floatfns.c 25.8 KB
Newer Older
Mike Rowan's avatar
Mike Rowan committed
1
/* Primitive operations on floating point for GNU Emacs Lisp interpreter.
2
   Copyright (C) 1988, 1993, 1994, 1999 Free Software Foundation, Inc.
Mike Rowan's avatar
Mike Rowan committed
3 4 5 6 7

This file is part of GNU Emacs.

GNU Emacs is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
Jim Blandy's avatar
Jim Blandy committed
8
the Free Software Foundation; either version 2, or (at your option)
Mike Rowan's avatar
Mike Rowan committed
9 10 11 12 13 14 15 16 17
any later version.

GNU Emacs is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with GNU Emacs; see the file COPYING.  If not, write to
18 19
the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA.  */
Mike Rowan's avatar
Mike Rowan committed
20 21


22 23 24 25 26 27
/* ANSI C requires only these float functions:
   acos, asin, atan, atan2, ceil, cos, cosh, exp, fabs, floor, fmod,
   frexp, ldexp, log, log10, modf, pow, sin, sinh, sqrt, tan, tanh.

   Define HAVE_INVERSE_HYPERBOLIC if you have acosh, asinh, and atanh.
   Define HAVE_CBRT if you have cbrt.
28
   Define HAVE_RINT if you have a working rint.
29 30 31 32 33 34 35 36 37 38 39 40
   If you don't define these, then the appropriate routines will be simulated.

   Define HAVE_MATHERR if on a system supporting the SysV matherr callback.
   (This should happen automatically.)

   Define FLOAT_CHECK_ERRNO if the float library routines set errno.
   This has no effect if HAVE_MATHERR is defined.

   Define FLOAT_CATCH_SIGILL if the float library routines signal SIGILL.
   (What systems actually do this?  Please let us know.)

   Define FLOAT_CHECK_DOMAIN if the float library doesn't handle errors by
Karl Heuer's avatar
Karl Heuer committed
41
   either setting errno, or signaling SIGFPE/SIGILL.  Otherwise, domain and
42 43 44 45 46
   range checking will happen before calling the float routines.  This has
   no effect if HAVE_MATHERR is defined (since matherr will be called when
   a domain error occurs.)
 */

47
#include <config.h>
48
#include <signal.h>
49 50 51
#include "lisp.h"
#include "syssignal.h"

52 53 54 55
#if STDC_HEADERS
#include <float.h>
#endif

56 57 58 59 60 61 62 63 64 65
/* If IEEE_FLOATING_POINT isn't defined, default it from FLT_*. */
#ifndef IEEE_FLOATING_POINT
#if (FLT_RADIX == 2 && FLT_MANT_DIG == 24 \
     && FLT_MIN_EXP == -125 && FLT_MAX_EXP == 128)
#define IEEE_FLOATING_POINT 1
#else
#define IEEE_FLOATING_POINT 0
#endif
#endif

66 67 68 69 70 71 72 73 74 75
/* Work around a problem that happens because math.h on hpux 7
   defines two static variables--which, in Emacs, are not really static,
   because `static' is defined as nothing.  The problem is that they are
   defined both here and in lread.c.
   These macros prevent the name conflict.  */
#if defined (HPUX) && !defined (HPUX8)
#define _MAXLDBL floatfns_maxldbl
#define _NMAXLDBL floatfns_nmaxldbl
#endif

Mike Rowan's avatar
Mike Rowan committed
76
#include <math.h>
77

78
/* This declaration is omitted on some systems, like Ultrix.  */
79
#if !defined (HPUX) && defined (HAVE_LOGB) && !defined (logb)
80
extern double logb ();
81
#endif /* not HPUX and HAVE_LOGB and no logb macro */
82

83 84 85 86 87 88 89
#if defined(DOMAIN) && defined(SING) && defined(OVERFLOW)
    /* If those are defined, then this is probably a `matherr' machine. */
# ifndef HAVE_MATHERR
#  define HAVE_MATHERR
# endif
#endif

Richard M. Stallman's avatar
Richard M. Stallman committed
90
#ifdef NO_MATHERR
91 92 93
#undef HAVE_MATHERR
#endif

94 95 96 97 98 99 100 101 102 103 104 105 106 107 108
#ifdef HAVE_MATHERR
# ifdef FLOAT_CHECK_ERRNO
#  undef FLOAT_CHECK_ERRNO
# endif
# ifdef FLOAT_CHECK_DOMAIN
#  undef FLOAT_CHECK_DOMAIN
# endif
#endif

#ifndef NO_FLOAT_CHECK_ERRNO
#define FLOAT_CHECK_ERRNO
#endif

#ifdef FLOAT_CHECK_ERRNO
# include <errno.h>
Jim Blandy's avatar
Jim Blandy committed
109 110

extern int errno;
111
#endif
Jim Blandy's avatar
Jim Blandy committed
112 113 114 115 116 117 118 119 120 121 122

/* Avoid traps on VMS from sinh and cosh.
   All the other functions set errno instead.  */

#ifdef VMS
#undef cosh
#undef sinh
#define cosh(x) ((exp(x)+exp(-x))*0.5)
#define sinh(x) ((exp(x)-exp(-x))*0.5)
#endif /* VMS */

Jim Blandy's avatar
Jim Blandy committed
123
static SIGTYPE float_error ();
Mike Rowan's avatar
Mike Rowan committed
124 125 126 127 128 129 130

/* Nonzero while executing in floating point.
   This tells float_error what to do.  */

static int in_float;

/* If an argument is out of range for a mathematical function,
Richard M. Stallman's avatar
Richard M. Stallman committed
131 132 133
   here is the actual argument value to use in the error message.
   These variables are used only across the floating point library call
   so there is no need to staticpro them.  */
Mike Rowan's avatar
Mike Rowan committed
134

135 136 137
static Lisp_Object float_error_arg, float_error_arg2;

static char *float_error_fn_name;
Mike Rowan's avatar
Mike Rowan committed
138

Jim Blandy's avatar
Jim Blandy committed
139 140 141
/* Evaluate the floating point expression D, recording NUM
   as the original argument for error messages.
   D is normally an assignment expression.
142 143 144 145 146
   Handle errors which may result in signals or may set errno.

   Note that float_error may be declared to return void, so you can't
   just cast the zero after the colon to (SIGTYPE) to make the types
   check properly.  */
Jim Blandy's avatar
Jim Blandy committed
147

148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174
#ifdef FLOAT_CHECK_ERRNO
#define IN_FLOAT(d, name, num)				\
  do {							\
    float_error_arg = num;				\
    float_error_fn_name = name;				\
    in_float = 1; errno = 0; (d); in_float = 0;		\
    switch (errno) {					\
    case 0: break;					\
    case EDOM:	 domain_error (float_error_fn_name, float_error_arg);	\
    case ERANGE: range_error (float_error_fn_name, float_error_arg);	\
    default:	 arith_error (float_error_fn_name, float_error_arg);	\
    }							\
  } while (0)
#define IN_FLOAT2(d, name, num, num2)			\
  do {							\
    float_error_arg = num;				\
    float_error_arg2 = num2;				\
    float_error_fn_name = name;				\
    in_float = 1; errno = 0; (d); in_float = 0;		\
    switch (errno) {					\
    case 0: break;					\
    case EDOM:	 domain_error (float_error_fn_name, float_error_arg);	\
    case ERANGE: range_error (float_error_fn_name, float_error_arg);	\
    default:	 arith_error (float_error_fn_name, float_error_arg);	\
    }							\
  } while (0)
#else
175
#define IN_FLOAT(d, name, num) (in_float = 1, (d), in_float = 0)
176 177 178
#define IN_FLOAT2(d, name, num, num2) (in_float = 1, (d), in_float = 0)
#endif

179 180 181 182 183
/* Convert float to Lisp_Int if it fits, else signal a range error
   using the given arguments.  */
#define FLOAT_TO_INT(x, i, name, num)					\
  do									\
    {									\
184 185
      if ((x) >= (((EMACS_INT) 1) << (VALBITS-1)) ||			\
	  (x) <= - (((EMACS_INT) 1) << (VALBITS-1)) - 1)		\
186
	range_error (name, num);					\
187
      XSETINT (i,  (EMACS_INT)(x));					\
188 189 190 191 192
    }									\
  while (0)
#define FLOAT_TO_INT2(x, i, name, num1, num2)				\
  do									\
    {									\
193 194
      if ((x) >= (((EMACS_INT) 1) << (VALBITS-1)) ||			\
	  (x) <= - (((EMACS_INT) 1) << (VALBITS-1)) - 1)		\
195
	range_error2 (name, num1, num2);				\
196
      XSETINT (i,  (EMACS_INT)(x));					\
197 198 199
    }									\
  while (0)

200 201 202 203
#define arith_error(op,arg) \
  Fsignal (Qarith_error, Fcons (build_string ((op)), Fcons ((arg), Qnil)))
#define range_error(op,arg) \
  Fsignal (Qrange_error, Fcons (build_string ((op)), Fcons ((arg), Qnil)))
204 205 206
#define range_error2(op,a1,a2) \
  Fsignal (Qrange_error, Fcons (build_string ((op)), \
				Fcons ((a1), Fcons ((a2), Qnil))))
207 208 209
#define domain_error(op,arg) \
  Fsignal (Qdomain_error, Fcons (build_string ((op)), Fcons ((arg), Qnil)))
#define domain_error2(op,a1,a2) \
210 211
  Fsignal (Qdomain_error, Fcons (build_string ((op)), \
				 Fcons ((a1), Fcons ((a2), Qnil))))
Mike Rowan's avatar
Mike Rowan committed
212 213 214 215 216 217 218 219 220

/* Extract a Lisp number as a `double', or signal an error.  */

double
extract_float (num)
     Lisp_Object num;
{
  CHECK_NUMBER_OR_FLOAT (num, 0);

221
  if (FLOATP (num))
222
    return XFLOAT_DATA (num);
Mike Rowan's avatar
Mike Rowan committed
223 224
  return (double) XINT (num);
}
225 226

/* Trig functions.  */
Mike Rowan's avatar
Mike Rowan committed
227 228 229

DEFUN ("acos", Facos, Sacos, 1, 1, 0,
  "Return the inverse cosine of ARG.")
230 231
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
232
{
233 234 235 236 237 238
  double d = extract_float (arg);
#ifdef FLOAT_CHECK_DOMAIN
  if (d > 1.0 || d < -1.0)
    domain_error ("acos", arg);
#endif
  IN_FLOAT (d = acos (d), "acos", arg);
Mike Rowan's avatar
Mike Rowan committed
239 240 241
  return make_float (d);
}

242 243
DEFUN ("asin", Fasin, Sasin, 1, 1, 0,
  "Return the inverse sine of ARG.")
244 245
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
246
{
247 248 249 250 251 252
  double d = extract_float (arg);
#ifdef FLOAT_CHECK_DOMAIN
  if (d > 1.0 || d < -1.0)
    domain_error ("asin", arg);
#endif
  IN_FLOAT (d = asin (d), "asin", arg);
Mike Rowan's avatar
Mike Rowan committed
253 254 255
  return make_float (d);
}

256 257
DEFUN ("atan", Fatan, Satan, 1, 1, 0,
  "Return the inverse tangent of ARG.")
258 259
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
260
{
261 262
  double d = extract_float (arg);
  IN_FLOAT (d = atan (d), "atan", arg);
Mike Rowan's avatar
Mike Rowan committed
263 264 265
  return make_float (d);
}

266 267
DEFUN ("cos", Fcos, Scos, 1, 1, 0,
  "Return the cosine of ARG.")
268 269
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
270
{
271 272
  double d = extract_float (arg);
  IN_FLOAT (d = cos (d), "cos", arg);
Mike Rowan's avatar
Mike Rowan committed
273 274 275
  return make_float (d);
}

276 277
DEFUN ("sin", Fsin, Ssin, 1, 1, 0,
  "Return the sine of ARG.")
278 279
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
280
{
281 282
  double d = extract_float (arg);
  IN_FLOAT (d = sin (d), "sin", arg);
Mike Rowan's avatar
Mike Rowan committed
283 284 285
  return make_float (d);
}

286 287
DEFUN ("tan", Ftan, Stan, 1, 1, 0,
  "Return the tangent of ARG.")
288 289 290 291 292 293 294 295 296 297
  (arg)
     register Lisp_Object arg;
{
  double d = extract_float (arg);
  double c = cos (d);
#ifdef FLOAT_CHECK_DOMAIN
  if (c == 0.0)
    domain_error ("tan", arg);
#endif
  IN_FLOAT (d = sin (d) / c, "tan", arg);
Mike Rowan's avatar
Mike Rowan committed
298 299 300
  return make_float (d);
}

301 302
#if 0 /* Leave these out unless we find there's a reason for them.  */

Mike Rowan's avatar
Mike Rowan committed
303 304
DEFUN ("bessel-j0", Fbessel_j0, Sbessel_j0, 1, 1, 0,
  "Return the bessel function j0 of ARG.")
305 306
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
307
{
308 309
  double d = extract_float (arg);
  IN_FLOAT (d = j0 (d), "bessel-j0", arg);
Mike Rowan's avatar
Mike Rowan committed
310 311 312 313 314
  return make_float (d);
}

DEFUN ("bessel-j1", Fbessel_j1, Sbessel_j1, 1, 1, 0,
  "Return the bessel function j1 of ARG.")
315 316
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
317
{
318 319
  double d = extract_float (arg);
  IN_FLOAT (d = j1 (d), "bessel-j1", arg);
Mike Rowan's avatar
Mike Rowan committed
320 321 322 323 324 325
  return make_float (d);
}

DEFUN ("bessel-jn", Fbessel_jn, Sbessel_jn, 2, 2, 0,
  "Return the order N bessel function output jn of ARG.\n\
The first arg (the order) is truncated to an integer.")
326 327
  (n, arg)
     register Lisp_Object n, arg;
Mike Rowan's avatar
Mike Rowan committed
328
{
329 330
  int i1 = extract_float (n);
  double f2 = extract_float (arg);
Mike Rowan's avatar
Mike Rowan committed
331

332
  IN_FLOAT (f2 = jn (i1, f2), "bessel-jn", n);
Mike Rowan's avatar
Mike Rowan committed
333 334 335 336 337
  return make_float (f2);
}

DEFUN ("bessel-y0", Fbessel_y0, Sbessel_y0, 1, 1, 0,
  "Return the bessel function y0 of ARG.")
338 339
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
340
{
341 342
  double d = extract_float (arg);
  IN_FLOAT (d = y0 (d), "bessel-y0", arg);
Mike Rowan's avatar
Mike Rowan committed
343 344 345 346 347
  return make_float (d);
}

DEFUN ("bessel-y1", Fbessel_y1, Sbessel_y1, 1, 1, 0,
  "Return the bessel function y1 of ARG.")
348 349
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
350
{
351 352
  double d = extract_float (arg);
  IN_FLOAT (d = y1 (d), "bessel-y0", arg);
Mike Rowan's avatar
Mike Rowan committed
353 354 355 356 357 358
  return make_float (d);
}

DEFUN ("bessel-yn", Fbessel_yn, Sbessel_yn, 2, 2, 0,
  "Return the order N bessel function output yn of ARG.\n\
The first arg (the order) is truncated to an integer.")
359 360
  (n, arg)
     register Lisp_Object n, arg;
Mike Rowan's avatar
Mike Rowan committed
361
{
362 363
  int i1 = extract_float (n);
  double f2 = extract_float (arg);
Mike Rowan's avatar
Mike Rowan committed
364

365
  IN_FLOAT (f2 = yn (i1, f2), "bessel-yn", n);
Mike Rowan's avatar
Mike Rowan committed
366 367 368
  return make_float (f2);
}

369 370 371
#endif

#if 0 /* Leave these out unless we see they are worth having.  */
Mike Rowan's avatar
Mike Rowan committed
372 373 374

DEFUN ("erf", Ferf, Serf, 1, 1, 0,
  "Return the mathematical error function of ARG.")
375 376
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
377
{
378 379
  double d = extract_float (arg);
  IN_FLOAT (d = erf (d), "erf", arg);
Mike Rowan's avatar
Mike Rowan committed
380 381 382 383 384
  return make_float (d);
}

DEFUN ("erfc", Ferfc, Serfc, 1, 1, 0,
  "Return the complementary error function of ARG.")
385 386
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
387
{
388 389
  double d = extract_float (arg);
  IN_FLOAT (d = erfc (d), "erfc", arg);
Mike Rowan's avatar
Mike Rowan committed
390 391 392 393 394
  return make_float (d);
}

DEFUN ("log-gamma", Flog_gamma, Slog_gamma, 1, 1, 0,
  "Return the log gamma of ARG.")
395 396
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
397
{
398 399
  double d = extract_float (arg);
  IN_FLOAT (d = lgamma (d), "log-gamma", arg);
Mike Rowan's avatar
Mike Rowan committed
400 401 402
  return make_float (d);
}

403
DEFUN ("cube-root", Fcube_root, Scube_root, 1, 1, 0,
404
  "Return the cube root of ARG.")
405 406
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
407
{
408 409 410 411 412 413 414 415 416
  double d = extract_float (arg);
#ifdef HAVE_CBRT
  IN_FLOAT (d = cbrt (d), "cube-root", arg);
#else
  if (d >= 0.0)
    IN_FLOAT (d = pow (d, 1.0/3.0), "cube-root", arg);
  else
    IN_FLOAT (d = -pow (-d, 1.0/3.0), "cube-root", arg);
#endif
Mike Rowan's avatar
Mike Rowan committed
417 418 419
  return make_float (d);
}

Richard M. Stallman's avatar
Richard M. Stallman committed
420 421
#endif

422 423
DEFUN ("exp", Fexp, Sexp, 1, 1, 0,
  "Return the exponential base e of ARG.")
424 425 426 427 428 429 430 431 432 433 434 435
  (arg)
     register Lisp_Object arg;
{
  double d = extract_float (arg);
#ifdef FLOAT_CHECK_DOMAIN
  if (d > 709.7827)   /* Assume IEEE doubles here */
    range_error ("exp", arg);
  else if (d < -709.0)
    return make_float (0.0);
  else
#endif
    IN_FLOAT (d = exp (d), "exp", arg);
Mike Rowan's avatar
Mike Rowan committed
436 437 438 439
  return make_float (d);
}

DEFUN ("expt", Fexpt, Sexpt, 2, 2, 0,
Richard M. Stallman's avatar
Richard M. Stallman committed
440
  "Return the exponential ARG1 ** ARG2.")
441 442
  (arg1, arg2)
     register Lisp_Object arg1, arg2;
Mike Rowan's avatar
Mike Rowan committed
443 444 445
{
  double f1, f2;

446 447
  CHECK_NUMBER_OR_FLOAT (arg1, 0);
  CHECK_NUMBER_OR_FLOAT (arg2, 0);
448 449
  if (INTEGERP (arg1)     /* common lisp spec */
      && INTEGERP (arg2)) /* don't promote, if both are ints */
Mike Rowan's avatar
Mike Rowan committed
450
    {				/* this can be improved by pre-calculating */
451
      EMACS_INT acc, x, y;	/* some binary powers of x then accumulating */
452 453
      Lisp_Object val;

454 455
      x = XINT (arg1);
      y = XINT (arg2);
Mike Rowan's avatar
Mike Rowan committed
456 457 458 459
      acc = 1;
      
      if (y < 0)
	{
460 461 462 463 464 465
	  if (x == 1)
	    acc = 1;
	  else if (x == -1)
	    acc = (y & 1) ? -1 : 1;
	  else
	    acc = 0;
Mike Rowan's avatar
Mike Rowan committed
466 467 468
	}
      else
	{
469 470 471 472 473 474 475
	  while (y > 0)
	    {
	      if (y & 1)
		acc *= x;
	      x *= x;
	      y = (unsigned)y >> 1;
	    }
Mike Rowan's avatar
Mike Rowan committed
476
	}
477
      XSETINT (val, acc);
478
      return val;
Mike Rowan's avatar
Mike Rowan committed
479
    }
480 481
  f1 = FLOATP (arg1) ? XFLOAT_DATA (arg1) : XINT (arg1);
  f2 = FLOATP (arg2) ? XFLOAT_DATA (arg2) : XINT (arg2);
482 483 484 485 486 487 488
  /* Really should check for overflow, too */
  if (f1 == 0.0 && f2 == 0.0)
    f1 = 1.0;
#ifdef FLOAT_CHECK_DOMAIN
  else if ((f1 == 0.0 && f2 < 0.0) || (f1 < 0 && f2 != floor(f2)))
    domain_error2 ("expt", arg1, arg2);
#endif
Richard M. Stallman's avatar
Richard M. Stallman committed
489
  IN_FLOAT2 (f1 = pow (f1, f2), "expt", arg1, arg2);
Mike Rowan's avatar
Mike Rowan committed
490 491
  return make_float (f1);
}
492

493
DEFUN ("log", Flog, Slog, 1, 2, 0,
494 495 496 497
  "Return the natural logarithm of ARG.\n\
If second optional argument BASE is given, return log ARG using that base.")
  (arg, base)
     register Lisp_Object arg, base;
Mike Rowan's avatar
Mike Rowan committed
498
{
499
  double d = extract_float (arg);
500

501 502 503 504
#ifdef FLOAT_CHECK_DOMAIN
  if (d <= 0.0)
    domain_error2 ("log", arg, base);
#endif
505
  if (NILP (base))
506
    IN_FLOAT (d = log (d), "log", arg);
507 508 509 510
  else
    {
      double b = extract_float (base);

511 512 513 514 515 516 517
#ifdef FLOAT_CHECK_DOMAIN
      if (b <= 0.0 || b == 1.0)
	domain_error2 ("log", arg, base);
#endif
      if (b == 10.0)
	IN_FLOAT2 (d = log10 (d), "log", arg, base);
      else
518
	IN_FLOAT2 (d = log (d) / log (b), "log", arg, base);
519
    }
Mike Rowan's avatar
Mike Rowan committed
520 521 522
  return make_float (d);
}

523 524
DEFUN ("log10", Flog10, Slog10, 1, 1, 0,
  "Return the logarithm base 10 of ARG.")
525 526
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
527
{
528 529 530 531 532 533
  double d = extract_float (arg);
#ifdef FLOAT_CHECK_DOMAIN
  if (d <= 0.0)
    domain_error ("log10", arg);
#endif
  IN_FLOAT (d = log10 (d), "log10", arg);
534 535 536
  return make_float (d);
}

Mike Rowan's avatar
Mike Rowan committed
537 538
DEFUN ("sqrt", Fsqrt, Ssqrt, 1, 1, 0,
  "Return the square root of ARG.")
539 540
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
541
{
542 543 544 545 546 547
  double d = extract_float (arg);
#ifdef FLOAT_CHECK_DOMAIN
  if (d < 0.0)
    domain_error ("sqrt", arg);
#endif
  IN_FLOAT (d = sqrt (d), "sqrt", arg);
Mike Rowan's avatar
Mike Rowan committed
548 549
  return make_float (d);
}
550

Richard M. Stallman's avatar
Richard M. Stallman committed
551
#if 0 /* Not clearly worth adding.  */
Mike Rowan's avatar
Mike Rowan committed
552

553 554
DEFUN ("acosh", Facosh, Sacosh, 1, 1, 0,
  "Return the inverse hyperbolic cosine of ARG.")
555 556
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
557
{
558 559 560 561 562 563 564 565 566 567
  double d = extract_float (arg);
#ifdef FLOAT_CHECK_DOMAIN
  if (d < 1.0)
    domain_error ("acosh", arg);
#endif
#ifdef HAVE_INVERSE_HYPERBOLIC
  IN_FLOAT (d = acosh (d), "acosh", arg);
#else
  IN_FLOAT (d = log (d + sqrt (d*d - 1.0)), "acosh", arg);
#endif
568 569 570 571 572
  return make_float (d);
}

DEFUN ("asinh", Fasinh, Sasinh, 1, 1, 0,
  "Return the inverse hyperbolic sine of ARG.")
573 574
  (arg)
     register Lisp_Object arg;
575
{
576 577 578 579 580 581
  double d = extract_float (arg);
#ifdef HAVE_INVERSE_HYPERBOLIC
  IN_FLOAT (d = asinh (d), "asinh", arg);
#else
  IN_FLOAT (d = log (d + sqrt (d*d + 1.0)), "asinh", arg);
#endif
582 583 584 585 586
  return make_float (d);
}

DEFUN ("atanh", Fatanh, Satanh, 1, 1, 0,
  "Return the inverse hyperbolic tangent of ARG.")
587 588
  (arg)
     register Lisp_Object arg;
589
{
590 591 592 593 594 595 596 597 598 599
  double d = extract_float (arg);
#ifdef FLOAT_CHECK_DOMAIN
  if (d >= 1.0 || d <= -1.0)
    domain_error ("atanh", arg);
#endif
#ifdef HAVE_INVERSE_HYPERBOLIC
  IN_FLOAT (d = atanh (d), "atanh", arg);
#else
  IN_FLOAT (d = 0.5 * log ((1.0 + d) / (1.0 - d)), "atanh", arg);
#endif
600 601 602 603 604
  return make_float (d);
}

DEFUN ("cosh", Fcosh, Scosh, 1, 1, 0,
  "Return the hyperbolic cosine of ARG.")
605 606
  (arg)
     register Lisp_Object arg;
607
{
608 609 610 611 612 613
  double d = extract_float (arg);
#ifdef FLOAT_CHECK_DOMAIN
  if (d > 710.0 || d < -710.0)
    range_error ("cosh", arg);
#endif
  IN_FLOAT (d = cosh (d), "cosh", arg);
614 615 616 617 618
  return make_float (d);
}

DEFUN ("sinh", Fsinh, Ssinh, 1, 1, 0,
  "Return the hyperbolic sine of ARG.")
619 620
  (arg)
     register Lisp_Object arg;
621
{
622 623 624 625 626 627
  double d = extract_float (arg);
#ifdef FLOAT_CHECK_DOMAIN
  if (d > 710.0 || d < -710.0)
    range_error ("sinh", arg);
#endif
  IN_FLOAT (d = sinh (d), "sinh", arg);
Mike Rowan's avatar
Mike Rowan committed
628 629 630 631 632
  return make_float (d);
}

DEFUN ("tanh", Ftanh, Stanh, 1, 1, 0,
  "Return the hyperbolic tangent of ARG.")
633 634
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
635
{
636 637
  double d = extract_float (arg);
  IN_FLOAT (d = tanh (d), "tanh", arg);
Mike Rowan's avatar
Mike Rowan committed
638 639
  return make_float (d);
}
640
#endif
Mike Rowan's avatar
Mike Rowan committed
641 642 643

DEFUN ("abs", Fabs, Sabs, 1, 1, 0,
  "Return the absolute value of ARG.")
644 645
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
646
{
647
  CHECK_NUMBER_OR_FLOAT (arg, 0);
Mike Rowan's avatar
Mike Rowan committed
648

649
  if (FLOATP (arg))
650
    IN_FLOAT (arg = make_float (fabs (XFLOAT_DATA (arg))), "abs", arg);
651
  else if (XINT (arg) < 0)
652
    XSETINT (arg, - XINT (arg));
Mike Rowan's avatar
Mike Rowan committed
653

654
  return arg;
Mike Rowan's avatar
Mike Rowan committed
655 656 657 658
}

DEFUN ("float", Ffloat, Sfloat, 1, 1, 0,
  "Return the floating point number equal to ARG.")
659 660
  (arg)
     register Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
661
{
662
  CHECK_NUMBER_OR_FLOAT (arg, 0);
Mike Rowan's avatar
Mike Rowan committed
663

664
  if (INTEGERP (arg))
665
    return make_float ((double) XINT (arg));
Mike Rowan's avatar
Mike Rowan committed
666
  else				/* give 'em the same float back */
667
    return arg;
Mike Rowan's avatar
Mike Rowan committed
668 669 670
}

DEFUN ("logb", Flogb, Slogb, 1, 1, 0,
Richard M. Stallman's avatar
Richard M. Stallman committed
671
  "Returns largest integer <= the base 2 log of the magnitude of ARG.\n\
Mike Rowan's avatar
Mike Rowan committed
672
This is the same as the exponent of a float.")
673 674
     (arg)
     Lisp_Object arg;
Mike Rowan's avatar
Mike Rowan committed
675
{
676
  Lisp_Object val;
677
  EMACS_INT value;
678
  double f = extract_float (arg);
679

680 681 682 683
  if (f == 0.0)
    value = -(VALMASK >> 1);
  else
    {
684
#ifdef HAVE_LOGB
685
      IN_FLOAT (value = logb (f), "logb", arg);
686 687
#else
#ifdef HAVE_FREXP
688 689 690
      int ivalue;
      IN_FLOAT (frexp (f, &ivalue), "logb", arg);
      value = ivalue - 1;
691
#else
692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710
      int i;
      double d;
      if (f < 0.0)
	f = -f;
      value = -1;
      while (f < 0.5)
	{
	  for (i = 1, d = 0.5; d * d >= f; i += i)
	    d *= d;
	  f /= d;
	  value -= i;
	}
      while (f >= 1.0)
	{
	  for (i = 1, d = 2.0; d * d <= f; i += i)
	    d *= d;
	  f /= d;
	  value += i;
	}
711
#endif
712
#endif
713
    }
714
  XSETINT (val, value);
715
  return val;
Mike Rowan's avatar
Mike Rowan committed
716 717
}

718

719 720 721 722
/* the rounding functions  */

static Lisp_Object
rounding_driver (arg, divisor, double_round, int_round2, name)
723
     register Lisp_Object arg, divisor;
724 725 726
     double (*double_round) ();
     EMACS_INT (*int_round2) ();
     char *name;
Mike Rowan's avatar
Mike Rowan committed
727
{
728
  CHECK_NUMBER_OR_FLOAT (arg, 0);
Mike Rowan's avatar
Mike Rowan committed
729

730 731
  if (! NILP (divisor))
    {
732
      EMACS_INT i1, i2;
733 734 735

      CHECK_NUMBER_OR_FLOAT (divisor, 1);

736
      if (FLOATP (arg) || FLOATP (divisor))
737 738 739
	{
	  double f1, f2;

740 741
	  f1 = FLOATP (arg) ? XFLOAT_DATA (arg) : XINT (arg);
	  f2 = (FLOATP (divisor) ? XFLOAT_DATA (divisor) : XINT (divisor));
742
	  if (! IEEE_FLOATING_POINT && f2 == 0)
743 744
	    Fsignal (Qarith_error, Qnil);

745 746
	  IN_FLOAT2 (f1 = (*double_round) (f1 / f2), name, arg, divisor);
	  FLOAT_TO_INT2 (f1, arg, name, arg, divisor);
747 748 749 750 751 752 753 754 755
	  return arg;
	}

      i1 = XINT (arg);
      i2 = XINT (divisor);

      if (i2 == 0)
	Fsignal (Qarith_error, Qnil);

756
      XSETINT (arg, (*int_round2) (i1, i2));
757 758 759
      return arg;
    }

760
  if (FLOATP (arg))
761 762
    {
      double d;
763

764
      IN_FLOAT (d = (*double_round) (XFLOAT_DATA (arg)), name, arg);
765
      FLOAT_TO_INT (d, arg, name, arg);
766
    }
Mike Rowan's avatar
Mike Rowan committed
767

768
  return arg;
Mike Rowan's avatar
Mike Rowan committed
769 770
}

771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817
/* With C's /, the result is implementation-defined if either operand
   is negative, so take care with negative operands in the following
   integer functions.  */

static EMACS_INT
ceiling2 (i1, i2)
     EMACS_INT i1, i2;
{
  return (i2 < 0
	  ? (i1 < 0  ?  ((-1 - i1) / -i2) + 1  :  - (i1 / -i2))
	  : (i1 <= 0  ?  - (-i1 / i2)  :  ((i1 - 1) / i2) + 1));
}

static EMACS_INT
floor2 (i1, i2)
     EMACS_INT i1, i2;
{
  return (i2 < 0
	  ? (i1 <= 0  ?  -i1 / -i2  :  -1 - ((i1 - 1) / -i2))
	  : (i1 < 0  ?  -1 - ((-1 - i1) / i2)  :  i1 / i2));
}

static EMACS_INT
truncate2 (i1, i2)
     EMACS_INT i1, i2;
{
  return (i2 < 0
	  ? (i1 < 0  ?  -i1 / -i2  :  - (i1 / -i2))
	  : (i1 < 0  ?  - (-i1 / i2)  :  i1 / i2));
}

static EMACS_INT
round2 (i1, i2)
     EMACS_INT i1, i2;
{
  /* The C language's division operator gives us one remainder R, but
     we want the remainder R1 on the other side of 0 if R1 is closer
     to 0 than R is; because we want to round to even, we also want R1
     if R and R1 are the same distance from 0 and if C's quotient is
     odd.  */
  EMACS_INT q = i1 / i2;
  EMACS_INT r = i1 % i2;
  EMACS_INT abs_r = r < 0 ? -r : r;
  EMACS_INT abs_r1 = (i2 < 0 ? -i2 : i2) - abs_r;
  return q + (abs_r + (q & 1) <= abs_r1 ? 0 : (i2 ^ r) < 0 ? -1 : 1);
}

818 819 820 821 822
/* The code uses emacs_rint, so that it works to undefine HAVE_RINT
   if `rint' exists but does not work right.  */
#ifdef HAVE_RINT
#define emacs_rint rint
#else
823
static double
824
emacs_rint (d)
825 826
     double d;
{
Richard M. Stallman's avatar
Richard M. Stallman committed
827
  return floor (d + 0.5);
828 829 830
}
#endif

831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861
static double
double_identity (d)
     double d;
{
  return d;
}

DEFUN ("ceiling", Fceiling, Sceiling, 1, 2, 0,
  "Return the smallest integer no less than ARG.  (Round toward +inf.)\n\
With optional DIVISOR, return the smallest integer no less than ARG/DIVISOR.")
  (arg, divisor)
     Lisp_Object arg, divisor;
{
  return rounding_driver (arg, divisor, ceil, ceiling2, "ceiling");
}

DEFUN ("floor", Ffloor, Sfloor, 1, 2, 0,
  "Return the largest integer no greater than ARG.  (Round towards -inf.)\n\
With optional DIVISOR, return the largest integer no greater than ARG/DIVISOR.")
  (arg, divisor)
     Lisp_Object arg, divisor;
{
  return rounding_driver (arg, divisor, floor, floor2, "floor");
}

DEFUN ("round", Fround, Sround, 1, 2, 0,
  "Return the nearest integer to ARG.\n\
With optional DIVISOR, return the nearest integer to ARG/DIVISOR.")
  (arg, divisor)
     Lisp_Object arg, divisor;
{
862
  return rounding_driver (arg, divisor, emacs_rint, round2, "round");
863 864 865 866 867 868 869 870 871 872 873 874 875
}

DEFUN ("truncate", Ftruncate, Struncate, 1, 2, 0,
       "Truncate a floating point number to an int.\n\
Rounds ARG toward zero.\n\
With optional DIVISOR, truncate ARG/DIVISOR.")
  (arg, divisor)
     Lisp_Object arg, divisor;
{
  return rounding_driver (arg, divisor, double_identity, truncate2,
			  "truncate");
}

876

877 878 879 880 881 882
Lisp_Object
fmod_float (x, y)
     register Lisp_Object x, y;
{
  double f1, f2;

883 884
  f1 = FLOATP (x) ? XFLOAT_DATA (x) : XINT (x);
  f2 = FLOATP (y) ? XFLOAT_DATA (y) : XINT (y);
885 886 887 888 889 890 891 892 893 894

  if (! IEEE_FLOATING_POINT && f2 == 0)
    Fsignal (Qarith_error, Qnil);

  /* If the "remainder" comes out with the wrong sign, fix it.  */
  IN_FLOAT2 ((f1 = fmod (f1, f2),
	      f1 = (f2 < 0 ? f1 > 0 : f1 < 0) ? f1 + f2 : f1),
	     "mod", x, y);
  return make_float (f1);
}
895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918

/* It's not clear these are worth adding.  */

DEFUN ("fceiling", Ffceiling, Sfceiling, 1, 1, 0,
  "Return the smallest integer no less than ARG, as a float.\n\
\(Round toward +inf.\)")
  (arg)
     register Lisp_Object arg;
{
  double d = extract_float (arg);
  IN_FLOAT (d = ceil (d), "fceiling", arg);
  return make_float (d);
}

DEFUN ("ffloor", Fffloor, Sffloor, 1, 1, 0,
  "Return the largest integer no greater than ARG, as a float.\n\
\(Round towards -inf.\)")
  (arg)
     register Lisp_Object arg;
{
  double d = extract_float (arg);
  IN_FLOAT (d = floor (d), "ffloor", arg);
  return make_float (d);
}
Mike Rowan's avatar
Mike Rowan committed
919

920 921 922 923 924 925
DEFUN ("fround", Ffround, Sfround, 1, 1, 0,
  "Return the nearest integer to ARG, as a float.")
  (arg)
     register Lisp_Object arg;
{
  double d = extract_float (arg);
926
  IN_FLOAT (d = emacs_rint (d), "fround", arg);
927 928 929 930
  return make_float (d);
}

DEFUN ("ftruncate", Fftruncate, Sftruncate, 1, 1, 0,
931
  "Truncate a floating point number to an integral float value.\n\
932 933 934 935 936 937 938 939
Rounds the value toward zero.")
  (arg)
     register Lisp_Object arg;
{
  double d = extract_float (arg);
  if (d >= 0.0)
    IN_FLOAT (d = floor (d), "ftruncate", arg);
  else
940
    IN_FLOAT (d = ceil (d), "ftruncate", arg);
941
  return make_float (d);
Mike Rowan's avatar
Mike Rowan committed
942 943
}

944
#ifdef FLOAT_CATCH_SIGILL
Jim Blandy's avatar
Jim Blandy committed
945
static SIGTYPE
Mike Rowan's avatar
Mike Rowan committed
946 947 948 949 950 951
float_error (signo)
     int signo;
{
  if (! in_float)
    fatal_error_signal (signo);

952
#ifdef BSD_SYSTEM
Mike Rowan's avatar
Mike Rowan committed
953 954 955
#ifdef BSD4_1
  sigrelse (SIGILL);
#else /* not BSD4_1 */
Jim Blandy's avatar
Jim Blandy committed
956
  sigsetmask (SIGEMPTYMASK);
Mike Rowan's avatar
Mike Rowan committed
957
#endif /* not BSD4_1 */
Jim Blandy's avatar
Jim Blandy committed
958 959 960
#else
  /* Must reestablish handler each time it is called.  */
  signal (SIGILL, float_error);
961
#endif /* BSD_SYSTEM */
Mike Rowan's avatar
Mike Rowan committed
962 963 964 965 966 967

  in_float = 0;

  Fsignal (Qarith_error, Fcons (float_error_arg, Qnil));
}

968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002
/* Another idea was to replace the library function `infnan'
   where SIGILL is signaled.  */

#endif /* FLOAT_CATCH_SIGILL */

#ifdef HAVE_MATHERR
int 
matherr (x)
     struct exception *x;
{
  Lisp_Object args;
  if (! in_float)
    /* Not called from emacs-lisp float routines; do the default thing. */
    return 0;
  if (!strcmp (x->name, "pow"))
    x->name = "expt";

  args
    = Fcons (build_string (x->name),
	     Fcons (make_float (x->arg1),
		    ((!strcmp (x->name, "log") || !strcmp (x->name, "pow"))
		     ? Fcons (make_float (x->arg2), Qnil)
		     : Qnil)));
  switch (x->type)
    {
    case DOMAIN:	Fsignal (Qdomain_error, args);		break;
    case SING:		Fsignal (Qsingularity_error, args);	break;
    case OVERFLOW:	Fsignal (Qoverflow_error, args);	break;
    case UNDERFLOW:	Fsignal (Qunderflow_error, args);	break;
    default:		Fsignal (Qarith_error, args);		break;
    }
  return (1);	/* don't set errno or print a message */
}
#endif /* HAVE_MATHERR */

Andreas Schwab's avatar
Andreas Schwab committed
1003
void
Mike Rowan's avatar
Mike Rowan committed
1004 1005
init_floatfns ()
{
1006
#ifdef FLOAT_CATCH_SIGILL
Mike Rowan's avatar
Mike Rowan committed
1007
  signal (SIGILL, float_error);
1008
#endif 
Mike Rowan's avatar
Mike Rowan committed
1009 1010 1011
  in_float = 0;
}

Andreas Schwab's avatar
Andreas Schwab committed
1012
void
Mike Rowan's avatar
Mike Rowan committed
1013 1014 1015 1016 1017
syms_of_floatfns ()
{
  defsubr (&Sacos);
  defsubr (&Sasin);
  defsubr (&Satan);
1018 1019 1020 1021 1022 1023
  defsubr (&Scos);
  defsubr (&Ssin);
  defsubr (&Stan);
#if 0
  defsubr (&Sacosh);
  defsubr (&Sasinh);
Mike Rowan's avatar
Mike Rowan committed
1024
  defsubr (&Satanh);
1025 1026 1027
  defsubr (&Scosh);
  defsubr (&Ssinh);
  defsubr (&Stanh);
Mike Rowan's avatar
Mike Rowan committed
1028 1029 1030 1031 1032 1033 1034 1035
  defsubr (&Sbessel_y0);
  defsubr (&Sbessel_y1);
  defsubr (&Sbessel_yn);
  defsubr (&Sbessel_j0);
  defsubr (&Sbessel_j1);
  defsubr (&Sbessel_jn);
  defsubr (&Serf);
  defsubr (&Serfc);
1036
  defsubr (&Slog_gamma);
1037
  defsubr (&Scube_root);
1038
#endif
1039 1040 1041 1042
  defsubr (&Sfceiling);
  defsubr (&Sffloor);
  defsubr (&Sfround);
  defsubr (&Sftruncate);
Mike Rowan's avatar
Mike Rowan committed
1043
  defsubr (&Sexp);
1044
  defsubr (&Sexpt);
Mike Rowan's avatar
Mike Rowan committed
1045 1046 1047 1048 1049 1050 1051 1052
  defsubr (&Slog);
  defsubr (&Slog10);
  defsubr (&Ssqrt);

  defsubr (&Sabs);
  defsubr (&Sfloat);
  defsubr (&Slogb);
  defsubr (&Sceiling);
1053
  defsubr (&Sfloor);
Mike Rowan's avatar
Mike Rowan committed
1054 1055 1056
  defsubr (&Sround);
  defsubr (&Struncate);
}