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date Mon, 13 Aug 2007 08:45:50 +0200
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1 /* Primitive operations on floating point for XEmacs Lisp interpreter.
2 Copyright (C) 1988, 1993, 1994 Free Software Foundation, Inc.
3
4 This file is part of XEmacs.
5
6 XEmacs is free software; you can redistribute it and/or modify it
7 under the terms of the GNU General Public License as published by the
8 Free Software Foundation; either version 2, or (at your option) any
9 later version.
10
11 XEmacs is distributed in the hope that it will be useful, but WITHOUT
12 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 for more details.
15
16 You should have received a copy of the GNU General Public License
17 along with XEmacs; see the file COPYING. If not, write to
18 the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
19 Boston, MA 02111-1307, USA. */
20
21 /* Synched up with: FSF 19.30. */
22
23 /* ANSI C requires only these float functions:
24 acos, asin, atan, atan2, ceil, cos, cosh, exp, fabs, floor, fmod,
25 frexp, ldexp, log, log10, modf, pow, sin, sinh, sqrt, tan, tanh.
26
27 Define HAVE_INVERSE_HYPERBOLIC if you have acosh, asinh, and atanh.
28 Define HAVE_CBRT if you have cbrt().
29 Define HAVE_RINT if you have rint().
30 If you don't define these, then the appropriate routines will be simulated.
31
32 Define HAVE_MATHERR if on a system supporting the SysV matherr() callback.
33 (This should happen automatically.)
34
35 Define FLOAT_CHECK_ERRNO if the float library routines set errno.
36 This has no effect if HAVE_MATHERR is defined.
37
38 Define FLOAT_CATCH_SIGILL if the float library routines signal SIGILL.
39 (What systems actually do this? Let me know. -jwz)
40
41 Define FLOAT_CHECK_DOMAIN if the float library doesn't handle errors by
42 either setting errno, or signalling SIGFPE/SIGILL. Otherwise, domain and
43 range checking will happen before calling the float routines. This has
44 no effect if HAVE_MATHERR is defined (since matherr will be called when
45 a domain error occurs).
46 */
47
48 #include <config.h>
49 #include "lisp.h"
50 #include "syssignal.h"
51
52 #ifdef LISP_FLOAT_TYPE
53
54 /* Need to define a differentiating symbol -- see sysfloat.h */
55 #define THIS_FILENAME floatfns
56 #include "sysfloat.h"
57
58 #ifndef HAVE_RINT
59 static double
60 rint (double x)
61 {
62 double r = floor (x + 0.5);
63 double diff = fabs (r - x);
64 /* Round to even and correct for any roundoff errors. */
65 if (diff >= 0.5 && (diff > 0.5 || r != 2.0 * floor (r / 2.0)))
66 r += r < x ? 1.0 : -1.0;
67 return r;
68 }
69 #endif
70
71 /* Nonzero while executing in floating point.
72 This tells float_error what to do. */
73 static int in_float;
74
75 /* If an argument is out of range for a mathematical function,
76 here is the actual argument value to use in the error message. */
77 static Lisp_Object float_error_arg, float_error_arg2;
78 static CONST char *float_error_fn_name;
79
80 /* Evaluate the floating point expression D, recording NUM
81 as the original argument for error messages.
82 D is normally an assignment expression.
83 Handle errors which may result in signals or may set errno.
84
85 Note that float_error may be declared to return void, so you can't
86 just cast the zero after the colon to (SIGTYPE) to make the types
87 check properly. */
88 #ifdef FLOAT_CHECK_ERRNO
89 #define IN_FLOAT(d, name, num) \
90 do { \
91 float_error_arg = num; \
92 float_error_fn_name = name; \
93 in_float = 1; errno = 0; (d); in_float = 0; \
94 if (errno != 0) in_float_error (); \
95 } while (0)
96 #define IN_FLOAT2(d, name, num, num2) \
97 do { \
98 float_error_arg = num; \
99 float_error_arg2 = num2; \
100 float_error_fn_name = name; \
101 in_float = 2; errno = 0; (d); in_float = 0; \
102 if (errno != 0) in_float_error (); \
103 } while (0)
104 #else
105 #define IN_FLOAT(d, name, num) (in_float = 1, (d), in_float = 0)
106 #define IN_FLOAT2(d, name, num, num2) (in_float = 2, (d), in_float = 0)
107 #endif
108
109
110 #define arith_error(op,arg) \
111 Fsignal (Qarith_error, list2 (build_string ((op)), (arg)))
112 #define range_error(op,arg) \
113 Fsignal (Qrange_error, list2 (build_string ((op)), (arg)))
114 #define range_error2(op,a1,a2) \
115 Fsignal (Qrange_error, list3 (build_string ((op)), (a1), (a2)))
116 #define domain_error(op,arg) \
117 Fsignal (Qdomain_error, list2 (build_string ((op)), (arg)))
118 #define domain_error2(op,a1,a2) \
119 Fsignal (Qdomain_error, list3 (build_string ((op)), (a1), (a2)))
120
121
122 /* Convert float to Lisp_Int if it fits, else signal a range error
123 using the given arguments. */
124 static Lisp_Object
125 float_to_int (double x, CONST char *name, Lisp_Object num, Lisp_Object num2)
126 {
127 if (x >= ((EMACS_INT) 1 << (VALBITS-1))
128 || x <= - ((EMACS_INT) 1 << (VALBITS-1)) - (EMACS_INT) 1)
129 {
130 if (!UNBOUNDP (num2))
131 range_error2 (name, num, num2);
132 else
133 range_error (name, num);
134 }
135 return (make_int ((EMACS_INT) x));
136 }
137
138
139 static void
140 in_float_error (void)
141 {
142 switch (errno)
143 {
144 case 0:
145 break;
146 case EDOM:
147 if (in_float == 2)
148 domain_error2 (float_error_fn_name, float_error_arg, float_error_arg2);
149 else
150 domain_error (float_error_fn_name, float_error_arg);
151 break;
152 case ERANGE:
153 range_error (float_error_fn_name, float_error_arg);
154 break;
155 default:
156 arith_error (float_error_fn_name, float_error_arg);
157 break;
158 }
159 }
160
161
162
163 static Lisp_Object mark_float (Lisp_Object, void (*) (Lisp_Object));
164 extern void print_float (Lisp_Object, Lisp_Object, int);
165 static int float_equal (Lisp_Object o1, Lisp_Object o2, int depth);
166 static unsigned long float_hash (Lisp_Object obj, int depth);
167 DEFINE_BASIC_LRECORD_IMPLEMENTATION ("float", float,
168 mark_float, print_float, 0, float_equal,
169 float_hash, struct Lisp_Float);
170
171 static Lisp_Object
172 mark_float (Lisp_Object obj, void (*markobj) (Lisp_Object))
173 {
174 return (Qnil);
175 }
176
177 static int
178 float_equal (Lisp_Object o1, Lisp_Object o2, int depth)
179 {
180 return (extract_float (o1) == extract_float (o2));
181 }
182
183 static unsigned long
184 float_hash (Lisp_Object obj, int depth)
185 {
186 /* mod the value down to 32-bit range */
187 /* #### change for 64-bit machines */
188 return (unsigned long) fmod (extract_float (obj), 4e9);
189 }
190
191
192 /* Extract a Lisp number as a `double', or signal an error. */
193
194 double
195 extract_float (Lisp_Object num)
196 {
197 CHECK_INT_OR_FLOAT (num);
198
199 if (FLOATP (num))
200 return (float_data (XFLOAT (num)));
201 return (double) XINT (num);
202 }
203 #endif /* LISP_FLOAT_TYPE */
204
205
206 /* Trig functions. */
207 #ifdef LISP_FLOAT_TYPE
208
209 DEFUN ("acos", Facos, Sacos, 1, 1, 0 /*
210 Return the inverse cosine of ARG.
211 */ )
212 (arg)
213 Lisp_Object arg;
214 {
215 double d = extract_float (arg);
216 #ifdef FLOAT_CHECK_DOMAIN
217 if (d > 1.0 || d < -1.0)
218 domain_error ("acos", arg);
219 #endif
220 IN_FLOAT (d = acos (d), "acos", arg);
221 return make_float (d);
222 }
223
224 DEFUN ("asin", Fasin, Sasin, 1, 1, 0 /*
225 Return the inverse sine of ARG.
226 */ )
227 (arg)
228 Lisp_Object arg;
229 {
230 double d = extract_float (arg);
231 #ifdef FLOAT_CHECK_DOMAIN
232 if (d > 1.0 || d < -1.0)
233 domain_error ("asin", arg);
234 #endif
235 IN_FLOAT (d = asin (d), "asin", arg);
236 return make_float (d);
237 }
238
239 DEFUN ("atan", Fatan, Satan, 1, 2, 0 /*
240 Return the inverse tangent of ARG.
241 */ )
242 (arg1, arg2)
243 Lisp_Object arg1, arg2;
244 {
245 double d = extract_float (arg1);
246
247 if (NILP (arg2))
248 IN_FLOAT (d = atan (d), "atan", arg1);
249 else
250 {
251 double d2 = extract_float (arg2);
252 #ifdef FLOAT_CHECK_DOMAIN
253 if (d == 0.0 && d2 == 0.0)
254 domain_error2 ("atan", arg1, arg2);
255 #endif
256 IN_FLOAT2 (d = atan2 (d, d2), "atan", arg1, arg2);
257 }
258 return make_float (d);
259 }
260
261 DEFUN ("cos", Fcos, Scos, 1, 1, 0 /*
262 Return the cosine of ARG.
263 */ )
264 (arg)
265 Lisp_Object arg;
266 {
267 double d = extract_float (arg);
268 IN_FLOAT (d = cos (d), "cos", arg);
269 return make_float (d);
270 }
271
272 DEFUN ("sin", Fsin, Ssin, 1, 1, 0 /*
273 Return the sine of ARG.
274 */ )
275 (arg)
276 Lisp_Object arg;
277 {
278 double d = extract_float (arg);
279 IN_FLOAT (d = sin (d), "sin", arg);
280 return make_float (d);
281 }
282
283 DEFUN ("tan", Ftan, Stan, 1, 1, 0 /*
284 Return the tangent of ARG.
285 */ )
286 (arg)
287 Lisp_Object arg;
288 {
289 double d = extract_float (arg);
290 double c = cos (d);
291 #ifdef FLOAT_CHECK_DOMAIN
292 if (c == 0.0)
293 domain_error ("tan", arg);
294 #endif
295 IN_FLOAT (d = (sin (d) / c), "tan", arg);
296 return make_float (d);
297 }
298 #endif /* LISP_FLOAT_TYPE (trig functions) */
299
300
301 /* Bessel functions */
302 #if 0 /* Leave these out unless we find there's a reason for them. */
303 /* #ifdef LISP_FLOAT_TYPE */
304
305 DEFUN ("bessel-j0", Fbessel_j0, Sbessel_j0, 1, 1, 0 /*
306 Return the bessel function j0 of ARG.
307 */ )
308 (arg)
309 Lisp_Object arg;
310 {
311 double d = extract_float (arg);
312 IN_FLOAT (d = j0 (d), "bessel-j0", arg);
313 return make_float (d);
314 }
315
316 DEFUN ("bessel-j1", Fbessel_j1, Sbessel_j1, 1, 1, 0 /*
317 Return the bessel function j1 of ARG.
318 */ )
319 (arg)
320 Lisp_Object arg;
321 {
322 double d = extract_float (arg);
323 IN_FLOAT (d = j1 (d), "bessel-j1", arg);
324 return make_float (d);
325 }
326
327 DEFUN ("bessel-jn", Fbessel_jn, Sbessel_jn, 2, 2, 0 /*
328 Return the order N bessel function output jn of ARG.
329 The first arg (the order) is truncated to an integer.
330 */ )
331 (arg1, arg2)
332 Lisp_Object arg1, arg2;
333 {
334 int i1 = extract_float (arg1);
335 double f2 = extract_float (arg2);
336
337 IN_FLOAT (f2 = jn (i1, f2), "bessel-jn", arg1);
338 return make_float (f2);
339 }
340
341 DEFUN ("bessel-y0", Fbessel_y0, Sbessel_y0, 1, 1, 0 /*
342 Return the bessel function y0 of ARG.
343 */ )
344 (arg)
345 Lisp_Object arg;
346 {
347 double d = extract_float (arg);
348 IN_FLOAT (d = y0 (d), "bessel-y0", arg);
349 return make_float (d);
350 }
351
352 DEFUN ("bessel-y1", Fbessel_y1, Sbessel_y1, 1, 1, 0 /*
353 Return the bessel function y1 of ARG.
354 */ )
355 (arg)
356 Lisp_Object arg;
357 {
358 double d = extract_float (arg);
359 IN_FLOAT (d = y1 (d), "bessel-y0", arg);
360 return make_float (d);
361 }
362
363 DEFUN ("bessel-yn", Fbessel_yn, Sbessel_yn, 2, 2, 0 /*
364 Return the order N bessel function output yn of ARG.
365 The first arg (the order) is truncated to an integer.
366 */ )
367 (arg1, arg2)
368 Lisp_Object arg1, arg2;
369 {
370 int i1 = extract_float (arg1);
371 double f2 = extract_float (arg2);
372
373 IN_FLOAT (f2 = yn (i1, f2), "bessel-yn", arg1);
374 return make_float (f2);
375 }
376
377 #endif /* 0 (bessel functions) */
378
379 /* Error functions. */
380 #if 0 /* Leave these out unless we see they are worth having. */
381 /* #ifdef LISP_FLOAT_TYPE */
382
383 DEFUN ("erf", Ferf, Serf, 1, 1, 0 /*
384 Return the mathematical error function of ARG.
385 */ )
386 (arg)
387 Lisp_Object arg;
388 {
389 double d = extract_float (arg);
390 IN_FLOAT (d = erf (d), "erf", arg);
391 return make_float (d);
392 }
393
394 DEFUN ("erfc", Ferfc, Serfc, 1, 1, 0 /*
395 Return the complementary error function of ARG.
396 */ )
397 (arg)
398 Lisp_Object arg;
399 {
400 double d = extract_float (arg);
401 IN_FLOAT (d = erfc (d), "erfc", arg);
402 return make_float (d);
403 }
404
405 DEFUN ("log-gamma", Flog_gamma, Slog_gamma, 1, 1, 0 /*
406 Return the log gamma of ARG.
407 */ )
408 (arg)
409 Lisp_Object arg;
410 {
411 double d = extract_float (arg);
412 IN_FLOAT (d = lgamma (d), "log-gamma", arg);
413 return make_float (d);
414 }
415
416 #endif /* 0 (error functions) */
417
418
419 /* Root and Log functions. */
420
421 #ifdef LISP_FLOAT_TYPE
422 DEFUN ("exp", Fexp, Sexp, 1, 1, 0 /*
423 Return the exponential base e of ARG.
424 */ )
425 (arg)
426 Lisp_Object arg;
427 {
428 double d = extract_float (arg);
429 #ifdef FLOAT_CHECK_DOMAIN
430 if (d > 709.7827) /* Assume IEEE doubles here */
431 range_error ("exp", arg);
432 else if (d < -709.0)
433 return make_float (0.0);
434 else
435 #endif
436 IN_FLOAT (d = exp (d), "exp", arg);
437 return make_float (d);
438 }
439 #endif /* LISP_FLOAT_TYPE */
440
441
442 DEFUN ("expt", Fexpt, Sexpt, 2, 2, 0 /*
443 Return the exponential ARG1 ** ARG2.
444 */ )
445 (arg1, arg2)
446 Lisp_Object arg1, arg2;
447 {
448 double f1, f2;
449
450 CHECK_INT_OR_FLOAT (arg1);
451 CHECK_INT_OR_FLOAT (arg2);
452 if ((INTP (arg1)) && /* common lisp spec */
453 (INTP (arg2))) /* don't promote, if both are ints */
454 {
455 EMACS_INT acc, x, y;
456 x = XINT (arg1);
457 y = XINT (arg2);
458
459 if (y < 0)
460 {
461 if (x == 1)
462 acc = 1;
463 else if (x == -1)
464 acc = (y & 1) ? -1 : 1;
465 else
466 acc = 0;
467 }
468 else
469 {
470 acc = 1;
471 while (y > 0)
472 {
473 if (y & 1)
474 acc *= x;
475 x *= x;
476 y = (unsigned EMACS_INT) y >> 1;
477 }
478 }
479 return (make_int (acc));
480 }
481 #ifdef LISP_FLOAT_TYPE
482 f1 = (FLOATP (arg1)) ? float_data (XFLOAT (arg1)) : XINT (arg1);
483 f2 = (FLOATP (arg2)) ? float_data (XFLOAT (arg2)) : XINT (arg2);
484 /* Really should check for overflow, too */
485 if (f1 == 0.0 && f2 == 0.0)
486 f1 = 1.0;
487 # ifdef FLOAT_CHECK_DOMAIN
488 else if ((f1 == 0.0 && f2 < 0.0) || (f1 < 0 && f2 != floor(f2)))
489 domain_error2 ("expt", arg1, arg2);
490 # endif /* FLOAT_CHECK_DOMAIN */
491 IN_FLOAT2 (f1 = pow (f1, f2), "expt", arg1, arg2);
492 return make_float (f1);
493 #else /* !LISP_FLOAT_TYPE */
494 abort ();
495 #endif /* LISP_FLOAT_TYPE */
496 }
497
498 #ifdef LISP_FLOAT_TYPE
499 DEFUN ("log", Flog, Slog, 1, 2, 0 /*
500 Return the natural logarithm of ARG.
501 If second optional argument BASE is given, return log ARG using that base.
502 */ )
503 (arg, base)
504 Lisp_Object arg, base;
505 {
506 double d = extract_float (arg);
507 #ifdef FLOAT_CHECK_DOMAIN
508 if (d <= 0.0)
509 domain_error2 ("log", arg, base);
510 #endif
511 if (NILP (base))
512 IN_FLOAT (d = log (d), "log", arg);
513 else
514 {
515 double b = extract_float (base);
516 #ifdef FLOAT_CHECK_DOMAIN
517 if (b <= 0.0 || b == 1.0)
518 domain_error2 ("log", arg, base);
519 #endif
520 if (b == 10.0)
521 IN_FLOAT2 (d = log10 (d), "log", arg, base);
522 else
523 IN_FLOAT2 (d = (log (d) / log (b)), "log", arg, base);
524 }
525 return make_float (d);
526 }
527
528
529 DEFUN ("log10", Flog10, Slog10, 1, 1, 0 /*
530 Return the logarithm base 10 of ARG.
531 */ )
532 (arg)
533 Lisp_Object arg;
534 {
535 double d = extract_float (arg);
536 #ifdef FLOAT_CHECK_DOMAIN
537 if (d <= 0.0)
538 domain_error ("log10", arg);
539 #endif
540 IN_FLOAT (d = log10 (d), "log10", arg);
541 return make_float (d);
542 }
543
544
545 DEFUN ("sqrt", Fsqrt, Ssqrt, 1, 1, 0 /*
546 Return the square root of ARG.
547 */ )
548 (arg)
549 Lisp_Object arg;
550 {
551 double d = extract_float (arg);
552 #ifdef FLOAT_CHECK_DOMAIN
553 if (d < 0.0)
554 domain_error ("sqrt", arg);
555 #endif
556 IN_FLOAT (d = sqrt (d), "sqrt", arg);
557 return make_float (d);
558 }
559
560
561 DEFUN ("cube-root", Fcube_root, Scube_root, 1, 1, 0 /*
562 Return the cube root of ARG.
563 */ )
564 (arg)
565 Lisp_Object arg;
566 {
567 double d = extract_float (arg);
568 #ifdef HAVE_CBRT
569 IN_FLOAT (d = cbrt (d), "cube-root", arg);
570 #else
571 if (d >= 0.0)
572 IN_FLOAT (d = pow (d, 1.0/3.0), "cube-root", arg);
573 else
574 IN_FLOAT (d = -pow (-d, 1.0/3.0), "cube-root", arg);
575 #endif
576 return make_float (d);
577 }
578 #endif /* LISP_FLOAT_TYPE */
579
580
581 /* Inverse trig functions. */
582 #ifdef LISP_FLOAT_TYPE
583 /* #if 0 Not clearly worth adding... */
584
585 DEFUN ("acosh", Facosh, Sacosh, 1, 1, 0 /*
586 Return the inverse hyperbolic cosine of ARG.
587 */ )
588 (arg)
589 Lisp_Object arg;
590 {
591 double d = extract_float (arg);
592 #ifdef FLOAT_CHECK_DOMAIN
593 if (d < 1.0)
594 domain_error ("acosh", arg);
595 #endif
596 #ifdef HAVE_INVERSE_HYPERBOLIC
597 IN_FLOAT (d = acosh (d), "acosh", arg);
598 #else
599 IN_FLOAT (d = log (d + sqrt (d*d - 1.0)), "acosh", arg);
600 #endif
601 return make_float (d);
602 }
603
604 DEFUN ("asinh", Fasinh, Sasinh, 1, 1, 0 /*
605 Return the inverse hyperbolic sine of ARG.
606 */ )
607 (arg)
608 Lisp_Object arg;
609 {
610 double d = extract_float (arg);
611 #ifdef HAVE_INVERSE_HYPERBOLIC
612 IN_FLOAT (d = asinh (d), "asinh", arg);
613 #else
614 IN_FLOAT (d = log (d + sqrt (d*d + 1.0)), "asinh", arg);
615 #endif
616 return make_float (d);
617 }
618
619 DEFUN ("atanh", Fatanh, Satanh, 1, 1, 0 /*
620 Return the inverse hyperbolic tangent of ARG.
621 */ )
622 (arg)
623 Lisp_Object arg;
624 {
625 double d = extract_float (arg);
626 #ifdef FLOAT_CHECK_DOMAIN
627 if (d >= 1.0 || d <= -1.0)
628 domain_error ("atanh", arg);
629 #endif
630 #ifdef HAVE_INVERSE_HYPERBOLIC
631 IN_FLOAT (d = atanh (d), "atanh", arg);
632 #else
633 IN_FLOAT (d = 0.5 * log ((1.0 + d) / (1.0 - d)), "atanh", arg);
634 #endif
635 return make_float (d);
636 }
637
638 DEFUN ("cosh", Fcosh, Scosh, 1, 1, 0 /*
639 Return the hyperbolic cosine of ARG.
640 */ )
641 (arg)
642 Lisp_Object arg;
643 {
644 double d = extract_float (arg);
645 #ifdef FLOAT_CHECK_DOMAIN
646 if (d > 710.0 || d < -710.0)
647 range_error ("cosh", arg);
648 #endif
649 IN_FLOAT (d = cosh (d), "cosh", arg);
650 return make_float (d);
651 }
652
653 DEFUN ("sinh", Fsinh, Ssinh, 1, 1, 0 /*
654 Return the hyperbolic sine of ARG.
655 */ )
656 (arg)
657 Lisp_Object arg;
658 {
659 double d = extract_float (arg);
660 #ifdef FLOAT_CHECK_DOMAIN
661 if (d > 710.0 || d < -710.0)
662 range_error ("sinh", arg);
663 #endif
664 IN_FLOAT (d = sinh (d), "sinh", arg);
665 return make_float (d);
666 }
667
668 DEFUN ("tanh", Ftanh, Stanh, 1, 1, 0 /*
669 Return the hyperbolic tangent of ARG.
670 */ )
671 (arg)
672 Lisp_Object arg;
673 {
674 double d = extract_float (arg);
675 IN_FLOAT (d = tanh (d), "tanh", arg);
676 return make_float (d);
677 }
678 #endif /* LISP_FLOAT_TYPE (inverse trig functions) */
679
680 /* Rounding functions */
681
682 DEFUN ("abs", Fabs, Sabs, 1, 1, 0 /*
683 Return the absolute value of ARG.
684 */ )
685 (arg)
686 Lisp_Object arg;
687 {
688 CHECK_INT_OR_FLOAT (arg);
689
690 #ifdef LISP_FLOAT_TYPE
691 if (FLOATP (arg))
692 {
693 IN_FLOAT (arg = make_float ((double) fabs (float_data (XFLOAT (arg)))),
694 "abs", arg);
695 return (arg);
696 }
697 else
698 #endif /* LISP_FLOAT_TYPE */
699 if (XINT (arg) < 0)
700 return (make_int (- XINT (arg)));
701 else
702 return (arg);
703 }
704
705 #ifdef LISP_FLOAT_TYPE
706 DEFUN ("float", Ffloat, Sfloat, 1, 1, 0 /*
707 Return the floating point number equal to ARG.
708 */ )
709 (arg)
710 Lisp_Object arg;
711 {
712 CHECK_INT_OR_FLOAT (arg);
713
714 if (INTP (arg))
715 return make_float ((double) XINT (arg));
716 else /* give 'em the same float back */
717 return arg;
718 }
719 #endif /* LISP_FLOAT_TYPE */
720
721
722 #ifdef LISP_FLOAT_TYPE
723 DEFUN ("logb", Flogb, Slogb, 1, 1, 0 /*
724 Return largest integer <= the base 2 log of the magnitude of ARG.
725 This is the same as the exponent of a float.
726 */ )
727 (arg)
728 Lisp_Object arg;
729 {
730 double f = extract_float (arg);
731
732 if (f == 0.0)
733 return (make_int (- (((EMACS_UINT) 1) << (VALBITS - 1)))); /* most-negative-fixnum */
734 #ifdef HAVE_LOGB
735 {
736 Lisp_Object val;
737 IN_FLOAT (val = make_int (logb (f)), "logb", arg);
738 return (val);
739 }
740 #else
741 #ifdef HAVE_FREXP
742 {
743 int exqp;
744 IN_FLOAT (frexp (f, &exqp), "logb", arg);
745 return (make_int (exqp - 1));
746 }
747 #else
748 {
749 int i;
750 double d;
751 EMACS_INT val;
752 if (f < 0.0)
753 f = -f;
754 val = -1;
755 while (f < 0.5)
756 {
757 for (i = 1, d = 0.5; d * d >= f; i += i)
758 d *= d;
759 f /= d;
760 val -= i;
761 }
762 while (f >= 1.0)
763 {
764 for (i = 1, d = 2.0; d * d <= f; i += i)
765 d *= d;
766 f /= d;
767 val += i;
768 }
769 return (make_int (val));
770 }
771 #endif /* ! HAVE_FREXP */
772 #endif /* ! HAVE_LOGB */
773 }
774 #endif /* LISP_FLOAT_TYPE */
775
776
777 DEFUN ("ceiling", Fceiling, Sceiling, 1, 1, 0 /*
778 Return the smallest integer no less than ARG. (Round toward +inf.)
779 */ )
780 (arg)
781 Lisp_Object arg;
782 {
783 CHECK_INT_OR_FLOAT (arg);
784
785 #ifdef LISP_FLOAT_TYPE
786 if (FLOATP (arg))
787 {
788 double d;
789 IN_FLOAT ((d = ceil (float_data (XFLOAT (arg)))), "ceiling", arg);
790 return (float_to_int (d, "ceiling", arg, Qunbound));
791 }
792 #endif /* LISP_FLOAT_TYPE */
793
794 return arg;
795 }
796
797
798 DEFUN ("floor", Ffloor, Sfloor, 1, 2, 0 /*
799 Return the largest integer no greater than ARG. (Round towards -inf.)
800 With optional DIVISOR, return the largest integer no greater than ARG/DIVISOR.
801 */ )
802 (arg, divisor)
803 Lisp_Object arg, divisor;
804 {
805 CHECK_INT_OR_FLOAT (arg);
806
807 if (! NILP (divisor))
808 {
809 EMACS_INT i1, i2;
810
811 CHECK_INT_OR_FLOAT (divisor);
812
813 #ifdef LISP_FLOAT_TYPE
814 if (FLOATP (arg) || FLOATP (divisor))
815 {
816 double f1, f2;
817
818 f1 = ((FLOATP (arg)) ? float_data (XFLOAT (arg)) : XINT (arg));
819 f2 = ((FLOATP (divisor)) ? float_data (XFLOAT (divisor)) : XINT (divisor));
820 if (f2 == 0)
821 Fsignal (Qarith_error, Qnil);
822
823 IN_FLOAT2 (f1 = floor (f1 / f2), "floor", arg, divisor);
824 return float_to_int (f1, "floor", arg, divisor);
825 }
826 #endif /* LISP_FLOAT_TYPE */
827
828 i1 = XINT (arg);
829 i2 = XINT (divisor);
830
831 if (i2 == 0)
832 Fsignal (Qarith_error, Qnil);
833
834 /* With C's /, the result is implementation-defined if either operand
835 is negative, so use only nonnegative operands. */
836 i1 = (i2 < 0
837 ? (i1 <= 0 ? -i1 / -i2 : -1 - ((i1 - 1) / -i2))
838 : (i1 < 0 ? -1 - ((-1 - i1) / i2) : i1 / i2));
839
840 return (make_int (i1));
841 }
842
843 #ifdef LISP_FLOAT_TYPE
844 if (FLOATP (arg))
845 {
846 double d;
847 IN_FLOAT ((d = floor (float_data (XFLOAT (arg)))), "floor", arg);
848 return (float_to_int (d, "floor", arg, Qunbound));
849 }
850 #endif /* LISP_FLOAT_TYPE */
851
852 return arg;
853 }
854
855 DEFUN ("round", Fround, Sround, 1, 1, 0 /*
856 Return the nearest integer to ARG.
857 */ )
858 (arg)
859 Lisp_Object arg;
860 {
861 CHECK_INT_OR_FLOAT (arg);
862
863 #ifdef LISP_FLOAT_TYPE
864 if (FLOATP (arg))
865 {
866 double d;
867 /* Screw the prevailing rounding mode. */
868 IN_FLOAT ((d = rint (float_data (XFLOAT (arg)))), "round", arg);
869 return (float_to_int (d, "round", arg, Qunbound));
870 }
871 #endif /* LISP_FLOAT_TYPE */
872
873 return arg;
874 }
875
876 DEFUN ("truncate", Ftruncate, Struncate, 1, 1, 0 /*
877 Truncate a floating point number to an integer.
878 Rounds the value toward zero.
879 */ )
880 (arg)
881 Lisp_Object arg;
882 {
883 CHECK_INT_OR_FLOAT (arg);
884
885 #ifdef LISP_FLOAT_TYPE
886 if (FLOATP (arg))
887 return (float_to_int (float_data (XFLOAT (arg)),
888 "truncate", arg, Qunbound));
889 #endif /* LISP_FLOAT_TYPE */
890
891 return arg;
892 }
893
894 /* Float-rounding functions. */
895 #ifdef LISP_FLOAT_TYPE
896 /* #if 1 It's not clear these are worth adding... */
897
898 DEFUN ("fceiling", Ffceiling, Sfceiling, 1, 1, 0 /*
899 Return the smallest integer no less than ARG, as a float.
900 \(Round toward +inf.\)
901 */ )
902 (arg)
903 Lisp_Object arg;
904 {
905 double d = extract_float (arg);
906 IN_FLOAT (d = ceil (d), "fceiling", arg);
907 return make_float (d);
908 }
909
910 DEFUN ("ffloor", Fffloor, Sffloor, 1, 1, 0 /*
911 Return the largest integer no greater than ARG, as a float.
912 \(Round towards -inf.\)
913 */ )
914 (arg)
915 Lisp_Object arg;
916 {
917 double d = extract_float (arg);
918 IN_FLOAT (d = floor (d), "ffloor", arg);
919 return make_float (d);
920 }
921
922 DEFUN ("fround", Ffround, Sfround, 1, 1, 0 /*
923 Return the nearest integer to ARG, as a float.
924 */ )
925 (arg)
926 Lisp_Object arg;
927 {
928 double d = extract_float (arg);
929 IN_FLOAT (d = rint (d), "fround", arg);
930 return make_float (d);
931 }
932
933 DEFUN ("ftruncate", Fftruncate, Sftruncate, 1, 1, 0 /*
934 Truncate a floating point number to an integral float value.
935 Rounds the value toward zero.
936 */ )
937 (arg)
938 Lisp_Object arg;
939 {
940 double d = extract_float (arg);
941 if (d >= 0.0)
942 IN_FLOAT (d = floor (d), "ftruncate", arg);
943 else
944 IN_FLOAT (d = ceil (d), "ftruncate", arg);
945 return make_float (d);
946 }
947
948 #endif /* LISP_FLOAT_TYPE (float-rounding functions) */
949
950
951 #ifdef LISP_FLOAT_TYPE
952 #ifdef FLOAT_CATCH_SIGILL
953 static SIGTYPE
954 float_error (int signo)
955 {
956 if (! in_float)
957 fatal_error_signal (signo);
958
959 EMACS_REESTABLISH_SIGNAL (signo, arith_error);
960 EMACS_UNBLOCK_SIGNAL (signo);
961
962 in_float = 0;
963
964 /* Was Fsignal(), but it just doesn't make sense for an error
965 occurring inside a signal handler to be restartable, considering
966 that anything could happen when the error is signaled and trapped
967 and considering the asynchronous nature of signal handlers. */
968 signal_error (Qarith_error, list1 (float_error_arg));
969 }
970
971 /* Another idea was to replace the library function `infnan'
972 where SIGILL is signaled. */
973
974 #endif /* FLOAT_CATCH_SIGILL */
975
976 #ifdef HAVE_MATHERR
977 int
978 matherr (struct exception *x)
979 {
980 Lisp_Object args;
981 if (! in_float)
982 /* Not called from emacs-lisp float routines; do the default thing. */
983 return 0;
984
985 /* if (!strcmp (x->name, "pow")) x->name = "expt"; */
986
987 args = Fcons (build_string (x->name),
988 Fcons (make_float (x->arg1),
989 ((in_float == 2)
990 ? Fcons (make_float (x->arg2), Qnil)
991 : Qnil)));
992 switch (x->type)
993 {
994 case DOMAIN: Fsignal (Qdomain_error, args); break;
995 case SING: Fsignal (Qsingularity_error, args); break;
996 case OVERFLOW: Fsignal (Qoverflow_error, args); break;
997 case UNDERFLOW: Fsignal (Qunderflow_error, args); break;
998 default: Fsignal (Qarith_error, args); break;
999 }
1000 return (1); /* don't set errno or print a message */
1001 }
1002 #endif /* HAVE_MATHERR */
1003 #endif /* LISP_FLOAT_TYPE */
1004
1005
1006 void
1007 init_floatfns_very_early (void)
1008 {
1009 #ifdef LISP_FLOAT_TYPE
1010 # ifdef FLOAT_CATCH_SIGILL
1011 signal (SIGILL, float_error);
1012 # endif
1013 in_float = 0;
1014 #endif /* LISP_FLOAT_TYPE */
1015 }
1016
1017 void
1018 syms_of_floatfns (void)
1019 {
1020
1021 /* Trig functions. */
1022
1023 #ifdef LISP_FLOAT_TYPE
1024 defsubr (&Sacos);
1025 defsubr (&Sasin);
1026 defsubr (&Satan);
1027 defsubr (&Scos);
1028 defsubr (&Ssin);
1029 defsubr (&Stan);
1030 #endif /* LISP_FLOAT_TYPE */
1031
1032 /* Bessel functions */
1033
1034 #if 0
1035 defsubr (&Sbessel_y0);
1036 defsubr (&Sbessel_y1);
1037 defsubr (&Sbessel_yn);
1038 defsubr (&Sbessel_j0);
1039 defsubr (&Sbessel_j1);
1040 defsubr (&Sbessel_jn);
1041 #endif /* 0 */
1042
1043 /* Error functions. */
1044
1045 #if 0
1046 defsubr (&Serf);
1047 defsubr (&Serfc);
1048 defsubr (&Slog_gamma);
1049 #endif /* 0 */
1050
1051 /* Root and Log functions. */
1052
1053 #ifdef LISP_FLOAT_TYPE
1054 defsubr (&Sexp);
1055 #endif /* LISP_FLOAT_TYPE */
1056 defsubr (&Sexpt);
1057 #ifdef LISP_FLOAT_TYPE
1058 defsubr (&Slog);
1059 defsubr (&Slog10);
1060 defsubr (&Ssqrt);
1061 defsubr (&Scube_root);
1062 #endif /* LISP_FLOAT_TYPE */
1063
1064 /* Inverse trig functions. */
1065
1066 #ifdef LISP_FLOAT_TYPE
1067 defsubr (&Sacosh);
1068 defsubr (&Sasinh);
1069 defsubr (&Satanh);
1070 defsubr (&Scosh);
1071 defsubr (&Ssinh);
1072 defsubr (&Stanh);
1073 #endif /* LISP_FLOAT_TYPE */
1074
1075 /* Rounding functions */
1076
1077 defsubr (&Sabs);
1078 #ifdef LISP_FLOAT_TYPE
1079 defsubr (&Sfloat);
1080 defsubr (&Slogb);
1081 #endif /* LISP_FLOAT_TYPE */
1082 defsubr (&Sceiling);
1083 defsubr (&Sfloor);
1084 defsubr (&Sround);
1085 defsubr (&Struncate);
1086
1087 /* Float-rounding functions. */
1088
1089 #ifdef LISP_FLOAT_TYPE
1090 defsubr (&Sfceiling);
1091 defsubr (&Sffloor);
1092 defsubr (&Sfround);
1093 defsubr (&Sftruncate);
1094 #endif /* LISP_FLOAT_TYPE */
1095 }
1096
1097 void
1098 vars_of_floatfns (void)
1099 {
1100 #ifdef LISP_FLOAT_TYPE
1101 Fprovide (intern ("lisp-float-type"));
1102 #endif
1103 }