SCM_INUMP (y)) { | |
3512 | long int yy = SCM_INUM (y); | |
3513 | long int z = xx + yy; | |
3514 | if (SCM_FIXABLE (z)) { | |
3515 | return SCM_MAKINUM (z); | |
3516 | } else { | |
3517 | #ifdef SCM_BIGDIG | |
1be6b49c | 3518 | return scm_i_long2big (z); |
98cb6e75 DH |
3519 | #else /* SCM_BIGDIG */ |
3520 | return scm_make_real ((double) z); | |
3521 | #endif /* SCM_BIGDIG */ | |
3522 | } | |
3523 | } else if (SCM_BIGP (y)) { | |
3524 | intbig: | |
f872b822 | 3525 | { |
98cb6e75 DH |
3526 | long int xx = SCM_INUM (x); |
3527 | #ifndef SCM_DIGSTOOBIG | |
3528 | long z = scm_pseudolong (xx); | |
3529 | return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
3530 | (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, 0); | |
3531 | #else /* SCM_DIGSTOOBIG */ | |
3532 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; | |
3533 | scm_longdigs (xx, zdigs); | |
3534 | return scm_addbig (zdigs, SCM_DIGSPERLONG, | |
3535 | (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, 0); | |
3536 | #endif /* SCM_DIGSTOOBIG */ | |
0f2d19dd | 3537 | } |
98cb6e75 DH |
3538 | } else if (SCM_REALP (y)) { |
3539 | return scm_make_real (xx + SCM_REAL_VALUE (y)); | |
3540 | } else if (SCM_COMPLEXP (y)) { | |
3541 | return scm_make_complex (xx + SCM_COMPLEX_REAL (y), | |
3542 | SCM_COMPLEX_IMAG (y)); | |
3543 | } else { | |
3544 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 3545 | } |
98cb6e75 DH |
3546 | } else if (SCM_BIGP (x)) { |
3547 | if (SCM_INUMP (y)) { | |
3548 | SCM_SWAP (x, y); | |
3549 | goto intbig; | |
3550 | } else if (SCM_BIGP (y)) { | |
3551 | if (SCM_NUMDIGS (x) > SCM_NUMDIGS (y)) { | |
3552 | SCM_SWAP (x, y); | |
3553 | } | |
3554 | return scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
3555 | SCM_BIGSIGN (x), y, 0); | |
3556 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3557 | return scm_make_real (scm_i_big2dbl (x) + SCM_REAL_VALUE (y)); |
98cb6e75 | 3558 | } else if (SCM_COMPLEXP (y)) { |
1be6b49c | 3559 | return scm_make_complex (scm_i_big2dbl (x) + SCM_COMPLEX_REAL (y), |
98cb6e75 DH |
3560 | SCM_COMPLEX_IMAG (y)); |
3561 | } else { | |
3562 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
f872b822 | 3563 | } |
98cb6e75 DH |
3564 | } else if (SCM_REALP (x)) { |
3565 | if (SCM_INUMP (y)) { | |
3566 | return scm_make_real (SCM_REAL_VALUE (x) + SCM_INUM (y)); | |
3567 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3568 | return scm_make_real (SCM_REAL_VALUE (x) + scm_i_big2dbl (y)); |
98cb6e75 DH |
3569 | } else if (SCM_REALP (y)) { |
3570 | return scm_make_real (SCM_REAL_VALUE (x) + SCM_REAL_VALUE (y)); | |
3571 | } else if (SCM_COMPLEXP (y)) { | |
3572 | return scm_make_complex (SCM_REAL_VALUE (x) + SCM_COMPLEX_REAL (y), | |
3573 | SCM_COMPLEX_IMAG (y)); | |
3574 | } else { | |
3575 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
3576 | } | |
3577 | } else if (SCM_COMPLEXP (x)) { | |
3578 | if (SCM_INUMP (y)) { | |
3579 | return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_INUM (y), | |
3580 | SCM_COMPLEX_IMAG (x)); | |
3581 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3582 | return scm_make_complex (SCM_COMPLEX_REAL (x) + scm_i_big2dbl (y), |
98cb6e75 DH |
3583 | SCM_COMPLEX_IMAG (x)); |
3584 | } else if (SCM_REALP (y)) { | |
3585 | return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_REAL_VALUE (y), | |
3586 | SCM_COMPLEX_IMAG (x)); | |
3587 | } else if (SCM_COMPLEXP (y)) { | |
3588 | return scm_make_complex (SCM_COMPLEX_REAL (x) + SCM_COMPLEX_REAL (y), | |
3589 | SCM_COMPLEX_IMAG (x) + SCM_COMPLEX_IMAG (y)); | |
3590 | } else { | |
3591 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARGn, s_sum); | |
3592 | } | |
3593 | } else { | |
3594 | SCM_WTA_DISPATCH_2 (g_sum, x, y, SCM_ARG1, s_sum); | |
3595 | } | |
0f2d19dd JB |
3596 | } |
3597 | ||
3598 | ||
9de33deb | 3599 | SCM_GPROC1 (s_difference, "-", scm_tc7_asubr, scm_difference, g_difference); |
609c3d30 MG |
3600 | /* If called with one argument @var{z1}, -@var{z1} returned. Otherwise |
3601 | * the sum of all but the first argument are subtracted from the first | |
3602 | * argument. */ | |
c05e97b7 | 3603 | #define FUNC_NAME s_difference |
0f2d19dd | 3604 | SCM |
6e8d25a6 | 3605 | scm_difference (SCM x, SCM y) |
0f2d19dd | 3606 | { |
98cb6e75 | 3607 | if (SCM_UNBNDP (y)) { |
c05e97b7 MV |
3608 | if (SCM_UNBNDP (x)) { |
3609 | SCM_WTA_DISPATCH_0 (g_difference, s_difference); | |
3610 | } else if (SCM_INUMP (x)) { | |
98cb6e75 DH |
3611 | long xx = -SCM_INUM (x); |
3612 | if (SCM_FIXABLE (xx)) { | |
3613 | return SCM_MAKINUM (xx); | |
3614 | } else { | |
f872b822 | 3615 | #ifdef SCM_BIGDIG |
1be6b49c | 3616 | return scm_i_long2big (xx); |
f3ae5d60 | 3617 | #else |
98cb6e75 | 3618 | return scm_make_real ((double) xx); |
f3ae5d60 | 3619 | #endif |
f3ae5d60 | 3620 | } |
98cb6e75 | 3621 | } else if (SCM_BIGP (x)) { |
1be6b49c | 3622 | SCM z = scm_i_copybig (x, !SCM_BIGSIGN (x)); |
98cb6e75 DH |
3623 | unsigned int digs = SCM_NUMDIGS (z); |
3624 | unsigned int size = digs * SCM_BITSPERDIG / SCM_CHAR_BIT; | |
1be6b49c | 3625 | return size <= sizeof (SCM) ? scm_i_big2inum (z, digs) : z; |
98cb6e75 DH |
3626 | } else if (SCM_REALP (x)) { |
3627 | return scm_make_real (-SCM_REAL_VALUE (x)); | |
3628 | } else if (SCM_COMPLEXP (x)) { | |
3629 | return scm_make_complex (-SCM_COMPLEX_REAL (x), -SCM_COMPLEX_IMAG (x)); | |
3630 | } else { | |
3631 | SCM_WTA_DISPATCH_1 (g_difference, x, SCM_ARG1, s_difference); | |
f872b822 | 3632 | } |
98cb6e75 DH |
3633 | } |
3634 | ||
3635 | if (SCM_INUMP (x)) { | |
3636 | long int xx = SCM_INUM (x); | |
3637 | if (SCM_INUMP (y)) { | |
3638 | long int yy = SCM_INUM (y); | |
3639 | long int z = xx - yy; | |
3640 | if (SCM_FIXABLE (z)) { | |
3641 | return SCM_MAKINUM (z); | |
3642 | } else { | |
f872b822 | 3643 | #ifdef SCM_BIGDIG |
1be6b49c | 3644 | return scm_i_long2big (z); |
f872b822 | 3645 | #else |
98cb6e75 | 3646 | return scm_make_real ((double) z); |
f872b822 | 3647 | #endif |
98cb6e75 DH |
3648 | } |
3649 | } else if (SCM_BIGP (y)) { | |
3650 | #ifndef SCM_DIGSTOOBIG | |
3651 | long z = scm_pseudolong (xx); | |
3652 | return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
3653 | (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, SCM_BIGSIGNFLAG); | |
f872b822 | 3654 | #else |
98cb6e75 DH |
3655 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
3656 | scm_longdigs (xx, zdigs); | |
3657 | return scm_addbig (zdigs, SCM_DIGSPERLONG, | |
3658 | (xx < 0) ? SCM_BIGSIGNFLAG : 0, y, SCM_BIGSIGNFLAG); | |
f872b822 | 3659 | #endif |
98cb6e75 DH |
3660 | } else if (SCM_REALP (y)) { |
3661 | return scm_make_real (xx - SCM_REAL_VALUE (y)); | |
3662 | } else if (SCM_COMPLEXP (y)) { | |
3663 | return scm_make_complex (xx - SCM_COMPLEX_REAL (y), | |
3664 | -SCM_COMPLEX_IMAG (y)); | |
3665 | } else { | |
3666 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
f872b822 | 3667 | } |
98cb6e75 DH |
3668 | } else if (SCM_BIGP (x)) { |
3669 | if (SCM_INUMP (y)) { | |
3670 | long int yy = SCM_INUM (y); | |
3671 | #ifndef SCM_DIGSTOOBIG | |
3672 | long z = scm_pseudolong (yy); | |
3673 | return scm_addbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
3674 | (yy < 0) ? 0 : SCM_BIGSIGNFLAG, x, 0); | |
f872b822 | 3675 | #else |
98cb6e75 DH |
3676 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
3677 | scm_longdigs (yy, zdigs); | |
3678 | return scm_addbig (zdigs, SCM_DIGSPERLONG, | |
3679 | (yy < 0) ? 0 : SCM_BIGSIGNFLAG, x, 0); | |
0f2d19dd | 3680 | #endif |
98cb6e75 DH |
3681 | } else if (SCM_BIGP (y)) { |
3682 | return (SCM_NUMDIGS (x) < SCM_NUMDIGS (y)) | |
3683 | ? scm_addbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
3684 | SCM_BIGSIGN (x), y, SCM_BIGSIGNFLAG) | |
3685 | : scm_addbig (SCM_BDIGITS (y), SCM_NUMDIGS (y), | |
3686 | SCM_BIGSIGN (y) ^ SCM_BIGSIGNFLAG, x, 0); | |
3687 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3688 | return scm_make_real (scm_i_big2dbl (x) - SCM_REAL_VALUE (y)); |
98cb6e75 | 3689 | } else if (SCM_COMPLEXP (y)) { |
1be6b49c | 3690 | return scm_make_complex (scm_i_big2dbl (x) - SCM_COMPLEX_REAL (y), |
98cb6e75 DH |
3691 | - SCM_COMPLEX_IMAG (y)); |
3692 | } else { | |
3693 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
3694 | } | |
3695 | } else if (SCM_REALP (x)) { | |
3696 | if (SCM_INUMP (y)) { | |
3697 | return scm_make_real (SCM_REAL_VALUE (x) - SCM_INUM (y)); | |
3698 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3699 | return scm_make_real (SCM_REAL_VALUE (x) - scm_i_big2dbl (y)); |
98cb6e75 DH |
3700 | } else if (SCM_REALP (y)) { |
3701 | return scm_make_real (SCM_REAL_VALUE (x) - SCM_REAL_VALUE (y)); | |
3702 | } else if (SCM_COMPLEXP (y)) { | |
3703 | return scm_make_complex (SCM_REAL_VALUE (x) - SCM_COMPLEX_REAL (y), | |
3704 | -SCM_COMPLEX_IMAG (y)); | |
3705 | } else { | |
3706 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
3707 | } | |
3708 | } else if (SCM_COMPLEXP (x)) { | |
3709 | if (SCM_INUMP (y)) { | |
3710 | return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_INUM (y), | |
3711 | SCM_COMPLEX_IMAG (x)); | |
3712 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3713 | return scm_make_complex (SCM_COMPLEX_REAL (x) - scm_i_big2dbl (y), |
98cb6e75 DH |
3714 | SCM_COMPLEX_IMAG (x)); |
3715 | } else if (SCM_REALP (y)) { | |
3716 | return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_REAL_VALUE (y), | |
3717 | SCM_COMPLEX_IMAG (x)); | |
3718 | } else if (SCM_COMPLEXP (y)) { | |
3719 | return scm_make_complex (SCM_COMPLEX_REAL (x) - SCM_COMPLEX_REAL (y), | |
3720 | SCM_COMPLEX_IMAG (x) - SCM_COMPLEX_IMAG (y)); | |
3721 | } else { | |
3722 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARGn, s_difference); | |
3723 | } | |
3724 | } else { | |
3725 | SCM_WTA_DISPATCH_2 (g_difference, x, y, SCM_ARG1, s_difference); | |
3726 | } | |
0f2d19dd | 3727 | } |
c05e97b7 | 3728 | #undef FUNC_NAME |
0f2d19dd | 3729 | |
9de33deb | 3730 | SCM_GPROC1 (s_product, "*", scm_tc7_asubr, scm_product, g_product); |
942e5b91 MG |
3731 | /* "Return the product of all arguments. If called without arguments,\n" |
3732 | * "1 is returned." | |
3733 | */ | |
0f2d19dd | 3734 | SCM |
6e8d25a6 | 3735 | scm_product (SCM x, SCM y) |
0f2d19dd | 3736 | { |
f4c627b3 DH |
3737 | if (SCM_UNBNDP (y)) { |
3738 | if (SCM_UNBNDP (x)) { | |
3739 | return SCM_MAKINUM (1L); | |
3740 | } else if (SCM_NUMBERP (x)) { | |
f872b822 | 3741 | return x; |
f4c627b3 DH |
3742 | } else { |
3743 | SCM_WTA_DISPATCH_1 (g_product, x, SCM_ARG1, s_product); | |
f872b822 | 3744 | } |
f4c627b3 DH |
3745 | } |
3746 | ||
3747 | if (SCM_INUMP (x)) { | |
3748 | long xx; | |
3749 | ||
3750 | intbig: | |
3751 | xx = SCM_INUM (x); | |
3752 | ||
3753 | if (xx == 0) { | |
f872b822 | 3754 | return x; |
f4c627b3 DH |
3755 | } else if (xx == 1) { |
3756 | return y; | |
3757 | } | |
3758 | ||
3759 | if (SCM_INUMP (y)) { | |
3760 | long yy = SCM_INUM (y); | |
3761 | long kk = xx * yy; | |
3762 | SCM k = SCM_MAKINUM (kk); | |
3763 | if (kk != SCM_INUM (k) || kk / xx != yy) { | |
f872b822 | 3764 | #ifdef SCM_BIGDIG |
f4c627b3 | 3765 | int sgn = (xx < 0) ^ (yy < 0); |
f872b822 | 3766 | #ifndef SCM_DIGSTOOBIG |
f4c627b3 DH |
3767 | long i = scm_pseudolong (xx); |
3768 | long j = scm_pseudolong (yy); | |
f872b822 MD |
3769 | return scm_mulbig ((SCM_BIGDIG *) & i, SCM_DIGSPERLONG, |
3770 | (SCM_BIGDIG *) & j, SCM_DIGSPERLONG, sgn); | |
3771 | #else /* SCM_DIGSTOOBIG */ | |
f4c627b3 DH |
3772 | SCM_BIGDIG xdigs [SCM_DIGSPERLONG]; |
3773 | SCM_BIGDIG ydigs [SCM_DIGSPERLONG]; | |
3774 | scm_longdigs (xx, xdigs); | |
3775 | scm_longdigs (yy, ydigs); | |
3776 | return scm_mulbig (xdigs, SCM_DIGSPERLONG, | |
3777 | ydigs, SCM_DIGSPERLONG, | |
f872b822 MD |
3778 | sgn); |
3779 | #endif | |
f4c627b3 DH |
3780 | #else |
3781 | return scm_make_real (((double) xx) * ((double) yy)); | |
3782 | #endif | |
3783 | } else { | |
3784 | return k; | |
0f2d19dd | 3785 | } |
f4c627b3 DH |
3786 | } else if (SCM_BIGP (y)) { |
3787 | #ifndef SCM_DIGSTOOBIG | |
3788 | long z = scm_pseudolong (xx); | |
3789 | return scm_mulbig ((SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
3790 | SCM_BDIGITS (y), SCM_NUMDIGS (y), | |
3791 | SCM_BIGSIGN (y) ? (xx > 0) : (xx < 0)); | |
0f2d19dd | 3792 | #else |
f4c627b3 DH |
3793 | SCM_BIGDIG zdigs [SCM_DIGSPERLONG]; |
3794 | scm_longdigs (xx, zdigs); | |
3795 | return scm_mulbig (zdigs, SCM_DIGSPERLONG, | |
3796 | SCM_BDIGITS (y), SCM_NUMDIGS (y), | |
3797 | SCM_BIGSIGN (y) ? (xx > 0) : (xx < 0)); | |
0f2d19dd | 3798 | #endif |
f4c627b3 DH |
3799 | } else if (SCM_REALP (y)) { |
3800 | return scm_make_real (xx * SCM_REAL_VALUE (y)); | |
3801 | } else if (SCM_COMPLEXP (y)) { | |
3802 | return scm_make_complex (xx * SCM_COMPLEX_REAL (y), | |
3803 | xx * SCM_COMPLEX_IMAG (y)); | |
3804 | } else { | |
3805 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
3806 | } | |
3807 | } else if (SCM_BIGP (x)) { | |
3808 | if (SCM_INUMP (y)) { | |
3809 | SCM_SWAP (x, y); | |
3810 | goto intbig; | |
3811 | } else if (SCM_BIGP (y)) { | |
3812 | return scm_mulbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
3813 | SCM_BDIGITS (y), SCM_NUMDIGS (y), | |
3814 | SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y)); | |
3815 | } else if (SCM_REALP (y)) { | |
1be6b49c | 3816 | return scm_make_real (scm_i_big2dbl (x) * SCM_REAL_VALUE (y)); |
f4c627b3 | 3817 | } else if (SCM_COMPLEXP (y)) { |
1be6b49c | 3818 | double z = scm_i_big2dbl (x); |
f4c627b3 DH |
3819 | return scm_make_complex (z * SCM_COMPLEX_REAL (y), |
3820 | z * SCM_COMPLEX_IMAG (y)); | |
3821 | } else { | |
3822 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
3823 | } | |
3824 | } else if (SCM_REALP (x)) { | |
3825 | if (SCM_INUMP (y)) { | |
3826 | return scm_make_real (SCM_INUM (y) * SCM_REAL_VALUE (x)); | |
3827 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3828 | return scm_make_real (scm_i_big2dbl (y) * SCM_REAL_VALUE (x)); |
f4c627b3 DH |
3829 | } else if (SCM_REALP (y)) { |
3830 | return scm_make_real (SCM_REAL_VALUE (x) * SCM_REAL_VALUE (y)); | |
3831 | } else if (SCM_COMPLEXP (y)) { | |
3832 | return scm_make_complex (SCM_REAL_VALUE (x) * SCM_COMPLEX_REAL (y), | |
3833 | SCM_REAL_VALUE (x) * SCM_COMPLEX_IMAG (y)); | |
3834 | } else { | |
3835 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
3836 | } | |
3837 | } else if (SCM_COMPLEXP (x)) { | |
3838 | if (SCM_INUMP (y)) { | |
3839 | return scm_make_complex (SCM_INUM (y) * SCM_COMPLEX_REAL (x), | |
3840 | SCM_INUM (y) * SCM_COMPLEX_IMAG (x)); | |
3841 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 3842 | double z = scm_i_big2dbl (y); |
f4c627b3 DH |
3843 | return scm_make_complex (z * SCM_COMPLEX_REAL (x), |
3844 | z * SCM_COMPLEX_IMAG (x)); | |
3845 | } else if (SCM_REALP (y)) { | |
3846 | return scm_make_complex (SCM_REAL_VALUE (y) * SCM_COMPLEX_REAL (x), | |
3847 | SCM_REAL_VALUE (y) * SCM_COMPLEX_IMAG (x)); | |
3848 | } else if (SCM_COMPLEXP (y)) { | |
3849 | return scm_make_complex (SCM_COMPLEX_REAL (x) * SCM_COMPLEX_REAL (y) | |
3850 | - SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_IMAG (y), | |
3851 | SCM_COMPLEX_REAL (x) * SCM_COMPLEX_IMAG (y) | |
3852 | + SCM_COMPLEX_IMAG (x) * SCM_COMPLEX_REAL (y)); | |
3853 | } else { | |
3854 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARGn, s_product); | |
3855 | } | |
3856 | } else { | |
3857 | SCM_WTA_DISPATCH_2 (g_product, x, y, SCM_ARG1, s_product); | |
0f2d19dd JB |
3858 | } |
3859 | } | |
3860 | ||
3861 | ||
0f2d19dd | 3862 | double |
6e8d25a6 | 3863 | scm_num2dbl (SCM a, const char *why) |
f4c627b3 | 3864 | #define FUNC_NAME why |
0f2d19dd | 3865 | { |
f4c627b3 | 3866 | if (SCM_INUMP (a)) { |
0f2d19dd | 3867 | return (double) SCM_INUM (a); |
f4c627b3 | 3868 | } else if (SCM_BIGP (a)) { |
1be6b49c | 3869 | return scm_i_big2dbl (a); |
f4c627b3 DH |
3870 | } else if (SCM_REALP (a)) { |
3871 | return (SCM_REAL_VALUE (a)); | |
3872 | } else { | |
3873 | SCM_WRONG_TYPE_ARG (SCM_ARGn, a); | |
3874 | } | |
0f2d19dd | 3875 | } |
f4c627b3 | 3876 | #undef FUNC_NAME |
0f2d19dd | 3877 | |
7351e207 MV |
3878 | #if ((defined (HAVE_ISINF) && defined (HAVE_ISNAN)) \ |
3879 | || (defined (HAVE_FINITE) && defined (HAVE_ISNAN))) | |
3880 | #define ALLOW_DIVIDE_BY_ZERO | |
3881 | /* #define ALLOW_DIVIDE_BY_EXACT_ZERO */ | |
3882 | #endif | |
0f2d19dd | 3883 | |
ba74ef4e MV |
3884 | /* The code below for complex division is adapted from the GNU |
3885 | libstdc++, which adapted it from f2c's libF77, and is subject to | |
3886 | this copyright: */ | |
3887 | ||
3888 | /**************************************************************** | |
3889 | Copyright 1990, 1991, 1992, 1993 by AT&T Bell Laboratories and Bellcore. | |
3890 | ||
3891 | Permission to use, copy, modify, and distribute this software | |
3892 | and its documentation for any purpose and without fee is hereby | |
3893 | granted, provided that the above copyright notice appear in all | |
3894 | copies and that both that the copyright notice and this | |
3895 | permission notice and warranty disclaimer appear in supporting | |
3896 | documentation, and that the names of AT&T Bell Laboratories or | |
3897 | Bellcore or any of their entities not be used in advertising or | |
3898 | publicity pertaining to distribution of the software without | |
3899 | specific, written prior permission. | |
3900 | ||
3901 | AT&T and Bellcore disclaim all warranties with regard to this | |
3902 | software, including all implied warranties of merchantability | |
3903 | and fitness. In no event shall AT&T or Bellcore be liable for | |
3904 | any special, indirect or consequential damages or any damages | |
3905 | whatsoever resulting from loss of use, data or profits, whether | |
3906 | in an action of contract, negligence or other tortious action, | |
3907 | arising out of or in connection with the use or performance of | |
3908 | this software. | |
3909 | ****************************************************************/ | |
3910 | ||
9de33deb | 3911 | SCM_GPROC1 (s_divide, "/", scm_tc7_asubr, scm_divide, g_divide); |
609c3d30 MG |
3912 | /* Divide the first argument by the product of the remaining |
3913 | arguments. If called with one argument @var{z1}, 1/@var{z1} is | |
3914 | returned. */ | |
c05e97b7 | 3915 | #define FUNC_NAME s_divide |
0f2d19dd | 3916 | SCM |
6e8d25a6 | 3917 | scm_divide (SCM x, SCM y) |
0f2d19dd | 3918 | { |
f8de44c1 DH |
3919 | double a; |
3920 | ||
3921 | if (SCM_UNBNDP (y)) { | |
3922 | if (SCM_UNBNDP (x)) { | |
c05e97b7 | 3923 | SCM_WTA_DISPATCH_0 (g_divide, s_divide); |
f8de44c1 | 3924 | } else if (SCM_INUMP (x)) { |
164826d3 DH |
3925 | long xx = SCM_INUM (x); |
3926 | if (xx == 1 || xx == -1) { | |
f8de44c1 | 3927 | return x; |
7351e207 | 3928 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
164826d3 DH |
3929 | } else if (xx == 0) { |
3930 | scm_num_overflow (s_divide); | |
7351e207 | 3931 | #endif |
f8de44c1 | 3932 | } else { |
164826d3 | 3933 | return scm_make_real (1.0 / (double) xx); |
f8de44c1 | 3934 | } |
f8de44c1 | 3935 | } else if (SCM_BIGP (x)) { |
1be6b49c | 3936 | return scm_make_real (1.0 / scm_i_big2dbl (x)); |
f8de44c1 | 3937 | } else if (SCM_REALP (x)) { |
5eec27e9 | 3938 | double xx = SCM_REAL_VALUE (x); |
7351e207 | 3939 | #ifndef ALLOW_DIVIDE_BY_ZERO |
5eec27e9 DH |
3940 | if (xx == 0.0) |
3941 | scm_num_overflow (s_divide); | |
3942 | else | |
7351e207 | 3943 | #endif |
5eec27e9 | 3944 | return scm_make_real (1.0 / xx); |
f8de44c1 DH |
3945 | } else if (SCM_COMPLEXP (x)) { |
3946 | double r = SCM_COMPLEX_REAL (x); | |
3947 | double i = SCM_COMPLEX_IMAG (x); | |
ba74ef4e MV |
3948 | if (r <= i) { |
3949 | double t = r / i; | |
3950 | double d = i * (1.0 + t * t); | |
3951 | return scm_make_complex (t / d, -1.0 / d); | |
3952 | } else { | |
3953 | double t = i / r; | |
3954 | double d = r * (1.0 + t * t); | |
3955 | return scm_make_complex (1.0 / d, -t / d); | |
3956 | } | |
f8de44c1 DH |
3957 | } else { |
3958 | SCM_WTA_DISPATCH_1 (g_divide, x, SCM_ARG1, s_divide); | |
3959 | } | |
3960 | } | |
3961 | ||
3962 | if (SCM_INUMP (x)) { | |
3963 | long xx = SCM_INUM (x); | |
3964 | if (SCM_INUMP (y)) { | |
3965 | long yy = SCM_INUM (y); | |
3966 | if (yy == 0) { | |
7351e207 | 3967 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
f4c627b3 | 3968 | scm_num_overflow (s_divide); |
7351e207 MV |
3969 | #else |
3970 | return scm_make_real ((double) xx / (double) yy); | |
3971 | #endif | |
f8de44c1 DH |
3972 | } else if (xx % yy != 0) { |
3973 | return scm_make_real ((double) xx / (double) yy); | |
3974 | } else { | |
3975 | long z = xx / yy; | |
3976 | if (SCM_FIXABLE (z)) { | |
3977 | return SCM_MAKINUM (z); | |
3978 | } else { | |
f872b822 | 3979 | #ifdef SCM_BIGDIG |
1be6b49c | 3980 | return scm_i_long2big (z); |
f872b822 | 3981 | #else |
f8de44c1 | 3982 | return scm_make_real ((double) xx / (double) yy); |
f872b822 | 3983 | #endif |
f872b822 | 3984 | } |
f8de44c1 | 3985 | } |
f8de44c1 | 3986 | } else if (SCM_BIGP (y)) { |
1be6b49c | 3987 | return scm_make_real ((double) xx / scm_i_big2dbl (y)); |
f8de44c1 | 3988 | } else if (SCM_REALP (y)) { |
5eec27e9 | 3989 | double yy = SCM_REAL_VALUE (y); |
7351e207 | 3990 | #ifndef ALLOW_DIVIDE_BY_ZERO |
5eec27e9 DH |
3991 | if (yy == 0.0) |
3992 | scm_num_overflow (s_divide); | |
3993 | else | |
7351e207 | 3994 | #endif |
5eec27e9 | 3995 | return scm_make_real ((double) xx / yy); |
f8de44c1 DH |
3996 | } else if (SCM_COMPLEXP (y)) { |
3997 | a = xx; | |
3998 | complex_div: /* y _must_ be a complex number */ | |
3999 | { | |
4000 | double r = SCM_COMPLEX_REAL (y); | |
4001 | double i = SCM_COMPLEX_IMAG (y); | |
ba74ef4e MV |
4002 | if (r <= i) { |
4003 | double t = r / i; | |
4004 | double d = i * (1.0 + t * t); | |
4005 | return scm_make_complex ((a * t) / d, -a / d); | |
4006 | } else { | |
4007 | double t = i / r; | |
4008 | double d = r * (1.0 + t * t); | |
4009 | return scm_make_complex (a / d, -(a * t) / d); | |
4010 | } | |
f8de44c1 DH |
4011 | } |
4012 | } else { | |
4013 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
4014 | } | |
f8de44c1 DH |
4015 | } else if (SCM_BIGP (x)) { |
4016 | if (SCM_INUMP (y)) { | |
4017 | long int yy = SCM_INUM (y); | |
4018 | if (yy == 0) { | |
7351e207 | 4019 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
f8de44c1 | 4020 | scm_num_overflow (s_divide); |
7351e207 MV |
4021 | #else |
4022 | if (scm_bigcomp (x, scm_i_int2big (0)) == 0) | |
4023 | return scm_nan (); | |
4024 | else | |
4025 | return scm_inf (); | |
4026 | #endif | |
f8de44c1 DH |
4027 | } else if (yy == 1) { |
4028 | return x; | |
4029 | } else { | |
4030 | long z = yy < 0 ? -yy : yy; | |
4031 | if (z < SCM_BIGRAD) { | |
1be6b49c | 4032 | SCM w = scm_i_copybig (x, SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0)); |
f8de44c1 DH |
4033 | return scm_divbigdig (SCM_BDIGITS (w), SCM_NUMDIGS (w), |
4034 | (SCM_BIGDIG) z) | |
1be6b49c ML |
4035 | ? scm_make_real (scm_i_big2dbl (x) / (double) yy) |
4036 | : scm_i_normbig (w); | |
f8de44c1 DH |
4037 | } else { |
4038 | SCM w; | |
4039 | #ifndef SCM_DIGSTOOBIG | |
4040 | z = scm_pseudolong (z); | |
4041 | w = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
4042 | (SCM_BIGDIG *) & z, SCM_DIGSPERLONG, | |
4043 | SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0), 3); | |
f872b822 | 4044 | #else |
f8de44c1 DH |
4045 | SCM_BIGDIG zdigs[SCM_DIGSPERLONG]; |
4046 | scm_longdigs (z, zdigs); | |
4047 | w = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
4048 | zdigs, SCM_DIGSPERLONG, | |
4049 | SCM_BIGSIGN (x) ? (yy > 0) : (yy < 0), 3); | |
f872b822 | 4050 | #endif |
f4c627b3 DH |
4051 | return (!SCM_UNBNDP (w)) |
4052 | ? w | |
1be6b49c | 4053 | : scm_make_real (scm_i_big2dbl (x) / (double) yy); |
f872b822 | 4054 | } |
f8de44c1 DH |
4055 | } |
4056 | } else if (SCM_BIGP (y)) { | |
4057 | SCM w = scm_divbigbig (SCM_BDIGITS (x), SCM_NUMDIGS (x), | |
4058 | SCM_BDIGITS (y), SCM_NUMDIGS (y), | |
4059 | SCM_BIGSIGN (x) ^ SCM_BIGSIGN (y), 3); | |
f4c627b3 DH |
4060 | return (!SCM_UNBNDP (w)) |
4061 | ? w | |
1be6b49c | 4062 | : scm_make_real (scm_i_big2dbl (x) / scm_i_big2dbl (y)); |
f8de44c1 | 4063 | } else if (SCM_REALP (y)) { |
5eec27e9 | 4064 | double yy = SCM_REAL_VALUE (y); |
7351e207 | 4065 | #ifndef ALLOW_DIVIDE_BY_ZERO |
5eec27e9 DH |
4066 | if (yy == 0.0) |
4067 | scm_num_overflow (s_divide); | |
4068 | else | |
7351e207 | 4069 | #endif |
5eec27e9 | 4070 | return scm_make_real (scm_i_big2dbl (x) / yy); |
f8de44c1 | 4071 | } else if (SCM_COMPLEXP (y)) { |
1be6b49c | 4072 | a = scm_i_big2dbl (x); |
f8de44c1 DH |
4073 | goto complex_div; |
4074 | } else { | |
4075 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4076 | } |
f8de44c1 DH |
4077 | } else if (SCM_REALP (x)) { |
4078 | double rx = SCM_REAL_VALUE (x); | |
4079 | if (SCM_INUMP (y)) { | |
5eec27e9 | 4080 | long int yy = SCM_INUM (y); |
7351e207 MV |
4081 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
4082 | if (yy == 0) | |
5eec27e9 | 4083 | scm_num_overflow (s_divide); |
7351e207 MV |
4084 | else |
4085 | #endif | |
5eec27e9 | 4086 | return scm_make_real (rx / (double) yy); |
f8de44c1 | 4087 | } else if (SCM_BIGP (y)) { |
1be6b49c | 4088 | return scm_make_real (rx / scm_i_big2dbl (y)); |
f8de44c1 | 4089 | } else if (SCM_REALP (y)) { |
5eec27e9 | 4090 | double yy = SCM_REAL_VALUE (y); |
7351e207 | 4091 | #ifndef ALLOW_DIVIDE_BY_ZERO |
5eec27e9 DH |
4092 | if (yy == 0.0) |
4093 | scm_num_overflow (s_divide); | |
4094 | else | |
7351e207 | 4095 | #endif |
5eec27e9 | 4096 | return scm_make_real (rx / yy); |
f8de44c1 DH |
4097 | } else if (SCM_COMPLEXP (y)) { |
4098 | a = rx; | |
4099 | goto complex_div; | |
4100 | } else { | |
4101 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
f872b822 | 4102 | } |
f8de44c1 DH |
4103 | } else if (SCM_COMPLEXP (x)) { |
4104 | double rx = SCM_COMPLEX_REAL (x); | |
4105 | double ix = SCM_COMPLEX_IMAG (x); | |
4106 | if (SCM_INUMP (y)) { | |
5eec27e9 | 4107 | long int yy = SCM_INUM (y); |
7351e207 MV |
4108 | #ifndef ALLOW_DIVIDE_BY_EXACT_ZERO |
4109 | if (yy == 0) | |
5eec27e9 | 4110 | scm_num_overflow (s_divide); |
7351e207 MV |
4111 | else |
4112 | #endif | |
4113 | { | |
5eec27e9 DH |
4114 | double d = yy; |
4115 | return scm_make_complex (rx / d, ix / d); | |
4116 | } | |
f8de44c1 | 4117 | } else if (SCM_BIGP (y)) { |
1be6b49c | 4118 | double d = scm_i_big2dbl (y); |
f8de44c1 | 4119 | return scm_make_complex (rx / d, ix / d); |
f8de44c1 | 4120 | } else if (SCM_REALP (y)) { |
5eec27e9 | 4121 | double yy = SCM_REAL_VALUE (y); |
7351e207 | 4122 | #ifndef ALLOW_DIVIDE_BY_ZERO |
5eec27e9 DH |
4123 | if (yy == 0.0) |
4124 | scm_num_overflow (s_divide); | |
4125 | else | |
7351e207 | 4126 | #endif |
5eec27e9 | 4127 | return scm_make_complex (rx / yy, ix / yy); |
f8de44c1 DH |
4128 | } else if (SCM_COMPLEXP (y)) { |
4129 | double ry = SCM_COMPLEX_REAL (y); | |
4130 | double iy = SCM_COMPLEX_IMAG (y); | |
ba74ef4e MV |
4131 | if (ry <= iy) { |
4132 | double t = ry / iy; | |
4133 | double d = iy * (1.0 + t * t); | |
4134 | return scm_make_complex ((rx * t + ix) / d, (ix * t - rx) / d); | |
4135 | } else { | |
4136 | double t = iy / ry; | |
4137 | double d = ry * (1.0 + t * t); | |
4138 | return scm_make_complex ((rx + ix * t) / d, (ix - rx * t) / d); | |
4139 | } | |
f8de44c1 DH |
4140 | } else { |
4141 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARGn, s_divide); | |
4142 | } | |
4143 | } else { | |
4144 | SCM_WTA_DISPATCH_2 (g_divide, x, y, SCM_ARG1, s_divide); | |
0f2d19dd JB |
4145 | } |
4146 | } | |
c05e97b7 | 4147 | #undef FUNC_NAME |
0f2d19dd | 4148 | |
9de33deb | 4149 | SCM_GPROC1 (s_asinh, "$asinh", scm_tc7_cxr, (SCM (*)()) scm_asinh, g_asinh); |
942e5b91 MG |
4150 | /* "Return the inverse hyperbolic sine of @var{x}." |
4151 | */ | |
0f2d19dd | 4152 | double |
6e8d25a6 | 4153 | scm_asinh (double x) |
0f2d19dd | 4154 | { |
f872b822 | 4155 | return log (x + sqrt (x * x + 1)); |
0f2d19dd JB |
4156 | } |
4157 | ||
4158 | ||
4159 | ||
4160 | ||
9de33deb | 4161 | SCM_GPROC1 (s_acosh, "$acosh", scm_tc7_cxr, (SCM (*)()) scm_acosh, g_acosh); |
942e5b91 MG |
4162 | /* "Return the inverse hyperbolic cosine of @var{x}." |
4163 | */ | |
0f2d19dd | 4164 | double |
6e8d25a6 | 4165 | scm_acosh (double x) |
0f2d19dd | 4166 | { |
f872b822 | 4167 | return log (x + sqrt (x * x - 1)); |
0f2d19dd JB |
4168 | } |
4169 | ||
4170 | ||
4171 | ||
4172 | ||
9de33deb | 4173 | SCM_GPROC1 (s_atanh, "$atanh", scm_tc7_cxr, (SCM (*)()) scm_atanh, g_atanh); |
942e5b91 MG |
4174 | /* "Return the inverse hyperbolic tangent of @var{x}." |
4175 | */ | |
0f2d19dd | 4176 | double |
6e8d25a6 | 4177 | scm_atanh (double x) |
0f2d19dd | 4178 | { |
f872b822 | 4179 | return 0.5 * log ((1 + x) / (1 - x)); |
0f2d19dd JB |
4180 | } |
4181 | ||
4182 | ||
4183 | ||
4184 | ||
9de33deb | 4185 | SCM_GPROC1 (s_truncate, "truncate", scm_tc7_cxr, (SCM (*)()) scm_truncate, g_truncate); |
942e5b91 MG |
4186 | /* "Round the inexact number @var{x} towards zero." |
4187 | */ | |
0f2d19dd | 4188 | double |
6e8d25a6 | 4189 | scm_truncate (double x) |
0f2d19dd | 4190 | { |
f872b822 MD |
4191 | if (x < 0.0) |
4192 | return -floor (-x); | |
4193 | return floor (x); | |
0f2d19dd JB |
4194 | } |
4195 | ||
4196 | ||
4197 | ||
9de33deb | 4198 | SCM_GPROC1 (s_round, "round", scm_tc7_cxr, (SCM (*)()) scm_round, g_round); |
942e5b91 MG |
4199 | /* "Round the inexact number @var{x}. If @var{x} is halfway between two\n" |
4200 | * "numbers, round towards even." | |
4201 | */ | |
0f2d19dd | 4202 | double |
6e8d25a6 | 4203 | scm_round (double x) |
0f2d19dd JB |
4204 | { |
4205 | double plus_half = x + 0.5; | |
f872b822 | 4206 | double result = floor (plus_half); |
0f2d19dd | 4207 | /* Adjust so that the scm_round is towards even. */ |
f872b822 | 4208 | return (plus_half == result && plus_half / 2 != floor (plus_half / 2)) |
0f2d19dd JB |
4209 | ? result - 1 : result; |
4210 | } | |
4211 | ||
4212 | ||
9de33deb | 4213 | SCM_GPROC1 (s_i_floor, "floor", scm_tc7_cxr, (SCM (*)()) floor, g_i_floor); |
942e5b91 MG |
4214 | /* "Round the number @var{x} towards minus infinity." |
4215 | */ | |
9de33deb | 4216 | SCM_GPROC1 (s_i_ceil, "ceiling", scm_tc7_cxr, (SCM (*)()) ceil, g_i_ceil); |
942e5b91 MG |
4217 | /* "Round the number @var{x} towards infinity." |
4218 | */ | |
9de33deb | 4219 | SCM_GPROC1 (s_i_sqrt, "$sqrt", scm_tc7_cxr, (SCM (*)()) sqrt, g_i_sqrt); |
942e5b91 MG |
4220 | /* "Return the square root of the real number @var{x}." |
4221 | */ | |
9de33deb | 4222 | SCM_GPROC1 (s_i_abs, "$abs", scm_tc7_cxr, (SCM (*)()) fabs, g_i_abs); |
942e5b91 MG |
4223 | /* "Return the absolute value of the real number @var{x}." |
4224 | */ | |
9de33deb | 4225 | SCM_GPROC1 (s_i_exp, "$exp", scm_tc7_cxr, (SCM (*)()) exp, g_i_exp); |
942e5b91 MG |
4226 | /* "Return the @var{x}th power of e." |
4227 | */ | |
9de33deb | 4228 | SCM_GPROC1 (s_i_log, "$log", scm_tc7_cxr, (SCM (*)()) log, g_i_log); |
b3fcac34 | 4229 | /* "Return the natural logarithm of the real number @var{x}." |
942e5b91 | 4230 | */ |
9de33deb | 4231 | SCM_GPROC1 (s_i_sin, "$sin", scm_tc7_cxr, (SCM (*)()) sin, g_i_sin); |
942e5b91 MG |
4232 | /* "Return the sine of the real number @var{x}." |
4233 | */ | |
9de33deb | 4234 | SCM_GPROC1 (s_i_cos, "$cos", scm_tc7_cxr, (SCM (*)()) cos, g_i_cos); |
942e5b91 MG |
4235 | /* "Return the cosine of the real number @var{x}." |
4236 | */ | |
9de33deb | 4237 | SCM_GPROC1 (s_i_tan, "$tan", scm_tc7_cxr, (SCM (*)()) tan, g_i_tan); |
942e5b91 MG |
4238 | /* "Return the tangent of the real number @var{x}." |
4239 | */ | |
9de33deb | 4240 | SCM_GPROC1 (s_i_asin, "$asin", scm_tc7_cxr, (SCM (*)()) asin, g_i_asin); |
942e5b91 MG |
4241 | /* "Return the arc sine of the real number @var{x}." |
4242 | */ | |
9de33deb | 4243 | SCM_GPROC1 (s_i_acos, "$acos", scm_tc7_cxr, (SCM (*)()) acos, g_i_acos); |
942e5b91 MG |
4244 | /* "Return the arc cosine of the real number @var{x}." |
4245 | */ | |
9de33deb | 4246 | SCM_GPROC1 (s_i_atan, "$atan", scm_tc7_cxr, (SCM (*)()) atan, g_i_atan); |
942e5b91 MG |
4247 | /* "Return the arc tangent of the real number @var{x}." |
4248 | */ | |
9de33deb | 4249 | SCM_GPROC1 (s_i_sinh, "$sinh", scm_tc7_cxr, (SCM (*)()) sinh, g_i_sinh); |
942e5b91 MG |
4250 | /* "Return the hyperbolic sine of the real number @var{x}." |
4251 | */ | |
9de33deb | 4252 | SCM_GPROC1 (s_i_cosh, "$cosh", scm_tc7_cxr, (SCM (*)()) cosh, g_i_cosh); |
942e5b91 MG |
4253 | /* "Return the hyperbolic cosine of the real number @var{x}." |
4254 | */ | |
9de33deb | 4255 | SCM_GPROC1 (s_i_tanh, "$tanh", scm_tc7_cxr, (SCM (*)()) tanh, g_i_tanh); |
942e5b91 MG |
4256 | /* "Return the hyperbolic tangent of the real number @var{x}." |
4257 | */ | |
f872b822 MD |
4258 | |
4259 | struct dpair | |
4260 | { | |
4261 | double x, y; | |
4262 | }; | |
4263 | ||
27c37006 NJ |
4264 | static void scm_two_doubles (SCM x, |
4265 | SCM y, | |
3eeba8d4 JB |
4266 | const char *sstring, |
4267 | struct dpair * xy); | |
f872b822 MD |
4268 | |
4269 | static void | |
27c37006 NJ |
4270 | scm_two_doubles (SCM x, SCM y, const char *sstring, struct dpair *xy) |
4271 | { | |
4272 | if (SCM_INUMP (x)) { | |
4273 | xy->x = SCM_INUM (x); | |
4274 | } else if (SCM_BIGP (x)) { | |
1be6b49c | 4275 | xy->x = scm_i_big2dbl (x); |
27c37006 NJ |
4276 | } else if (SCM_REALP (x)) { |
4277 | xy->x = SCM_REAL_VALUE (x); | |
98cb6e75 | 4278 | } else { |
27c37006 | 4279 | scm_wrong_type_arg (sstring, SCM_ARG1, x); |
98cb6e75 DH |
4280 | } |
4281 | ||
27c37006 NJ |
4282 | if (SCM_INUMP (y)) { |
4283 | xy->y = SCM_INUM (y); | |
4284 | } else if (SCM_BIGP (y)) { | |
1be6b49c | 4285 | xy->y = scm_i_big2dbl (y); |
27c37006 NJ |
4286 | } else if (SCM_REALP (y)) { |
4287 | xy->y = SCM_REAL_VALUE (y); | |
98cb6e75 | 4288 | } else { |
27c37006 | 4289 | scm_wrong_type_arg (sstring, SCM_ARG2, y); |
98cb6e75 | 4290 | } |
0f2d19dd JB |
4291 | } |
4292 | ||
4293 | ||
a1ec6916 | 4294 | SCM_DEFINE (scm_sys_expt, "$expt", 2, 0, 0, |
27c37006 NJ |
4295 | (SCM x, SCM y), |
4296 | "Return @var{x} raised to the power of @var{y}. This\n" | |
0137a31b | 4297 | "procedure does not accept complex arguments.") |
1bbd0b84 | 4298 | #define FUNC_NAME s_scm_sys_expt |
0f2d19dd JB |
4299 | { |
4300 | struct dpair xy; | |
27c37006 | 4301 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
f8de44c1 | 4302 | return scm_make_real (pow (xy.x, xy.y)); |
0f2d19dd | 4303 | } |
1bbd0b84 | 4304 | #undef FUNC_NAME |
0f2d19dd JB |
4305 | |
4306 | ||
a1ec6916 | 4307 | SCM_DEFINE (scm_sys_atan2, "$atan2", 2, 0, 0, |
27c37006 NJ |
4308 | (SCM x, SCM y), |
4309 | "Return the arc tangent of the two arguments @var{x} and\n" | |
4310 | "@var{y}. This is similar to calculating the arc tangent of\n" | |
4311 | "@var{x} / @var{y}, except that the signs of both arguments\n" | |
0137a31b MG |
4312 | "are used to determine the quadrant of the result. This\n" |
4313 | "procedure does not accept complex arguments.") | |
1bbd0b84 | 4314 | #define FUNC_NAME s_scm_sys_atan2 |
0f2d19dd JB |
4315 | { |
4316 | struct dpair xy; | |
27c37006 | 4317 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
f8de44c1 | 4318 | return scm_make_real (atan2 (xy.x, xy.y)); |
0f2d19dd | 4319 | } |
1bbd0b84 | 4320 | #undef FUNC_NAME |
0f2d19dd JB |
4321 | |
4322 | ||
a1ec6916 | 4323 | SCM_DEFINE (scm_make_rectangular, "make-rectangular", 2, 0, 0, |
bb628794 | 4324 | (SCM real, SCM imaginary), |
942e5b91 MG |
4325 | "Return a complex number constructed of the given @var{real} and\n" |
4326 | "@var{imaginary} parts.") | |
1bbd0b84 | 4327 | #define FUNC_NAME s_scm_make_rectangular |
0f2d19dd JB |
4328 | { |
4329 | struct dpair xy; | |
bb628794 | 4330 | scm_two_doubles (real, imaginary, FUNC_NAME, &xy); |
f8de44c1 | 4331 | return scm_make_complex (xy.x, xy.y); |
0f2d19dd | 4332 | } |
1bbd0b84 | 4333 | #undef FUNC_NAME |
0f2d19dd JB |
4334 | |
4335 | ||
4336 | ||
a1ec6916 | 4337 | SCM_DEFINE (scm_make_polar, "make-polar", 2, 0, 0, |
27c37006 | 4338 | (SCM x, SCM y), |
942e5b91 | 4339 | "Return the complex number @var{x} * e^(i * @var{y}).") |
1bbd0b84 | 4340 | #define FUNC_NAME s_scm_make_polar |
0f2d19dd JB |
4341 | { |
4342 | struct dpair xy; | |
27c37006 | 4343 | scm_two_doubles (x, y, FUNC_NAME, &xy); |
f8de44c1 | 4344 | return scm_make_complex (xy.x * cos (xy.y), xy.x * sin (xy.y)); |
0f2d19dd | 4345 | } |
1bbd0b84 | 4346 | #undef FUNC_NAME |
0f2d19dd JB |
4347 | |
4348 | ||
152f82bf | 4349 | SCM_GPROC (s_real_part, "real-part", 1, 0, 0, scm_real_part, g_real_part); |
942e5b91 MG |
4350 | /* "Return the real part of the number @var{z}." |
4351 | */ | |
0f2d19dd | 4352 | SCM |
6e8d25a6 | 4353 | scm_real_part (SCM z) |
0f2d19dd | 4354 | { |
c2ff8ab0 DH |
4355 | if (SCM_INUMP (z)) { |
4356 | return z; | |
4357 | } else if (SCM_BIGP (z)) { | |
4358 | return z; | |
4359 | } else if (SCM_REALP (z)) { | |
4360 | return z; | |
4361 | } else if (SCM_COMPLEXP (z)) { | |
4362 | return scm_make_real (SCM_COMPLEX_REAL (z)); | |
4363 | } else { | |
4364 | SCM_WTA_DISPATCH_1 (g_real_part, z, SCM_ARG1, s_real_part); | |
4365 | } | |
0f2d19dd JB |
4366 | } |
4367 | ||
4368 | ||
152f82bf | 4369 | SCM_GPROC (s_imag_part, "imag-part", 1, 0, 0, scm_imag_part, g_imag_part); |
942e5b91 MG |
4370 | /* "Return the imaginary part of the number @var{z}." |
4371 | */ | |
0f2d19dd | 4372 | SCM |
6e8d25a6 | 4373 | scm_imag_part (SCM z) |
0f2d19dd | 4374 | { |
c2ff8ab0 | 4375 | if (SCM_INUMP (z)) { |
f872b822 | 4376 | return SCM_INUM0; |
c2ff8ab0 | 4377 | } else if (SCM_BIGP (z)) { |
f872b822 | 4378 | return SCM_INUM0; |
c2ff8ab0 DH |
4379 | } else if (SCM_REALP (z)) { |
4380 | return scm_flo0; | |
4381 | } else if (SCM_COMPLEXP (z)) { | |
4382 | return scm_make_real (SCM_COMPLEX_IMAG (z)); | |
4383 | } else { | |
4384 | SCM_WTA_DISPATCH_1 (g_imag_part, z, SCM_ARG1, s_imag_part); | |
4385 | } | |
0f2d19dd JB |
4386 | } |
4387 | ||
4388 | ||
9de33deb | 4389 | SCM_GPROC (s_magnitude, "magnitude", 1, 0, 0, scm_magnitude, g_magnitude); |
942e5b91 MG |
4390 | /* "Return the magnitude of the number @var{z}. This is the same as\n" |
4391 | * "@code{abs} for real arguments, but also allows complex numbers." | |
4392 | */ | |
0f2d19dd | 4393 | SCM |
6e8d25a6 | 4394 | scm_magnitude (SCM z) |
0f2d19dd | 4395 | { |
c2ff8ab0 | 4396 | if (SCM_INUMP (z)) { |
5986c47d DH |
4397 | long int zz = SCM_INUM (z); |
4398 | if (zz >= 0) { | |
4399 | return z; | |
4400 | } else if (SCM_POSFIXABLE (-zz)) { | |
4401 | return SCM_MAKINUM (-zz); | |
4402 | } else { | |
4403 | #ifdef SCM_BIGDIG | |
1be6b49c | 4404 | return scm_i_long2big (-zz); |
5986c47d DH |
4405 | #else |
4406 | scm_num_overflow (s_magnitude); | |
4407 | #endif | |
4408 | } | |
c2ff8ab0 | 4409 | } else if (SCM_BIGP (z)) { |
5986c47d DH |
4410 | if (!SCM_BIGSIGN (z)) { |
4411 | return z; | |
4412 | } else { | |
1be6b49c | 4413 | return scm_i_copybig (z, 0); |
5986c47d | 4414 | } |
c2ff8ab0 DH |
4415 | } else if (SCM_REALP (z)) { |
4416 | return scm_make_real (fabs (SCM_REAL_VALUE (z))); | |
4417 | } else if (SCM_COMPLEXP (z)) { | |
4418 | double r = SCM_COMPLEX_REAL (z); | |
4419 | double i = SCM_COMPLEX_IMAG (z); | |
4420 | return scm_make_real (sqrt (i * i + r * r)); | |
4421 | } else { | |
4422 | SCM_WTA_DISPATCH_1 (g_magnitude, z, SCM_ARG1, s_magnitude); | |
4423 | } | |
0f2d19dd JB |
4424 | } |
4425 | ||
4426 | ||
9de33deb | 4427 | SCM_GPROC (s_angle, "angle", 1, 0, 0, scm_angle, g_angle); |
942e5b91 MG |
4428 | /* "Return the angle of the complex number @var{z}." |
4429 | */ | |
0f2d19dd | 4430 | SCM |
6e8d25a6 | 4431 | scm_angle (SCM z) |
0f2d19dd | 4432 | { |
f4c627b3 DH |
4433 | if (SCM_INUMP (z)) { |
4434 | if (SCM_INUM (z) >= 0) { | |
4435 | return scm_make_real (atan2 (0.0, 1.0)); | |
4436 | } else { | |
4437 | return scm_make_real (atan2 (0.0, -1.0)); | |
f872b822 | 4438 | } |
f4c627b3 DH |
4439 | } else if (SCM_BIGP (z)) { |
4440 | if (SCM_BIGSIGN (z)) { | |
4441 | return scm_make_real (atan2 (0.0, -1.0)); | |
4442 | } else { | |
4443 | return scm_make_real (atan2 (0.0, 1.0)); | |
0f2d19dd | 4444 | } |
f4c627b3 DH |
4445 | } else if (SCM_REALP (z)) { |
4446 | return scm_make_real (atan2 (0.0, SCM_REAL_VALUE (z))); | |
4447 | } else if (SCM_COMPLEXP (z)) { | |
4448 | return scm_make_real (atan2 (SCM_COMPLEX_IMAG (z), SCM_COMPLEX_REAL (z))); | |
4449 | } else { | |
4450 | SCM_WTA_DISPATCH_1 (g_angle, z, SCM_ARG1, s_angle); | |
4451 | } | |
0f2d19dd JB |
4452 | } |
4453 | ||
4454 | ||
3c9a524f DH |
4455 | SCM_GPROC (s_exact_to_inexact, "exact->inexact", 1, 0, 0, scm_exact_to_inexact, g_exact_to_inexact); |
4456 | /* Convert the number @var{x} to its inexact representation.\n" | |
4457 | */ | |
4458 | SCM | |
4459 | scm_exact_to_inexact (SCM z) | |
4460 | { | |
4461 | if (SCM_INUMP (z)) | |
4462 | return scm_make_real ((double) SCM_INUM (z)); | |
4463 | else if (SCM_BIGP (z)) | |
4464 | return scm_make_real (scm_i_big2dbl (z)); | |
4465 | else if (SCM_INEXACTP (z)) | |
4466 | return z; | |
4467 | else | |
4468 | SCM_WTA_DISPATCH_1 (g_exact_to_inexact, z, 1, s_exact_to_inexact); | |
4469 | } | |
4470 | ||
4471 | ||
a1ec6916 | 4472 | SCM_DEFINE (scm_inexact_to_exact, "inexact->exact", 1, 0, 0, |
1bbd0b84 | 4473 | (SCM z), |
1e6808ea | 4474 | "Return an exact number that is numerically closest to @var{z}.") |
1bbd0b84 | 4475 | #define FUNC_NAME s_scm_inexact_to_exact |
0f2d19dd | 4476 | { |
c2ff8ab0 | 4477 | if (SCM_INUMP (z)) { |
f872b822 | 4478 | return z; |
c2ff8ab0 | 4479 | } else if (SCM_BIGP (z)) { |
f872b822 | 4480 | return z; |
c2ff8ab0 DH |
4481 | } else if (SCM_REALP (z)) { |
4482 | double u = floor (SCM_REAL_VALUE (z) + 0.5); | |
4483 | long lu = (long) u; | |
4484 | if (SCM_FIXABLE (lu)) { | |
4485 | return SCM_MAKINUM (lu); | |
f872b822 | 4486 | #ifdef SCM_BIGDIG |
fc194577 | 4487 | } else if (isfinite (u) && !xisnan (u)) { |
1be6b49c | 4488 | return scm_i_dbl2big (u); |
f872b822 | 4489 | #endif |
c2ff8ab0 DH |
4490 | } else { |
4491 | scm_num_overflow (s_scm_inexact_to_exact); | |
4492 | } | |
4493 | } else { | |
4494 | SCM_WRONG_TYPE_ARG (1, z); | |
4495 | } | |
0f2d19dd | 4496 | } |
1bbd0b84 | 4497 | #undef FUNC_NAME |
0f2d19dd JB |
4498 | |
4499 | ||
0f2d19dd | 4500 | #ifdef SCM_BIGDIG |
0f2d19dd | 4501 | /* d must be integer */ |
1cc91f1b | 4502 | |
0f2d19dd | 4503 | SCM |
1be6b49c | 4504 | scm_i_dbl2big (double d) |
0f2d19dd | 4505 | { |
1be6b49c | 4506 | size_t i = 0; |
0f2d19dd JB |
4507 | long c; |
4508 | SCM_BIGDIG *digits; | |
4509 | SCM ans; | |
f872b822 MD |
4510 | double u = (d < 0) ? -d : d; |
4511 | while (0 != floor (u)) | |
4512 | { | |
4513 | u /= SCM_BIGRAD; | |
4514 | i++; | |
4515 | } | |
1be6b49c | 4516 | ans = scm_i_mkbig (i, d < 0); |
f872b822 MD |
4517 | digits = SCM_BDIGITS (ans); |
4518 | while (i--) | |
4519 | { | |
4520 | u *= SCM_BIGRAD; | |
4521 | c = floor (u); | |
4522 | u -= c; | |
4523 | digits[i] = c; | |
4524 | } | |
cf7c17e9 | 4525 | #ifndef SCM_RECKLESS |
e1724d20 | 4526 | if (u != 0) |
52859adf | 4527 | scm_num_overflow ("dbl2big"); |
e1724d20 | 4528 | #endif |
0f2d19dd JB |
4529 | return ans; |
4530 | } | |
4531 | ||
0f2d19dd | 4532 | double |
1be6b49c | 4533 | scm_i_big2dbl (SCM b) |
0f2d19dd JB |
4534 | { |
4535 | double ans = 0.0; | |
1be6b49c | 4536 | size_t i = SCM_NUMDIGS (b); |
f872b822 MD |
4537 | SCM_BIGDIG *digits = SCM_BDIGITS (b); |
4538 | while (i--) | |
4539 | ans = digits[i] + SCM_BIGRAD * ans; | |
f3ae5d60 MD |
4540 | if (SCM_BIGSIGN (b)) |
4541 | return - ans; | |
0f2d19dd JB |
4542 | return ans; |
4543 | } | |
1cc91f1b | 4544 | |
f872b822 | 4545 | #endif |
0f2d19dd | 4546 | |
5c11cc9d | 4547 | #ifdef HAVE_LONG_LONGS |
1be6b49c ML |
4548 | # ifndef LLONG_MAX |
4549 | # define ULLONG_MAX ((unsigned long long) (-1)) | |
4550 | # define LLONG_MAX ((long long) (ULLONG_MAX >> 1)) | |
4551 | # define LLONG_MIN (~LLONG_MAX) | |
4552 | # endif | |
f872b822 | 4553 | #endif |
0f2d19dd | 4554 | |
3d2e8ceb MV |
4555 | /* Parameters for creating integer conversion routines. |
4556 | ||
4557 | Define the following preprocessor macros before including | |
4558 | "libguile/num2integral.i.c": | |
4559 | ||
4560 | NUM2INTEGRAL - the name of the function for converting from a | |
4561 | Scheme object to the integral type. This function | |
4562 | will be defined when including "num2integral.i.c". | |
4563 | ||
4564 | INTEGRAL2NUM - the name of the function for converting from the | |
4565 | integral type to a Scheme object. This function | |
4566 | will be defined. | |
4567 | ||
4568 | INTEGRAL2BIG - the name of an internal function that createas a | |
4569 | bignum from the integral type. This function will | |
4570 | be defined. The name should start with "scm_i_". | |
4571 | ||
4572 | ITYPE - the name of the integral type. | |
4573 | ||
4574 | UNSIGNED - Define this when ITYPE is an unsigned type. Do not | |
4575 | define it otherwise. | |
4576 | ||
4577 | UNSIGNED_ITYPE | |
4578 | - the name of the the unsigned variant of the | |
4579 | integral type. If you don't define this, it defaults | |
4580 | to "unsigned ITYPE" for signed types and simply "ITYPE" | |
4581 | for unsigned ones. | |
4582 | ||
4583 | SIZEOF_ITYPE - an expression giving the size of the integral type in | |
4584 | bytes. This expression must be computable by the | |
4585 | preprocessor. If you don't know a value for this, | |
4586 | don't define it. The purpose of this parameter is | |
4587 | mainly to suppress some warnings. The generated | |
4588 | code will work correctly without it. | |
4589 | */ | |
4590 | ||
1be6b49c ML |
4591 | #define NUM2INTEGRAL scm_num2short |
4592 | #define INTEGRAL2NUM scm_short2num | |
4593 | #define INTEGRAL2BIG scm_i_short2big | |
4594 | #define ITYPE short | |
3d2e8ceb | 4595 | #define SIZEOF_ITYPE SIZEOF_SHORT |
1be6b49c ML |
4596 | #include "libguile/num2integral.i.c" |
4597 | ||
4598 | #define NUM2INTEGRAL scm_num2ushort | |
4599 | #define INTEGRAL2NUM scm_ushort2num | |
4600 | #define INTEGRAL2BIG scm_i_ushort2big | |
4601 | #define UNSIGNED | |
4602 | #define ITYPE unsigned short | |
3d2e8ceb | 4603 | #define SIZEOF_ITYPE SIZEOF_SHORT |
1be6b49c ML |
4604 | #include "libguile/num2integral.i.c" |
4605 | ||
4606 | #define NUM2INTEGRAL scm_num2int | |
4607 | #define INTEGRAL2NUM scm_int2num | |
4608 | #define INTEGRAL2BIG scm_i_int2big | |
4609 | #define ITYPE int | |
3d2e8ceb | 4610 | #define SIZEOF_ITYPE SIZEOF_INT |
1be6b49c ML |
4611 | #include "libguile/num2integral.i.c" |
4612 | ||
4613 | #define NUM2INTEGRAL scm_num2uint | |
4614 | #define INTEGRAL2NUM scm_uint2num | |
4615 | #define INTEGRAL2BIG scm_i_uint2big | |
4616 | #define UNSIGNED | |
4617 | #define ITYPE unsigned int | |
3d2e8ceb | 4618 | #define SIZEOF_ITYPE SIZEOF_INT |
1be6b49c ML |
4619 | #include "libguile/num2integral.i.c" |
4620 | ||
4621 | #define NUM2INTEGRAL scm_num2long | |
4622 | #define INTEGRAL2NUM scm_long2num | |
4623 | #define INTEGRAL2BIG scm_i_long2big | |
4624 | #define ITYPE long | |
3d2e8ceb | 4625 | #define SIZEOF_ITYPE SIZEOF_LONG |
1be6b49c ML |
4626 | #include "libguile/num2integral.i.c" |
4627 | ||
4628 | #define NUM2INTEGRAL scm_num2ulong | |
4629 | #define INTEGRAL2NUM scm_ulong2num | |
4630 | #define INTEGRAL2BIG scm_i_ulong2big | |
4631 | #define UNSIGNED | |
4632 | #define ITYPE unsigned long | |
3d2e8ceb | 4633 | #define SIZEOF_ITYPE SIZEOF_LONG |
1be6b49c ML |
4634 | #include "libguile/num2integral.i.c" |
4635 | ||
1be6b49c ML |
4636 | #define NUM2INTEGRAL scm_num2ptrdiff |
4637 | #define INTEGRAL2NUM scm_ptrdiff2num | |
4638 | #define INTEGRAL2BIG scm_i_ptrdiff2big | |
4639 | #define ITYPE ptrdiff_t | |
3d2e8ceb MV |
4640 | #define UNSIGNED_ITYPE size_t |
4641 | #define SIZEOF_ITYPE SIZEOF_PTRDIFF_T | |
1be6b49c ML |
4642 | #include "libguile/num2integral.i.c" |
4643 | ||
4644 | #define NUM2INTEGRAL scm_num2size | |
4645 | #define INTEGRAL2NUM scm_size2num | |
4646 | #define INTEGRAL2BIG scm_i_size2big | |
4647 | #define UNSIGNED | |
4648 | #define ITYPE size_t | |
3d2e8ceb | 4649 | #define SIZEOF_ITYPE SIZEOF_SIZE_T |
1be6b49c | 4650 | #include "libguile/num2integral.i.c" |
0f2d19dd | 4651 | |
5c11cc9d | 4652 | #ifdef HAVE_LONG_LONGS |
1cc91f1b | 4653 | |
caf08e65 MV |
4654 | #ifndef ULONG_LONG_MAX |
4655 | #define ULONG_LONG_MAX (~0ULL) | |
4656 | #endif | |
4657 | ||
1be6b49c ML |
4658 | #define NUM2INTEGRAL scm_num2long_long |
4659 | #define INTEGRAL2NUM scm_long_long2num | |
4660 | #define INTEGRAL2BIG scm_i_long_long2big | |
4661 | #define ITYPE long long | |
3d2e8ceb | 4662 | #define SIZEOF_ITYPE SIZEOF_LONG_LONG |
1be6b49c ML |
4663 | #include "libguile/num2integral.i.c" |
4664 | ||
4665 | #define NUM2INTEGRAL scm_num2ulong_long | |
4666 | #define INTEGRAL2NUM scm_ulong_long2num | |
4667 | #define INTEGRAL2BIG scm_i_ulong_long2big | |
4668 | #define UNSIGNED | |
4669 | #define ITYPE unsigned long long | |
3d2e8ceb | 4670 | #define SIZEOF_ITYPE SIZEOF_LONG_LONG |
1be6b49c | 4671 | #include "libguile/num2integral.i.c" |
0f2d19dd | 4672 | |
1be6b49c | 4673 | #endif /* HAVE_LONG_LONGS */ |
caf08e65 | 4674 | |
5437598b MD |
4675 | #define NUM2FLOAT scm_num2float |
4676 | #define FLOAT2NUM scm_float2num | |
4677 | #define FTYPE float | |
4678 | #include "libguile/num2float.i.c" | |
4679 | ||
4680 | #define NUM2FLOAT scm_num2double | |
4681 | #define FLOAT2NUM scm_double2num | |
4682 | #define FTYPE double | |
4683 | #include "libguile/num2float.i.c" | |
4684 | ||
1be6b49c | 4685 | #ifdef GUILE_DEBUG |
caf08e65 | 4686 | |
6063dc1d SJ |
4687 | #ifndef SIZE_MAX |
4688 | #define SIZE_MAX ((size_t) (-1)) | |
4689 | #endif | |
4690 | #ifndef PTRDIFF_MIN | |
4691 | #define PTRDIFF_MIN \ | |
4692 | ((ptrdiff_t) ((ptrdiff_t) 1 << (sizeof (ptrdiff_t) * 8 - 1))) | |
4693 | #endif | |
4694 | #ifndef PTRDIFF_MAX | |
4695 | #define PTRDIFF_MAX (~ PTRDIFF_MIN) | |
4696 | #endif | |
4697 | ||
1be6b49c ML |
4698 | #define CHECK(type, v) \ |
4699 | do { \ | |
4700 | if ((v) != scm_num2##type (scm_##type##2num (v), 1, "check_sanity")) \ | |
4701 | abort (); \ | |
4702 | } while (0); | |
caf08e65 | 4703 | |
1be6b49c ML |
4704 | static void |
4705 | check_sanity () | |
4706 | { | |
4707 | CHECK (short, 0); | |
4708 | CHECK (ushort, 0U); | |
4709 | CHECK (int, 0); | |
4710 | CHECK (uint, 0U); | |
4711 | CHECK (long, 0L); | |
4712 | CHECK (ulong, 0UL); | |
4713 | CHECK (size, 0); | |
4714 | CHECK (ptrdiff, 0); | |
4715 | ||
4716 | CHECK (short, -1); | |
4717 | CHECK (int, -1); | |
4718 | CHECK (long, -1L); | |
4719 | CHECK (ptrdiff, -1); | |
4720 | ||
4721 | CHECK (short, SHRT_MAX); | |
4722 | CHECK (short, SHRT_MIN); | |
4723 | CHECK (ushort, USHRT_MAX); | |
4724 | CHECK (int, INT_MAX); | |
4725 | CHECK (int, INT_MIN); | |
4726 | CHECK (uint, UINT_MAX); | |
4727 | CHECK (long, LONG_MAX); | |
4728 | CHECK (long, LONG_MIN); | |
4729 | CHECK (ulong, ULONG_MAX); | |
4730 | CHECK (size, SIZE_MAX); | |
4731 | CHECK (ptrdiff, PTRDIFF_MAX); | |
4732 | CHECK (ptrdiff, PTRDIFF_MIN); | |
0f2d19dd | 4733 | |
1be6b49c ML |
4734 | #ifdef HAVE_LONG_LONGS |
4735 | CHECK (long_long, 0LL); | |
4736 | CHECK (ulong_long, 0ULL); | |
1be6b49c | 4737 | CHECK (long_long, -1LL); |
1be6b49c ML |
4738 | CHECK (long_long, LLONG_MAX); |
4739 | CHECK (long_long, LLONG_MIN); | |
4740 | CHECK (ulong_long, ULLONG_MAX); | |
4741 | #endif | |
0f2d19dd JB |
4742 | } |
4743 | ||
b10586f0 ML |
4744 | #undef CHECK |
4745 | ||
4746 | #define CHECK \ | |
4747 | scm_internal_catch (SCM_BOOL_T, check_body, &data, check_handler, &data); \ | |
4748 | if (!SCM_FALSEP (data)) abort(); | |
4749 | ||
4750 | static SCM | |
4751 | check_body (void *data) | |
4752 | { | |
4753 | SCM num = *(SCM *) data; | |
4754 | scm_num2ulong (num, 1, NULL); | |
4755 | ||
4756 | return SCM_UNSPECIFIED; | |
4757 | } | |
4758 | ||
4759 | static SCM | |
4760 | check_handler (void *data, SCM tag, SCM throw_args) | |
4761 | { | |
4762 | SCM *num = (SCM *) data; | |
4763 | *num = SCM_BOOL_F; | |
4764 | ||
4765 | return SCM_UNSPECIFIED; | |
4766 | } | |
4767 | ||
4768 | SCM_DEFINE (scm_sys_check_number_conversions, "%check-number-conversions", 0, 0, 0, | |
b4e15479 | 4769 | (void), |
b10586f0 ML |
4770 | "Number conversion sanity checking.") |
4771 | #define FUNC_NAME s_scm_sys_check_number_conversions | |
4772 | { | |
4773 | SCM data = SCM_MAKINUM (-1); | |
4774 | CHECK; | |
4775 | data = scm_int2num (INT_MIN); | |
4776 | CHECK; | |
4777 | data = scm_ulong2num (ULONG_MAX); | |
4778 | data = scm_difference (SCM_INUM0, data); | |
4779 | CHECK; | |
4780 | data = scm_ulong2num (ULONG_MAX); | |
4781 | data = scm_sum (SCM_MAKINUM (1), data); data = scm_difference (SCM_INUM0, data); | |
4782 | CHECK; | |
4783 | data = scm_int2num (-10000); data = scm_product (data, data); data = scm_product (data, data); | |
4784 | CHECK; | |
4785 | ||
4786 | return SCM_UNSPECIFIED; | |
4787 | } | |
4788 | #undef FUNC_NAME | |
4789 | ||
1be6b49c | 4790 | #endif |
0f2d19dd | 4791 | |
0f2d19dd JB |
4792 | void |
4793 | scm_init_numbers () | |
0f2d19dd | 4794 | { |
1be6b49c | 4795 | abs_most_negative_fixnum = scm_i_long2big (- SCM_MOST_NEGATIVE_FIXNUM); |
ac0c002c DH |
4796 | scm_permanent_object (abs_most_negative_fixnum); |
4797 | ||
a261c0e9 DH |
4798 | /* It may be possible to tune the performance of some algorithms by using |
4799 | * the following constants to avoid the creation of bignums. Please, before | |
4800 | * using these values, remember the two rules of program optimization: | |
4801 | * 1st Rule: Don't do it. 2nd Rule (experts only): Don't do it yet. */ | |
86d31dfe MV |
4802 | scm_c_define ("most-positive-fixnum", |
4803 | SCM_MAKINUM (SCM_MOST_POSITIVE_FIXNUM)); | |
4804 | scm_c_define ("most-negative-fixnum", | |
4805 | SCM_MAKINUM (SCM_MOST_NEGATIVE_FIXNUM)); | |
a261c0e9 | 4806 | |
f3ae5d60 MD |
4807 | scm_add_feature ("complex"); |
4808 | scm_add_feature ("inexact"); | |
5986c47d | 4809 | scm_flo0 = scm_make_real (0.0); |
f872b822 | 4810 | #ifdef DBL_DIG |
0f2d19dd | 4811 | scm_dblprec = (DBL_DIG > 20) ? 20 : DBL_DIG; |
f872b822 | 4812 | #else |
0f2d19dd JB |
4813 | { /* determine floating point precision */ |
4814 | double f = 0.1; | |
f872b822 | 4815 | double fsum = 1.0 + f; |
bb628794 DH |
4816 | while (fsum != 1.0) { |
4817 | if (++scm_dblprec > 20) { | |
4818 | fsum = 1.0; | |
4819 | } else { | |
f872b822 | 4820 | f /= 10.0; |
bb628794 | 4821 | fsum = f + 1.0; |
f872b822 | 4822 | } |
bb628794 | 4823 | } |
f872b822 | 4824 | scm_dblprec = scm_dblprec - 1; |
0f2d19dd | 4825 | } |
f872b822 | 4826 | #endif /* DBL_DIG */ |
1be6b49c ML |
4827 | |
4828 | #ifdef GUILE_DEBUG | |
4829 | check_sanity (); | |
4830 | #endif | |
4831 | ||
a0599745 | 4832 | #include "libguile/numbers.x" |
0f2d19dd | 4833 | } |
89e00824 ML |
4834 | |
4835 | /* | |
4836 | Local Variables: | |
4837 | c-file-style: "gnu" | |
4838 | End: | |
4839 | */ |